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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,416 | OWR-12697689-012 | Arc Hilbert–Poincaré Series of ADE Surface Singularities | Does the arc Hilbert–Poincaré series characterize ADE surface singularities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-012",
"literature-status:open",
"owr-year:2023"
] | The Arc Hilbert--Poincare series is computed for rational double points, but current literature continues to pose whether it characterizes them; this remains unresolved. | [
{
"url": "https://webusers.imj-prg.fr/~hussein.mourtada/PointDouble30Sept.pdf",
"label": "Mourtada, jet schemes of rational double points"
},
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Does the arc Hilbert–Poincaré series characterize ADE surface singularities? | Does the Arc Hilbert-Poincaré series characterize ADE surface sin- gularities? This series is an invariant of singularities (it detects regularity) and it contains different ingredients which motivate its study from the viewpoint of singularity theory [8]. But it is in general very difficult to compute, even though so... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,417 | OWR-12697689-013 | Specialness of Local Koszul Homomorphisms | Is every local Koszul homomorphism special Koszul? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-013",
"literature-status:open",
"owr-year:2023"
] | The known examples of local Koszul homomorphisms are special Koszul, but the cited primary discussion explicitly leaves the all-homomorphisms question unanswered. | [
{
"url": "https://doi.org/10.1017/FMS.2025.21",
"label": "Briggs--Cameron--Letz--Pollitz"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/11773ea5-b1e5-4e9e-b650-808e9d9dc944/content",
"label": "OWR-2023-6, Question 4"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Is every local Koszul homomorphism special Koszul? | Is any local Koszul homomorphism special Koszul? If ϕ is Koszul, then we can choose the A\infty -structure on A such that there exists a free, non-negatively graded module V and a summand W \subseteq V ⊗ V such that A\sim = Ta (V )/(W ) with m2 ⊗ k = µ ⊗ k and mn ⊗ k = 0 for n 6= 2 . Here the mn ’s are the higher multi... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,418 | OWR-12697689-014 | Koszulness from the Kähler Package | Is every Artinian quadratic Gorenstein algebra with the Kähler package Koszul? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-014",
"literature-status:open",
"owr-year:2023"
] | The Kähler-package examples from matroid Chow rings do not settle the universal assertion for all Artinian quadratic Gorenstein algebras; the question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR question"
},
{
"url": "https://arxiv.org/abs/2004.10237",
"label": "quadratic Gorenstein algebras with surprising properties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Is every Artinian quadratic Gorenstein algebra with the Kähler package Koszul? | This answered a question of Manin. It would be nice to have a way to unify these two results and so we ask the following question: Question 2. Is every Artinian, quadratic, Gorenstein algebra with the Kähler package Koszul? Resolutions in Local Algebra and Singularity Theory 379 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,419 | OWR-12697689-015 | Proxy-Small Modules and Cohomological Support Varieties | Let $R$ be a Noetherian local ring. Is $R$ a complete intersection whenever every finitely generated $R$-module $M$ is proxy small, meaning that there is an object $P\in\langle M\rangle\cap\langle R\rangle$ with the same ordinary support as $M$? More generally, how small can the cohomological support variety $V_R(M)$ b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-015",
"literature-status:open",
"owr-year:2023"
] | The report explicitly leaves open whether Pollitz's support-variety characterization can be restricted from all bounded complexes to finitely generated modules; later work on bounds and realizability does not resolve that restriction question. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2210.15574",
"label": "Briggs--Grifo--Pollitz, Bounds on cohomological support varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Let $R$ be a Noetherian local ring. Is $R$ a complete intersection whenever every finitely generated $R$-module $M$ is proxy small, meaning that there is an object $P\in\langle M\rangle\cap\langle R\rangle$ with the same ordinary support as $M$? More generally, how small can the cohomological support variety $V_R(M)$ b... | But Pollitz’ characterization was in terms of all M \in Db (R); the problem of whether this characterization can be restricted to finitely generated R-modules remains open. This prompts the question of when is VR (R) = An , or more generally of how small can VR (M ) be. Resolutions in Local Algebra and Singularity Theo... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,420 | OWR-12697689-016 | Vasconcelos Conjecture for Kähler Differentials | Let $k$ be a field of characteristic zero and let $S$ be a commutative Noetherian $k$-algebra essentially of finite type. If the module of Kähler differentials $\Omega^1_{S/k}$ has finite projective dimension over $S$, must $S$ be a reduced complete intersection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-016",
"literature-status:open",
"owr-year:2023"
] | The extracted record is only a truncated conjecture fragment followed by an example, so no definite mathematical claim is identifiable; under the prescribed uncertainty rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Let $k$ be a field of characteristic zero and let $S$ be a commutative Noetherian $k$-algebra essentially of finite type. If the module of Kähler differentials $\Omega^1_{S/k}$ has finite projective dimension over $S$, must $S$ be a reduced complete intersection? | conjecture (which was known to hold more generally). An interesting example is the coinvariant algebra for the symmetric group Sn acting by permuting the coordinates of k n , having a presentation S = k[x1 , . . . , xn ]/(x1 + \cdot \cdot \cdot + xn , . . . , xn1 + \cdot \cdot \cdot + xnn ), Jacobian criteria for class... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,421 | OWR-12697690-001 | Uniform Expansion Stability for Wild Quivers | Does every wild quiver $Q$ admit a stability condition $\mu$ such that $(Q,\mu)$ has uniform expansion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 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-12697690-001",
"literature-status:open",
"owr-year:2023"
] | The wild-quiver converse was still stated as a conjecture in the source report; the later paper proves it for broad special classes, but the searched literature does not establish the assertion for every wild quiver. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
},
{
"url": "https://ems.press/content/serial-article-files/47504",
"label": "J. Comb. Algebra 8 (2024), 111--119"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Does every wild quiver $Q$ admit a stability condition $\mu$ such that $(Q,\mu)$ has uniform expansion? | We conjecture that, conversely, every wild quiver Q admits a stability µ such that (Q, µ) exhibits uniform expansion. 1. Dimension expanders Consider the following result in linear algebra: Let k be an algebraically closed field. For every finite-dimensional k-vector space V , there exist linear operators F, G \in End(... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,422 | OWR-12697690-002 | Mutation Theories from Extriangulated Categories | Which established mutation theories can be recovered from the mutation theorem for $0$-Auslander extriangulated categories, and which new mutation operations arise from it? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 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-12697690-002",
"literature-status:open",
"owr-year:2023"
] | The extracted question asks whether Theorem 2 yields new mutations, but it gives no theorem or mutation data; no authoritative source located a resolution of this under-specified problem. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Which established mutation theories can be recovered from the mutation theorem for $0$-Auslander extriangulated categories, and which new mutation operations arise from it? | Can Theorem 2 be applied to discover new mutations? Representation Theory of Quivers and Finite-Dimensional Algebras 415 Disclaimer: The categorical structures arising from those examples are appar- ently of very different natures. The category (C, ∆T ) is a relative structure of a triangulated category; the category K... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,423 | OWR-12697690-005 | Birkhoff Classification over $mathbb Z/p^6mathbb Z$ | Classify monomorphisms of finite abelian groups over $\mathbb{Z}/p^6\mathbb{Z}$ up to Birkhoff equivalence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 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-12697690-005",
"literature-status:open",
"owr-year:2023"
] | The Birkhoff problem for monomorphisms over Z/p^6Z remains unresolved; modern surveys still describe the n=6 classification as open, despite finite-type results for n\leq5 and controlled wildness for n\geq7. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12640",
"label": "Gao--Külshammer--Kvamme--Psaroudakis, PLMS (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Classify monomorphisms of finite abelian groups over $\mathbb{Z}/p^6\mathbb{Z}$ up to Birkhoff equivalence. | An old open question is the “Birkhoff problem”, on describing the category mono(1 \to 2, mod Z/p6 Z)). where Ai is an object in A for all i \in Q0 , and where A\alpha : As(\alpha) \to At(\alpha) is a morphism in A for all \alpha \in Q1 . For simplicity we skip the index sets when writing representations. A morphism (Ai... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,424 | OWR-12697690-006 | Comparison of Integral and Truncated-Polynomial Birkhoff Categories | Compare the representation theory of $\operatorname{mono}(1\to2,\operatorname{mod}\mathbb{Z}/p^6\mathbb{Z})$ with that of $\operatorname{mono}(1\to2,\operatorname{mod}k[x]/(x^6))$. Are the two monomorphism categories equivalent in an appropriate representation-theoretic sense? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 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-12697690-006",
"literature-status:open",
"owr-year:2023"
] | The comparison between mono(1\to2, mod Z/p^6Z) and mono(1\to2, mod k[x]/(x^6)) remains an open boundary-case question; the latter category is understood much better, but no equivalence or matching structure has been proved. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12640",
"label": "Gao--Külshammer--Kvamme--Psaroudakis, PLMS (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Compare the representation theory of $\operatorname{mono}(1\to2,\operatorname{mod}\mathbb{Z}/p^6\mathbb{Z})$ with that of $\operatorname{mono}(1\to2,\operatorname{mod}k[x]/(x^6))$. Are the two monomorphism categories equivalent in an appropriate representation-theoretic sense? | question is attributed to the paper [1] by Birkhoff. In [7] the authors ask whether the structure of mono(1 \to 2, mod Z/p6 Z)) is similar to the structure of mono(1 \to 2, mod k[x]/(x6 )). 2. A (representation) equivalence Now assume A is an abelian category with enough injectives. Then the category rep(Q, A) is also ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,425 | OWR-12697690-007 | Uniqueness of Surface Models for Locally Gentle Algebras | Does every finite-dimensional locally gentle algebra admit a unique tiled-surface model up to rotations of the tiles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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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-12697690-007",
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] | The finite-dimensional-surface uniqueness conjecture for string-algebra tilings is stated in the report without a proof, and no later primary source located here establishes it in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Does every finite-dimensional locally gentle algebra admit a unique tiled-surface model up to rotations of the tiles? | We conjecture that if we choose B to be finite dimensional, the surface is unique, up to rotating certain collections of tiles. Theorem ([2]). The following are equivalent: (1) A is a string algebra. (2) A = B/R with B locally gentle and R is an ideal generated by paths of length \geq 2 such that every oriented cycle i... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,426 | OWR-12697690-008 | Higher-Auslander Koszul Duals of Auslander Algebras | For which representation-finite algebras is the Koszul dual of their Auslander algebra a higher Auslander algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697690-008",
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] | The report explicitly poses the question for which representation-finite algebras the Koszul dual of the Auslander algebra is higher Auslander; the cited work proves important hereditary and self-injective cases but not the general classification. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
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{
"url": "https://arxiv.org/abs/2210.06180",
"label": "Chan--Iyama--Marczinzik, Dominant Auslander--Gorenstein algebras"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | For which representation-finite algebras is the Koszul dual of their Auslander algebra a higher Auslander algebra? | This leads to the following open question: For which representation-finite algebra B is the Koszul dual of the Auslander algebra of B higher Auslander? Auslander regular algebras and Koszul duality René Marczinzik (joint work with Aaron Chan and Osamu Iyama) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,427 | OWR-12697690-009 | Module Parametrization by $F$-Polynomials | Is the parametrization map $\Phi$ associated with the $F$-polynomials of modules over $\Lambda\cong kQ/I$ an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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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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] | The record states only that a map Phi is conjectured to be an isomorphism, without defining the map or its source and target; no resolution can be verified from the extracted record. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Is the parametrization map $\Phi$ associated with the $F$-polynomials of modules over $\Lambda\cong kQ/I$ an isomorphism? | We conjecture that the map Φ is in fact an isomorphism. 4. Parametrization From now on, we assume moreover that k = C. We let Λ \sim = kQ/I with I an admissible ideal, and we let n be the number of vertices of Q. For any Λ-module M , its F -polynomial is X F (M ) = χ (Grd (M )) yd \in Z[y1 , . . . , yn ], d\inNn | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,428 | OWR-12697690-010 | Realizability of Complete Sign-Coherent Fans | Characterize the complete sign-coherent fans in $\mathbb R^d$ that can be realized as the $g$-fans of finite-dimensional algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486](https://doi.org/10.4171/owr/2023/7)
