id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,416 | OWR-14299521-008 | Gauge-Theoretic and Calibrated-Submanifold Counting Invariants | Define counting invariants for gauge-theoretic objects and calibrated submanifolds in $G_2$ geometry, and prove an equality between the two invariants. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-008",
"literature-status:open",
"owr-year:2025"
] | The construction of well-defined counting invariants simultaneously for gauge theory and calibrated submanifolds, and an equality between them, remains an explicitly open G2-geometric problem. | [
{
"url": "https://www.spp2026.de/projects/2nd-period/gauge-theoretic-methods-in-the-geometry-of-g2-manifolds.html",
"label": "DFG Gauge-theoretic methods in G2 geometry"
},
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Define counting invariants for gauge-theoretic objects and calibrated submanifolds in $G_2$ geometry, and prove an equality between the two invariants. | The big open question is whether we can define counting invariants for both the gauge theory and the calibrated submanifolds, and then prove some equality between the two invariants. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,417 | OWR-14299521-009 | Multiple Minimal Surfaces in Riemannian Three-Spheres | Beyond the established positive-Ricci-curvature cases, does every closed Riemannian three-sphere contain at least four minimal two-spheres and five minimal tori? More generally, must it contain multiple minimal surfaces of every genus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-009",
"literature-status:partially-solved",
"owr-year:2025"
] | The four-minimal-spheres and five-minimal-tori conjectures are proved for positive-Ricci and, for spheres, bumpy metrics, but the unrestricted claim for every closed Riemannian three-sphere remains open. | [
{
"url": "https://arxiv.org/abs/2305.08755",
"label": "Existence of four minimal spheres in S3 with a bumpy metric"
},
{
"url": "https://arxiv.org/abs/2409.09315",
"label": "Existence of 5 minimal tori in 3-spheres of positive Ricci curvature"
},
{
"url": "https://doi.org/10.4171/owr/202... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Beyond the established positive-Ricci-curvature cases, does every closed Riemannian three-sphere contain at least four minimal two-spheres and five minimal tori? More generally, must it contain multiple minimal surfaces of every genus? | conjecture. The topology of these moduli spaces motivated Yau (1982)[4] and White (1989)[5] to conjecture the existence of at least four minimal spheres and five minimal tori, respectively, in any closed Riemannian 3-sphere. For other topological types, Lawson (1970)[6] constructed minimal surfaces of arbitrary genus in... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,418 | OWR-14299521-010 | Stability of Noncollapsing Manifold Submetries | Let $P_i:M_i\to Y_i$ be manifold submetries, with compact $M_i$ of uniformly bounded geometry, converging without collapse to a submetry $P:M\to Y$. Are $P_i$ and $P_j$, for all sufficiently large $i,j$, equivalent up to homeomorphisms of their source and target spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-010",
"literature-status:open",
"owr-year:2025"
] | The stated stability conjecture for non-collapsing manifold submetries is recorded as a conjecture with only special cases known, and no general proof or counterexample was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Let $P_i:M_i\to Y_i$ be manifold submetries, with compact $M_i$ of uniformly bounded geometry, converging without collapse to a submetry $P:M\to Y$. Are $P_i$ and $P_j$, for all sufficiently large $i,j$, equivalent up to homeomorphisms of their source and target spaces? | stability argument, verifies the validity of the following conjecture in the case of one-dimensional base spaces. Other special cases of this theorem are provided by Perelman’s stability theorem [2], the equivariant stability theorem of Harvey [1] and the case of Riemannian submersions verified by Tapp [3]. Conjecture 1.... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,419 | OWR-14299521-012 | Infinitesimal Quasiconformality of Harmonic Spheres | Let $X$ be a compact quasiconvex metric space satisfying a local quadratic isoperimetric inequality, and assume that every continuous map $S^2\to X$ of sufficiently small diameter is null-homotopic. Is every harmonic map $u:S^2\to X$ infinitesimally quasiconformal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-012",
"literature-status:open",
"owr-year:2025"
] | The question concerns whether an arbitrary harmonic sphere in the stated metric setting is infinitesimally quasiconformal. The primary work proves this for energy minimizers on the sphere and explicitly leaves the general harmonic-sphere question open. | [
{
"url": "https://ems.press/content/serial-article-files/52249",
"label": "Meier--Vikman--Wenger Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2503.08553",
"label": "Energy minimizing harmonic spheres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Let $X$ be a compact quasiconvex metric space satisfying a local quadratic isoperimetric inequality, and assume that every continuous map $S^2\to X$ of sufficiently small diameter is null-homotopic. Is every harmonic map $u:S^2\to X$ infinitesimally quasiconformal? | Is it true that u is infinitesimally quasiconformal? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,420 | OWR-14299521-013 | Harmonic Two-Spheres in Compact Metric Spaces | Let $X$ be a compact metric space with a nontrivial $k$th homotopy group for some $k\geq 2$. What additional conditions on $X$ guarantee the existence of a nontrivial harmonic two-sphere? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-013",
"literature-status:open",
"owr-year:2025"
] | Sacks--Uhlenbeck gives the smooth closed-manifold result, while current metric-space work proves existence only under additional hypotheses. No general compact-metric-space criterion resolving the extracted question is established. | [
{
"url": "https://ems.press/content/serial-article-files/52249",
"label": "Oberwolfach Report 30"
},
{
"url": "https://arxiv.org/abs/2503.08553",
"label": "Energy minimizing harmonic spheres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Let $X$ be a compact metric space with a nontrivial $k$th homotopy group for some $k\geq 2$. What additional conditions on $X$ guarantee the existence of a nontrivial harmonic two-sphere? | Using the techniques developed in [6], Sacks-Uhlenbeck moreover showed that every closed Riemannian manifold with non-trivial k-th homotopy group for some k \geq 2 contains a non-trivial harmonic 2-sphere, see [6, Theorem 5.7]. It would be interesting to know whether a similar result holds in a metric setting. Question... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,421 | OWR-14299521-014 | Contractible Ricci-Nonnegative Four-Manifolds with Euclidean Growth | Let $(M^4,g)$ be a smooth, complete, contractible four-manifold with $\operatorname{Ric}\geq 0$ and Euclidean volume growth. Must $M$ be homeomorphic to $\mathbb{R}^4$, and must every asymptotic cross-section be homeomorphic to $S^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-014",
"literature-status:open",
"owr-year:2025"
] | The conjecture remains open: the 2026 survey still formulates the existence of a nonstandard contractible four-manifold with nonnegative Ricci curvature and Euclidean volume growth as an open question, while recent work gives structural and fundamental-group restrictions only. | [
{
"url": "https://doi.org/10.1016/j.indag.2025.04.003",
"label": "Brué--Pigati--Semola survey"
},
{
"url": "https://arxiv.org/abs/2502.03259",
"label": "Huang--Huang fundamental groups"
},
{
"url": "https://ems.press/content/serial-article-files/52249",
"label": "Oberwolfach Report 3... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Let $(M^4,g)$ be a smooth, complete, contractible four-manifold with $\operatorname{Ric}\geq 0$ and Euclidean volume growth. Must $M$ be homeomorphic to $\mathbb{R}^4$, and must every asymptotic cross-section be homeomorphic to $S^3$? | Conjecture 1. Let (M 4 , g) be a smooth, complete, contractible 4-manifold with Ric \geq 0 and Euclidean volume growth. Then the following hold: i) M 4 is homeomorphic to R4 ; ii) for every (Z, dZ ) \in C\infty , Z is homeomorphic to S 3 . The report passage is retained verbatim as the relevant context for this extract... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,422 | OWR-14299522-001 | Tensor-Factorization Uniqueness for SAW$^*$-Algebras | Let $A_i$ for $i<m$ and $B_j$ for $j<n$ be SAW$^*$-algebras such that $\bigotimes_{i<m}A_i\cong\bigotimes_{j<n}B_j$. Must $m=n$, and, after permuting the factors, must $A_i$ be stably isomorphic to $B_i$ for every $i$? In particular, for the Calkin algebra $\mathcal{Q}(H)$, is $\mathcal{Q}(H)\otimes\mathcal{Q}(H)$ isom... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** partially solv... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-001",
"literature-status:partially-solved",
"owr-year:2025"
] | Kania proved that the Calkin algebra cannot be decomposed as a tensor product of two infinite-dimensional C-star algebras, settling Wassermann's original decomposition question. The record's further ultrapower factorization and uniqueness questions remain open. | [
{
"url": "https://doi.org/10.1093/qmath/hav027",
"label": "Kania tensor decomposition theorem"
},
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Let $A_i$ for $i<m$ and $B_j$ for $j<n$ be SAW$^*$-algebras such that $\bigotimes_{i<m}A_i\cong\bigotimes_{j<n}B_j$. Must $m=n$, and, after permuting the factors, must $A_i$ be stably isomorphic to $B_i$ for every $i$? In particular, for the Calkin algebra $\mathcal{Q}(H)$, is $\mathcal{Q}(H)\otimes\mathcal{Q}(H)$ isom... | This was motivated by a question of Simon Wasserman, who asked whether the Calkin algebra Q(H) (defined as the quotient B(H)/K(H) for a separable, infinite-dimensional, Hilbert space H) is isomorphic to Q(H) ⊗ Q(H) (here and below ⊗ is the minimal tensor product). Is Q(H) ⊗ Q(H) \sim = Q(H) ⊗ Q(H) ⊗ Q(H)? A considerably ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,423 | OWR-14299522-006 | Selflessness and Strict Comparison for Reduced Group $C^*$-Algebras | For a discrete group $G$, is strict comparison for $C_r^*(G)$ equivalent to $C^*$-simplicity? Is selflessness equivalent to strict comparison together with $C^*$-simplicity? Find a dynamical characterization of selflessness, and more generally characterize selflessness of reduced crossed products through dynamics or st... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-006",
"literature-status:open",
"owr-year:2025"
] | Recent work proves selflessness and strict comparison for broad classes, including hyperbolic groups, but does not establish the proposed general equivalences or a general dynamical or stabilizer characterization. The primary paper explicitly leaves higher-rank cases open. | [
{
"url": "https://doi.org/10.1007/s00222-025-01366-5",
"label": "Strict comparison primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | For a discrete group $G$, is strict comparison for $C_r^*(G)$ equivalent to $C^*$-simplicity? Is selflessness equivalent to strict comparison together with $C^*$-simplicity? Find a dynamical characterization of selflessness, and more generally characterize selflessness of reduced crossed products through dynamics or st... | Whether strict comparison for C ∗ (G) is equivalent to C ∗ -simplicity or whether selflessness is equivalent to strict comparison plus C ∗ -simplicity are also open problems. In light of Ozawa’s result on extremely proximal actions [30], is there a dynamical condition charac- terizing selflessness? More generally, can on... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,424 | OWR-14299522-007 | Selflessness of the Reduced $C^*$-Algebra of $\mathrm{SL}_3(\mathbb{Z})$ | Is the reduced group $C^*$-algebra $C_r^*(\mathrm{SL}_3(\mathbb{Z}))$ selfless? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-007",
"literature-status:open",
"owr-year:2025"
] | Selflessness is proved for cocompact lattices in SL-three of the reals, but SL-three of the integers is a nonuniform higher-rank lattice and is not covered. The current primary literature leaves this higher-rank lattice direction open. | [
{
"url": "https://doi.org/10.1007/s00222-025-01366-5",
"label": "Strict comparison primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Is the reduced group $C^*$-algebra $C_r^*(\mathrm{SL}_3(\mathbb{Z}))$ selfless? | In contrast, (RD) remains open for many nonuniform lattices (e.g. Open question. Is Cr∗ (SL3 (Z)) selfless? commutes; i.e. Ψ ◦ ιA = ∆. A typical example of a selfless C ∗ -algebra is an infinite free product, e.g. Cr∗ (F\infty ) (see [5]). Beyond this, natural examples are harder to come by. For instance, until recently i... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,425 | OWR-14299522-008 | Local Lifting Properties of Free-Group Product $C^*$-Algebras | Does the full group $C^*$-algebra $C^*(F_2\times F_2)$ have the local lifting property or the lifting property? More generally, does a $C^*$-algebra $A$ have the local lifting property if and only if $\operatorname{Ext}(A)$ is a group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** partially solv... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-008",
"literature-status:partially-solved",
"owr-year:2025"
] | MIP-star equals RE refuted the Connes embedding problem, so the equivalent residual-finite-dimensionality assertion for the full group C-star algebra of the product of two free groups is false. The LLP question and the proposed general equivalence with the Ext group condition remain unresolved. | [
{
"url": "https://arxiv.org/abs/2001.04383",
"label": "MIP-star equals RE"
},
{
"url": "https://doi.org/10.7153/oam-2020-14-36",
"label": "Pop Ext and LLP results"
},
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Does the full group $C^*$-algebra $C^*(F_2\times F_2)$ have the local lifting property or the lifting property? More generally, does a $C^*$-algebra $A$ have the local lifting property if and only if $\operatorname{Ext}(A)$ is a group? | The Connes Embeding Problem is equivalent to the question of whether or not C ∗ (F2 \times F2 ) is residually finite-dimensional (RFD). The following is a long-standing open question. Does C ∗ (F2 \times F2 ) have the (L)LP? Does A have the LLP if and only if Ext(A) is a group? states that it is not known whether the LP... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,426 | OWR-14299522-010 | Selected Lifting and Perturbation Problems in Operator Algebras | Is there an automorphism $\alpha$ of $\mathcal{O}_\infty\otimes\mathcal{K}$ that fixes the diagonal and induces $-\mathrm{id}$ on $K_0$, and can such an automorphism have the Rokhlin property? Does there exist a relatively free group $G$ for which $C_r^*(G)$ is selfless? Does there exist a simple $C^*$-algebra that is ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-010",
"literature-status:open",
"owr-year:2025"
] | This record aggregates several unrelated open-problem-session questions and omits definitions and hypotheses for some of them. The source does not provide a single determinate claim, so the unresolved or unclear extraction is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Is there an automorphism $\alpha$ of $\mathcal{O}_\infty\otimes\mathcal{K}$ that fixes the diagonal and induces $-\mathrm{id}$ on $K_0$, and can such an automorphism have the Rokhlin property? Does there exist a relatively free group $G$ for which $C_r^*(G)$ is selfless? Does there exist a simple $C^*$-algebra that is ... | This informal session was devoted to collect and present a number of open problems in the area. Does the continuous part of the induced action Z y AU lift to ℓ\infty (A)? Is p ⊗ 1R \simMvN 1R ⊗ p in R ⊗ R? Is there an autormorphism \alpha on O\infty ⊗ K which fixes the diagonal and satisfies K0 (\alpha) = −id? Does there... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,427 | OWR-14299522-011 | Structural Problems for $C^*$- and von Neumann Algebras | Do the normalized random matrices $X_k$ converge strongly to a free circular distribution? Are $q$-Gaussian $C^*$-algebras selfless for $-1<q<1$ and $q\neq0$? Are the indicated tracial ultrapowers mutually isomorphic? Does there exist a group that has a mixed identity and whose reduced $C^*$-algebra is selfless? Does $... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-011",
"literature-status:open",
"owr-year:2025"
] | The record is a compound list of open problems spanning free circular limits, q-Gaussian selflessness, ultraproduct isomorphism, rapid decay, Choquet simplices, free group factors, and free-product isomorphism. Current literature gives partial results but no resolution of the listed collection. | [
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
},
{
"url": "https://doi.org/10.1007/s00222-025-01366-5",
"label": "Strict comparison primary paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Do the normalized random matrices $X_k$ converge strongly to a free circular distribution? Are $q$-Gaussian $C^*$-algebras selfless for $-1<q<1$ and $q\neq0$? Are the indicated tracial ultrapowers mutually isomorphic? Does there exist a group that has a mixed identity and whose reduced $C^*$-algebra is selfless? Does $... | Does Xk converge strongly to a free circular distribution? Are q-Gaussian C∗ -algebras selfless for −1 < q < 1, q 6= 0? Are any two of these algebras isomorphic? Does a group G exist which is not mixed identity-free and such that Cr∗ (G) is selfless? Does C ∗ (F2 \times F2 ) have the (local) lifting property? Does there ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,428 | OWR-14299522-012 | Single Generation and Free-Group $C^*$-Superrigidity | Is every unital simple separable $C^*$-algebra singly generated? Is the free group $F_2$ determined, among hyperbolic groups, by its reduced $C^*$-algebra, possibly in a superrigid sense? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948](https://doi.org/10.4171/owr/2025/35)
## Literature review (checked 2026-08-22)
**Status:** partially solv... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299522-012",
"literature-status:partially-solved",
"owr-year:2025"
] | The universal single-generation claim is disproved by an August 2026 construction of a simple unital separable AH algebra that is not singly generated. The separate C-star-superrigidity question for the free group of rank two within hyperbolic groups remains open. | [