## Literature review... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"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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"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-12697690-010",
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] | The extracted passage says only that a problem is posed and does not include its statement; the identifiable surrounding research questions on deformations and semigroup operations remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/7",
"label": "original OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/7 | null | null | null | Characterize the complete sign-coherent fans in $\mathbb R^d$ that can be realized as the $g$-fans of finite-dimensional algebras. | We pose the following problem. K0 (projA)R := K0 (projA) ⊗Z R ≃ R|A| . We call T = (T i , di ) \in Kb (projA) presilting if HomKb (projA) (T, T [ℓ]) = 0 for all positive integers ℓ, and silting if it is presilting and generates Kb (projA) as a thick subcategory. We call T 2-term if T i = 0 for all i 6= 0, −1. Definitio... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/7, pp. 397--486 |
30,005,429 | OWR-12697692-001 | Behavioral and Seasonal Effects on COVID-19 Transmission | How did behavioural patterns, seasonality and virus strains affect transmission during Covid-19? and Optimal intervention strategies for minimizing total incidence during an epidemic Tom Britton (joint work with Felix Gunther, Hilde Kjelgaard Brustad, Arnoldo Frigessi, Lasse Leskela) The first part concerns a project w... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Design and Analysis of Infectious Disease Studies (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/8, page range not supplied by EMS](https://doi.org/10.4171/owr/2023/8)
## Literature rev... | 3 | open | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The question is a presentation heading answered empirically in the following discussion of mobility, seasonality, and viral variants, not a ) | null | null | null | [
"owr",
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{
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"label": "Günther--Brustad--Frigessi--Britton, 2026 publication record"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/8 | null | null | null | null | How did behavioural patterns, seasonality and virus strains affect transmission during Covid-19? and Optimal intervention strategies for minimizing total incidence during an epidemic Tom Britton (joint work with Felix Gunther, Hilde Kjelgaard Brustad, Arnoldo Frigessi, Lasse Leskela) The first part concerns a project w... | unrecoverable | The question is a presentation heading answered empirically in the following discussion of mobility, seasonality, and viral variants, not a standalone mathematical conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Design and Analysis of Infectious Disease Studies (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/8, page range not supplied by EMS |
30,005,430 | OWR-12697692-002 | Exchangeability Tests for Branching in Timed Phylogenies | Does branching now imply branching next? In part 1 of the talk, titled Does branching now imply branching next? Testing for exchangeability in timed phylogenies, by C. Colijn (sole author), I develop a statistical test for exchangeability on timed phylogenies. The test is based on nodes in a phylogeny for which one of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Design and Analysis of Infectious Disease Studies (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/8, page range not supplied by EMS](https://doi.org/10.4171/owr/2023/8)
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"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The question is a talk heading introducing a developed exchangeability test for branching times, not an unresolved mathematical problem. No ) | null | null | null | [
"owr",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/8 | null | null | null | null | Does branching now imply branching next? In part 1 of the talk, titled Does branching now imply branching next? Testing for exchangeability in timed phylogenies, by C. Colijn (sole author), I develop a statistical test for exchangeability on timed phylogenies. The test is based on nodes in a phylogeny for which one of ... | unrecoverable | The question is a talk heading introducing a developed exchangeability test for branching times, not an unresolved mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Design and Analysis of Infectious Disease Studies (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/8, page range not supplied by EMS |
30,005,431 | OWR-12697693-001 | Smallest Solvable Group Excluded from Abelian-Type Skew Braces | Among solvable finite groups that are not the multiplicative group of any skew brace of abelian type, determine one of minimum order. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-12697693-001",
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"url": "https://cris.vub.be/ws/portalfiles/portal/119985424/birkjour.pdf",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Among solvable finite groups that are not the multiplicative group of any skew brace of abelian type, determine one of minimum order. | A skew brace is a triple (A, +, ◦), where (A, +) and (A, ◦) are groups and a ◦ (b + c) = a ◦ b − a + a ◦ c holds for all a, b, c \in A. We will mainly consider finite skew braces of abelian type, that is, finite skew braces where the group (A, +) is abelian. In [2], Etingof, Schedler and Soloviev proved that the multipli... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,432 | OWR-12697693-003 | The Property-s Elements of a Skew Brace | Let $B=(B,+,\circ)$ be a skew brace, write $a*b=-a+a\circ b-b$, and for $x\in B$ set $$\operatorname{Fix}^r(x)=\{b\in B:x*b=0\},\qquad \operatorname{Fix}^l(x)=\{b\in B:b*x=0\}.$$ If $C_x^+$ and $C_x^\circ$ are the centralizers of $x$ in $(B,+)$ and $(B,\circ)$, respectively, call $x$ an element with property $(s)$ when... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23292254",
"checked_at": "2026-10-11",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-11] I have released an unrefereed preprint, **The Elements with Property (s) of a Skew Brace Need Not Form an Ideal: On a Question of Colazzo, Ferrara and Trombetti** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23292254) | [
"owr",
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{
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"label": "Colazzo--Ferrara--Trombetti, Publ. Mat. 69 (2025)"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Let $B=(B,+,\circ)$ be a skew brace, write $a*b=-a+a\circ b-b$, and for $x\in B$ set $$\operatorname{Fix}^r(x)=\{b\in B:x*b=0\},\qquad \operatorname{Fix}^l(x)=\{b\in B:b*x=0\}.$$ If $C_x^+$ and $C_x^\circ$ are the centralizers of $x$ in $(B,+)$ and $(B,\circ)$, respectively, call $x$ an element with property $(s)$ when... | In the following, we will state some open problems. Is the set of all elements with property (s) an ideal? Derived-indecomposable solutions and skew braces whose elements have a finite number of conjugates Ilaria Colazzo (joint work with Maria Ferrara and Marco Trombetti) | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,433 | OWR-12697693-004 | Finiteness and Goodness for Property-S Skew Braces | Let $B=(B,+,\circ)$ be a skew brace, write $a*b=-a+a\circ b-b$, and define $$\operatorname{Fix}^r(x)=\{b\in B:x*b=0\},\qquad \operatorname{Fix}^l(x)=\{b\in B:b*x=0\}.$$ Say that $B$ has property $(S)$ when, for every $x\in B$, both $$[(B,+):\operatorname{Fix}^r(x)\cap C_x^+]\quad\text{and}\quad[(B,\circ):\operatorname{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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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"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-12697693-004",
"literature-status:open",
"owr-year:2023"
] | The finite-generation question for ideals, equivalently whether every skew brace with property (S) is good, is explicitly retained as an open question in the 2025 treatment. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
},
{
"url": "https://mat.uab.es/pubmat/fitxers/download/FileType%3Apdf/FolderName%3Av69%281%29/FileName%3A6912508.pdf",
"label": "Colazzo--Ferrara--Trombetti, Publ. Mat. 69 (2025)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Let $B=(B,+,\circ)$ be a skew brace, write $a*b=-a+a\circ b-b$, and define $$\operatorname{Fix}^r(x)=\{b\in B:x*b=0\},\qquad \operatorname{Fix}^l(x)=\{b\in B:b*x=0\}.$$ Say that $B$ has property $(S)$ when, for every $x\in B$, both $$[(B,+):\operatorname{Fix}^r(x)\cap C_x^+]\quad\text{and}\quad[(B,\circ):\operatorname{... | Is it true that any finitely generated ideal of B is finite? Is every periodic skew brace with property (S) good? Actually, as a consequence of Theorems 3.14, 3.25 and 3.27 in [1], it turns out that the previous question is equivalent to the following one: is every skew brace with property (S) good? The report passage ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,434 | OWR-12697693-005 | Semilattice Realizations by Wedge Semibraces | Which semilattices occur as the underlying semilattice of a $\wedge$-semibrace, and which occur when the $\wedge$-semibrace is also an $L$-algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-005",
"literature-status:open",
"owr-year:2023"
] | The semilattice-realization questions for wedge-semibraces, including the L-algebra case, remain open in the source literature; later work gives canonical closures and finite enumerations but not the requested characterization. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106314",
"label": "Rump, L-algebras with duality and structure groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Which semilattices occur as the underlying semilattice of a $\wedge$-semibrace, and which occur when the $\wedge$-semibrace is also an $L$-algebra? | As there is no (obvious) notion of trivial ∧-semibrace, the following question is far less trivial: Problem 3. It has been shown by Rump, that every L-algebra X is embedded as a sub- L-algebra into a self-similar L-algebra S(X) - its self-similar closure - such that S(X) is generated as a monoid by X. The self-similar ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,435 | OWR-12697693-006 | Non-Desarguesian Plane Lattices as Bricks | Can the subspace lattice of a non-Desarguesian projective plane be the underlying lattice of a brick? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-006",
"literature-status:open",
"owr-year:2023"
] | The report presents the non-Desarguesian-plane brick question as open and records only positive constructions for Desarguesian subspace lattices; no primary source located here supplies a brick on a non-Desarguesian plane lattice. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Can the subspace lattice of a non-Desarguesian projective plane be the underlying lattice of a brick? | Can the subspace lattice of a non-desarguesian plane be the under- lying lattice of a brick? 1. Special classes of L-algebras Definition 2. [6] A ∧-semibrace is a set X with two binary operations \cdot, ∧ and a distinguished element e \in X, such that (X, ∧) is a ∧-semilattice and the following conditions hold x \cdot ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,436 | OWR-12697693-007 | Structure Groups of Anisotropic Bilinear Forms | Let $b(v,w)=v^{\mathsf T}Aw$ be an anisotropic, not necessarily symmetric, bilinear form on $K^n$. Find a representation of the structure group $G(X(b))$ that generalizes the pure paraunitary model $$G(X(b))\cong\{\varphi(t)\in\operatorname{GL}_n(K[t,t^{-1}]):\varphi(t^{-1})^{\mathsf T}A\varphi(t)=A,\ \varphi(1)=I\}$$ ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-007",
"literature-status:open",
"owr-year:2023"
] | The requested representation of the structure group for a non-symmetric anisotropic bilinear form is posed as a problem in the report, and no authoritative later solution was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Let $b(v,w)=v^{\mathsf T}Aw$ be an anisotropic, not necessarily symmetric, bilinear form on $K^n$. Find a representation of the structure group $G(X(b))$ that generalizes the pure paraunitary model $$G(X(b))\cong\{\varphi(t)\in\operatorname{GL}_n(K[t,t^{-1}]):\varphi(t^{-1})^{\mathsf T}A\varphi(t)=A,\ \varphi(1)=I\}$$ ... | 2. Representations of L-algebras Let K be a field and b(v, w) = v ⊤ Aw an anisotropic K-bilinear form on K n , where A is a symmetric n \times n-matrix. The desarguesian lattice L(K, n) can then be equipped with the structure of an L-algebra X(b) by means of the Sasaki operation U \cdot V = U ⊥ + (U \cap V ) where U ⊥ =... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,437 | OWR-12697693-008 | Monoid and Group Invariants of qL-Algebras | Develop a theory of $qL$-algebras and their monoid-valued and group-valued invariants. Do these invariants carry Garside-like structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-008",
"literature-status:open",
"owr-year:2023"
] | The question asks whether the displayed relations admit a brace-like theory, but the extracted record omits the relations themselves and no verified general construction or classification was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Develop a theory of $qL$-algebras and their monoid-valued and group-valued invariants. Do these invariants carry Garside-like structures? | Can these relations be described in terms of a brace-like theory? 2. Representations of L-algebras Let K be a field and b(v, w) = v ⊤ Aw an anisotropic K-bilinear form on K n , where A is a symmetric n \times n-matrix. The desarguesian lattice L(K, n) can then be equipped with the structure of an L-algebra X(b) by means... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,438 | OWR-12697693-009 | Trivialization Structures for Nondegenerate Cycle Sets | For a nondegenerate cycle set $X$, develop a trivialization theory relating $X$ to $X_{\mathrm{tr}}$. Determine the relations between $S(X)$ and $S(X_{\mathrm{tr}})$ and between $G(X)$ and $G(X_{\mathrm{tr}})$, decide whether they admit a brace-like description, and study the $L$-algebra trivialization defined by $$x\m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697693-009",
"literature-status:open",
"owr-year:2023"
] | The record contains only the lead-in to Problem 11 and omits the actual question, so its status is unresolved and therefore open under the required normalization. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | For a nondegenerate cycle set $X$, develop a trivialization theory relating $X$ to $X_{\mathrm{tr}}$. Determine the relations between $S(X)$ and $S(X_{\mathrm{tr}})$ and between $G(X)$ and $G(X_{\mathrm{tr}})$, decide whether they admit a brace-like description, and study the $L$-algebra trivialization defined by $$x\m... | We pose the following question: Problem 11. Let (X, ◦) be a non-degenerate cycle set. Then X admits a trivialization Xtr on the same set X, given by x ◦tr y = y, which has the structure monoid M (Xtr ) = |X| \sim Z\geq0 and structure group G(Xtr ) = Z|X| . The bijective identifications M (X) \to \sim M (Xtr ) resp. G(X)... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,439 | OWR-12697693-010 | Cycle Set Deformations into Cycloids | Find further deformations of cycle sets into cycloids, and determine the commutative semigroup operations on the structure monoid $M(X)$ induced by these deformations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-010",