{
"url": "https://arxiv.org/abs/2608.13707",
"label": "Elliott--Li--Niu counterexample"
},
{
"url": "https://doi.org/10.4171/owr/2025/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/35 | null | null | null | Is every unital simple separable $C^*$-algebra singly generated? Is the free group $F_2$ determined, among hyperbolic groups, by its reduced $C^*$-algebra, possibly in a superrigid sense? | Is every unital simple separable C∗ -algebra singly generated? Is F2 Cr∗ -(super)rigid (within hyperbolic groups)? Consider \{Fijk | i, j = 1, . . . , n, k = 1, . . . , d\}, where Fijk are pairwise orthogo- nal. Define Xk = ( \sqrt{ }1n A(Fijk ))ni,j=1 \in Mn (M2\infty ). Does Xk converge strongly to a free circular dis... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | C*-Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/35, pp. 1887--1948 |
30,006,429 | OWR-14299523-001 | Cohomology Theory for Subalgebra Zeta Functions | Construct a cohomology theory for subalgebra zeta functions that unifies the arithmetic zeta-function theory with the combinatorial theory of flag Hilbert–Poincaré series. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-001",
"literature-status:open",
"owr-year:2025"
] | Recent work introduces cotype zeta functions that generalize and unify several counting zeta functions, but no bespoke cohomology theory unifying the two theories in the extracted question has been established. | [
{
"url": "https://arxiv.org/abs/2504.18908",
"label": "Lee--Lee cotype zeta functions"
},
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | Construct a cohomology theory for subalgebra zeta functions that unifies the arithmetic zeta-function theory with the combinatorial theory of flag Hilbert–Poincaré series. | Is there a bespoke cohomology theory for subalgebra zeta functions that unifies these two theories? 2. Flag Hilbert–Poincaré series Now we explore a more combinatorial zeta function within enumerative algebra. Let A be a finite set of hyperplanes in AnK with K a number field. Write L(A) for the set of all possible inters... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,430 | OWR-14299523-002 | Combinatorial Formulas for Graph Zeta Functions | For every graph $\Gamma$ on a fixed vertex set, find a meaningful combinatorial formula for its zeta function $W_\Gamma^-(X,T)$ that extends the known hypergraph formula for cographs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-002",
"literature-status:open",
"owr-year:2025"
] | A combinatorial Denef formula is known for cographs, while the 2025 discussion identifies sandwich comparisons as an obstruction for general graphs and reformulates the problem for families of graphs. No formula valid for all graphs is known. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
},
{
"url": "https://ems.press/content/serial-article-files/46914",
"label": "Earlier graphical zeta results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | For every graph $\Gamma$ on a fixed vertex set, find a meaningful combinatorial formula for its zeta function $W_\Gamma^-(X,T)$ that extends the known hypergraph formula for cographs. | Is there a meaningful com- binatorial formula (in the spirit of Theorem 1) for the functions WΓ− (X, T ) which is valid for all graphs on a given vertex set? One attempt at answering the previous question is to relate the order complex ∆(2[n] ) appearing in (1) to the face lattice of the permutohedron, which we denote ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,431 | OWR-14299523-003 | Regularity of Dedekind Zeta Functions in Zp-Extensions | Identify and prove further regularity phenomena for Dedekind zeta functions and their invariants along arbitrary $\mathbb{Z}_p$-extensions, beyond the known Iwasawa-type asymptotics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-003",
"literature-status:open",
"owr-year:2025"
] | Iwasawa's three-parameter asymptotic is established, and current work studies further regularity for Dedekind zeta functions and Euler--Kronecker constants, but the broad question of other regularities in arbitrary Z-p-extensions remains open. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4379/OWR_2025_38.pdf?sequence=1",
"label": "Primary report PDF"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | Identify and prove further regularity phenomena for Dedekind zeta functions and their invariants along arbitrary $\mathbb{Z}_p$-extensions, beyond the known Iwasawa-type asymptotics. | Are there other regularities in Zp -extensions? Analytic properties of the Dedekind zeta function over Zp -extensions Dohyeong Kim (joint work with Harin Jung) Cohomology Theories for Automorphic Forms and Enumerative Algebra 2095 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,432 | OWR-14299523-004 | Arithmetic Meaning of Euler-Kronecker Constants | For a number field $F$, determine what arithmetic information is encoded by its Euler–Kronecker constant $\gamma_F$, and characterize this information through primes, zeros, class-field data, or other intrinsic invariants of $F$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-004",
"literature-status:open",
"owr-year:2025"
] | The Euler--Kronecker constant has explicit formulas and known links to small prime norms, zero-free regions, and bounds, but no complete arithmetic interpretation is known; the extracted question remains open. | [
{
"url": "https://www.kurims.kyoto-u.ac.jp/~kenkyubu/emeritus/ihara/Publications-and-Recent-Preprints/RecentArticles/pdf-files/1A.pdf",
"label": "Ihara primary paper"
},
{
"url": "https://doi.org/10.1142/S1793042126500521",
"label": "Ghosh higher constants"
},
{
"url": "https://ems.press... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | For a number field $F$, determine what arithmetic information is encoded by its Euler–Kronecker constant $\gamma_F$, and characterize this information through primes, zeros, class-field data, or other intrinsic invariants of $F$. | What kind of arithmetic information does \gammaF encode? of the Euler–Kronecker constants along Zp -extensions. The aforementioned con- stant generalizes the better-known constant \gamma named after Euler and Mascheroni, which admits a concise definition:- 1 1 \gamma := lim 1 + + \cdot\cdot\cdot+ − log n . n\to\infty 2 ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,433 | OWR-14299523-005 | Degree of Topological Subalgebra Zeta Functions | Let $A$ be an algebra of dimension $d$ in the subalgebra-zeta setting. Prove the degree conjecture $\deg Z_A^{\mathrm{top}}(s)=-d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14299523-005",
"literature-status:open",
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] | The degree conjecture is still presented as a conjecture; known results cover special bases and classes through cone and Hilbert-series constructions, not all algebras in the extracted scope. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
},
{
"url": "https://torossmann.github.io/files/mfo25b.pdf",
"label": "Rossmann--Voll survey slides"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | Let $A$ be an algebra of dimension $d$ in the subalgebra-zeta setting. Prove the degree conjecture $\deg Z_A^{\mathrm{top}}(s)=-d$. | Degree conjecture ([8, Conj. I]). deg(ZA top (s)) = −d. Evseev [6, Prop. 4.1] showed that if A admits a particular type of basis, then there exists a d-dimensional cone C \subset Rd\geq0 such that the reduced zeta function ZA d red (T ) is the (coarse) Hilbert series of the affine monoid algebra Q[C \cap Z ]. Using the e... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,434 | OWR-14299523-006 | Gorenstein Hilbert Series for Reduced Subalgebra Zeta Functions | For every $d$-dimensional algebra $A$ in the subalgebra-zeta setting, construct a natural $\mathbb{N}_0$-graded Gorenstein algebra of dimension $d$ whose Hilbert series is the reduced subalgebra zeta function $Z_A^{\mathrm{red}}(T)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-006",
"literature-status:open",
"owr-year:2025"
] | The Hilbert-series conjecture remains unresolved in general. Evseev's cone construction proves the desired Gorenstein interpretation for a restricted basis class, which is only partial progress toward the extracted claim. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
},
{
"url": "https://torossmann.github.io/files/mfo25b.pdf",
"label": "Rossmann--Voll survey slides"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | For every $d$-dimensional algebra $A$ in the subalgebra-zeta setting, construct a natural $\mathbb{N}_0$-graded Gorenstein algebra of dimension $d$ whose Hilbert series is the reduced subalgebra zeta function $Z_A^{\mathrm{red}}(T)$. | In- spired by the preceding two conjectures, define mtop (A) := s−d ZA top (s −1 ) , mred (A) := (1 − T )d ZA red (T ) . s=0 T =1 The topological degree conjecture is equivalent to mtop (A) being nonzero and finite. Similarly, if the Hilbert series conjecture is true, then ZA red (T ) has a pole of order d at T = 1 whenc... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,435 | OWR-14299523-007 | Coincidence of Reduced and Topological Zeta Invariants | For a $d$-dimensional algebra $A$, define $m_{\mathrm{top}}(A)$ from the leading behavior of $Z_A^{\mathrm{top}}(s)$ at $s=0$ and $m_{\mathrm{red}}(A)$ from that of $Z_A^{\mathrm{red}}(T)$ at $T=1$. Prove that $m_{\mathrm{red}}(A)=m_{\mathrm{top}}(A)$ and that their common value is a positive rational number. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-007",
"literature-status:open",
"owr-year:2025"
] | The coincidence conjecture has been verified for selected families and supported by computations, but the report states that it has not been formally settled and no general proof is known. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
},
{
"url": "https://torossmann.github.io/files/mfo25b.pdf",
"label": "Rossmann--Voll survey slides"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | For a $d$-dimensional algebra $A$, define $m_{\mathrm{top}}(A)$ from the leading behavior of $Z_A^{\mathrm{top}}(s)$ at $s=0$ and $m_{\mathrm{red}}(A)$ from that of $Z_A^{\mathrm{red}}(T)$ at $T=1$. Prove that $m_{\mathrm{red}}(A)=m_{\mathrm{top}}(A)$ and that their common value is a positive rational number. | Coincidence conjecture. mred (A) = mtop (A) and the common value is a posi- tive rational number. The topological degree conjecture is equivalent to mtop (A) being nonzero and finite. Similarly, if the Hilbert series conjecture is true, then ZA red (T ) has a pole of order d at T = 1 whence mred (A) is nonzero and finite... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,436 | OWR-14299523-008 | Higher-Depth Mock Modular Forms and Polyharmonic Maass Forms | Relate higher-depth mixed mock modular forms and iterated integrals to polyharmonic weak Maass forms. Use this connection to explain the passage from finite-length representation theory for the modular group to a well-behaved representation theory for the ambient real Lie group. Determine first whether iterated Eisenst... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124](https://doi.org/10.4171/owr/2025/38)
## Literature r... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299523-008",
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] | Polyharmonic weak Maass forms and higher-depth mock modular forms each have substantial theories, but the requested general connection through iterated integrals and the resulting representation-theoretic explanation is explicitly unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/52251",
"label": "Oberwolfach Report 38"
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{
"url": "https://doi.org/10.1007/s11139-018-0057-0",
"label": "Matsusaka polyharmonic forms"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869324004289",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/38 | null | null | null | Relate higher-depth mixed mock modular forms and iterated integrals to polyharmonic weak Maass forms. Use this connection to explain the passage from finite-length representation theory for the modular group to a well-behaved representation theory for the ambient real Lie group. Determine first whether iterated Eisenst... | Problem: Connect higher-depth mixed mock modular forms and iterated integrals to polyharmonic weak Maass forms. Through this connection, explain the shift from a well-behaved representation theory for the modular group to a well-behaved representation theory for the real Lie group. Harmonic weak Maass forms also admit ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Cohomology Theories for Automorphic Forms and Enumerative Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/38, pp. 2065--2124 |
30,006,437 | OWR-14299525-001 | Formal Verification of AI-Generated Mathematical Proofs | Develop a reliable workflow that translates AI-generated mathematical arguments into Lean, checks every inferential detail, and diagnoses gaps rather than accepting persuasive but invalid prose. Determine how much of this verification and repair process can itself be automated. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350](https://doi.org/10.4171/owr/2025/43)
## Literature... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299525-001",
"literature-status:open",
"owr-year:2025"
] | Formal proof assistants can mechanically check a completed Lean proof, and current LLM provers remain unreliable on research-level formalization; no general system that validates the details of arbitrary AI-generated mathematical arguments is established. | [
{
"url": "https://doi.org/10.4171/owr/2025/43",
"label": "Oberwolfach Report 43/2025"
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{
"url": "https://arxiv.org/abs/2306.15626",
"label": "LeanDojo"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/43 | null | null | null | Develop a reliable workflow that translates AI-generated mathematical arguments into Lean, checks every inferential detail, and diagnoses gaps rather than accepting persuasive but invalid prose. Determine how much of this verification and repair process can itself be automated. | Can AI confirm the details in a Lean verified proof? (2) Check LLM’s arguments: Don’t trust, and verify. (3) Check all the arguments: I think the future is going to be filled with highly persuasive, incorrect mathematical text, and formalization is going to be required to keep mathematics mathematics. Boosting sphere pack... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350 |
30,006,438 | OWR-14299525-002 | Generative Sphere Packing across Dimensions and Periodic Geometries | Can one conditional generative model trained across different numbers of balls and dimensions extrapolate to larger sphere-packing instances while preserving or improving minimum separation after projection? Extend projection-corrected flow-matching methods from finite boxes to periodic packings and establish when the ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350](https://doi.org/10.4171/owr/2025/43)
## Literature... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299525-002",
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] | The report presents extrapolation across dimensions and ball counts and passage from finite boxes to periodic packings as open questions; the described diffusion and flow-matching method is a heuristic construction and does not prove either generalization. | [
{
"url": "https://doi.org/10.4171/owr/2025/43",
"label": "Oberwolfach Report 43/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/43 | null | null | null | Can one conditional generative model trained across different numbers of balls and dimensions extrapolate to larger sphere-packing instances while preserving or improving minimum separation after projection? Extend projection-corrected flow-matching methods from finite boxes to periodic packings and establish when the ... | Open questions and conjectures. (1) Generalization across n and d. Can a single conditional model, trained on a mixture of ball counts and dimensions, extrapolate to larger instances while maintaining or improving minimal separations after projection? (2) From finite boxes to periodic packings. • Projection-corrected sa... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350 |
30,006,439 | OWR-14299525-003 | Agentic and Neuro-Symbolic AI for Mathematical Research | Build an agentic AI system that carries out the full workflow of a mathematician, from exploring examples and formulating conjectures to selecting proof strategies, and determine whether it can solve research-level benchmarks such as FATE-X autonomously. Identify an effective architecture that combines neural pattern r... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350](https://doi.org/10.4171/owr/2025/43)
## Literature... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Computational complexity, algorithms, and theoretical CS.",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14299525-003",
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] | Agentic systems that autonomously reproduce the full research workflow and reliably generate human-readable formal proofs remain an active research goal; current formal benchmarks show a large gap between natural-language reasoning and verified proof construction. | [
{
"url": "https://doi.org/10.4171/owr/2025/43",
"label": "Oberwolfach Report 43/2025"
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{
"url": "https://arxiv.org/abs/2511.02872",
"label": "FATE benchmark"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/43 | null | null | null | Build an agentic AI system that carries out the full workflow of a mathematician, from exploring examples and formulating conjectures to selecting proof strategies, and determine whether it can solve research-level benchmarks such as FATE-X autonomously. Identify an effective architecture that combines neural pattern r... | A Vision and Open Questions for the Future Looking ahead, our vision for AI in mathematics extends beyond proof assistance. In this spirit, I would like to propose two key questions to promote new research: (1) How can we build an agentic AI system that effectively mimics the full workflow of a human mathematician¡ªfrom ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350 |