"literature-status:open",
"owr-year:2023"
] | The passage states the deformation problem for cycle sets and asks for further deformations and associated commutative semigroup operations; no complete classification or resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Find further deformations of cycle sets into cycloids, and determine the commutative semigroup operations on the structure monoid $M(X)$ induced by these deformations. | If the problem can be solved satisfyingly, we expect the following two conse- quences: • handy normal forms for non-involutive structure invariants, • a better understanding of elementary combinatorial properties, such as growth in structure invariants Non-degenerate cycle sets can be deformed into L-algebras; both str... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,440 | OWR-12697693-011 | Multiplicative p-Groups of Braces | Which finite $p$-groups occur as multiplicative groups of braces; in particular, what is a smallest counterexample and what necessary or sufficient conditions characterize such groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | open | null | 2,023 | 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-12697693-011",
"literature-status:open",
"owr-year:2023"
] | The report identifies the minimal-counterexample and p-group-realization questions for brace multiplicative groups as open; later work confirms positive results through order p^4 and known counterexamples but not the requested characterization or minimum. | [
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2016.01.011",
"label": "Bachiller, Counterexample to a conjecture about braces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Which finite $p$-groups occur as multiplicative groups of braces; in particular, what is a smallest counterexample and what necessary or sufficient conditions characterize such groups? | As the importance of Sylow subgroups in the theory of finite groups can not be overestimated, the following open problem is crucial. What is the minimal counterexample? Can one give a characterization or necessary condition for a p-group to be the multiplicative group of a brace? It is known that a skew brace that can b... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,441 | OWR-12697693-012 | Centrally Nilpotent Skew Braces of Maximal Class | Study centrally nilpotent skew braces of maximal nilpotency class, using the lower central series $$\Gamma_{n+1}(B)=\sum_{i=1}^{n}\bigl(\Gamma_i(B)*\Gamma_{n+1-i}(B)+[\Gamma_i(B),\Gamma_{n+1-i}(B)]_+\bigr).$$ Classify the braces that attain maximal class. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | partially_solved | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"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 | [
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"literature-status:partially-solved",
"owr-year:2023"
] | Central nilpotency and its lower and upper series are developed, with structural results for several low classes, but a classification of centrally nilpotent skew braces of maximal class remains absent. | [
{
"url": "https://arxiv.org/abs/2109.04389",
"label": "Bonatto--Jedlička, Central nilpotency of skew braces"
},
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Study centrally nilpotent skew braces of maximal nilpotency class, using the lower central series $$\Gamma_{n+1}(B)=\sum_{i=1}^{n}\bigl(\Gamma_i(B)*\Gamma_{n+1-i}(B)+[\Gamma_i(B),\Gamma_{n+1-i}(B)]_+\bigr).$$ Classify the braces that attain maximal class. | Problem 4. Study centrally nilpotent skew braces of maximal nilpotency class. It should be, of course, duly noted which nilpotency class to consider. The one derived from the aboveP series seems a natural choice, an equivalent version of this n series as Γ[n+1] (B) = i=1 Γ[i] ∗ Γ[n+1−i] + [Γ[i] , Γ[n+1−i] ]+ has proven... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,442 | OWR-12697693-013 | Semi-Affine Structures and Skew Brace Constructions | Classify cancellative semi-affine structures on groups, construct skew braces that are not bi-skew braces from groupal semi-affine structures, and construct two-sided skew braces by the same method. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563](https://doi.org/10.4171/owr/2023/9)
## Literature review (checked... | 3 | partially_solved | null | 2,023 | 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-12697693-013",
"literature-status:partially-solved",
"owr-year:2023"
] | The semi-affine correspondence gives a general categorical description and constructions of cancellative and groupal structures, including skew-brace examples, but the requested complete classifications and systematic constructions remain open. | [
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S002240492300066X",
"label": "Semi-affine structures on groups and semi-braces"
},
{
"url": "https://doi.org/10.4171/owr/2023/9",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/9 | null | null | null | Classify cancellative semi-affine structures on groups, construct skew braces that are not bi-skew braces from groupal semi-affine structures, and construct two-sided skew braces by the same method. | Problem 2. Let G be a group. Find all ”trivially decomposable” cancellative semi-affine structures on G to construct all cancellative semi-affine structures on G itself. Problem 3. Extend the description of cancellative semi-affine structures on groups to the general case. Problem 4. Find systematic constructions of sk... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Skew Braces and the Yang–Baxter Equation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/9, pp. 537--563 |
30,005,443 | OWR-12697706-001 | Zero–One Law for Directional Transience | For a random walk in a random environment, let $A_+$ be the event of directional transience in a fixed direction. Must $\mathbb P(A_+)\in\{0,1\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606](https://doi.org/10.4171/owr/2023/10)
## Literature review (checke... | 3 | open | null | 2,023 | 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-12697706-001",
"literature-status:open",
"owr-year:2023"
] | The extracted record combines the unresolved one-sided directional-transience zero--one question with the two-dimensional Bricmont--Kupiainen invariance-principle question; the cited theory proves only the union zero--one law and higher-dimensional perturbative results. | [
{
"url": "https://doi.org/10.4171/owr/2023/10",
"label": "original Oberwolfach report"
},
{
"url": "https://www.maths.tcd.ie/EMIS/journals/EJP-ECP/article/view/1060.html",
"label": "Zerner, A non-ballistic law of large numbers"
},
{
"url": "https://doi.org/10.1007/BF02102067",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/10 | null | null | null | For a random walk in a random environment, let $A_+$ be the event of directional transience in a fixed direction. Must $\mathbb P(A_+)\in\{0,1\}$? | 572 Oberwolfach Report 10/2023 Together with the fact that P A− \cup A+ \in \{0, 1\} (proved in [12]), this puts into focus the following open problem: Problem 1. Is P A+ \in \{0, 1\}? They are also important in stating several intriguing open questions, described in details in Berger’s lecture in these proceedings. Do... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606 |
30,005,444 | OWR-12697706-002 | Planar Bricmont–Kupiainen Invariance Principle | Does the full invariance principle hold under the Bricmont–Kupiainen conditions in dimension $d=2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606](https://doi.org/10.4171/owr/2023/10)
## Literature review (checke... | 3 | open | null | 2,023 | 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-12697706-002",
"literature-status:open",
"owr-year:2023"
] | Bricmont--Kupiainen prove the perturbative quenched invariance principle for d\geq3, while the report explicitly leaves the full d=2 case as a problem; no primary source located here closes that case. | [
{
"url": "https://doi.org/10.4171/owr/2023/10",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/BF02102067",
"label": "Bricmont--Kupiainen, Random walks in asymmetric random environments"
},
{
"url": "https://arxiv.org/abs/math/0607192",
"label": "Bolthaus... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/10 | null | null | null | Does the full invariance principle hold under the Bricmont–Kupiainen conditions in dimension $d=2$? | Does the full invariance principle hold under the Bricmont-Kupiainen conditions, for d = 2? under a weaker symmetry condition than that of Bricmont-Kupiainen. Work in progress of Bolthausen and the author will prove (1) in the case d = 2. This leads to the: Mini-Workshop: New Horizons in Motions in Random Media 573 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606 |
30,005,445 | OWR-12697706-003 | Invariance Principles for Perturbed Balanced Environments | Can one prove an invariance principle for a slightly perturbed balanced environment or for a balanced environment subjected to a percolation perturbation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606](https://doi.org/10.4171/owr/2023/10)
## Literature review (checke... | 3 | open | null | 2,023 | 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-12697706-003",
"literature-status:open",
"owr-year:2023"
] | The report presents invariance principles for established balanced or perturbative regimes, but identifies slightly perturbed balanced environments and percolation perturbations as unresolved extensions; no proof covering either extension was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/10",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.spa.2013.01.007",
"label": "random walks in random environments without ellipticity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/10 | null | null | null | Can one prove an invariance principle for a slightly perturbed balanced environment or for a balanced environment subjected to a percolation perturbation? | There are a few remaining open problems in this regime, but in my opinion, the most interesting open problems are in connecting this regime to other regimes, particularly the perturbative regime. For example, can we prove an invariance principle for a slightly perturbed balanced environment? can we prove it for a balan... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606 |
30,005,446 | OWR-12697706-004 | Critical Random Walks on Percolation Clusters | What is the anomalous behavior of random walks on percolation clusters at criticality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606](https://doi.org/10.4171/owr/2023/10)
## Literature review (checke... | 3 | open | null | 2,023 | 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"
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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-12697706-004",
"literature-status:open",
"owr-year:2023"
] | This is contextual prose rather than a precise conjecture; critical percolation clusters and anomalous random-walk scaling remain dimension- and model-dependent, so the extracted item is not a settled theorem. | [
{
"url": "https://doi.org/10.4171/owr/2023/10",
"label": "original Oberwolfach report"
},
{
"url": "https://www.maths.ox.ac.uk/node/4868",
"label": "Croydon, random walks on critical percolation clusters"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/10 | null | null | null | What is the anomalous behavior of random walks on percolation clusters at criticality? | Describing the expected anomalous behaviour of random walks on percolation clusters at criticality itself soon thereafter became a question of interest. Random walks on random graphs in critical regimes David A. Croydon | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: New Horizons in Motions in Random Media (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/10, pp. 565--606 |
30,005,447 | OWR-12697707-001 | Finite-Time Singularities in Free-Boundary Fluid Models | Determine whether finite-time singularities form in vortex patches, water waves, porous-media interface flows, Hele–Shaw cells, and atmospheric front dynamics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Free Boundary Problems Arising in Fluid Mechanics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/11, pp. 607--638](https://doi.org/10.4171/owr/2023/11)
## Literature revi... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"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-12697707-001",
"literature-status:open",
"owr-year:2023"
] | The record is a broad statement that finite-time singularity formation is fundamental in several free-boundary and fluid models, not a single formal problem; no general resolution exists across the listed models. | [
{
"url": "https://doi.org/10.4171/owr/2023/11",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/11 | null | null | null | Determine whether finite-time singularities form in vortex patches, water waves, porous-media interface flows, Hele–Shaw cells, and atmospheric front dynamics. | More precisely, we will address problems as the vortex- patch, the study of water waves, interface flows in porous media and Hele- Shaw cells as well as atmospheric front dynamics where the formation of finite time singularities is a fundamental open question. Mathematics Subject Classification (2020): 35Q35, 35R35, 76... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Free Boundary Problems Arising in Fluid Mechanics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/11, pp. 607--638 |
30,005,448 | OWR-12697708-001 | Unspecified Reinforced Random Process Problem | They then chaired a 1-hour discussion session during which the participants had the opportunity to ask questions about the model and discuss open problems. Plenty of time was left free in the program for participants to discuss the open problems informally in smaller groups during the week. We are hoping that these ope... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | open | null | 2,023 | 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"
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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 passage only describes the workshop's discussion sessions and lists contribution titles without stating a mathematical p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697708-001",
"literature-status:open",
"owr-year:2023"
] | The record only reports an informal discussion of reinforcement problems and states no specific mathematical claim; its unresolved content is therefore not verifiable as solved. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | null | They then chaired a 1-hour discussion session during which the participants had the opportunity to ask questions about the model and discuss open problems. Plenty of time was left free in the program for participants to discuss the open problems informally in smaller groups during the week. We are hoping that these ope... | unrecoverable | The official report passage only describes the workshop's discussion sessions and lists contribution titles without stating a mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,449 | OWR-12697708-002 | Deterministic Limits of Trace-Reinforced Ant Walks | On every finite graph, do the edge-weight sequences in the trace-reinforced ant model, normalized by the number of walks, converge almost surely to deterministic limits? Can the model be extended meaningfully to several food sources? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | open | null | 2,023 | 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"