30,006,440 | OWR-14299525-004 | Extremal Diameters of Symmetric-Group Cayley Graphs | Prove the proposed upper bound $\frac{1}{2}n^2+4n$ for diameters of undirected Cayley graphs of $S_n$. Prove or disprove that the explicit square-with-whiskers generating families maximize the diameter for every $n$, extending the computations through $n=15$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350](https://doi.org/10.4171/owr/2025/43)
## Literature... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299525-004",
"literature-status:open",
"owr-year:2025"
] | The refined symmetric-group Cayley-graph diameter bound and square-with-whiskers extremality are explicitly conjectured; exhaustive computation only reaches the finite range reported through n less than or equal to 15. | [
{
"url": "https://arxiv.org/abs/2509.19162",
"label": "CayleyPy Growth"
},
{
"url": "https://doi.org/10.4171/owr/2025/43",
"label": "Oberwolfach Report 43/2025"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/43 | null | null | null | Prove the proposed upper bound $\frac{1}{2}n^2+4n$ for diameters of undirected Cayley graphs of $S_n$. Prove or disprove that the explicit square-with-whiskers generating families maximize the diameter for every $n$, extending the computations through $n=15$. | We propose refinement of the Babai-type conjecture on diameters of Sn : 12 n2 +4n upper bounds for the diameters in the standard undirected case, as compared to prior conjectural bounds of O(n2 ). We also provide explicit generator families, related to involutions in a simple “square-with-whiskers” pattern, which we con... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350 |
30,006,441 | OWR-14299525-005 | Scaling Paradigms for Lean Autoformalization | Determine which combination of fine-grained tree search, whole-proof generation, iterative debugging, hierarchical decomposition, and reinforcement learning scales most effectively to large research-level theorem-proving and autoformalization tasks in Lean. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350](https://doi.org/10.4171/owr/2025/43)
## Literature... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299525-005",
"literature-status:open",
"owr-year:2025"
] | Type-checking and retrieval substantially improve autoformalization on benchmarks, but general feasibility and necessity at research scale are not theorem-level results and semantic correctness remains difficult. | [
{
"url": "https://doi.org/10.4171/owr/2025/43",
"label": "Oberwolfach Report 43/2025"
},
{
"url": "https://arxiv.org/abs/2406.07222",
"label": "Improving Autoformalization using Type Checking"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/43 | null | null | null | Determine which combination of fine-grained tree search, whole-proof generation, iterative debugging, hierarchical decomposition, and reinforcement learning scales most effectively to large research-level theorem-proving and autoformalization tasks in Lean. | Why Autoformalization Will Be Both Feasible and Necessary? Lean Method Zoo – Paradigms to Scale Formal Proving Fabien Glöckle I presented different methods to use language models with interactive theorem proving such as Lean. These methods include fine-level tree search, and reinforce- ment learning extensions: MCTS, wh... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Machine Learning and AI for Mathematics (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/43, pp. 2323--2350 |
30,006,442 | OWR-14299574-001 | Uniform Bounds for Transcendental Rational Points | Let $X\subseteq\mathbb{C}_p^n$ be definable in a Hensel-minimal structure. Can $\#X^{\mathrm{trans}}(\mathbb{Q},H)$ be bounded uniformly for all $H\geq1$, with bounds analogous to those known in dimension one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-001",
"literature-status:open",
"owr-year:2025"
] | The cited singularities report formulates uniform boundedness of the number of transcendental rational points as an open question; existing Pila--Wilkie-type estimates do not settle the stated uniform bound with the desired theorem-level constants. | [
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
},
{
"url": "https://www.wisdom.weizmann.ac.il/~dnovikov/Papers/Pfaff_Wilkie.pdf",
"label": "Effective Pila--Wilkie bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | Let $X\subseteq\mathbb{C}_p^n$ be definable in a Hensel-minimal structure. Can $\#X^{\mathrm{trans}}(\mathbb{Q},H)$ be bounded uniformly for all $H\geq1$, with bounds analogous to those known in dimension one? | Let me end this report with an open question, inspired by [15], where the one- dimensional case is treated. Is it possible to bound the number \#X trans (Q, H) uniformly in H ⩾ 1, with upper bounds as in Theorem 2? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,443 | OWR-14299574-002 | Generic Linear Projections and Dimensionality Type | For singularities of dimensionality type at least three, is a generic linear projection sufficiently generic that its discriminant computes the dimensionality type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-002",
"literature-status:open",
"owr-year:2025"
] | The generic-polynomial projection theorem and the dimensionality-type-two case are known, but whether generic linear projection suffices in dimensionality type three or higher remains open. | [
{
"url": "https://math.univ-cotedazur.fr/~parus/publis/JAG1439R1.pdf",
"label": "Zariski dimensionality type"
},
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | For singularities of dimensionality type at least three, is a generic linear projection sufficiently generic that its discriminant computes the dimensionality type? | The question whether a generic linear projection is always sufficient is still open for dimensionality type three and higher. Open problem. Is a generic linear projection generic, i.e. can its discriminant be used to compute the dimensionality type? Generic projection after Zariski. r+1 r The generic projection \piu = (\... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,444 | OWR-14299574-004 | Zero-Mutable Laurent Polynomials as Cluster Variables | Is every zero-mutable Laurent polynomial in two variables a cluster variable for a suitable quiver? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-004",
"literature-status:open",
"owr-year:2025"
] | The implication from zero-mutability to being a cluster variable for a suitable quiver is still stated as a conjecture; current work develops zero-mutable polynomials and proves important families of associated smoothing results, not the universal cluster-variable assertion. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/e0847358-34cd-4809-8330-e99d50f1e37e/download",
"label": "Oberwolfach Report 45/2025"
},
{
"url": "https://arxiv.org/abs/2503.18661",
"label": "Smoothings from zero-mutable Laurent polynomials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | Is every zero-mutable Laurent polynomial in two variables a cluster variable for a suitable quiver? | Conjecture (Gräfnitz-R., maybe soon a theorem). Every zero-mutable Laurent polynomial in 2-variables is a cluster variable in for a suitable quiver. 3. Singular Log Structures and Smoothings of Toroidal Crossing Fano Varieties Exercise in toric geometry. For an affine toric variety U\sigma = Spec C[\sigma ∨ \cap M ]: U\... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,445 | OWR-14299574-005 | Crepant Resolutions and Smoothings of Toroidal Fano Varieties | Do log schemes constructed from compatible facetwise zero-mutable Laurent polynomials admit both a log-crepant resolution and a smoothing? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-005",
"literature-status:partially-solved",
"owr-year:2025"
] | The universal conjecture for all log schemes of the stated type is not established, but the report proves the smoothing statement for all 105 smooth Fano threefolds in its constructed class and later work constructs log-crepant resolutions and smoothings in additional families. | [
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
},
{
"url": "https://www.cambridge.org/core/journals/moduli/article/how-to-make-log-structures/974D2003CB24AD0B7DCD4D7507A011E6",
"label": "How to make log structures"
},
{
"url": "https://arxiv.org/abs... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | Do log schemes constructed from compatible facetwise zero-mutable Laurent polynomials admit both a log-crepant resolution and a smoothing? | Conjecture (Corti-R.). Log schemes obtained as in (b) of the Proposition permit a log crepant log resolution and also a smoothing. Proposition. (a) A choice of zero-mutable Laurent polynomial on a facet ∆ of the dual P ∨ of P gives a singular generically log smooth structure at the one-dimensional stratum of Y correspo... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,446 | OWR-14299574-006 | Sharp Homological Bounds for Realizable Monomial Ideals | Is the homological-dimension lower bound for the number of realizations sharp for every realizable monomial ideal in $k[x_1,x_2]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-006",
"literature-status:open",
"owr-year:2025"
] | The homological-dimension lower bound is proved, but its sharpness for realizable monomial ideals in two variables is explicitly left as a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | Is the homological-dimension lower bound for the number of realizations sharp for every realizable monomial ideal in $k[x_1,x_2]$? | We conjecture that this bound is sharp for realizable monomial ideals of k[x1 , x2 ]. 3. Applications The Independence Theorem presents the possibility of categorifying numerical invariants defined as codimensions of realizable submodules. Normal surface singularities. Originally defined by Ágoston and Némethi in [1], ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,447 | OWR-14299574-007 | Motivic Igusa Series of Plane Curves | For a smooth curve $f$, compute the motivic Igusa series $Q_f(s,T)$; ultimately compute it for every reduced plane curve. For a reduced plane curve, also find an exponential relation between the cohomology of its restricted contact loci $X_{f,n}^0$ and its punctual Hilbert schemes $\operatorname{Hilb}_n(f)_0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-007",
"literature-status:open",
"owr-year:2025"
] | The report states that even the smooth-curve case requires a family of naive Igusa-zeta computations not then available in the literature, and leaves computation of the series and the exponential relation as questions. | [
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
},
{
"url": "https://arxiv.org/abs/2503.18449",
"label": "Discriminants and motivic integration"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | For a smooth curve $f$, compute the motivic Igusa series $Q_f(s,T)$; ultimately compute it for every reduced plane curve. For a reduced plane curve, also find an exponential relation between the cohomology of its restricted contact loci $X_{f,n}^0$ and its punctual Hilbert schemes $\operatorname{Hilb}_n(f)_0$. | for some formal parameter s. Unfortunately, already for a smooth curve f , com- puting Qf (s, T ) amounts to compute the naive Igusa zeta function for the discrim- inant of monic degree n polynomials for all n. To the best of our knowledge, such a computation is not in the literature, although some related work in the ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,448 | OWR-14299574-008 | Small Resolutions Detected by Symplectic Cohomology | Let $F$ be the Milnor fiber of an isolated compound Du Val singularity. Does the singularity admit a small resolution with $\ell$ irreducible exceptional components if and only if $\operatorname{rank}SH^k(F)=\ell$ in every negative degree $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The Evans--Lekili equivalence between small resolutions and negative-degree symplectic cohomology remains conjectural in general, while explicit calculations provide evidence and verify it for broad quasihomogeneous cA subfamilies. | [
{
"url": "https://doi.org/10.5802/ahl.177",
"label": "Symplectic cohomology of cDV singularities"
},
{
"url": "https://doi.org/10.1007/s00209-026-03943-7",
"label": "Symplectic cohomology of quasihomogeneous cA singularities"
},
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | Let $F$ be the Milnor fiber of an isolated compound Du Val singularity. Does the singularity admit a small resolution with $\ell$ irreducible exceptional components if and only if $\operatorname{rank}SH^k(F)=\ell$ in every negative degree $k$? | Conjecture 1.4], which predicts that, for an isolated compound Du Val (cDV) singularity, the existence of a small resolution can be detected by the symplectic cohomology of its Milnor fibre F . Isolated cDV singularities are terminal threefold hypersurface singularities and form the only class of Gorenstein singularitie... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,449 | OWR-14299574-009 | Proved Symplectic-Cohomology Factorization Fragment | Conjecture 5.3], and show that this refined version also holds for all the singularities we consider in [1]. Our findings can be summarised as follows. Theorem 3. Let p(x, y, z, w) = x2 + y 2 + g(z, w) be a suspended polynomial and let F (resp. L) denote the corresponding Milnor fibre (resp. link). Consider a small Q-fact... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490](https://doi.org/10.4171/owr/2025/45)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction states a refined conjecture only to report that it is proved for all quasihomogeneous comp) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299574-009",
"literature-status:partially-solved",
"owr-year:2025"
] | The refined symplectic-cohomology identity is proved for suspended polynomials in the considered quasihomogeneous cA families, but the extracted universal conjecture is not proved for all isolated cDV singularities. | [
{
"url": "https://doi.org/10.4171/owr/2025/45",
"label": "Oberwolfach Report 45/2025"
},
{
"url": "https://doi.org/10.1007/s00209-026-03943-7",
"label": "Symplectic cohomology of quasihomogeneous cA singularities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/45 | null | null | null | null | Conjecture 5.3], and show that this refined version also holds for all the singularities we consider in [1]. Our findings can be summarised as follows. Theorem 3. Let p(x, y, z, w) = x2 + y 2 + g(z, w) be a suspended polynomial and let F (resp. L) denote the corresponding Milnor fibre (resp. link). Consider a small Q-fact... | unrecoverable | The official report confirms that this extraction states a refined conjecture only to report that it is proved for all quasihomogeneous compound-$A_n$ singularities considered there; it is not a separately posed open problem. No separate clean statement is promoted; the original record remains publicly visible and reta... | null | null | null | null | null | Singularities (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/45, pp. 2413--2490 |
30,006,450 | OWR-14299575-001 | Negative Dependence for Random Spanning Forests | Let $G=(V,E)$ be a graph and let $\mathcal F$ be its family of spanning forests. Does the generating polynomial $p_{\mathcal F}(x)=\sum_{F\in\mathcal F}x^F$ satisfy the negative-dependence property $R(1,\{1\})$? More broadly, is there a class between real-stable and Lorentzian polynomials for which $R(c,\mathbb R_{\geq... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Combinatorial Hodge Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/47, pp. 2545--2592](https://doi.org/10.4171/owr/2025/47)
## Literature review (checked 202... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299575-001",
"literature-status:open",
"owr-year:2025"
] | The proposed search for a polynomial class interpolating real-stable and Lorentzian behavior with the stated correlation constant is presented as a general approach to open problems; the report supplies no proof of existence of such a class. | [
{
"url": "https://doi.org/10.4171/owr/2025/47",
"label": "Oberwolfach Report 47/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/47 | null | null | null | Let $G=(V,E)$ be a graph and let $\mathcal F$ be its family of spanning forests. Does the generating polynomial $p_{\mathcal F}(x)=\sum_{F\in\mathcal F}x^F$ satisfy the negative-dependence property $R(1,\{1\})$? More broadly, is there a class between real-stable and Lorentzian polynomials for which $R(c,\mathbb R_{\geq... | One general approach for both of these open problems is to find some new class of polynomials, possibly containing real stable polynomials and being contained in Lorentzian polynomials (or a closely related class), for which R(c, Rn\geq0 ) holds for some desired constant c \in [1, 2]. Conjecture 6 (Kahn, Grimmett–Winkle... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Combinatorial Hodge Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/47, pp. 2545--2592 |
30,006,451 | OWR-14299577-001 | Reversible Primes and Prime Palindromes | Are there infinitely many primes whose base-ten digit reversals are also prime? Are there infinitely many palindromic primes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-001",
"literature-status:open",
"owr-year:2025"
] | Infinitely many primes whose digit reversals are prime, and infinitely many prime palindromes, remain unproved; current sieve results reach almost-prime reversals and palindromic almost-primes rather than the prime assertions. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://academic.oup.com/imrn/article/2024/18/12466/7729537",
"label": "Infinitude of Palindromic Almost-Prime Numbers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Are there infinitely many primes whose base-ten digit reversals are also prime? Are there infinitely many palindromic primes? | Are there infinitely many prime numbers p whose reverse ← − p is also a prime number? This is an open problem which seems at least as difficult as the twin prime conjecture. Here again we conjecture the existence of infinitely many prime palin- dromes. Primes with almost prime reverse Cécile Dartyge (joint work with Joël... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,452 | OWR-14299577-002 | Limiting Distributions of Mixed Character Sums | For each prime $q$, let $\chi_q$ be the prescribed deterministic character and let $S(\chi_q,x,\theta)=\sum_{n\leq x}\chi_q(n)e(n\theta)$. When $\theta$ is uniform on $[0,1]$, determine the limiting distribution of this mixed character sum as $q\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-002",
"literature-status:open",
"owr-year:2025"
] | The cited work proves limiting process laws for shifted mixed character sums with characters sampled from families, but it does not determine the stated limit for the deterministic quadratic character as q tends to infinity with theta uniform. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://arxiv.org/abs/2510.06161",
"label": "Distribution of mixed character sums"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For each prime $q$, let $\chi_q$ be the prescribed deterministic character and let $S(\chi_q,x,\theta)=\sum_{n\leq x}\chi_q(n)e(n\theta)$. When $\theta$ is uniform on $[0,1]$, determine the limiting distribution of this mixed character sum as $q\to\infty$. | What is the limiting distribution of S(χq , x, \theta) when \theta \in [0, 1] is chosen uniformly at random and q \to \infty? We will report on the results in [1] and [2]. We develop an approach aiming to understand the mixed character sums X S(χ, x, \theta) = χ(n)e(n\theta), n\leqx For each integer k \in [0, q − 1] an... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,453 | OWR-14299577-003 | Maximum Normalized Mahler Measure of Littlewood Polynomials | Let $P_n(x)=\sum_{k=0}^n a_kx^k$ range over Littlewood polynomials with $a_k\in\{-1,1\}$. Determine the extremal limit superior $b_m=\limsup_{n\to\infty}M_0(P_n)/\sqrt{n}$, where $M_0$ denotes Mahler measure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The Mahler limsup for Littlewood polynomials is not determined, but the record has been improved by proving arbitrarily large degrees with normalized Mahler measure greater than 0.954. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://arxiv.org/abs/2510.06161",
"label": "Distribution of mixed character sums"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $P_n(x)=\sum_{k=0}^n a_kx^k$ range over Littlewood polynomials with $a_k\in\{-1,1\}$. Determine the extremal limit superior $b_m=\limsup_{n\to\infty}M_0(P_n)/\sqrt{n}$, where $M_0$ denotes Mahler measure. | What is M0 (Pn ) bm = lim sup \sqrt{ } , n\to\infty n Pn k where Pn (x) = k=0 ak x with ak = \pm1 for all k? where Y(l) are independent random variables uniformly distributed in \{−1, 1\}. Theorem 2. For each fixed \alpha and \beta, the random process Gq,\alpha,\beta converges in distribution to G\alpha,\beta as q \to \... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,454 | OWR-14299577-004 | Pointwise Convergence of Polynomial Ergodic Averages | Let $(X,\mathcal{B},\mu)$ be a probability space with commuting invertible measure-preserving transformations $T_1,\ldots,T_m$, and let $P_1,\ldots,P_m\in\mathbb{Z}[y]$. For $f_1,\ldots,f_m\in L^\infty(X)$, do the averages $\frac{1}{N}\sum_{n=1}^N\prod_{i=1}^m f_i(T_i^{P_i(n)}x)$ converge pointwise almost everywhere as... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-004",
"literature-status:partially-solved",
"owr-year:2025"
] | Walsh proved full L2 convergence, and recent work proves pointwise convergence when the polynomial degrees are distinct, but pointwise almost-everywhere convergence for arbitrary commuting polynomial data remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://arxiv.org/abs/2411.09478",
"label": "The multilinear circle method and a question of Bergelson"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $(X,\mathcal{B},\mu)$ be a probability space with commuting invertible measure-preserving transformations $T_1,\ldots,T_m$, and let $P_1,\ldots,P_m\in\mathbb{Z}[y]$. For $f_1,\ldots,f_m\in L^\infty(X)$, do the averages $\frac{1}{N}\sum_{n=1}^N\prod_{i=1}^m f_i(T_i^{P_i(n)}x)$ converge pointwise almost everywhere as... | Is it true that for any functions f1 , . . . , fm \in L\infty (X) the multilinear polynomial ergodic averages 1 X Y Pi (n) N m (1) fi Ti x , x \in X, N n=1 i=1 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,455 | OWR-14299577-005 | Moments of the Riemann Zeta Function | For every integer $k\geq1$, prove that there is an explicit polynomial $P_k$ of degree $k^2$ such that $\frac{1}{T}\int_0^T|\zeta(1/2+it)|^{2k}\,dt=P_k(\log T)+o(1)$ as $T\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-005",
"literature-status:open",
"owr-year:2025"
] | The Conrey--Farmer--Keating--Rubinstein--Snaith moment recipe is conjectural for the broad families referenced here; known special cases and function-field analogues do not prove the general family statement. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://doi.org/10.1112/S0024611505015174",
"label": "Integral moments of L-functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For every integer $k\geq1$, prove that there is an explicit polynomial $P_k$ of degree $k^2$ such that $\frac{1}{T}\int_0^T|\zeta(1/2+it)|^{2k}\,dt=P_k(\log T)+o(1)$ as $T\to\infty$. | T 0 In fact, this conjecture is a special case of a general “recipe” that is supposed to apply also to moments in families of L-functions. The following conjecture is due to Conrey–Farmer–Keating–Rubinstein–Snaith [1]: In fact, this conjecture is a special case of a general “recipe” that is supposed to apply also to mo... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,456 | OWR-14299577-006 | Moments of Quadratic Dirichlet L-Functions | For every integer $k\geq1$, prove that there is an explicit polynomial $Q_k$ of degree $k(k+1)/2$ such that $\frac1N\sum_{|d|\leq N,\ d\text{ squarefree}}L(1/2,\chi_d)^k=Q_k(\log N)+o(1)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The quadratic Dirichlet moment conjecture remains open in its full all-k form, although low moments, bounds, and related function-field results provide substantial partial progress. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
},
{
"url": "https://doi.org/10.1112/S0024611505015174",
"label": "Integral moments of L-functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For every integer $k\geq1$, prove that there is an explicit polynomial $Q_k$ of degree $k(k+1)/2$ such that $\frac1N\sum_{|d|\leq N,\ d\text{ squarefree}}L(1/2,\chi_d)^k=Q_k(\log N)+o(1)$. | Conjecture 2. For each integer k \geq 1 there exists an explicit polynomial Qk of degree k(k + 1)/2 such that 1 X L( 12 , χd )k = Qk (log N ) + o(1). N |d|\leqN d squarefree In fact, this conjecture is a special case of a general “recipe” that is supposed to apply also to moments in families of L-functions. One well-st... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,457 | OWR-14299577-007 | Moments of Quadratic L-Functions over Function Fields | Let $q$ be an odd prime power. For every integer $k\geq1$, prove that there is an explicit polynomial $R_{k,q}$ of degree $k(k+1)/2$ such that $q^{-(2g+1)}\sum_{d}L(1/2,\chi_d)^k=R_{k,q}(g)+o(1)$ as $g\to\infty$, where the sum is over monic squarefree $d\in\mathbb{F}_q[t]$ of degree $2g+1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-007",
"literature-status:partially-solved",
"owr-year:2025"
] | The function-field moment formula is proved with an explicit error term for q sufficiently large relative to k, but the extracted conjecture for every odd prime power and every k is not fully established. | [
{
"url": "https://arxiv.org/abs/2302.07664",
"label": "Hyperelliptic curves and moments"
},
{
"url": "https://arxiv.org/abs/2402.00354",
"label": "Uniform twisted homological stability"
},
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $q$ be an odd prime power. For every integer $k\geq1$, prove that there is an explicit polynomial $R_{k,q}$ of degree $k(k+1)/2$ such that $q^{-(2g+1)}\sum_{d}L(1/2,\chi_d)^k=R_{k,q}(g)+o(1)$ as $g\to\infty$, where the sum is over monic squarefree $d\in\mathbb{F}_q[t]$ of degree $2g+1$. | Conjecture 3. Let q be an odd prime power. For each integer k \geq 1 there exists an explicit polynomial Rk,q of degree k(k + 1)/2 such that 1 X L( 12 , χd )k = Rk,q (g) + o(1). q 2g+1 d\inFq [t] d squarefree, monic deg d=2g+1 The goal of the two papers [2, 3] is to prove Conjecture 3 for q sufficiently large with respec... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,458 | OWR-14299577-008 | Reported Uniform Stability Bound for Twisted Braid-Group Homology | Conjecture 3. We can compute this. • The trace of Frobenius on unstable homology gives rise to the error term. We can control this if we know a bound on unstable Betti numbers (this turns out to be easy) and a good enough range of stability. The sheaf Lk decomposes into summands V\lambda , indexed by irreducible repres... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report explains that the required uniform stability bound is proved in the cited work; this extraction is proof exposition surr) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The required uniform homological-stability range has now been proved in a linear range, yielding the predicted function-field moment asymptotics in a large-q regime; the full conjecture as stated for all odd prime powers is not thereby settled. | [
{
"url": "https://arxiv.org/abs/2402.00354",
"label": "Uniform twisted homological stability"
},
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | null | Conjecture 3. We can compute this. • The trace of Frobenius on unstable homology gives rise to the error term. We can control this if we know a bound on unstable Betti numbers (this turns out to be easy) and a good enough range of stability. The sheaf Lk decomposes into summands V\lambda , indexed by irreducible repres... | unrecoverable | The official report explains that the required uniform stability bound is proved in the cited work; this extraction is proof exposition surrounding that result, not a separate open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,459 | OWR-14299577-009 | Duplicate Reported Twisted Braid-Group Stability Result | The sheaf Lk decomposes into summands V\lambda , indexed by irreducible representa- tions of the symplectic group. The multiplicity of V\lambda in Lk depends on k and n, but the family of summands \{V\lambda \} are the same regardless.2 It is thus natural to study each summand H∗ (\betan ; V\lambda ) individually. What... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this overlapping extraction repeats the stable-homology calculation and uniform stability bound already de) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-009",
"literature-status:partially-solved",
"owr-year:2025"
] | The stable homology and a uniform stability range are computed, and these imply the associated moment formula in the large-q regime, but the full all-q conjectural asymptotic remains unresolved. | [
{
"url": "https://arxiv.org/abs/2302.07664",
"label": "Hyperelliptic curves and moments"
},
{
"url": "https://arxiv.org/abs/2402.00354",
"label": "Uniform twisted homological stability"
},
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach Report 51/2025"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | null | The sheaf Lk decomposes into summands V\lambda , indexed by irreducible representa- tions of the symplectic group. The multiplicity of V\lambda in Lk depends on k and n, but the family of summands \{V\lambda \} are the same regardless.2 It is thus natural to study each summand H∗ (\betan ; V\lambda ) individually. What... | unrecoverable | The official report confirms that this overlapping extraction repeats the stable-homology calculation and uniform stability bound already described in the preceding reported-result extraction. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,460 | OWR-14299577-010 | Reported Function-Field Moment Result | Conjecture 3. Then, Frobenius eigenvalues equidistribute according to a theorem of Deligne, and this allows you to prove e.g. that sums which should have lots of cancellation do have lots of cancellation. What we do in [2, 3] is also to exploit the freedom of varying q, but in a different way. Namely, Deligne’s bounds o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report states that the cited work proves the fixed-function-field moment formula for sufficiently large odd prime powers and de) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-010",
"literature-status:partially-solved",
"owr-year:2025"
] | The function-field moment conjecture is proved in a restricted regime, using uniform twisted homological stability and sufficiently large q, but the full fixed-q statement for every odd prime power remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
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{
"url": "https://arxiv.org/abs/2302.07664",
"label": "Bergström--Diaconu--Petersen--Westerland"
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{
"url": "https://arxiv.org/abs/2402.00354",
"label": "Miller--Patzt--Petersen--Randal-Williams... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | null | Conjecture 3. Then, Frobenius eigenvalues equidistribute according to a theorem of Deligne, and this allows you to prove e.g. that sums which should have lots of cancellation do have lots of cancellation. What we do in [2, 3] is also to exploit the freedom of varying q, but in a different way. Namely, Deligne’s bounds o... | unrecoverable | The official report states that the cited work proves the fixed-function-field moment formula for sufficiently large odd prime powers and describes extensions to shifted moments and ratios; this extracted proof discussion is not a standalone open problem. No separate clean statement is promoted; the original record rem... | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,461 | OWR-14299577-011 | Nonconstancy of the Multiplication-Table Limit Profile | For the limiting profile $f_{\mathrm{Mult}}$ governing the multiplication-table problem, prove that $\max_x f_{\mathrm{Mult}}(x)/\min_x f_{\mathrm{Mult}}(x)>1$; equivalently, prove that the profile is not constant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-011",
"literature-status:open",
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] | Green and Sawhney obtain the asymptotic and a rigorous upper ratio bound, but explicitly leave the strict nonconstancy inequality in the conjecture unproved. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
},
{
"url": "https://arxiv.org/abs/2604.28116",
"label": "Green--Sawhney, permutation model"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For the limiting profile $f_{\mathrm{Mult}}$ governing the multiplication-table problem, prove that $\max_x f_{\mathrm{Mult}}(x)/\min_x f_{\mathrm{Mult}}(x)>1$; equivalently, prove that the profile is not constant. | We have maxx fMult (x) maxx g(x) \leq < 1 + 2 \cdot 10−7 . minx fMult (x) minx g(x) We conjecture that max x fMult (x) minx fMult (x) > 1; an inequality of this type can be proved when studying divisors of smooth numbers in sufficiently short dyadic intervals. Let M (n) = |\{x \in [n] : x = x1 x2 with xi \leq n\}|. The q... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,462 | OWR-14299577-014 | Selberg Eigenvalue Conjecture for Congruence Groups | Prove that every nonzero Laplace eigenvalue of a Maass cusp form for a congruence subgroup is at least $1/4$, equivalently that exceptional Maass cusp forms with eigenvalue below $1/4$ do not exist. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-014",
"literature-status:open",
"owr-year:2025"
] | Selberg's eigenvalue conjecture, asserting the absence of exceptional Maass forms for congruence groups, remains unproved; current unconditional bounds are strictly weaker than 1/4. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
},
{
"url": "https://doi.org/10.1017/fmp.2026.10025",
"label": "Pascadi, exceptional Maass forms"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Prove that every nonzero Laplace eigenvalue of a Maass cusp form for a congruence subgroup is at least $1/4$, equivalently that exceptional Maass cusp forms with eigenvalue below $1/4$ do not exist. | In turn, bounding these exponential sums relies on the spectral theory of GL2 automorphic forms of level q, and in particular on large sieve inequalities for their Fourier coefficients. The dominant contribution in these estimates often comes from the ‘exceptional’ Maass cusp forms f , which are eigenforms of the hyperbo... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,463 | OWR-14299577-016 | Higher-Rank Shifted Convolution Sums | For Fourier coefficients $a(n)$ and $b(n)$ of higher-rank automorphic forms, obtain nontrivial estimates and asymptotic formulas for shifted convolution sums such as $\sum_{n\leq x}a(n)b(n+1)$ beyond the known low-rank cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-016",
"literature-status:open",
"owr-year:2025"
] | Shifted convolution asymptotics are known in important GL(3) times GL(2) cases, including the remaining divisor-function case reported there, but the general higher-rank formulation in the extracted record remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For Fourier coefficients $a(n)$ and $b(n)$ of higher-rank automorphic forms, obtain nontrivial estimates and asymptotic formulas for shifted convolution sums such as $\sum_{n\leq x}a(n)b(n+1)$ beyond the known low-rank cases. | where a(n) and b(n) are two arithmetic functions, usually of multiplicative nature. The shifted convolution problem is not only interesting on its own, such as the twin prime conjecture and the Chowla conjecture, but is also closely related to problems on moments of L-functions, the subconvexity problem as well as the ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,464 | OWR-14299577-017 | Short Coefficient Detection of Cusp-Form Norms | For every $\varepsilon>0$, prove that there is a constant $C=C(k,\varepsilon)>0$ such that every cusp form $f\in S_k(N)$ satisfies $\|f\|^2\ll_{k,\varepsilon}\sum_{n\leq C N^{1+\varepsilon}}|a_f(n)|^2$, without assuming squarefree level or Atkin–Lehner eigenform conditions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-017",
"literature-status:open",
"owr-year:2025"
] | The target N^{1+epsilon} coefficient-detection inequality is proved for square-free levels with Atkin--Lehner eigenforms and in general only with N^{2+epsilon}; the stated uniform bound is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | For every $\varepsilon>0$, prove that there is a constant $C=C(k,\varepsilon)>0$ such that every cusp form $f\in S_k(N)$ satisfies $\|f\|^2\ll_{k,\varepsilon}\sum_{n\leq C N^{1+\varepsilon}}|a_f(n)|^2$, without assuming squarefree level or Atkin–Lehner eigenform conditions. | Is it true that, for every ǫ > 0 there exists C > 0 depending only on k and ǫ such that X (1) kf k2 ≪k,ǫ |af (n)|2 for all f \in Sk (N )? n\leqC\cdotN 1+ǫ (Proposed by Edgar Assing) Let Sk (N ) be the space of cusp forms of level N and weight k, equipped with the Petersson norm Z kf k2 = |f (x + iy)|2 y k−2 dxdy. Γ0 (N... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,465 | OWR-14299577-018 | Difference Sets of Signed Representatives | Let $n\ge1$ and let $A\subseteq\{-n,\ldots,n\}\setminus\{0\}$ contain exactly one of $k$ and $-k$ for each $1\le k\le n$. Must $|(A-A)\cap[1,n]|=(1-o(1))n$? More strongly, for each $\varepsilon>0$ and every $B\subseteq[1,n]$ with $|B|\ge\varepsilon n$, must $\sum_{a,b\in A}\mathbf1_B(a-b)\gg_\varepsilon n^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | partially_solved | Christian Bernert and Nuno Arala Santos | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-018",