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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-12697708-002",
"literature-status:open",
"owr-year:2023"
] | The deterministic-limit conjecture for normalized trace-reinforced ant weights on every finite graph remains conjectural; primary work proves it only for several graph classes and examples. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
},
{
"url": "https://math.univ-lyon1.fr/~schapira/articlespdf/antsJEP.pdf",
"label": "Kious--Mailler--Schapira, trace-reinforced ants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | On every finite graph, do the edge-weight sequences in the trace-reinforced ant model, normalized by the number of walks, converge almost surely to deterministic limits? Can the model be extended meaningfully to several food sources? | all weight sequences normalized by the number of random walks, converge almost surely to some deterministic constants, and we conjecture that this is a general fact which should hold on any finite graph. Several problems on this model remain open, such as proving our main conjec- ture on general finite graphs, or exten... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,450 | OWR-12697708-003 | Persistent Hubs under Preferential-Attachment Removal | In preferential-attachment models with vertex removal, is the maximum-degree vertex eventually persistent, or does its identity change infinitely often? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | partially_solved | null | 2,023 | 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"
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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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"display_name": "Oberwolfach Reports Open Problems",
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"owr-year:2023"
] | Special removal mechanisms and several preferential-attachment local limits are analyzed, including a 2025 vertex-death model, but the general persistence and Bernoulli-limit questions in the record remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2503.08675",
"label": "Heydenreich--Lodewijks, preferential attachment with vertex death"
},
{
"url": "https://arxiv.org/abs/2212.05551",
"label": "universality o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | In preferential-attachment models with vertex removal, is the maximum-degree vertex eventually persistent, or does its identity change infinitely often? | Open problems. Here, we discuss some open problems for preferential attach- ment models. (a) Preferential attachment models with removal. Is the vertex with maximal degree persistent, or does it change with time? (b) Relation local limits preferential attachment models and Bernoulli model. Graph distances. We next inve... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,451 | OWR-12697708-004 | Local Limits of Preferential Attachment with Deterministic or Random Outdegree | Do the local limits of affine preferential-attachment graphs with fixed outdegree agree with those of the corresponding Bernoulli preferential-attachment model with Poisson outdegree, after attachment is based only on indegree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | partially_solved | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "probability",
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"id": 15,
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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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697708-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Local limits are identified for broad preferential-attachment families and for Bernoulli preferential attachment, with coupling and universality results, but the general relation asked in the extracted record is not a single fully resolved theorem. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2212.05551",
"label": "universality of the local limit of preferential attachment models"
},
{
"url": "https://arxiv.org/abs/0807.4904",
"label": "Dereich--Mörter... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | Do the local limits of affine preferential-attachment graphs with fixed outdegree agree with those of the corresponding Bernoulli preferential-attachment model with Poisson outdegree, after attachment is based only on indegree? | What is the relation between the local limits of the two models? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,452 | OWR-12697708-005 | Mathematical Characterization of Condensation in Reinforced Systems | What is condensation? 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:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | open | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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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 | null | Unrecoverable OWR statement (The extracted phrase is a section heading that the ensuing exposition answers by defining and illustrating condensation; it is not an open p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697708-005",
"literature-status:open",
"owr-year:2023"
] | The extracted item is only the definitional question What is condensation? and does not specify a mathematical conjecture or criterion whose solution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | null | What is condensation? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The extracted phrase is a section heading that the ensuing exposition answers by defining and illustrating condensation; it is not an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,453 | OWR-12697708-006 | Unique Equilibria for Subcritical Reinforcement on Infinite Graphs | For $\alpha<1$ on an infinite bounded-degree graph with bounded firing rates, is there a unique equilibrium $x$, and does $X_e(t)\to x_e$ almost surely for every edge $e$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | partially_solved | null | 2,023 | 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"
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"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-12697708-006",
"literature-status:partially-solved",
"owr-year:2023"
] | For the subcritical model, convergence is proved on bounded-degree graphs below alpha=1/2 and on Z for alpha<1, while unique-equilibrium convergence on arbitrary infinite graphs remains open. | [
{
"url": "https://arxiv.org/abs/2010.03347",
"label": "Couzinié--Hirsch, weakly reinforced Pólya urns"
},
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | For $\alpha<1$ on an infinite bounded-degree graph with bounded firing rates, is there a unique equilibrium $x$, and does $X_e(t)\to x_e$ almost surely for every edge $e$? | 2. Subcritical case: \alpha < 1 For a finite graph, the function L is concave, which implies the convergence of the vector (xeP(t))e\inE toPthe unique equilibrium (which maximises L on the simplex xe \geq 0, e xe = v p(v)). It is thus natural to ask if such a convergence takes place for general graphs: Conjecture 1. On... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,454 | OWR-12697708-007 | Critical Reinforcement Convergence on the Infinite Line | At $\alpha=1$, for $G=\mathbb Z$ with firing rates $p(v)=1$, does $x_v(t)\to1$ almost surely for every vertex $v$ as $t\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | open | null | 2,023 | 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",
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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-12697708-007",
"literature-status:open",
"owr-year:2023"
] | The critical alpha=1 conjecture for the infinite line is stated in the report, while known results concern subcritical regimes or finite graphs; no proof of pointwise convergence to one on Z was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2010.03347",
"label": "Couzinié--Hirsch, weakly reinforced Pólya urns"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | At $\alpha=1$, for $G=\mathbb Z$ with firing rates $p(v)=1$, does $x_v(t)\to1$ almost surely for every vertex $v$ as $t\to\infty$? | 3. Critical case: \alpha = 1 In the case \alpha = 1, the function L is non-strictly concave, and in some situations this leads to the non-uniqueness of an equilibrium. In particular, this happens on even-length cycle [8]. For instance, if the firing rates are uniform, p(v) ≡ 1, the equilibria on the cycle of length 2k ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,455 | OWR-12697708-008 | Sharp Reinforcement Thresholds for Tree and Whisker Components | For supercritical reinforcement, improve the threshold $\alpha>2$ guaranteeing that every surviving connected component is a tree, and the threshold $\alpha>25$ guaranteeing, under $p(v)=1$, that every component is a whisker. Is $\alpha>4/3$ sharp for both conclusions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | partially_solved | null | 2,023 | 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"
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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-12697708-008",
"literature-status:partially-solved",
"owr-year:2023"
] | Strong-reinforcement work proves finite surviving components and tree or whisker structure in sufficiently large-alpha regimes and exhibits phase transitions, but the sharp lower bounds requested by the two open problems remain unresolved. | [
{
"url": "https://doi.org/10.1088/1361-6544/acc9a0",
"label": "Hirsch--Holmes--Kleptsyn, Infinite WARM graphs III"
},
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | For supercritical reinforcement, improve the threshold $\alpha>2$ guaranteeing that every surviving connected component is a tree, and the threshold $\alpha>25$ guaranteeing, under $p(v)=1$, that every component is a whisker. Is $\alpha>4/3$ sharp for both conclusions? | Open Problem 1. Open Problem 2. This means that the lower bounds \alpha > \alpha0 (with \alpha0 = 2 and \alpha0 = 25) in the open problems above are not true in general if \alpha0 < 4/3. 3. Critical case: \alpha = 1 In the case \alpha = 1, the function L is non-strictly concave, and in some situations this leads to the... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,456 | OWR-12697708-009 | Finite Surviving Components under Supercritical Reinforcement | Suppose the firing rates $p(v)$ are bounded away from zero and infinity and $\alpha>1$. Does $\lim_{t\to\infty}X_e(t)$ exist almost surely for every edge $e$, with the surviving edges forming finite connected components? For $\alpha>2$, are those components trees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | partially_solved | null | 2,023 | 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"
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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-12697708-009",
"literature-status:partially-solved",
"owr-year:2023"
] | For bounded-degree graphs and sufficiently strong reinforcement, primary work proves convergence and finite surviving components in important regimes, but Conjecture 3 for every alpha>1 with firing rates bounded above and below is not established in full. | [
{
"url": "https://doi.org/10.1088/1361-6544/acc9a0",
"label": "Hirsch--Holmes--Kleptsyn, Infinite WARM graphs III"
},
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | Suppose the firing rates $p(v)$ are bounded away from zero and infinity and $\alpha>1$. Does $\lim_{t\to\infty}X_e(t)$ exist almost surely for every edge $e$, with the surviving edges forming finite connected components? For $\alpha>2$, are those components trees? | Conjecture 3. Assume that firing rates p(v) are bounded away from zero and from infinity, and that \alpha > 1. Then the limit limt\to\infty Xe (t) exists almost surely for each e, and the surviving edges form finite connected components. In particular, for \alpha > 2 they are trees. For infinite graphs the Lyapunov fun... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,457 | OWR-12697708-010 | Reinforcement Counterexamples on Integer Lattices | Can a supercritical-reinforcement example on a regular tree with infinitely many infinite surviving components be adapted to $\mathbb{Z}^d$ for some $d\geq2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679](https://doi.org/10.4171/owr/2023/12)
## Litera... | 3 | open | null | 2,023 | 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-12697708-010",
"literature-status:open",
"owr-year:2023"
] | The extracted item is only Open Problem 3 referring to whether the regular-tree counterexample can be transferred to Z^d for d\geq2; no such construction or impossibility theorem was found. | [
{
"url": "https://arxiv.org/abs/2009.07682",
"label": "Hirsch--Holmes--Kleptsyn, WARM percolation on a regular tree"
},
{
"url": "https://doi.org/10.4171/owr/2023/12",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/12 | null | null | null | Can a supercritical-reinforcement example on a regular tree with infinitely many infinite surviving components be adapted to $\mathbb{Z}^d$ for some $d\geq2$? | Open Problem 3. Also, it is interesting to know whether the example on the regular tree can be modified for the case of Zd for some d \geq 2. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Stochastic Reinforcement Processes and Graphs (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/12, pp. 639--679 |
30,005,458 | OWR-12697709-001 | Unspecified Weak Space-Time PDE Optimization Problem | We start with an example from a paper of Casas and Chrysafinos [1]. We aim to minimize Z 1 T \gamma \lambda J(y, u) = ky − yd k8L4 (Ω) dx + ky(T ) − yΩ k2L2 (Ω) + kuk2L2(Q) 8 0 2 2 subject to the instationary Navier-Stokes equations yt − ν∆y + (y \cdot ∇)y + ∇p = f +u in Q div y = 0 in Q y(0) = y0 in Ω y = 0 on Σ and a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimization Problems for PDEs in Weak Space-Time Form (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/13, pp. 681--740](https://doi.org/10.4171/owr/2023/13)
## Literature review (checke... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"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 | Unrecoverable OWR statement (The official report passage presents optimization models and proved first-order conditions but does not state an unresolved mathematical que) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697709-001",
"literature-status:open",
"owr-year:2023"