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] | Ferudun’s unrefereed preprint claims both answers: at most two elements of $[1,n]$ are absent from $A-A$, and the number of ordered pairs with difference in $B$ is at least $\lfloor(|B|-1)^2/4\rfloor$. Independent checks of all 2,046 signed sets for n≤10 support the claims but do not prove the general theorem. The manu... | [
{
"url": "https://doi.org/10.5281/zenodo.23006720",
"label": "Alper Ferudun (2026), Differences of Signed Representatives — unrefereed preprint"
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{
"url": "https://eulersolve.org/papers/owr-14299577-018/",
"label": "EulerSolve manuscript, source, and verification materials"
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{
"url":... | 2026-09-28T00:00:00 | Alper Ferudun (2026), Differences of Signed Representatives — unrefereed preprint: https://doi.org/10.5281/zenodo.23006720
EulerSolve manuscript, source, and verification materials: https://eulersolve.org/papers/owr-14299577-018/
Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--276... | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $n\ge1$ and let $A\subseteq\{-n,\ldots,n\}\setminus\{0\}$ contain exactly one of $k$ and $-k$ for each $1\le k\le n$. Must $|(A-A)\cap[1,n]|=(1-o(1))n$? More strongly, for each $\varepsilon>0$ and every $B\subseteq[1,n]$ with $|B|\ge\varepsilon n$, must $\sum_{a,b\in A}\mathbf1_B(a-b)\gg_\varepsilon n^2$? | Let n≥1 and A⊂{−n,…,n}\{0} have size n and contain one of k and −k for every 1≤k≤n. Is |(A−A)∩[1,n]|=(1−o(1))n? If B⊆{1,…,n} has |B|≥εn, is the sum of 1_B(a−b) over a,b∈A ≫_ε n²? | corrected_verified | Checked OWR 51/2025, p. 2756. Restored the bounded signed-representative setup, removed neighbouring Assing text, and recorded the named proposers. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,466 | OWR-14299577-019 | Three-Full Sums and the Erdős–Ingham Dirichlet Zero Problem | Let $A$ be the set of integers representable as a sum of three $3$-full numbers. Does $A$ have positive density, and does it contain every sufficiently large integer? Separately, for $f(s)=1+2^{-s}+3^{-s}+5^{-s}$, does there exist $t\in\mathbb{R}$ with $f(1+it)=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-019",
"literature-status:open",
"owr-year:2025"
] | The extracted record combines unresolved questions on sums of three 3-full numbers with the Erdős--Ingham zero problem for 1+2^{-s}+3^{-s}+5^{-s}; no authoritative proof resolving either question was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $A$ be the set of integers representable as a sum of three $3$-full numbers. Does $A$ have positive density, and does it contain every sufficiently large integer? Separately, for $f(s)=1+2^{-s}+3^{-s}+5^{-s}$, does there exist $t\in\mathbb{R}$ with $f(1+it)=0$? | Is this easier to prove for the sum of three 3-full numbers?) (b) Are all sufficiently large integers in A? (Presumably not – indeed, probably the density of A is < 1. Are there any t \in R such that f (1 + it) = 0? (Presumably not.) This was asked by Erdős and Ingham in connection with Tauberian theorems. (Proposed by ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,467 | OWR-14299577-020 | Counting Palindromic and Digit-Reversible Squares | Determine the asymptotic number of palindromic squares in $[1,X]$, and decide whether infinitely many exist outside the four known infinite families. Determine the number of nonpalindromic squares whose digit reversal is also a square, and decide whether there are infinitely many. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-020",
"literature-status:partially-solved",
"owr-year:2025"
] | Infinitely many non-palindromic reversible squares are known through an explicit family, but the broader counting and classification question for palindromic squares beyond the four families remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
},
{
"url": "https://oeis.org/A035090",
"label": "OEIS A035090"
},
{
"url": "https://oeis.org/A002778/a002778_1.pdf",
"label": "Keith, Classification and enumeration of palindromic squares"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Determine the asymptotic number of palindromic squares in $[1,X]$, and decide whether infinitely many exist outside the four known infinite families. Determine the number of nonpalindromic squares whose digit reversal is also a square, and decide whether there are infinitely many. | Editor’s note: Keith [9] has given four infi- nite families of palindromic squares, and asks whether there are infinitely many aside from these. (2) How many non-palindromic squares are there which remain a square when the digits are reversed? Are there infinitely many? (a) Does A have positive density? (Presumably yes, s... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,468 | OWR-14299577-021 | Rational Points on a Singular Twisted Cayley Cubic | Let $N(B)$ count primitive integer solutions $(x,y,z,w)\in[-B,B]^4$ with $x\neq0$ to $x^3+2xyz+xw^2-y^2w+wz^2=0$. Prove an asymptotic $N(B)\sim(c_1+c_2)B(\log B)^3$ with explicit positive constants, where $c_1$ is the predicted product of local densities and $c_2$ accounts for the Zariski-dense thin set. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299577-021",
"literature-status:open",
"owr-year:2025"
] | The requested asymptotic for primitive points on the twisted four-singularity Cayley cubic is presented as an open problem; the thin-set contribution is specifically identified as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $N(B)$ count primitive integer solutions $(x,y,z,w)\in[-B,B]^4$ with $x\neq0$ to $x^3+2xyz+xw^2-y^2w+wz^2=0$. Prove an asymptotic $N(B)\sim(c_1+c_2)B(\log B)^3$ with explicit positive constants, where $c_1$ is the predicted product of local densities and $c_2$ accounts for the Zariski-dense thin set. | What is the proper generalisation of this to higher dimensions? (Proposed by Tim Browning) Let N (B) count the number of solutions to x3 + 2xyz + xw2 − y 2 w + wz 2 = 0 with x 6= 0 and gcd(x, y, z, w) = 1 with x, y, z, w \in Z4 \cap [−B, B]4 . This has 4 sin- gularities, and is a twisted form of the Cayley cubic surfac... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,469 | OWR-14299577-022 | Primitive-Root Orders of Elliptic-Curve Frobenius Traces | Let $E$ be an elliptic curve and, for each prime $p$ of good reduction, let $a_p$ be its Frobenius trace. Are there infinitely many $p$ for which $a_p$ is a primitive root modulo $p$? Are there infinitely many $p$ for which the multiplicative order of $a_p$ modulo $p$ is at least six? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764](https://doi.org/10.4171/owr/2025/51)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (partially_solved) | null | null | [Discussion #4 literature review, 2026-09-29] keep **partially_solved**. | [
"owr",
"oberwolfach-reports",
"OWR-14299577-022",
"literature-status:partially-solved",
"owr-year:2025"
] | The workshop report records a sketched solution for the order-at-least-six question, but provides no published complete proof for it or for the stronger primitive-root assertion, so the pair is not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2025/51",
"label": "Oberwolfach report 51/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/51 | null | null | null | Let $E$ be an elliptic curve and, for each prime $p$ of good reduction, let $a_p$ be its Frobenius trace. Are there infinitely many $p$ for which $a_p$ is a primitive root modulo $p$? Are there infinitely many $p$ for which the multiplicative order of $a_p$ modulo $p$ is at least six? | One can show by an elementary computation that if p does not divide the discriminant (or the conductor) of E, and if ap is non-zero, then the multiplicative order of ap modulo p coincides with the degree of the extension of Fp generated by the p-torsion points of E over Fp . (1) Are there infinitely many p such that ap ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/51, pp. 2701--2764 |
30,006,470 | OWR-14299578-002 | Optimal Bounds for Pairs of Commuting Integer Matrices | For $X\in M_n(\mathbb{Z})$, let $|X|$ be the maximum absolute value of its entries, and define $N(T)=\#\{(X,Y)\in M_n(\mathbb{Z})^2:|X|\leq T,\ |Y|\leq T,\ XY=YX\}$. Prove that, for every $\varepsilon>0$, $N(T)\ll_\varepsilon T^{n^2+1+\varepsilon}$ for arbitrary $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-002",
"literature-status:partially-solved",
"owr-year:2025"
] | The commuting-matrix conjecture has the conjectured exponent for n at most 3, while the reported general theorem gives a weaker exponent n/2+2-2/(n+1); the optimal general bound remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | For $X\in M_n(\mathbb{Z})$, let $|X|$ be the maximum absolute value of its entries, and define $N(T)=\#\{(X,Y)\in M_n(\mathbb{Z})^2:|X|\leq T,\ |Y|\leq T,\ XY=YX\}$. Prove that, for every $\varepsilon>0$, $N(T)\ll_\varepsilon T^{n^2+1+\varepsilon}$ for arbitrary $n$. | conjecture. 2 Conjecture. For any \varepsilon > 0 we have N (T ) ≪\varepsilon T n +1+\varepsilon . For n \leq 3 it is possible to prove the conjectured bound by examining the underlying system of n2 quadratic equations in 2n2 variables, but it seems too complicated to do so when n is large. The following is our main re... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,471 | OWR-14299578-003 | Character Sums for General Polynomial Families | Extend the available stratification and cancellation estimates for multiplicative character sums from the treated polynomial family to broad, explicitly characterized families of multivariable polynomials. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-003",
"literature-status:open",
"owr-year:2025"
] | The report explicitly describes generalization of the proved character-sum theorem to other polynomial families as work in progress, so the extracted question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Extend the available stratification and cancellation estimates for multiplicative character sums from the treated polynomial family to broad, explicitly characterized families of multivariable polynomials. | A natural question is to generalize Theorem 1 to other families of polynomials. Σ(u, v) is very intricate. However we benefit from the fact that we are summing over (u, v) as follows. Introduce the following sum p X 2r Y Λ := χi xk y ℓ (sxm + ty n ) x,y=1 j=1 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,472 | OWR-14299578-004 | Rank Distribution in Quadratic-Twist Families | Fix an elliptic curve $E$ over a global field $K$, a norm $\operatorname{Nm}$ on $K$, and $j\geq0$. If $\mathcal{F}(X)$ is the set of quadratic extensions $K(\sqrt{d})/K$ with squarefree $d$ and $\operatorname{Nm}(d)\leq X$, determine the limit as $X\to\infty$ of the proportion for which $\operatorname{rk}E(K(\sqrt{d})... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-004",
"literature-status:open",
"owr-year:2025"
] | The limiting rank distribution in quadratic-twist families is the Goldfeld problem; the report records major conditional and Selmer-theoretic progress but not a proof of the stated distribution in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
},
{
"url": "https://arxiv.org/abs/2503.17619",
"label": "Smith, BSD implies Goldfeld"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Fix an elliptic curve $E$ over a global field $K$, a norm $\operatorname{Nm}$ on $K$, and $j\geq0$. If $\mathcal{F}(X)$ is the set of quadratic extensions $K(\sqrt{d})/K$ with squarefree $d$ and $\operatorname{Nm}(d)\leq X$, determine the limit as $X\to\infty$ of the proportion for which $\operatorname{rk}E(K(\sqrt{d})... | X\to\infty \#F (X) We note that the above question is equivalent to the problem of computing the dis- tribution of algebraic ranks of K-rational points of quadratic twist families \{Ed \}d of E over K. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,473 | OWR-14299578-005 | Poonen-Rains Selmer Distributions in Twist Families | Let $E/K$ be an elliptic curve and let $E_d$ range through a natural family of twists. Prove that the dimensions of the $p$-Selmer groups $\operatorname{Sel}_p(E_d/K)$ have the Poonen–Rains limiting distribution for the full family, beyond the currently proved primes, fields, and conditional regimes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Poonen--Rains-type Selmer distributions are proved in several important twist and function-field settings, and the 2026 cyclic-extension work gives conditional rank bounds, but the full stated distribution over the broad family remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
},
{
"url": "https://arxiv.org/abs/2607.01126",
"label": "Keliher--Park, Selmer ranks in prime cyclic extensions"
},
{
"url": "https://doi.org/10.1090/S0894-0347-2011-00710-8",
"label": "Poonen--Rai... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Let $E/K$ be an elliptic curve and let $E_d$ range through a natural family of twists. Prove that the dimensions of the $p$-Selmer groups $\operatorname{Sel}_p(E_d/K)$ have the Poonen–Rains limiting distribution for the full family, beyond the currently proved primes, fields, and conditional regimes. | The above construction can be generalized to any endomorphism of E defined over K. For the family of quadratic twists of E and p = 2, the elements of Sel2 (Ed /K) can be described more explicitly: they parametrize bi-quadratic extensions over the field K(E[2]) with certain ramification conditions at places v | 2d∆E \infty... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,474 | OWR-14299578-006 | Effective Mordell Bounds for Rational Points | Give an effective form of the Mordell conjecture: for every smooth projective curve $C$ of genus at least two over a number field $K$, compute an explicit bound for the heights and number of points in $C(K)$ from effective arithmetic data of $C$ and $K$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-006",
"literature-status:open",
"owr-year:2025"
] | Faltings proves finiteness of rational points, but the effective or explicit Mordell problem remains open in general, exactly as stated in the source report. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Give an effective form of the Mordell conjecture: for every smooth projective curve $C$ of genus at least two over a number field $K$, compute an explicit bound for the heights and number of points in $C(K)$ from effective arithmetic data of $C$ and $K$. | This remains a difficult open problem, in the context of the so-called effective or explicit Mordell conjecture. Bogomolov and Lehmer type bounds and rational points of small rank on algebraic varieties Evelina Viada | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,475 | OWR-14299578-007 | Torsion-Anomalous Conjecture for Semiabelian Varieties | Let $V$ be an irreducible subvariety of a semiabelian variety $G$. Prove that $V$ contains only finitely many maximal $V$-torsion-anomalous subvarieties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-007",
"literature-status:open",
"owr-year:2025"
] | The torsion-anomalous conjecture is proved for curves in abelian varieties and some codimension-two cases, but not for the general varieties described in the record. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
},
{
"url": "https://doi.org/10.1093/imrn/1999.20.1119",
"label": "Bombieri--Masser--Zannier"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Let $V$ be an irreducible subvariety of a semiabelian variety $G$. Prove that $V$ contains only finitely many maximal $V$-torsion-anomalous subvarieties. | Conjecture. The case of hypersufaces reduces to the Manin-Mumford Conjecture. Unfortunately, the TAC is only proven for curves in abelian varieties, and for varieties of codi- mension 2 in Gnm and E N . However, some cases are proven in an effective way and this has consequences on the effective Mordell-Lang Conjecture. ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,476 | OWR-14299578-008 | Finiteness of R-Equivalence Classes in Nonabelian Cohomology | Let $K$ be a number field and $G$ a finite solvable group. Is the quotient $H^1(K,G)/R$ by $R$-equivalence finite? If so, relate its cardinality to the minimum number of torsors over a purely transcendental extension of $K$ needed to parametrize $H^1(K,G)$ densely. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-008",
"literature-status:open",
"owr-year:2025"
] | Finiteness of H^1(K,G) modulo R-equivalence for finite solvable G over number fields is explicitly posed as an open problem, including preservation under split extensions. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Let $K$ be a number field and $G$ a finite solvable group. Is the quotient $H^1(K,G)/R$ by $R$-equivalence finite? If so, relate its cardinality to the minimum number of torsors over a purely transcendental extension of $K$ needed to parametrize $H^1(K,G)$ densely. | Then the number r of R-equivalence classes in H1 (K, A)/R is finite, and it is the minimal number of torsors over K(t1 , . . . , td ) needed to densely parametrize H1 (K, A), for all sufficiently large Our work motivates the following open question: Problem 5. Is r := H1 (K, G)/R finite? Applying stratification theorems to ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,477 | OWR-14299578-009 | Asymptotic Density for Quaternary Quadratic Forms | For a quaternary quadratic form $Q$, choose the appropriate main term $M_T(r)$ and determine whether the normalized error in the count $\#\{x\in\mathbb{Z}^4\cap[-r,r]^4:Q(x)=0\}-M_T(r)$ has an asymptotic density as $r\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-009",
"literature-status:open",
"owr-year:2025"