] | The record is an optimization example and a statement of first-order conditions, not a well-formed open problem; because its intended unresolved claim cannot be identified, it is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/13",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/13 | null | null | null | null | We start with an example from a paper of Casas and Chrysafinos [1]. We aim to minimize Z 1 T \gamma \lambda J(y, u) = ky − yd k8L4 (Ω) dx + ky(T ) − yΩ k2L2 (Ω) + kuk2L2(Q) 8 0 2 2 subject to the instationary Navier-Stokes equations yt − ν∆y + (y \cdot ∇)y + ∇p = f +u in Q div y = 0 in Q y(0) = y0 in Ω y = 0 on Σ and a... | unrecoverable | The official report passage presents optimization models and proved first-order conditions but does not state an unresolved mathematical question. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Optimization Problems for PDEs in Weak Space-Time Form (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/13, pp. 681--740 |
30,005,459 | OWR-12697710-003 | Positivity of Noncommutative State Polynomials on Convex Sets | Are matrix evaluations sufficient to test positivity of noncommutative state polynomials on a convex set $K_C$, and is there a Krivine–Stengle-type Positivstellensatz using evaluations on unbounded self-adjoint operators? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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-12697710-003",
"literature-status:open",
"owr-year:2023"
] | The matrix-evaluation sufficiency and unbounded-self-adjoint-operator Positivstellensatz questions are stated as open in the source, and no primary result located here resolves either question for the stated noncommutative state-polynomial setting. | [
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | Are matrix evaluations sufficient to test positivity of noncommutative state polynomials on a convex set $K_C$, and is there a Krivine–Stengle-type Positivstellensatz using evaluations on unbounded self-adjoint operators? | Since Theo- rem 1 characterizes only positive state polynomials but not noncommutative state polynomials, one is left with the following open problem. Are matrix evaluations sufficient for checking positivity on a con- vex KC ? Is there an analog of Krivine-Stengle Positivstellensatz for KC if one considers evaluations... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,460 | OWR-12697710-006 | Convexity of Odd-Power Sum-of-Squares Cones | Is $\Sigma_{n,m}(2k+1)$ a closed convex cone? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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 | {
"source_url": "https://zenodo.org/records/23298476",
"checked_at": "2026-10-11",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-11] I have released an unrefereed preprint, **On Reznick's Question about the Cone of Forms with a Sum-of-Squares Odd Power: Explicit Non-Convexity for Sextics in Five and Quartics in Seven Variables** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23298476) | [
"owr",
"oberwolfach-reports",
"OWR-12697710-006",
"literature-status:open",
"owr-year:2023"
] | The source proves closedness of the odd-power SOS-root set but leaves convexity as difficult and conjectural; no primary result found here establishes or refutes convexity for the stated general set. | [
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | Is $\Sigma_{n,m}(2k+1)$ a closed convex cone? | A natural question is whether Σn,m (2k + 1) is a closed convex cone. Real Algebraic Geometry with a View toward Koopman Operator Methods 779 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,461 | OWR-12697710-007 | Mixed Odd Powers of Sum-of-Squares Polynomials | If $p^{2i+1}$ and $q^{2j+1}$ are sums of squares, must $(p+q)^{2i+2j+1}$ also be a sum of squares? In addition, define $c_k$ with $0\leq c_k<3$ by $$\left\{c:\left(x^4y^2+x^2y^4+1-cx^2y^2\right)^{2k+1}\text{ is a sum of squares}\right\}=\{c:c\leq c_k\}.$$ What is $\lim_{k\to\infty}c_k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | solved | null | 2,023 | 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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; the limit is 3 by our argument)**. B. Reznick (OWR 14/2023, pp. 778–780) conjectures that if p^{2i+1} and q^{2j+1} are sums of squares (sos), so is (p+q)^{2i+2j+1}, and asks for lim c_k, c_k being the largest c with M_c^{2k+1} sos, M_c = x⁴y² + x²y⁴ + z⁶ − cx... | [
"owr",
"oberwolfach-reports",
"OWR-12697710-007",
"literature-status:open",
"owr-year:2023"
] | The report proves only the common-exponent special case and records the mixed-exponent assertion and the limit question as conjectural; no later primary result located here settles either the conjecture or the limit. | [
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report and stated conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | If $p^{2i+1}$ and $q^{2j+1}$ are sums of squares, must $(p+q)^{2i+2j+1}$ also be a sum of squares? In addition, define $c_k$ with $0\leq c_k<3$ by $$\left\{c:\left(x^4y^2+x^2y^4+1-cx^2y^2\right)^{2k+1}\text{ is a sum of squares}\right\}=\{c:c\leq c_k\}.$$ What is $\lim_{k\to\infty}c_k$? | More generally, I conjecture that if p2i+1 and q 2j+1 are sos, then so is (p + q)2i+2j+1 . What is limk\to\infty ck ? Theorem. Suppose p and q are polynomials and p2k+1 and q are both sos. Then (p + q)2k+1 is also sos. As a hint of the proof, (p + q)3 = p3 + q(3p2 + 3pq + q 2 ) and moreover also 3p + 3pq + q 2 = 34 (2p... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,462 | OWR-12697710-008 | Compactly Supported Representing Measures for Linear Functionals | Let $A$ be a unital commutative real algebra with nonempty character space $X(A)$, and let $L:A\to\mathbb R$ be linear with $L(1)=1$. Characterize when there is a compactly supported Radon measure $\nu$ on $X(A)$ such that $$L(a)=\int_{X(A)}\alpha(a)\,d\nu(\alpha)$$ for every $a\in A$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | partially_solved | null | 2,023 | 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-12697710-008",
"literature-status:partially-solved",
"owr-year:2023"
] | The unrestricted existence question is false without positivity and growth hypotheses, while the cited work gives necessary and sufficient intrinsic conditions for compactly supported representing measures and identifies their support. | [
{
"url": "https://academic.oup.com/imrn/article/2023/3/2281/6881771",
"label": "Infusino--Kuhlmann--Kuna--Michalski, IMRN"
},
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | Let $A$ be a unital commutative real algebra with nonempty character space $X(A)$, and let $L:A\to\mathbb R$ be linear with $L(1)=1$. Characterize when there is a compactly supported Radon measure $\nu$ on $X(A)$ such that $$L(a)=\int_{X(A)}\alpha(a)\,d\nu(\alpha)$$ for every $a\in A$. | Given a linear functional L : A \to R with L(1) = 1, does there exist a Radon measure ν on X(A) such that Z (1) L(a) = \alpha(a)dν(\alpha) for all a \in A X(A) An Intrinsic Characterization of Moment Functionals in the Compact Case Maria Infusino (joint work with S. Kuhlmann, T. Kuna, P. Michalski) and the support of ν... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,463 | OWR-12697710-009 | Dagger Closure of Trace-Positive Noncommutative Polynomials | For the cone $K$ of trace-positive noncommutative polynomials, is $K=K^\dagger$, where $K^\dagger=\{f:\exists g\text{ such that }f+\varepsilon g\in K\text{ for every }\varepsilon>0\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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-12697710-009",
"literature-status:open",
"owr-year:2023"
] | The trace-positive noncommutative polynomial results establish closure characterizations and exhibit that K is not closed, but the proposed equality of K with its dagger closure remains explicitly open. | [
{
"url": "https://arxiv.org/abs/2205.05959",
"label": "Klep--Scheiderer--Volcic, tracial moment problem"
},
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | For the cone $K$ of trace-positive noncommutative polynomials, is $K=K^\dagger$, where $K^\dagger=\{f:\exists g\text{ such that }f+\varepsilon g\in K\text{ for every }\varepsilon>0\}$? | One possible candidate is the so-called dagger closure often considered in real algebraic geometry: Open Problem. Is K = K† , where K† := \{f | there is an nc polynomial g such that f + \varepsilong \in K for every \varepsilon > 0\}? Namely, M is a sum of commutators c and sums of hermitian squares s with denominators ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,464 | OWR-12697710-010 | Context-Free Open-Problem Label | Open Problem. Real Algebraic Geometry with a View toward Koopman Operator Methods 787 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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 contains only the words “Open Problem” at this extraction boundary, with no recoverable mathematical content. No separat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697710-010",
"literature-status:open",
"owr-year:2023"
] | The extracted record contains only the words Open Problem and no mathematical proposition, so its truth or resolution cannot be identified; under the required rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | null | Open Problem. Real Algebraic Geometry with a View toward Koopman Operator Methods 787 | unrecoverable | The official report contains only the words “Open Problem” at this extraction boundary, with no recoverable mathematical content. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,465 | OWR-12697710-012 | Intersection of Sum-of-Squares and SONC Cones | Characterize the intersection $\Sigma_{n,2d}\cap C_{n,2d}$ of the sum-of-squares and SONC cones. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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-12697710-012",
"literature-status:open",
"owr-year:2023"
] | The surrounding SOS+SONC equality questions were resolved, but the report and subsequent primary paper still leave a general characterization of the intersection of the SOS and SONC cones as an open question. | [
{
"url": "https://doi.org/10.1515/advgeom-2024-0031",
"label": "Dressler--Kuhlmann--Schick, Advances in Geometry"
},
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | Characterize the intersection $\Sigma_{n,2d}\cap C_{n,2d}$ of the sum-of-squares and SONC cones. | An open question regarding the interplay of the cones Σn,2d and Cn,2d is a char- acterization of their intersection Σn,2d \cap Cn,2d . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,466 | OWR-12697710-013 | Heat Flows into Sum-of-Squares Cones | For which $d\in\mathbb{N}$ does heat flow send every positive binary form of degree $2d$ into the sum-of-squares cone after a uniform time, and which linear flows have the analogous property for general $(n,d)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | partially_solved | null | 2,023 | 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 | {
"source_url": "https://doi.org/10.4171/OWR/2023/14",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (OP1: only d ≤ 2, by our argument; OP2: yes, by the proposer's unrefereed preprint)**. P. J. di Dio (joint with R. Curto, M. Korda, V. Magron; [OWR 14/2023](https://doi.org/10.4171/OWR/2023/14), p. 794) asks (OP1) for which d some τ ≥ 0 gives e^{τΔ}Pos(2,2d) ⊆ SOS(... | [
"owr",
"oberwolfach-reports",
"OWR-12697710-013",
"literature-status:open",
"owr-year:2023"
] | Heat-flow results settle the quadratic and ternary-quartic cases and give obstructions, but the stated existence questions for bivariate higher degrees and general linear operators remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report and results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | For which $d\in\mathbb{N}$ does heat flow send every positive binary form of degree $2d$ into the sum-of-squares cone after a uniform time, and which linear flows have the analogous property for general $(n,d)$? | Open Problem 1. For which d \in N does there exist a \tau2,2d \geq 0 such that e\tau2,2d \cdot∆ Pos(2, 2d) \subseteq SOS(2, 2d). Hence, we have the following second open problem. Open Problem 2. For (n, d) \in N \times 2N is there an (linear) operator A such that there exists a \taun,d (A) \geq 0 such that et\cdotA Pos... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,467 | OWR-12697710-014 | Images of Principal Minor Maps for Square Matrices | What equations describe the image of $\mathbb{C}^{5\times5}$ under the principal-minor map, and can the image for $\mathbb{C}^{n\times n}$ be cut out using the action of $\operatorname{SL}_2(\mathbb{C})^n\rtimes S_n$ and compatible combinatorial structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | partially_solved | null | 2,023 | 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-12697710-014",
"literature-status:partially-solved",
"owr-year:2023"
] | The complex symmetric principal-minor problem and its invariant equations are characterized, and Hermitian images receive finite equation-and-inequality descriptions, but the general square-matrix image and the full bundled converse questions remain unresolved. | [
{
"url": "https://arxiv.org/abs/2105.13444",
"label": "Al Ahmadieh--Vinzant, symmetric principal minors"
},
{
"url": "https://arxiv.org/abs/2205.05267",
"label": "Al Ahmadieh--Vinzant, determinantal representations"
},
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR rep... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | What equations describe the image of $\mathbb{C}^{5\times5}$ under the principal-minor map, and can the image for $\mathbb{C}^{n\times n}$ be cut out using the action of $\operatorname{SL}_2(\mathbb{C})^n\rtimes S_n$ and compatible combinatorial structures? | Does the converse hold? What are equations describing the image of C5\times5 under the principal minor map? Can the image of Cn\timesn be cut out by equations obtained from the action of SL2 (C)n ⋊ Sn and some increasing combinatorial structures? The report passage is retained verbatim as the relevant context for this ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,468 | OWR-12697710-015 | Rational Certificates for Truncated Moment Nonrepresentability | Let $K=\{x\in\mathbb R^n:g_1(x),\ldots,g_r(x)\geq0\}$ and let $Q(g)$ be the quadratic module generated by $g_1,\ldots,g_r$. For a rational truncated moment vector that is not representable by a measure on $K$, can there be a rational separating polynomial $p\in1+Q(g)$ for which every sum-of-squares certificate of membe... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811](https://doi.org/10.4171/owr/2023/14)
## Literature r... | 3 | open | null | 2,023 | 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-12697710-015",
"literature-status:open",
"owr-year:2023"
] | Scheiderer proved that rational positive certificates can fail to have rational SOS certificates, but the report question whether this phenomenon occurs for the specified truncated-moment certificates remains open. | [
{
"url": "https://doi.org/10.4171/JEMS/620",
"label": "Scheiderer, JEMS"
},
{
"url": "https://doi.org/10.4171/owr/2023/14",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/14 | null | null | null | Let $K=\{x\in\mathbb R^n:g_1(x),\ldots,g_r(x)\geq0\}$ and let $Q(g)$ be the quadratic module generated by $g_1,\ldots,g_r$. For a rational truncated moment vector that is not representable by a measure on $K$, can there be a rational separating polynomial $p\in1+Q(g)$ for which every sum-of-squares certificate of membe... | It is an open question whether such phenomenon can actually occur in this context. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry with a View toward Koopman Operator Methods (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/14, pp. 741--811 |
30,005,469 | OWR-12697711-001 | Real Algebraic Geometry Workshop Overview | 2. Computability and Complexity Tools from real algebraic geometry are very well suited for studying computability and complexity questions. For example Annie Raymond spoke about the unde- cidability of the general problem of deciding algebraic inequalities between graph homomorphism densities. Evelyne Hubert spoke abo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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 is a workshop-summary paragraph and contains no standalone open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697711-001",
"literature-status:open",
"owr-year:2023"
] | The record is an introductory survey paragraph listing topics and results rather than a specific conjecture or question; no uniquely triageable mathematical claim is extracted, so it remains open by the required normalization. | [
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | null | 2. Computability and Complexity Tools from real algebraic geometry are very well suited for studying computability and complexity questions. For example Annie Raymond spoke about the unde- cidability of the general problem of deciding algebraic inequalities between graph homomorphism densities. Evelyne Hubert spoke abo... | unrecoverable | The official report confirms that this extraction is a workshop-summary paragraph and contains no standalone open problem. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,470 | OWR-12697711-002 | Analytic Hilbert Seventeenth Problem | Is every positive-semidefinite real-analytic function $f:\mathbb R^n\to\mathbb R$ a sum of squares of real-analytic meromorphic functions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,023 | 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-12697711-002",
"literature-status:partially-solved",
"owr-year:2023"
] | The analytic Hilbert-seventeenth analogue is known in dimensions at most two and under compactness hypotheses; recent work removes compactness for Stein surfaces, but the global higher-dimensional statement remains unresolved. | [
{
"url": "https://doi.org/10.1515/crelle-2025-0071",
"label": "Fernando, meromorphic functions on Stein surfaces"
},
{
"url": "https://doi.org/10.1007/s12220-021-00721-1",
"label": "Fernando, positive semidefinite analytic functions on surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Is every positive-semidefinite real-analytic function $f:\mathbb R^n\to\mathbb R$ a sum of squares of real-analytic meromorphic functions? | In real-analytic geometry, where one considers real-analytic functions (locally given by convergent power series) instead of polynomials, even the analogue of Artin’s theorem is still an open problem. Open question 1. Are all positive semidefinite real-analytic functions f : Rn \to R sums of squares of real-analytic me... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,471 | OWR-12697711-003 | Positive Weighted Graph Homomorphism Densities | Characterize the finite graphs $H$ for which $t(H,G_w)\geq 0$ for every weighted graph $G_w$, allowing real edge weights. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-003",
"literature-status:open",
"owr-year:2023"
] | The positive-graph paper formulates the symmetric-graph characterization as a conjecture and proves it only for classes including trees and all graphs up to a finite size bound; no general characterization was found. | [
{
"url": "https://doi.org/10.1016/j.ejc.2015.07.007",
"label": "Camarena--Csoka--Hubai--Lippner--Lovasz, Positive graphs"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Characterize the finite graphs $H$ for which $t(H,G_w)\geq 0$ for every weighted graph $G_w$, allowing real edge weights. | For instance, it is still an open question to characterize all graphs H such that t(H, Gw ) \geq 0 for all weighted graphs Gw [Lov]. X t(f, G) = c\phi p∗ (x1 (\phi), y1 (\phi), . . . , xk (\phi), yk (\phi)) \phi | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,472 | OWR-12697711-005 | Algorithmic Recognition of Zonoids | Given a polynomial $p$ for which $K=\{x\in\mathbb R^d:p(x)\geq 0\}$ is a centrally symmetric convex body, decide algorithmically whether $K$ is a zonoid. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-005",
"literature-status:open",
"owr-year:2023"
] | Zonoid membership is tame or definable in broad families and has substantial geometric necessary conditions, but no general decision algorithm for polynomially described centrally symmetric convex bodies of the stated form is established. | [
{
"url": "https://doi.org/10.1016/j.jfa.2021.109341",
"label": "Lerario--Mathis, On tameness of zonoids"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Given a polynomial $p$ for which $K=\{x\in\mathbb R^d:p(x)\geq 0\}$ is a centrally symmetric convex body, decide algorithmically whether $K$ is a zonoid. | Can we decide if K is a zonoid? We denote by E the closure in the Zariski topology of the set of exposed points of D. This is by definition an algebraic variety, contained in the algebraic boundary of D, and we are interested in characterizing its dimension and degree. In particular, since we are interested in exposed ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,473 | OWR-12697711-006 | Irreducibility of Exposed-Point Varieties of Generic Discotopes | Let $D=D_1+\cdots+D_N$ be a generic discotope with $\dim D_i\geq 2$, and let $E$ be the Zariski closure of its exposed points. Prove that $E$ is irreducible. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-006",
"literature-status:open",
"owr-year:2023"
] | Irreducibility of the exposed-point variety is proved for two-dimensional discs and several low-codimension cases, but the conjecture for generic discotopes with higher-dimensional discs remains open. | [
{
"url": "https://arxiv.org/abs/2111.01241",
"label": "Gesmundo--Meroni, The Geometry of Discotopes"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Let $D=D_1+\cdots+D_N$ be a generic discotope with $\dim D_i\geq 2$, and let $E$ be the Zariski closure of its exposed points. Prove that $E$ is irreducible. | Conjecture 8.2]. Conjecture 1. Let D be a generic discotope with dim Di \geq 2 for all i = 1, . . . , N . Then, E is irreducible. The proof of the first part of the Theorem 2 relies on the construction of geometric joins of varieties. The second part, when (⋆) > d−1, is based on an interpretation of E as a determinanta... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,474 | OWR-12697711-007 | Orphaned Discotope Conjecture Label | conjecture. 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:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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 confirms that the extraction is only an orphaned conjecture label; the complete conjecture is preserved in the adjacent ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697711-007",
"literature-status:open",
"owr-year:2023"
] | The extracted record contains only the word conjecture and no identifiable mathematical statement, so the claim cannot be resolved and is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that the extraction is only an orphaned conjecture label; the complete conjecture is preserved in the adjacent record. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,475 | OWR-12697711-008 | Semialgebraicity of Finite Rank-One Convex Hulls | Prove that the rank-one convex hull of every finite set of matrices is semialgebraic. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,023 | 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-12697711-008",
"literature-status:partially-solved",
"owr-year:2023"
] | Semialgebraicity is proved for diagonal cases, finite-ray directional settings, and finite sets of 2 by 2 triangular matrices, but the universal higher-dimensional rank-one convex-hull conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2509.07541",
"label": "Meroni--Raita, semialgebraic rank-one convex hulls"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Prove that the rank-one convex hull of every finite set of matrices is semialgebraic. | Conjecture 2. The rank-one convex hull of a finite set is semialgebraic. This result is true in R2 , identified with the space of diagonal 2 \times 2 matrices. In fact, [4, Theorem 1.1] proves that this holds for more general cones in R2 , with a finite number of rays, and provides an algorithm for the computation of t... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,476 | OWR-12697711-010 | Spectrality of Infinite Symmetric Orbit-Space Quotients | Is the Kolmogorov quotient $\operatorname{KQ}(A_{\mathbb K,\infty}^n/G)$ a spectral space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-010",
"literature-status:open",
"owr-year:2023"
] | The 2025 primary paper still states the Kolmogorov-quotient spectral-space assertion as a conjecture; no proof or counterexample resolving it was found. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.11.016",
"label": "Kummer--Riener, Journal of Algebra"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Is the Kolmogorov quotient $\operatorname{KQ}(A_{\mathbb K,\infty}^n/G)$ a spectral space? | Is the Kolmogorov quotient KQ(AnK,\infty /G) a spectral space? which is a diffeomorphism when restricted to the relative interior of any face of bd C(n, d). The vertices of S are the images of the vertices of C(n, d) The connection to cyclic polytopes was observed experimentally by Melánová, Sturmfels, and Winter [10... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,477 | OWR-12697711-012 | Stable Division and Arveson–Douglas Essential Normality | If a homogeneous ideal $I\subset\mathbb C[z_1,\ldots,z_d]$ gives an essentially normal compressed coordinate tuple, must $I$ have the stable division property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-012",
"literature-status:open",
"owr-year:2023"
] | Stable division is established as sufficient for essential normality and many cases of essential normality are known, but the converse implication stated in the record remains an open question. | [
{
"url": "https://doi.org/10.1112/jlms/jdq054",
"label": "Shalit, Stable polynomial division and essential normality"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | If a homogeneous ideal $I\subset\mathbb C[z_1,\ldots,z_d]$ gives an essentially normal compressed coordinate tuple, must $I$ have the stable division property? | Nowadays, this question is the first part of the Arveson-Douglas essential normality conjecture. It is an open question whether the converse holds. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,478 | OWR-12697711-014 | Algorithms for Amoeba Dimensions from Tropical Fans | Given a $d$-dimensional rational polyhedral fan with support $F\subseteq\mathbb R^n$, compute $\min_U\{2\dim_{\mathbb R}(U+F)-\dim_{\mathbb R}U\}$ over subspaces $U$ spanned by rational vectors. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,023 | 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-12697711-014",
"literature-status:partially-solved",
"owr-year:2023"
] | The requested expression is computable in polynomial time for matroid fans arising from linear spaces, but no algorithm for arbitrary rational polyhedral fans with the same input-output specification was established. | [
{
"url": "https://doi.org/10.1090/proc/16744",
"label": "Draisma--Eggleston--Pendavingh--Rau--Yuen, Proceedings of the AMS"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | Given a $d$-dimensional rational polyhedral fan with support $F\subseteq\mathbb R^n$, compute $\min_U\{2\dim_{\mathbb R}(U+F)-\dim_{\mathbb R}U\}$ over subspaces $U$ spanned by rational vectors. | Open question 1. Is there an algorithm that takes as input a d-dimensional rational polyhedral fan with support F and computes the expression in the corollary with Trop(X) replaced by F ? 2. Amoeba dimensions of linear spaces Now assume that V \subseteq Cn is a linear subspace for which X := V \cap (C∗ )n is nonempty. ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,479 | OWR-12697711-015 | Equality of Tropical and Matroidal Amoeba-Dimension Formulas | For a loopless matroid $M$ on $[n]$ with matroid-fan support $F\subseteq\mathbb R^n$, prove that $\min_U\{2\dim_{\mathbb R}(U+F)-\dim_{\mathbb R}U\}$ equals $\min_{\bigsqcup_{i=1}^kP_i=[n]}\sum_{i=1}^k(2\operatorname{rk}_M(P_i)-1)$, where $U$ ranges over rationally spanned subspaces and every $P_i$ is nonempty. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,023 | 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 | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **The Amoeba Dimension of an Arbitrary Loopless Matroid** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23058144) | [
"owr",
"oberwolfach-reports",
"OWR-12697711-015",
"literature-status:partially-solved",
"owr-year:2023"
] | The equality is proved for matroids realizable over the complex numbers, including the linear-space amoeba formula, while the record asks for all loopless matroids and the non-realizable case remains conjectural. | [
{
"url": "https://doi.org/10.1090/proc/16744",
"label": "Draisma--Eggleston--Pendavingh--Rau--Yuen, Proceedings of the AMS"
},
{
"url": "https://arxiv.org/abs/2303.13143",
"label": "primary preprint"
},
{
"url": "https://doi.org/10.4171/owr/2023/15",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | For a loopless matroid $M$ on $[n]$ with matroid-fan support $F\subseteq\mathbb R^n$, prove that $\min_U\{2\dim_{\mathbb R}(U+F)-\dim_{\mathbb R}U\}$ equals $\min_{\bigsqcup_{i=1}^kP_i=[n]}\sum_{i=1}^k(2\operatorname{rk}_M(P_i)-1)$, where $U$ ranges over rationally spanned subspaces and every $P_i$ is nonempty. | Open question 2. Is it true that min\{2 dimR (U + F ) − dimR U | U subspace of (R)n spanned by rational vectors\} equals k X G min\{ (2 rkM (Pi ) − 1) | Pi = [n] and all Pi 6= \varnothing\}? i=1 i It is not hard to see \leq by taking for U the space spanned by the characteristic vectors of the Pi . For the converse we ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,480 | OWR-12697711-016 | Characterizations of Symmetrically Hyperbolic Hook-Shaped Polynomials | For a diagonal map $T:\mathbb R[t]_{n,0}\to\mathbb R[t]_{d,0}$, prove that $T((x-1)^{n-1}(x+n-1))$ is real-rooted with $d-1$ roots of one sign exactly when $T$ preserves zero-sum hyperbolicity. Also prove that a hook-shaped symmetric polynomial $p$ is symmetrically hyperbolic exactly when $\Delta_{\mathbf 1,\mathbf 1}p... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-016",
"literature-status:open",
"owr-year:2023"
] | The report identifies this as an open problem; current work gives evidence and low-degree or special-case results, but no general characterization. | [
{
"url": "https://ems.press/content/serial-article-files/47009?nt=1",
"label": "OWR 2023 report"
},
{
"url": "https://arxiv.org/abs/2308.09653",
"label": "Symmetric Hyperbolic Polynomials"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2025.107869",