] | Circle-method results determine appropriate main terms and secondary terms in some cases, but the existence of the requested asymptotic density for general quadratic forms in four variables remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | For a quaternary quadratic form $Q$, choose the appropriate main term $M_T(r)$ and determine whether the normalized error in the count $\#\{x\in\mathbb{Z}^4\cap[-r,r]^4:Q(x)=0\}-M_T(r)$ has an asymptotic density as $r\to\infty$. | Is there an asymptotic density for \# x \in Z4 \cap [−r, r]4 : Q(x) = 0 − MT r where MT is an appropriate main term? 7. Mayank Pandey Denote by Kn0 ,n1 ,n2 ,n3 the splitting field of n0 + n1 x + n2 x2 + n3 x3 . The question is to provide bounds for X 1 S(X) = ζKn0 ,n1 ,n2 ,n3 2 |n0 |,|n1 |,|n2 |,|n3 |\leqX | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,478 | OWR-14299578-010 | Curves with Unbounded Rational-Point-to-Genus Ratio | Construct, or prove impossible, a sequence of smooth projective curves $C_n/\mathbb{Q}$ with genus $g(C_n)\geq2$ such that $\#C_n(\mathbb{Q})/g(C_n)\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842](https://doi.org/10.4171/owr/2025/52)
## Literature review (checked 2026-08... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299578-010",
"literature-status:open",
"owr-year:2025"
] | Uniformity results bound rational points in important low-rank or conditional settings, but no construction or impossibility theorem is known for a sequence over Q whose rational-point-to-genus ratio tends to infinity. | [
{
"url": "https://doi.org/10.4171/owr/2025/52",
"label": "Oberwolfach report 52/2025"
},
{
"url": "https://annals.math.princeton.edu/2021/194-1/p05",
"label": "Dimitrov--Gao--Habegger, uniformity in Mordell--Lang"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/52 | null | null | null | Construct, or prove impossible, a sequence of smooth projective curves $C_n/\mathbb{Q}$ with genus $g(C_n)\geq2$ such that $\#C_n(\mathbb{Q})/g(C_n)\to\infty$. | Michael Stoll Can one construct a sequence (Cn )n\geq1 of nice curves over Q of genus g(Cn ) \geq 2 such that \#Cn (Q) lim \to \infty? n\to\infty g(Cn ) where ζKn0 ,n1 ,n2 ,n3 is the Dedekind zeta function. Using convexity estimate for each term individually, one can obtain S(X) ≪ X 5 . Applying known subconvexity boun... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Statistics for Algebraic Objects (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/52, pp. 2765--2842 |
30,006,479 | OWR-14299579-001 | Sharp Second-Order Energy of Hard-Sphere Bosons | Prove the upper bound with the Lee–Huang–Yang constant in the second-order ground-state energy expansion for the dilute hard-sphere Bose gas. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544](https://doi.org/10.4171/owr/2025/46)
## Literature review (... | 3 | partially_solved | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s00205-024-02049-w",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (unrefereed preprint)**. S. Schraven (OWR 46/2025, p. 2504) calls an upper bound with the correct Lee–Huang–Yang constant for hard-sphere bosons in the thermodynamic limit an important open problem; the best published bound has the right order (ρa³)^{1/2} but not t... | [
"owr",
"oberwolfach-reports",
"OWR-14299579-001",
"literature-status:open",
"owr-year:2025"
] | The leading-order ground-state energy is known and the second-order upper bound has the correct order but wrong constant; establishing the correct constant is explicitly still an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2025/46",
"label": "Oberwolfach report 46/2025"
},
{
"url": "https://arxiv.org/abs/2506.04153",
"label": "Brooks--Oldenburg--Saint Aubin--Schlein, third-order upper bound"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/46 | null | null | null | Prove the upper bound with the Lee–Huang–Yang constant in the second-order ground-state energy expansion for the dilute hard-sphere Bose gas. | It remains an important open problem to establish such an upper bound with the correct constant. where the infimum is taken over all \psiN \in L2 (ΛN L ) which are symmetric, i.e. \psiN (x1 , . . . , xN ) = \psiN (x\sigma(1) , . . . , x\sigma(N ) ) for all permutations \sigma \in SN , and which satisfy the hard-core con... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544 |
30,006,480 | OWR-14299579-002 | Quasi-Bosonic Ground States and Excitation Spectra | Can the quasi-bosonic approximation established for the first eigenvalue be extended to the true many-body ground state, possibly after suitable unitary transformations, and does it yield a quasi-bosonic description of the higher excitation spectrum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544](https://doi.org/10.4171/owr/2025/46)
## Literature review (... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299579-002",
"literature-status:open",
"owr-year:2025"
] | The report presents the true-ground-state quasi-bosonic estimate and excitation-spectrum extension as questions, with no complete proof supplied; these claims therefore remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/46",
"label": "Oberwolfach report 46/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/46 | null | null | null | Can the quasi-bosonic approximation established for the first eigenvalue be extended to the true many-body ground state, possibly after suitable unitary transformations, and does it yield a quasi-bosonic description of the higher excitation spectrum? | Could something like (5) hold for the true ground state? Is there any change this quasi bosonic picture is correct beyond the first eigenvalue, with a quasi bosonic excitation spectrum? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544 |
30,006,481 | OWR-14299579-003 | Huang–Yang Derivation Fragment | where F (1) = 2 35 (9\pi) 3 3 (11−2 log 2) in agreement with the Huang-Yang conjecture (1). In the following, we will discuss the main ideas emploied in [2] to prove (1). First, let us define the model. We consider a spin- 21 system of N = N↑ + N↓ fermions in a box Λ = [−L/2, L/2]3 \subset R3 with periodic boundary cond... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544](https://doi.org/10.4171/owr/2025/46)
## Literature review (... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a formula and exposition from the derivation of a proved Huang–Yang energy expansion, n) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299579-003",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a fragment of the Huang--Yang derivation rather than a standalone theorem or resolved question; no independent closure of the underlying claim is established, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/46",
"label": "Oberwolfach Report 46/2025"
},
{
"url": "https://doi.org/10.1007/s00220-023-04672-2",
"label": "Rigorous upper bound for the Gell--Mann--Brueckner formula"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/46 | null | null | null | null | where F (1) = 2 35 (9\pi) 3 3 (11−2 log 2) in agreement with the Huang-Yang conjecture (1). In the following, we will discuss the main ideas emploied in [2] to prove (1). First, let us define the model. We consider a spin- 21 system of N = N↑ + N↓ fermions in a box Λ = [−L/2, L/2]3 \subset R3 with periodic boundary cond... | unrecoverable | The official report confirms that this extraction is a formula and exposition from the derivation of a proved Huang–Yang energy expansion, not an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544 |
30,006,482 | OWR-14299579-004 | Huang–Yang Completion-of-Squares Fragment | conjecture. On the other hand, Q3 cannot be treated directly as an error term since a standard Cauchy-Schwarz estimate shows that the expectation value is bounded by O(L3 ρ7/3 ) while the cor- responding expectation value on the trial state is zero. Instead, a completion of the square method is emploied. The Hamiltonia... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544](https://doi.org/10.4171/owr/2025/46)
## Literature review (... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a technical proof fragment describing a completion-of-squares argument, not an open pro) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299579-004",
"literature-status:open",
"owr-year:2025"
] | The extracted record is an intermediate completion-of-squares estimate in the Huang--Yang analysis and does not state a completed independent result; the unresolved extracted claim is therefore classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/46",
"label": "Oberwolfach Report 46/2025"
},
{
"url": "https://doi.org/10.1007/s00220-023-04672-2",
"label": "Rigorous upper bound for the Gell--Mann--Brueckner formula"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/46 | null | null | null | null | conjecture. On the other hand, Q3 cannot be treated directly as an error term since a standard Cauchy-Schwarz estimate shows that the expectation value is bounded by O(L3 ρ7/3 ) while the cor- responding expectation value on the trial state is zero. Instead, a completion of the square method is emploied. The Hamiltonia... | unrecoverable | The official report confirms that this extraction is a technical proof fragment describing a completion-of-squares argument, not an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544 |
30,006,483 | OWR-14299579-005 | The Gell–Mann–Brueckner Formula in the Thermodynamic Limit | Establish the Gell–Mann–Brueckner formula in the thermodynamic limit. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544](https://doi.org/10.4171/owr/2025/46)
## Literature review (... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299579-005",
"literature-status:open",
"owr-year:2025"
] | The report explicitly states that establishing the Gell--Mann--Brueckner formula in the thermodynamic limit remains open; existing rigorous results cover the mean-field regime but not this target. | [
{
"url": "https://doi.org/10.4171/owr/2025/46",
"label": "Oberwolfach Report 46/2025"
},
{
"url": "https://doi.org/10.1007/s00220-023-04672-2",
"label": "Rigorous upper bound in the mean-field regime"
},
{
"url": "https://arxiv.org/abs/2405.01386",
"label": "Rigorous lower bound in t... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/46 | null | null | null | Establish the Gell–Mann–Brueckner formula in the thermodynamic limit. | Though the analysis of the lower bound even goes slightly beyond the mean-field regime, covering prefactors of the form kF−1+\varepsilon for \varepsilon > 0 small, it re- mains an open problem to establish the Gell–Mann–Brueckner formula in the thermodynamic limit. The report passage is retained verbatim as the relevant... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Analysis of Many-body Quantum Systems (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/46, pp. 2491--2544 |
30,006,484 | OWR-14299580-001 | Open Problems on Spectral-Parameter Yang–Baxter Solutions | Let $V$ be a possibly infinite-dimensional vector space and let $R:\mathbb R\to\operatorname{GL}(V\otimes V)$ satisfy the Yang–Baxter equation with spectral parameter. Can such families be studied by a unified algebraic or categorical theory, and how do analytic properties of $R(x)$ control the associated braided or qu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-001",
"literature-status:open",
"owr-year:2025"
] | The listed structural, categorical, and spectral-parameter questions for Yang--Baxter solutions and Nichols algebras are posed as broad open directions; no complete classification or general theory resolving them was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Let $V$ be a possibly infinite-dimensional vector space and let $R:\mathbb R\to\operatorname{GL}(V\otimes V)$ satisfy the Yang–Baxter equation with spectral parameter. Can such families be studied by a unified algebraic or categorical theory, and how do analytic properties of $R(x)$ control the associated braided or qu... | Open problems and directions We collect here a (non-exhaustive) list of open problems related to solutions of the Yang–Baxter equation, grouped by theme. What can be said about the structure of the Nichols algebras associated to such braidings? Are these braidings in any sense limits of rigid braidings? (2) Nichols alg... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,485 | OWR-14299580-002 | Classification and Applications of Yang–Baxter Operators | Classify $3\times3$ Yang–Baxter operators up to Drinfeld twists, equivalence of their braid-group representations, and spectral data. What geometry do the irreducible components, dimensions, and singularities of the variety of Yang–Baxter operators have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-002",
"literature-status:open",
"owr-year:2025"
] | The requested classifications of Sklyanin-type realizations, Yang--Baxter operators, braid-group images, and internal automorphism objects for skew braces remain open research problems. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Classify $3\times3$ Yang–Baxter operators up to Drinfeld twists, equivalence of their braid-group representations, and spectral data. What geometry do the irreducible components, dimensions, and singularities of the variety of Yang–Baxter operators have? | Are Sklyanin algebras (or suit- able generalizations of them) realizable as Nichols algebras with respect to Yang–Baxter operators with spectral parameter? Can one classify Yang– Baxter operators up to equivalences such as Drinfeld twist, equivalence induced by isomorphic braid group representations, conditions on the ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,486 | OWR-14299580-003 | Recomposition and Cabling of Set-Theoretic Yang–Baxter Solutions | Can indecomposable set-theoretic Yang–Baxter solutions be systematically recomposed into new solutions? Can these solutions be classified up to cabling, or distinguished by computable invariants of cabling equivalence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-003",
"literature-status:open",
"owr-year:2025"
] | The report presents recomposition, integral-unit-group, and cabling classification as open questions; recent work gives partial constructions and criteria but not the requested general classification. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/2410.23821",
"label": "Cabling of non-involutive solutions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Can indecomposable set-theoretic Yang–Baxter solutions be systematically recomposed into new solutions? Can these solutions be classified up to cabling, or distinguished by computable invariants of cabling equivalence? | Is there a sys- tematic way to “recompose” or stitch together indecomposable set-theoretic solutions of the YBE to obtain new ones? (4) Structure algebras of set-theoretic solutions. What can be said about the integral unit group of the multiplicative group of B? (6) Classification up to cabling. Can one classify solu- ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,487 | OWR-14299580-004 | Truncated Yang–Baxter Conjecture | conjecture . . . . . . . . . . . . . . . . . . 2656 Silvia Properzi (joint with C. Dietzel, E. Feingesicht and C. Dietzel, S. Trappeniers) Skew braces, indecomposability and Dehornoy’s representations for solutions to the Yang-Baxter equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2657 Isabela Reci... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extracted fragment contains only a reference to a conjecture and no recoverable formulation. No separa) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-004",
"literature-status:open",
"owr-year:2025"
] | The extracted value is a malformed table-of-contents or conjecture fragment and does not identify a resolved mathematical assertion; under the conservative triage rule its unresolved content is open. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . 2656 Silvia Properzi (joint with C. Dietzel, E. Feingesicht and C. Dietzel, S. Trappeniers) Skew braces, indecomposability and Dehornoy’s representations for solutions to the Yang-Baxter equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2657 Isabela Reci... | unrecoverable | The official report confirms that the extracted fragment contains only a reference to a conjecture and no recoverable formulation. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,488 | OWR-14299580-005 | Noetherian Enveloping Algebras of Lie Algebras | If the universal enveloping algebra $U(\mathfrak g)$ of a Lie algebra $\mathfrak g$ is Noetherian, must $\mathfrak g$ be finite-dimensional? If a group algebra $kG$ is Noetherian, must $G$ be polycyclic-by-finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-005",
"literature-status:open",
"owr-year:2025"
] | The Noetherian enveloping-algebra conjecture for Lie algebras is explicitly identified as a difficult classical open problem; known non-Noetherian examples and graded results do not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://doi.org/10.1016/j.aim.2014.05.007",
"label": "Universal enveloping algebra of the Witt algebra"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | If the universal enveloping algebra $U(\mathfrak g)$ of a Lie algebra $\mathfrak g$ is Noetherian, must $\mathfrak g$ be finite-dimensional? If a group algebra $kG$ is Noetherian, must $G$ be polycyclic-by-finite? | Introduction There have been advances in the classification of Hopf algebras with finite Gelfand- Kirillov dimension but the analogous question for Noetherian Hopf algebras en- counters at the very start difficult classical open problems, namely: Conjecture 1. The report passage is retained verbatim as the relevant context... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,489 | OWR-14299580-006 | Drinfeld-Twist Classification of Set-Theoretic Solutions | Classify set-theoretic Yang–Baxter solutions up to Drinfeld twists. In particular, if two rack solutions on the same set are related by a Drinfeld twist, must they coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-006",
"literature-status:open",
"owr-year:2025"
] | The underlying question is classification of set-theoretic Yang--Baxter solutions up to Drinfeld twists; the literature states this classification remains open, including for rack solutions. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/2109.04978",
"label": "YB-semitrusses and set-theoretic solutions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Classify set-theoretic Yang–Baxter solutions up to Drinfeld twists. In particular, if two rack solutions on the same set are related by a Drinfeld twist, must they coincide? | Racks and an open question. moreover, for all a, b, c \in G, (gdt1) Φ(1, b, c) = (1, b, c), Ψ(a, b, 1) = (a, b, 1), (gdt2) F (a, 1) = (a, 1), F (1, b) = (1, b), (gdt3) m23 Φ = F m23 , (gdt4) m12 Ψ = F m12 , where m : G \times G \to G is the multiplication. Given a braided group (G, m, 1, r) with multiplication m, neutr... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,490 | OWR-14299580-007 | Normal Complements in Integral Group-Ring Units | For a finite nilpotent group $G$, does $G$ have a normal complement in the normalized unit group $U_1(\mathbb Z[G])$? If so, can the complement be chosen torsion-free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-007",