"label": "Journal of Pure and Applied... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | For a diagonal map $T:\mathbb R[t]_{n,0}\to\mathbb R[t]_{d,0}$, prove that $T((x-1)^{n-1}(x+n-1))$ is real-rooted with $d-1$ roots of one sign exactly when $T$ preserves zero-sum hyperbolicity. Also prove that a hook-shaped symmetric polynomial $p$ is symmetrically hyperbolic exactly when $\Delta_{\mathbf 1,\mathbf 1}p... | Open Problems Our results leave open several interesting questions. Finally, we will say more about a quintic example. Theorem 9. Let p = 4500e5 − 220e1e4 + 7e21 e3 , which is in 5 variables. Then, • p is symmetrically hyperbolic. • p’s associated operator is not extendable • ∆\textasciitilde{}1\textasciitilde{}1 p is ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,481 | OWR-12697711-017 | Extendability of Operators Associated with Hook-Shaped Polynomials | If $p$ is hook-shaped and symmetrically hyperbolic, prove that its associated operator is extendable if and only if $p$ is weakly sum-of-squares hyperbolic. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881](https://doi.org/10.4171/owr/2023/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,023 | 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-12697711-017",
"literature-status:open",
"owr-year:2023"
] | The report states this conjecture as open; the available degree-three and degree-four classifications and computational evidence do not prove it in general. | [
{
"url": "https://ems.press/content/serial-article-files/47009?nt=1",
"label": "OWR 2023 report"
},
{
"url": "https://arxiv.org/abs/2308.09653",
"label": "Symmetric Hyperbolic Polynomials"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2025.107869",
"label": "Journal of Pure and Applied... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/15 | null | null | null | If $p$ is hook-shaped and symmetrically hyperbolic, prove that its associated operator is extendable if and only if $p$ is weakly sum-of-squares hyperbolic. | A more speculative conjecture is as follows: Conjecture 3. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | New Directions in Real Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/15, pp. 813--881 |
30,005,482 | OWR-12697712-001 | Complexity of Counting versus Recovering Planted Communities | Is it easier to count communities than find them? A pair (G, H) of correlated Erdős-Rényi random graphs on n vertices is generated by drawing independently for each of the n(n − 1)/2 couples on vertices a pair of correlated Bernouilli random variables of mean \lambda/n and of correlation parameter s, and including th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914](https://doi.org/10.4171/owr/2023/16)
## Literature... | 3 | partially_solved | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The contribution asks whether community statistics can be easier to infer than communities themselves and then states that its low-degree lo) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697712-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Low-degree tests establish hardness of recovery-versus-testing for a broad planted-community framework, but this does not settle the general algorithmic question. | [
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.94",
"label": "ITCS 2023 paper"
},
{
"url": "https://arxiv.org/abs/2212.10872",
"label": "Community inference paper"
},
{
"url": "https://ems.press/content/serial-article-files/47010?nt=1",
"label": "OWR 2... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/16 | null | null | null | null | Is it easier to count communities than find them? A pair (G, H) of correlated Erdős-Rényi random graphs on n vertices is generated by drawing independently for each of the n(n − 1)/2 couples on vertices a pair of correlated Bernouilli random variables of mean \lambda/n and of correlation parameter s, and including th... | unrecoverable | The contribution asks whether community statistics can be easier to infer than communities themselves and then states that its low-degree lower bounds answer the question negatively. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914 |
30,005,483 | OWR-12697712-002 | Successive Edge-Disjoint Spanning Trees in Random Graphs | In the successive edge-disjoint minimum-spanning-tree process, do the largest-component profiles satisfy $\rho_k(2k+t)\to\rho_\infty(t)$ as $k\to\infty$, and do the limiting tree weights satisfy $\gamma_k\to2k-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914](https://doi.org/10.4171/owr/2023/16)
## Literature... | 3 | open | null | 2,023 | 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-12697712-002",
"literature-status:open",
"owr-year:2023"
] | The extracted statement is an incomplete conjectural fragment, so its intended claim cannot be established unambiguously; under the stated rule it remains open. | [
{
"url": "https://ems.press/content/serial-article-files/47010?nt=1",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/16 | null | null | null | In the successive edge-disjoint minimum-spanning-tree process, do the largest-component profiles satisfy $\rho_k(2k+t)\to\rho_\infty(t)$ as $k\to\infty$, and do the limiting tree weights satisfy $\gamma_k\to2k-1$? | We conjecture that for Random Graphs: Combinatorics, Complex Networks and Disordered Systems 903 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914 |
30,005,484 | OWR-12697712-003 | Chromatic Numbers of Exchangeable Graphon Random Graphs | We give an extension of Bollobás’ classical result on the chromatic number of the binomial random graph to exchangeable random graphs associated with graphons. The asymptotic value was conjectured by Martinsson, Panagiotou, Su, and Trujić. We confirm this conjecture for block graphons and a special class of graphons t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914](https://doi.org/10.4171/owr/2023/16)
## Literature... | 3 | partially_solved | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The passage summarizes proved results for block and approximable graphons and does not itself state the complete general conjecture; the con) | [
"OWR-12697712-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697712-003",
"literature-status:partially-solved",
"owr-year:2023"
] | The cited work extends the chromatic polynomial expectation to block graphons and gives upper bounds for general graphons, but the full general statement is not proved. | [
{
"url": "https://arxiv.org/abs/2109.07773",
"label": "Graphon chromatic polynomials"
},
{
"url": "https://ems.press/content/serial-article-files/47010?nt=1",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/16 | null | null | null | null | We give an extension of Bollobás’ classical result on the chromatic number of the binomial random graph to exchangeable random graphs associated with graphons. The asymptotic value was conjectured by Martinsson, Panagiotou, Su, and Trujić. We confirm this conjecture for block graphons and a special class of graphons t... | unrecoverable | The passage summarizes proved results for block and approximable graphons and does not itself state the complete general conjecture; the concrete convergence question is retained in OWR-12697712-004. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914 |
30,005,485 | OWR-12697712-004 | Convergence of Expected Graphon Chromatic Numbers | For a graphon $W$, does $(\log n/n)\mathbb{E}[\chi(G(n,W))]$ converge as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914](https://doi.org/10.4171/owr/2023/16)
## Literature... | 3 | partially_solved | null | 2,023 | 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... | [
"OWR-12697712-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697712-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Convergence is proved for several graphon classes and general bounds are known, but the stated convergence question remains unresolved in full generality. | [
{
"url": "https://arxiv.org/abs/2109.07773",
"label": "Graphon chromatic polynomials"
},
{
"url": "https://ems.press/content/serial-article-files/47010?nt=1",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/16 | null | null | null | For a graphon $W$, does $(\log n/n)\mathbb{E}[\chi(G(n,W))]$ converge as $n\to\infty$? | Is it true that logn n E[χ(G(n, W ))] converges as n \to \infty? Resilience of perfect matchings in random hypergraphs Matthew Kwan Let Gk (n, p) be the Erdős–Rényi k-uniform random hypergraph with n vertices and edge probability p. Johansson, Kahn and Vu famously answered Shamir’s problem, showing that for any fixed ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914 |
30,005,486 | OWR-12697712-005 | Local Resilience of Random-Hypergraph Perfect Matchings | For every fixed $k$, do sufficiently large $C$ and sufficiently small $\varepsilon>0$ ensure that, with high probability, deleting at most an $\varepsilon$-fraction of the incident hyperedges at every vertex of $G_k(n,C\log n/n^{k-1})$ still leaves a perfect matching? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914](https://doi.org/10.4171/owr/2023/16)
## Literature... | 3 | partially_solved | null | 2,023 | 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-12697712-005",
"literature-status:partially-solved",
"owr-year:2023"
] | The stated local resilience conjecture remains unresolved; related random-hypergraph resilience and transference theorems prove substantial special cases. | [
{
"url": "https://arxiv.org/abs/1908.01435",
"label": "Hypergraph matching resilience"
},
{
"url": "https://arxiv.org/abs/2006.04370",
"label": "Random hypergraph Dirac theorems"
},
{
"url": "https://ems.press/content/serial-article-files/47010?nt=1",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/16 | null | null | null | For every fixed $k$, do sufficiently large $C$ and sufficiently small $\varepsilon>0$ ensure that, with high probability, deleting at most an $\varepsilon$-fraction of the incident hyperedges at every vertex of $G_k(n,C\log n/n^{k-1})$ still leaves a perfect matching? | Asaf Ferber and I conjectured a resilience version of this theorem. Coloring inhomogeneous random graphs Mikhail Isaev Given a graphon W : [0, 1]2 \to (\varepsilon, 1 − \varepsilon), where 0 < \varepsilon < 1/2, consider the exchangeable random graph G(n, W ) on vertex set \{1, 2, . . . , n\} defined as follows: 1) samp... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Random Graphs: Combinatorics, Complex Networks and Disordered Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/16, pp. 883--914 |
30,005,487 | OWR-13750327-001 | Campana–Peternell Conjecture for Fano Manifolds | Is every Fano manifold with nef tangent bundle a rational homogeneous variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 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-13750327-001",
"literature-status:partially-solved",
"owr-year:2023"
] | An abundance-type weak form is known and low-dimensional cases are established, but the broad Fano classification with nef tangent bundle remains open in general. | [
{
"url": "https://arxiv.org/abs/2408.03799",
"label": "Wang 2024"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Is every Fano manifold with nef tangent bundle a rational homogeneous variety? | This conjecture is known to be true in dimension at most five, but in general it is wide open. This is a report on joint work with Andreas Höring, [5] and [6]. Given a compact Kähler manifold (M, \omega), the class [\omega] \in H 1 (M, ΩM ) defines a non-split extension | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,488 | OWR-13750327-002 | Ax–Schanuel and Zilber–Pink for Abelian-Differential Strata | Prove the Ax–Schanuel conjecture for a stratum $S_\alpha$ of abelian differentials. Does $S_\alpha$ contain only finitely many arithmetic points of rank at least $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | open | null | 2,023 | 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-13750327-002",
"literature-status:open",
"owr-year:2023"
] | The Ax-Schanuel and Zilber-Pink directions described in the report remain conjectural; current results cover important special bi-algebraic settings rather than the stated general problem. | [
{
"url": "https://arxiv.org/abs/2303.00642",
"label": "Deroin and Matheus"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Prove the Ax–Schanuel conjecture for a stratum $S_\alpha$ of abelian differentials. Does $S_\alpha$ contain only finitely many arithmetic points of rank at least $3$? | A tantalizing open question is to prove the Ax-Schanuel conjecture for S\alpha and attack the following Zilber-Pink conjecture for S\alpha : The stratum S\alpha contains only finitely many arithmetic points of rank at least 3. In [Ler21] and [KL22], the authors develop for S\alpha the first steps of the bi-algebraic he... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,489 | OWR-13750327-004 | Full Support for Singular Hitchin Systems | Does $R\chi(n,0)_*\operatorname{IC}_{M_{\mathrm{Dol}}(n,0)}$ have full support on the entire Hitchin base $A_n$, meaning that none of its direct summands is properly supported on a subvariety of $A_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 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-13750327-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Full support is proved on the reduced Hitchin base in degree zero and for important families, but the conjecture on the entire Hitchin base remains open. | [
{
"url": "https://arxiv.org/abs/2209.00621",
"label": "Combinatorial decomposition theorem"
},
{
"url": "https://arxiv.org/abs/2502.04966",
"label": "Hitchin fibrations are Ngô fibrations"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Does $R\chi(n,0)_*\operatorname{IC}_{M_{\mathrm{Dol}}(n,0)}$ have full support on the entire Hitchin base $A_n$, meaning that none of its direct summands is properly supported on a subvariety of $A_n$? | conjecture. where Ln (d) is a local system on Sn◦ which coincides as \pi1 (Sn◦ )-representation with the top homology of the geometric realization of the poset of non d-integral partitions m \geq n, up to a twist by the sign representation of \pi1 (Sn◦ ) = Aut(n). Further, if d = e is coprime with n, Wn is a general no... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,490 | OWR-13750327-005 | Determination of Hitchin Complexes from Open Restrictions | Is the complex $R\chi(n,0)_*\operatorname{IC}_{M_{\mathrm{Dol}}(n,0)}$ determined by its restriction to every nonempty open subset of $A_n$, in particular the smooth locus of the Hitchin fibration? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 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"
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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-13750327-005",
"literature-status:partially-solved",
"owr-year:2023"
] | Known full-support results on the reduced base do not establish determination by every nonempty open subset, especially the smooth Hitchin locus; the stated question remains unresolved. | [
{
"url": "https://arxiv.org/abs/2209.00621",
"label": "Combinatorial decomposition theorem"
},
{
"url": "https://arxiv.org/abs/2502.04966",
"label": "Hitchin fibrations are Ngô fibrations"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Is the complex $R\chi(n,0)_*\operatorname{IC}_{M_{\mathrm{Dol}}(n,0)}$ determined by its restriction to every nonempty open subset of $A_n$, in particular the smooth locus of the Hitchin fibration? | In other words, we ask whether the complex Rχ(n, 0)∗ ICMDol (n,0) is determined by the restriction to any open subset of An , in particular the locus over which the Hitchin fibration is smooth. The result is a refinement of the celebrated Ngô support theorem; see [19, §7]. The main issue is to determine the support Sn... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,491 | OWR-13750327-006 | Zero-Free One-Forms on Compact Kähler Varieties | Does the threefold classification for smooth projective varieties whose underlying differentiable manifolds fiber over the circle extend to compact Kähler threefolds? More generally, does every smooth complex projective variety of nonnegative Kodaira dimension with a nowhere-vanishing holomorphic one-form have a birati... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | open | null | 2,023 | 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-13750327-006",