"literature-status:open",
"owr-year:2025"
] | For finite nilpotent groups the existence of a normal complement in the normalized units of the integral group ring is still reported as unknown in general; positive results cover special families only. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://annals.math.princeton.edu/articles/10997",
"label": "Counterexample to the integral group-ring isomorphism problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | For a finite nilpotent group $G$, does $G$ have a normal complement in the normalized unit group $U_1(\mathbb Z[G])$? If so, can the complement be chosen torsion-free? | The aim is to make it accessible to all participants and to highlight the link be- tween braces and group rings, in particular via some old open problems on the isomorphism problem of integral group rings. Recall Problem 29 in [2] for a finite (nilpotent) group G and the group of normalised units U1 (Z[G]) of the integr... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,491 | OWR-14299580-008 | Welding Set-Theoretic Yang–Baxter Solutions | When does a set-theoretic Yang–Baxter solution admit an extension of its braid-group actions to welded braid groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The basic welded-pair representation question is answered by an explicit isomorphism to a derived pair with the twist solution, but the weighted 2-cocycle and further welded-pair classification questions in the same record remain open. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/1707.02250",
"label": "Yang--Baxter 2-cocycle invariants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | When does a set-theoretic Yang–Baxter solution admit an extension of its braid-group actions to welded braid groups? | Can we weld a YBE solution? A set-theoretic YBE solution (X, r) gives rise to an action of every braid group Bn on the nth power of X, hence to a representation of Bn . It is natural to ask when such actions extend to the welded braid groups W Bn . The letter groups can be seen topologically as the motion groups of n u... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,492 | OWR-14299580-009 | Cocycle-Weighted Representations of Welded Braid Groups | For a welded pair $(X,r,s)$, do cocycle weights make the second solution $s$ representation-theoretically relevant? Are the resulting representations of the welded braid group isomorphic to representations arising from a welded pair $(X,r',q)$ built from the derived solution $r'$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-009",
"literature-status:open",
"owr-year:2025"
] | The extracted questions about weighted representations and replacement of the second welded component are explicitly left as questions after the unweighted reduction theorem; no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://doi.org/10.18910/73356",
"label": "Yang--Baxter 2-cocycle invariants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | For a welded pair $(X,r,s)$, do cocycle weights make the second solution $s$ representation-theoretically relevant? Are the resulting representations of the welded braid group isomorphic to representations arising from a welded pair $(X,r',q)$ built from the derived solution $r'$? | This answers an open question from [1]. Does using general second components s become relevant when one enriches the induced representations with weights computed using 2-cocycles, in the spirit of [4]? Are the W Bn -representations induced by a welded pair (X, r, s) isomorphic to ones induced by a welded pair (X, r′ ,... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,493 | OWR-14299580-010 | Structure Objects and Deformations of Welded Pairs | What object plays for a welded pair the role that the structure skew brace plays for a solution? Is there a common framework for the two families of deformations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-010",
"literature-status:open",
"owr-year:2025"
] | The report proposes finding an object for welded pairs and a common framework for two deformation families as open questions; no subsequent general framework resolving either was located. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | What object plays for a welded pair the role that the structure skew brace plays for a solution? Is there a common framework for the two families of deformations? | What object plays for a welded pair the same role as the structure skew brace plays for a solution? Is there a common framework embracing the two families of solution deformations above? The Yang–Baxter Equation and Representations of Braid Groups 2655 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,494 | OWR-14299580-011 | Unidentified Hecke-Type Equivalence Class | The task of determining whether the last class exists was posed as an open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks whether the last item in an unpublished classification list is realizable, but it does not identify that equivalenc) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-011",
"literature-status:open",
"owr-year:2025"
] | The last possible equivalence class of non-involutive Hecke-type unitary Yang--Baxter matrices is still described as an existence question; no construction or impossibility proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://doi.org/10.1007/S00220-011-1386-7",
"label": "Localization of unitary braid group representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | null | The task of determining whether the last class exists was posed as an open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report asks whether the last item in an unpublished classification list is realizable, but it does not identify that equivalence class mathematically; a self-contained statement cannot be restored from the public report. No separate clean statement is promoted; the original record remains publicly visible ... | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,495 | OWR-14299580-012 | Root Systems and Classification of Generalized Nichols Algebras | Develop a root-system and Weyl-groupoid theory for Nichols algebra objects in arbitrary braided tensor categories, and classify the resulting generalized Nichols algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-012",
"literature-status:partially-solved",
"owr-year:2025"
] | The logarithmic Kazhdan--Lusztig correspondence has a general algebraic proof under explicit analytic and categorical hypotheses, but the unconditional analytic hypotheses are not established in full generality. | [
{
"url": "https://arxiv.org/abs/2501.10735",
"label": "Conditional algebraic proof of the logarithmic Kazhdan--Lusztig correspondence"
},
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Develop a root-system and Weyl-groupoid theory for Nichols algebra objects in arbitrary braided tensor categories, and classify the resulting generalized Nichols algebras. | conjecture. In my talk I present a proof. A main step is essentially proving that braided tensor categories with large commutative algebras often look like Drinfeld centers of Nichols algebras. This general picture suggests many other interesting cases, for example for C the category related to an affine Lie algebra at i... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,496 | OWR-14299580-014 | Virtual Abelianity of Unitary Yang–Baxter Braid Images | Let $(R,V)$ be a unitary solution of the Yang–Baxter equation. Is the braid-group image $\rho_R(B_n)$ virtually abelian for every $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-014",
"literature-status:open",
"owr-year:2025"
] | The virtually-abelian image statement for every unitary Yang--Baxter operator is presented as a decategorified conjecture with only substantial evidence and special-case proofs; it remains unresolved in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/1009.0241",
"label": "Localization of unitary braid group representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Let $(R,V)$ be a unitary solution of the Yang–Baxter equation. Is the braid-group image $\rho_R(B_n)$ virtually abelian for every $n$? | Evidence and examples. • In many weakly integral settings, explicit unitary R-matrix realisations (Gaussian/Clifford-like) yield localisation and finite braid images; see, e.g., doubles of finite groups [6], extraspecial 2-group images [7], and property F for SO(N )2 [11]. • For FPdim(X)2 \in / N it has been verified for m... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,497 | OWR-14299580-015 | Classification of Monoidal Functors from the Braid Category | Fix a monoidal subcategory $\mathcal Y$ of the matrix category. Classify the strict monoidal functors in $\operatorname{MonFun}(\mathcal B,\mathcal Y)$, up to the appropriate equivalences. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-015",
"literature-status:open",
"owr-year:2025"
] | The requested classification of monoidal functors from the braid category into an arbitrary fixed matrix subcategory is stated as an organizational problem and is not solved in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/2112.04533",
"label": "Classification of spin-chain braid representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Fix a monoidal subcategory $\mathcal Y$ of the matrix category. Classify the strict monoidal functors in $\operatorname{MonFun}(\mathcal B,\mathcal Y)$, up to the appropriate equivalences. | problem: Problem 1. Fix a subcategory Y of Mat. Classify functors in MonFun(B, Y), up to appropriate equivalences. The category MonFun(B, Mat) has additional categorical structure that facili- tates a more general perspective of the problem above. Theorem 2. The category MonFun(B, Mat) is a strict monoidal category und... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,498 | OWR-14299580-016 | Classifiable Subcategories of Braid-Category Monoidal Functors | Which subcategories of $\operatorname{MonFun}(\mathcal B,\operatorname{Mat})$ admit a tractable classification? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-016",
"literature-status:open",
"owr-year:2025"
] | Some subcategories, including group-type and involutive examples, are understood, but finding subcategories of the full monoidal-functor category that admit classification remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/2112.04533",
"label": "Classification of spin-chain braid representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Which subcategories of $\operatorname{MonFun}(\mathcal B,\operatorname{Mat})$ admit a tractable classification? | Problem 4. Find subcategories of MonFun(B, Mat) amenable to classification. For example, functors associated with group-type solutions [8] to the Yang- Baxter equation provide such a subcategory, although they are not closed under composition. Similarly involutive (i.e., R2 = Id) solutions do not form a subcat- egory of... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,499 | OWR-14299580-017 | Nichols Algebras over Simple Groups | Let $G$ be a finite simple group and let $V$ be a nonzero Yetter–Drinfeld module over $\mathbb C G$. Must the Nichols algebra $\mathcal B(V)$ be infinite-dimensional? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672](https://doi.org/10.4171/owr/2025/49)
## Li... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299580-017",
"literature-status:open",
"owr-year:2025"
] | The conjecture that every nonzero Yetter--Drinfeld module over a finite simple group has infinite-dimensional Nichols algebra remains open; alternating, most sporadic, and many Lie-type cases are known but do not cover all simple groups. | [
{
"url": "https://doi.org/10.4171/owr/2025/49",
"label": "Oberwolfach Report 49/2025"
},
{
"url": "https://arxiv.org/abs/2306.02989",
"label": "Finite-dimensional Nichols algebras of prime dimension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/49 | null | null | null | Let $G$ be a finite simple group and let $V$ be a nonzero Yetter–Drinfeld module over $\mathbb C G$. Must the Nichols algebra $\mathcal B(V)$ be infinite-dimensional? | I will also briefly mention a conjecture of [1] concerning Nichols algebras over simple groups: Conjecture 1. The conjecture remains open. One is never too old to learn about Nichols algebras Leandro Vendramin (joint work with A. Andruskiewitsch, I. Heckenberger, E. Meir) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/49, pp. 2633--2672 |
30,006,500 | OWR-14299582-002 | Sharp Hilbert-Transform Bounds for UMD Spaces | For a UMD Banach space $X$, let $h_p(X)$ be the $L^p(X)$ operator norm of the Hilbert transform and let $m_p(X)$ be the UMD-$p$ constant. Determine the sharp dependence of $h_p(X)$ on $m_p(X)$; in particular, decide whether $h_p(X)$ and $m_p(X)$ are comparable up to universal linear factors. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916](https://doi.org/10.4171/owr/2025/53)
## L... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299582-002",
"literature-status:open",
"owr-year:2025"
] | The Bourgain--Burkholder bounds and later linear reductions give important partial progress, but the sharp dependence of the Hilbert-transform norm on the UMD constant remains the stated UMD conjecture. | [
{
"url": "https://arxiv.org/abs/2604.11273",
"label": "Two-sided linear estimate and dyadic reduction of the UMD conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2025/53",
"label": "Oberwolfach Report 53/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/53 | null | null | null | For a UMD Banach space $X$, let $h_p(X)$ be the $L^p(X)$ operator norm of the Hilbert transform and let $m_p(X)$ be the UMD-$p$ constant. Determine the sharp dependence of $h_p(X)$ on $m_p(X)$; in particular, decide whether $h_p(X)$ and $m_p(X)$ are comparable up to universal linear factors. | It is an open question whether these inequalities are sharp. A two sided linear estimate and a dyadic reduction of the UMD conjecture Komla Domelevo (joint work with Stefanie Petermichl) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916 |
30,006,501 | OWR-14299582-003 | Dimension-Independent Analyticity Bounds for K-Convex Spaces | Let $X$ be a $K$-convex Banach space. For every $1<p<\infty$, do there exist an angle $\theta>0$ and a bound independent of the dimension $d$ such that $\sup_{d\geq1}M_{p,d,\theta}^X<\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916](https://doi.org/10.4171/owr/2025/53)
## L... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299582-003",
"literature-status:open",
"owr-year:2025"
] | Dimension-dependent estimates are available, but the proposed dimension-independent bounds for all K-convex spaces and all p remain an explicit open problem. | [
{
"url": "https://doi.org/10.4171/owr/2025/53",
"label": "Oberwolfach Report 53/2025"
},
{
"url": "https://doi.org/10.4171/JEMS/1430",
"label": "Holomorphic functional calculus and vector-valued Littlewood--Paley theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/53 | null | null | null | Let $X$ be a $K$-convex Banach space. For every $1<p<\infty$, do there exist an angle $\theta>0$ and a bound independent of the dimension $d$ such that $\sup_{d\geq1}M_{p,d,\theta}^X<\infty$? | Is it true that for all 1 < p < \infty one has dimension-independent constants, that is, X sup Mp,d,\theta p < \infty? d\geq1 Pisier [10] proved that the Banach space X is K-convex if and only if there exists an angle 0 < \theta \leq \thetap such that for some all (equivalently: for some) 1 < p < \infty one has X sup M... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916 |
30,006,502 | OWR-14299582-004 | Dimension-Free Bounds and Optimal Ornstein-Uhlenbeck Calculus Angles | If $X$ is $K$-convex, are the bounds $\sup_{d\geq1}M_{p,d,\theta}^X$ finite for every $1<p<\infty$ and every $0<\theta<\theta_p$, possibly even at $\theta=\theta_p$? If $X$ is UMD, does the Ornstein–Uhlenbeck operator $-L_X$ have a bounded $H^\infty(\Sigma_\theta)$ functional calculus for every $0<\theta<\theta_p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916](https://doi.org/10.4171/owr/2025/53)
## L... | 3 | partially_solved | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299582-004",
"literature-status:partially-solved",
"owr-year:2025"
] | For UMD spaces a bounded H-infinity calculus is known at some suboptimal sector angle, while the requested optimal-angle statement remains open; hence the problem has a partial result but is not solved. | [
{
"url": "https://doi.org/10.4171/owr/2025/53",
"label": "Oberwolfach Report 53/2025"
},
{
"url": "https://doi.org/10.4171/JEMS/1430",
"label": "Holomorphic functional calculus and vector-valued Littlewood--Paley theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/53 | null | null | null | If $X$ is $K$-convex, are the bounds $\sup_{d\geq1}M_{p,d,\theta}^X$ finite for every $1<p<\infty$ and every $0<\theta<\theta_p$, possibly even at $\theta=\theta_p$? If $X$ is UMD, does the Ornstein–Uhlenbeck operator $-L_X$ have a bounded $H^\infty(\Sigma_\theta)$ functional calculus for every $0<\theta<\theta_p$? | If X is K-convex, is it true that for all 1 < p < \infty one has X sup Mp,d,\theta <\infty d\geq1 for all 0 < \theta < \thetap , or even X sup Mp,d,\theta p < \infty? d\geq1 Similar questions may be asked with regard to the optimal angle for bounded- ness of the H \infty -calculus of −LX . If X is UMD, Is it true that ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916 |
30,006,503 | OWR-14299582-005 | Optimal Sector Angles for UMD Ornstein-Uhlenbeck Calculus | Let $X$ be a UMD Banach space. For every $1<p<\infty$, does the Ornstein–Uhlenbeck operator $-L_X$ admit a bounded $H^\infty(\Sigma_\theta)$ functional calculus for every sector angle $0<\theta<\theta_p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916](https://doi.org/10.4171/owr/2025/53)
## L... | 3 | partially_solved | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299582-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Kalton--Weis theory supplies bounded H-infinity calculus for some angle below the optimal scalar angle, but the all-angles-below-the-threshold assertion in the extracted problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/53",
"label": "Oberwolfach Report 53/2025"
},
{
"url": "https://doi.org/10.4171/JEMS/1430",
"label": "Holomorphic functional calculus and vector-valued Littlewood--Paley theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/53 | null | null | null | Let $X$ be a UMD Banach space. For every $1<p<\infty$, does the Ornstein–Uhlenbeck operator $-L_X$ admit a bounded $H^\infty(\Sigma_\theta)$ functional calculus for every sector angle $0<\theta<\theta_p$? | If X is UMD, Is it true that for all 1 < p < \infty that −LX has a bounded H \infty (Σ\theta )-calculus for all 0 < \theta < \thetap ? for all 0 < \theta < \thetap , or even X sup Mp,d,\theta p < \infty? d\geq1 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in SPDEs and BSDEs meet Harmonic and Functional Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/53, pp. 2843--2916 |
30,006,504 | OWR-14299583-001 | Functional Inequalities Workshop Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2931 Patricia Alonso Ruiz (joint with Fabrice Baudoin) An isoperimetric inequality for (fractal) spaces with different micro- and macrostructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2934 ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-001",
"literature-status:open",
"owr-year:2025"
] | The exact record is an OCR table-of-contents fragment and does not state an identifiable mathematical claim whose truth can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2025/54",
"label": "Oberwolfach Report 2025/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2931 Patricia Alonso Ruiz (joint with Fabrice Baudoin) An isoperimetric inequality for (fractal) spaces with different micro- and macrostructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2934 ... | unrecoverable | The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,505 | OWR-14299583-003 | Detecting Geometric Scales in Fractal Measurements | Given a space with different microscopic and macroscopic geometries, develop an intrinsic procedure for detecting the correct scale at which to measure volume, perimeter, and isoperimetric behavior. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-003",
"literature-status:open",
"owr-year:2025"
] | Existing fractal-space isoperimetric results require specified structures and scales; no general theorem answering the extracted scale-detection question was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/54",
"label": "Oberwolfach Report 2025/54"
},
{
"url": "https://arxiv.org/abs/1903.10078",
"label": "Alonso Ruiz--Baudoin, Besov classes on Dirichlet spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | Given a space with different microscopic and macroscopic geometries, develop an intrinsic procedure for detecting the correct scale at which to measure volume, perimeter, and isoperimetric behavior. | How to “detect” the correct scale when performing measurements? An isoperimetric inequality for (fractal) spaces with different micro- and macrostructure Patricia Alonso Ruiz (joint work with Fabrice Baudoin) Figure 1. Approximation of a Sierpinski gasket cable system | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,506 | OWR-14299583-004 | Lattice Packing Conjecture for Origin-Symmetric Convex Bodies | Prove that there is a universal constant $c>0$ such that every origin-symmetric convex body $K\subset\mathbb{R}^n$ with $\operatorname{Vol}_n(K)=cn^2$ admits a covolume-one lattice $L\subset\mathbb{R}^n$ satisfying $L\cap K=\{0\}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-004",
"literature-status:open",
"owr-year:2025"
] | The Euclidean-ball and ellipsoid cases are proved, but the stated extension to every origin-symmetric convex body remains a conjecture. | [
{
"url": "https://link.springer.com/article/10.1007/s00222-026-01412-w",
"label": "Lattice packing of spheres using a stochastically evolving ellipsoid"
},
{
"url": "https://doi.org/10.4171/owr/2025/54",
"label": "Oberwolfach Report 2025/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | Prove that there is a universal constant $c>0$ such that every origin-symmetric convex body $K\subset\mathbb{R}^n$ with $\operatorname{Vol}_n(K)=cn^2$ admits a covolume-one lattice $L\subset\mathbb{R}^n$ satisfying $L\cap K=\{0\}$. | We conjecture that the conclusion remains true for any origin- symmetric convex body K satisfying (2), and not only for Euclidean balls or ellipsoids; compare with earlier work of Schmidt under the weaker assumption Voln (K) \leq cn [18, 19]. Functional Inequalities: Geometric Calculus meets Stochastic Analysis 2939 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,507 | OWR-14299583-005 | Banach–Mazur Diameter of Nonsymmetric Convex Bodies | Determine the diameter of the Banach–Mazur compactum of $n$-dimensional convex bodies, equivalently the maximum possible Banach–Mazur distance between two nonsymmetric convex bodies in dimension $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-005",
"literature-status:partially-solved",
"owr-year:2025"
] | The exact Banach--Mazur diameter for nonsymmetric convex bodies is still unknown, although current work gives bounds optimal up to polylogarithmic factors. | [
{
"url": "https://arxiv.org/abs/2510.20511",
"label": "Bizeul, Distances between non-symmetric convex bodies"
},
{
"url": "https://doi.org/10.4171/owr/2025/54",
"label": "Oberwolfach Report 2025/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | Determine the diameter of the Banach–Mazur compactum of $n$-dimensional convex bodies, equivalently the maximum possible Banach–Mazur distance between two nonsymmetric convex bodies in dimension $n$. | A fundamental question is to determine the diameter of the Banach–Mazur compactum, that is, the maximal possible distance between two convex bodies in dimension n. The Banach–Mazur distance provides a quantitative way to compare convex bodies in high dimension up to affine transformations. Given two convex bodies K, L \s... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,508 | OWR-14299583-006 | Reported Mean-Norm Bound for Nonsymmetric Convex Bodies | It was a long standing open problem to provide a similar result in the nonsymmetric case, where Pisier’s argument is known to fail. Functional Inequalities: Geometric Calculus meets Stochastic Analysis 2943 Theorem 2. If K is a convex body in isotropic position, then C log n M (K) \leq \sqrt{ } , n for some universal c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report identifies the nonsymmetric case as a formerly open problem and then states the authors’ theorem $M(K)\leq C\log(n)/\sqr) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The nonsymmetric analogue now has an almost optimal general bound, but the exact optimal estimate and the remaining logarithmic factors are unresolved. | [
{
"url": "https://arxiv.org/abs/2510.20511",
"label": "Bizeul, Distances between non-symmetric convex bodies"
},
{
"url": "https://doi.org/10.4171/owr/2025/54",
"label": "Oberwolfach Report 2025/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | null | It was a long standing open problem to provide a similar result in the nonsymmetric case, where Pisier’s argument is known to fail. Functional Inequalities: Geometric Calculus meets Stochastic Analysis 2943 Theorem 2. If K is a convex body in isotropic position, then C log n M (K) \leq \sqrt{ } , n for some universal c... | unrecoverable | The official report identifies the nonsymmetric case as a formerly open problem and then states the authors’ theorem $M(K)\leq C\log(n)/\sqrt{n}$; it does not pose removal of the logarithm as a new problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance... | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,509 | OWR-14299583-007 | Reported Nonexistence of Critical Loop-Soup Double Points | famous Mandelbrot’s conjecture. Finally, it was proved by Kiefer \sqrt{ }and Mörters [8] that the dimension of double points on the Brownian frontier is ( 97 + 1)/24. The computation of the exact Hausdorff dimensions of the Brownian frontier and double points on the Brownian frontier relied on a so-called Brownian disc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994](https://doi.org/10.4171/owr/2025/54)
## Literatu... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report first motivates the critical double-point question and then states the authors’ result proving that such double points d) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299583-007",
"literature-status:open",
"owr-year:2025"
] | For subcritical intensity the double points are understood, but at critical intensity one the existence of double points remains unresolved. | [
{
"url": "https://arxiv.org/abs/2205.11468",
"label": "Gao--Li--Qian, Multiple points on Brownian loop-soup cluster boundaries"
},
{
"url": "https://doi.org/10.1214/25-AOP1765",
"label": "Annals of Probability, Multiple points on Brownian loop-soup cluster boundaries"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/54 | null | null | null | null | famous Mandelbrot’s conjecture. Finally, it was proved by Kiefer \sqrt{ }and Mörters [8] that the dimension of double points on the Brownian frontier is ( 97 + 1)/24. The computation of the exact Hausdorff dimensions of the Brownian frontier and double points on the Brownian frontier relied on a so-called Brownian disc... | unrecoverable | The official report first motivates the critical double-point question and then states the authors’ result proving that such double points do not exist, so the extraction is not an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Functional Inequalities: Geometric Calculus meets Stochastic Analysis (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/54, pp. 2917--2994 |
30,006,510 | OWR-14299586-001 | Typical Cells in Hyperbolic Tessellations with Unbounded Cells | Extend the notions of cell intensity and typical cell naturally to hyperbolic tessellations containing unbounded cells. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hyperbolic meets Stochastic Geometry (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/57, pp. 3031--3062](https://doi.org/10.4171/owr/2025/57)
## Literature review (checked... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299586-001",
"literature-status:open",
"owr-year:2025"
] | Specific hyperbolic tessellations with unbounded cells are studied, but no natural general extension of cell intensity and typical cell was established. | [
{
"url": "https://ems.press/content/serial-article-files/52444",
"label": "Oberwolfach Report on stochastic geometry"
},
{
"url": "https://arxiv.org/abs/2303.16831",
"label": "Ideal Poisson--Voronoi tessellations in hyperbolic spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/57 | null | null | null | Extend the notions of cell intensity and typical cell naturally to hyperbolic tessellations containing unbounded cells. | One open problem is to find a natural extension of the notions of cell intensity and the typical cell to the case when T contains unbounded cells. unique invariant probability measure on I(Hd , o, x). Then the typical cell Ctyp (T ) of T is a random polytope with distribution hXZ i −1 P(Ctyp (T ) \in \cdot) = \gammad (T... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Hyperbolic meets Stochastic Geometry (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/57, pp. 3031--3062 |
30,006,511 | OWR-14299586-002 | Large-Genus Hyperbolic Surfaces Above the One-Quarter Spectral Threshold | Do there exist closed hyperbolic surfaces of arbitrarily large genus whose first positive Laplace eigenvalue is greater than $1/4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hyperbolic meets Stochastic Geometry (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/57, pp. 3031--3062](https://doi.org/10.4171/owr/2025/57)
## Literature review (checked... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299586-002",
"literature-status:open",
"owr-year:2025"
] | Large-genus constructions approach the one-quarter threshold from below, but existence of arbitrarily large genus with first eigenvalue greater than one-quarter remains unresolved. | [
{
"url": "https://arxiv.org/abs/1406.1080",
"label": "Mondal, On largeness and multiplicity of the first eigenvalue"
},
{
"url": "https://arxiv.org/abs/2302.02540",
"label": "Fortier Bourque--Petri, Linear programming bounds for hyperbolic surfaces"
},
{
"url": "https://arxiv.org/abs/210... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/57 | null | null | null | Do there exist closed hyperbolic surfaces of arbitrarily large genus whose first positive Laplace eigenvalue is greater than $1/4$? | One of the main open problems about hyperbolic surfaces of large genus is whether it is possible to find X \in Mg for arbitrarily large with first positive eigenvalue of the Laplacian \lambda1 (X) > 41 (which is asymptotically optimal). Mini-Workshop: Hyperbolic meets Stochastic Geometry 3051 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Hyperbolic meets Stochastic Geometry (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/57, pp. 3031--3062 |
30,006,512 | OWR-14299587-001 | Constraint-Satisfaction Dichotomy for Homogeneous Structures | Does the finite-domain constraint-satisfaction dichotomy extend to reducts of finitely bounded homogeneous structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | open | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-001",
"literature-status:open",
"owr-year:2025"
] | The finite-domain constraint-satisfaction dichotomy is known, but the analogous dichotomy for homogeneous structures remains open. | [
{
"url": "https://doi.org/10.4171/OWR/2025/58",
"label": "Oberwolfach Report 2025/58"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | Does the finite-domain constraint-satisfaction dichotomy extend to reducts of finitely bounded homogeneous structures? | An analogous conjecture for homogeneous structures remains open despite growing structural insights. Mathematics Subject Classification (2020): 03Cxx, 08Axx. License: Unless otherwise noted, the content of this report is licensed under CC BY SA 4.0. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,513 | OWR-14299587-002 | Finite Length of Permutation Modules over Arbitrary Fields | Let $M$ be an $\omega$-categorical structure, let $G=\operatorname{Aut}(M)$, and let $W$ be an oligomorphic $G$-set. Is the permutation module $F[W]$ of finite length over $FG$ for every field $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-002",
"literature-status:partially-solved",
"owr-year:2025"
] | Finite composition length is proved for the Rado graph and several broad classes, while the question for every finite-relational homogeneous structure remains open. | [
{
"url": "https://arxiv.org/abs/2603.29606",
"label": "Evans, Permutation modules for Ramsey structures"
},
{
"url": "https://www.cs.ox.ac.uk/people/bartek.klin/papers/lics26.pdf",
"label": "Yang--Bojańczyk--Klin, The Finite Length Property of the Rado Graph and Friends"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | Let $M$ be an $\omega$-categorical structure, let $G=\operatorname{Aut}(M)$, and let $W$ be an oligomorphic $G$-set. Is the permutation module $F[W]$ of finite length over $FG$ for every field $F$? | Is F W of finite length for every field F ? So (i) would give a negative answer to a question of Macpherson (Question 2.2.7 (4) in [13]) and (ii) would give a counterexample to a well-known conjecture of Simon Thomas [14] on reducts of finitely homogeneous structures. 2. Ramsey structures and a decision procedure If M is ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,514 | OWR-14299587-003 | Structural Characterization of Exceptional Borel Graphs | What structural property characterizes Borel graphs for which the general results fail? Is there an analogous characterization for Borel graphs whose Borel chromatic number is at most a fixed $k\in\mathbb{N}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The Gowers--Kechris dichotomy handles the basic uncountable-chromatic case, and later work gives complexity results for fixed finite bounds, but no general structural characterization is known. | [
{
"url": "https://link.springer.com/article/10.1007/s00222-021-01047-z",
"label": "Todorčević--Vidnyánszky, A complexity problem for Borel graphs"
},
{
"url": "https://arxiv.org/abs/2111.03683",
"label": "Brandt et al., On Homomorphism Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | What structural property characterizes Borel graphs for which the general results fail? Is there an analogous characterization for Borel graphs whose Borel chromatic number is at most a fixed $k\in\mathbb{N}$? | What does it mean, however, if no such generalization exists? Can we find a reasonable struc- tural characterization of Borel graphs for which these general results fail? Is there a similar characterization for Borel graphs of Borel chromatic number at most some fixed k \in N? Homogeneous Structures: Model Theory meets U... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,515 | OWR-14299587-004 | Reconstructing Structures from Topological Symmetry Monoids | What information about an infinite structure can be reconstructed from its topological automorphism group or from the topological monoid of its elementary self-embeddings? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-004",
"literature-status:partially-solved",
"owr-year:2025"
] | For omega-categorical structures, topological automorphism and elementary-embedding monoids recover the structure up to bi-interpretability, but stronger exact reconstruction is not general. | [
{
"url": "https://doi.org/10.1016/0168-0072(86)90037-0",
"label": "Ahlbrandt--Ziegler, Quasi finitely axiomatizable totally categorical theories"
},
{
"url": "https://arxiv.org/abs/2603.28419",
"label": "de la Nuez Gonzalez et al., Minimal and intrinsic topologies on monoids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | What information about an infinite structure can be reconstructed from its topological automorphism group or from the topological monoid of its elementary self-embeddings? | What information can we recover about the original structure A from a given space of symmetries (as a topological group/monoid)? On the topological reconstruction of monoids of elementary embeddings of \omega-categorical structures Paolo Marimon (joint work with J. de la Nuez Gonzales, Zaniar Ghadernezhad, and Michael ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
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