"literature-status:open",
"owr-year:2023"
] | The report explicitly states that both the compact Kähler extension conjecture and the birational or étale-cover expectation remain open. | [
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Does the threefold classification for smooth projective varieties whose underlying differentiable manifolds fiber over the circle extend to compact Kähler threefolds? More generally, does every smooth complex projective variety of nonnegative Kodaira dimension with a nowhere-vanishing holomorphic one-form have a birati... | Both conjectures remain open for the moment. Komplexe Analysis – Differential and Algebraic methods in Kähler spaces 995 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,492 | OWR-13750327-007 | Hermitian–Symplectic Structures on Non-Kähler Manifolds | Does any non-Kähler compact complex manifold admit a Hermitian–symplectic structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | open | null | 2,023 | 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-13750327-007",
"literature-status:open",
"owr-year:2023"
] | Examples and obstructions are known for several non-Kähler classes, but the existence and classification question for Hermitian-Symplectic structures remains open in general. | [
{
"url": "https://sites.math.rutgers.edu/~cl1412/papers/Kahler-submersion.pdf",
"label": "Kähler submersion paper"
},
{
"url": "https://arxiv.org/abs/2409.09425",
"label": "Streets-Tian conjecture"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Does any non-Kähler compact complex manifold admit a Hermitian–symplectic structure? | The question is still open in general, though there are negative results which say that there are no such examples among complex surfaces ([8, 10]), nilmanifolds with invariant complex structures ([5]), twistor spaces ([11]), Moishezon manifolds and complex manifolds of Fujiki class ([9, 2]). We end with an open proble... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,493 | OWR-13750327-008 | Local Fundamental Groups of Algebraic Singularities | For each natural class $\mathcal C_n$ of $n$-dimensional complex algebraic singularities, characterize the finitely presented groups that occur as local fundamental groups $\pi_1(X;x)$ of members of $\mathcal C_n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 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"
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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 | [
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"OWR-13750327-008",
"literature-status:partially-solved",
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] | Normal and several special classes of singularities have strong fundamental-group realizability theorems, while the stated broad classification across singularity classes remains incomplete. | [
{
"url": "https://doi.org/10.1090/S0894-0347-2014-00807-9",
"label": "Kapovich and Kollar"
},
{
"url": "https://arxiv.org/abs/2302.11790",
"label": "Low-dimensional lc singularities"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
"label": "OWR 2023 report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | For each natural class $\mathcal C_n$ of $n$-dimensional complex algebraic singularities, characterize the finitely presented groups that occur as local fundamental groups $\pi_1(X;x)$ of members of $\mathcal C_n$. | What fundamental groups can we find among the singularities in Cn ? Komplexe Analysis – Differential and Algebraic methods in Kähler spaces 1007 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,494 | OWR-13750327-009 | Local Fundamental Groups of Rational Singularities | Which finitely presented groups occur as local fundamental groups of rational complex algebraic singularities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"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-13750327-009",
"literature-status:partially-solved",
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] | The report gives complete realizability for normal isolated threefold singularities and partial rational and Cohen-Macaulay classifications, but not a complete answer for all singularities in the question. | [
{
"url": "https://doi.org/10.1090/S0894-0347-2014-00807-9",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Which finitely presented groups occur as local fundamental groups of rational complex algebraic singularities? | Question 1. However, due to the work of Kollár and Kapovich, we can understand the fundamental group of their dual complexes. The dual complex, denoted by D(X; x), is a combinatorial object that encodes the intersection of the exceptional divisors on a resolution. Theorem 7. Let (X; x) be a rational singularity. Then ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,495 | OWR-13750327-010 | Fundamental Groups of Five-Dimensional Log-Canonical Singularities | Does every finitely presented group occur as the local fundamental group of a five-dimensional log-canonical singularity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
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"description": "Geometric objects defined by polynomial equations.",
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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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750327-010",
"literature-status:open",
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] | The five-dimensional log-canonical realizability question for arbitrary finitely presented groups remains unresolved; current low-dimensional results do not reach this claim. | [
{
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"label": "Low-dimensional lc singularities"
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Does every finitely presented group occur as the local fundamental group of a five-dimensional log-canonical singularity? | Does any finitely presented group appear as the fundamental group of a 5-dimensional lc singularity? Komplexe Analysis – Differential and Algebraic methods in Kähler spaces 1009 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,496 | OWR-13750327-011 | Virtual Nilpotence of Rational Log-Canonical Local Groups | For every rational log-canonical singularity $(X;x)$, is the local fundamental group $\pi_1(X;x)$ virtually nilpotent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | open | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"slug": "algebraic-geometry",
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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-13750327-011",
"literature-status:open",
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] | No general proof that local fundamental groups of log-canonical rational singularities are virtually nilpotent was found; the report presents this as an open question. | [
{
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"label": "Low-dimensional lc singularities"
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | For every rational log-canonical singularity $(X;x)$, is the local fundamental group $\pi_1(X;x)$ virtually nilpotent? | In a similar vein, we propose the following question. Is \pi1 (X; x) virtually nilpo- tent? Komplexe Analysis – Differential and Algebraic methods in Kähler spaces 1009 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,497 | OWR-13750327-012 | Equality Cases for Singularities of Theta Divisors | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety. If $\dim\operatorname{Sing}_m(\Theta)=\dim A-2m+1$ for some $m\geq2$, must $A$ be either a hyperelliptic Jacobian or the intermediate Jacobian of a cubic threefold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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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",
"oberwolfach-reports",
"OWR-13750327-012",
"literature-status:partially-solved",
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] | The dimension bound and equality problem for principally polarized abelian varieties is proved in Prym, low-dimensional, and isolated-singularity cases, but remains open in general. | [
{
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"label": "Schnell and Yang"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety. If $\dim\operatorname{Sing}_m(\Theta)=\dim A-2m+1$ for some $m\geq2$, must $A$ be either a hyperelliptic Jacobian or the intermediate Jacobian of a cubic threefold? | Moreover, if the equality is achieved in (1) by any m \geq 2, is it true that A is either the Jacobian of a hyperelliptic curve or the intermediate Jacobian of a cubic threefold? If this question is true, then it implies a conjecture of Debarre, proposed by Grushevsky [8, Conjecture 5.5] and a conjecture of Grushevsky ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,498 | OWR-13750327-014 | Dimension Bounds for Theta Divisor Singularities | For every indecomposable principally polarized abelian variety $(A,\Theta)$ and every $m\geq2$, is $\dim\operatorname{Sing}_m(\Theta)\leq\dim A-2m+1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030](https://doi.org/10.4171/owr/2023/18)
## Literat... | 3 | partially_solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-13750327-014",
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] | The dimension bound is known for Prym varieties, in dimension at most five, and for isolated singularities, with further conditional results; the general equality classification remains open. | [
{
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"label": "Schnell and Yang"
},
{
"url": "https://ems.press/content/serial-article-files/47013",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/18 | null | null | null | For every indecomposable principally polarized abelian variety $(A,\Theta)$ and every $m\geq2$, is $\dim\operatorname{Sing}_m(\Theta)\leq\dim A-2m+1$? | Question 1. If (A, Θ) is a principally polarized abelian variety, Kollár [9, Theorem 17.13] showed that lct(Θ) = 1, i.e. (A, Θ) is log canonical, which implies that dim Singm (Θ) \leq dim A − m, \forallm \geq 2. Later, Ein and Lazarsfeld [7] proved that if one assumes (A, Θ) is indecomposable, then Θ is normal and has... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis – Differential and Algebraic methods in Kähler spaces (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/18, pp. 965--1030 |
30,005,499 | OWR-13750328-001 | Representation-Theory Workshop Overview | conjecture. Regarding the Galois version of the Alperin-McKay conjecture, C. Vallejo estab- lished the fields of values of the 2-height zero characters, providing a surprising new consequence of and support for the conjecture. Finally, regarding the so- called “counting conjectures,” J. Semeraro, in joint work with Kess... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is a workshop overview and contains no standalone open problem.) | null | null | null | [
"owr",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | null | conjecture. Regarding the Galois version of the Alperin-McKay conjecture, C. Vallejo estab- lished the fields of values of the 2-height zero characters, providing a surprising new consequence of and support for the conjecture. Finally, regarding the so- called “counting conjectures,” J. Semeraro, in joint work with Kess... | unrecoverable | The official report confirms that this extraction is a workshop overview and contains no standalone open problem. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,500 | OWR-13750328-002 | Representation-Theory Table-of-Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043 Shigeo Koshitani (joint with Caroline Lassueur, Benjamin Sambale) Splendid Morita equivalences for principal 2-blocks with wreathed defect groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment, not a standalone open problem.) | null | null | null | [
"owr",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043 Shigeo Koshitani (joint with Caroline Lassueur, Benjamin Sambale) Splendid Morita equivalences for principal 2-blocks with wreathed defect groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment, not a standalone open problem. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,501 | OWR-13750328-003 | First Hochschild Cohomology of Nontrivial-Defect Blocks | For every block $B$ of a finite group with nontrivial defect group, is $HH^1(B)$ nonzero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-13750328-003",
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{
"url": "https://arxiv.org/abs/2301.03185",
"label": "Benson--Kessar--Linckelmann, Hochschild cohomology II"
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{
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"label": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For every block $B$ of a finite group with nontrivial defect group, is $HH^1(B)$ nonzero? | It remains an open question (cf. [9, Question 7.4]), whether for every block B of a finite group with non-trivial defect groups we have HH 1 (B) 6= 0. If p ⩾ 3, then w−1 X dimk HH 1 (B) = dimFp (Z(Bpj )). j=0 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,502 | OWR-13750328-004 | Hochschild Cohomology of Symmetric-Group Algebras | Prove that $HH^1(\mathbb F_pS_n)$ is a solvable Lie algebra for every $n\geq 1$, and extend the known Hochschild-cohomology generating functions to blocks of alternating groups, finite Coxeter groups, Hecke algebras, and diagram algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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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] | The solvability conjecture for the Lie algebra HH1(Fp Sn) has substantial criteria and computations, including recent block-theoretic criteria, but no general proof for every n and p is established. | [
{
"url": "https://arxiv.org/abs/2503.16697",
"label": "Linckelmann--Wang, solvability of HH1 for blocks"
},
{
"url": "https://arxiv.org/abs/2301.03185",
"label": "Benson--Kessar--Linckelmann, Hochschild cohomology II"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberw... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Prove that $HH^1(\mathbb F_pS_n)$ is a solvable Lie algebra for every $n\geq 1$, and extend the known Hochschild-cohomology generating functions to blocks of alternating groups, finite Coxeter groups, Hecke algebras, and diagram algebras. | The authors conjecture that HH 1 (Fp Sn ) should be a solvable Lie algebra, for any positive integer n. This raises the question whether the above results on generating functions for Hochschild cohomology can be extended to (blocks of) alternating groups, other finite Coxeter groups, Hecke algebras, and diagram algebras... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,503 | OWR-13750328-006 | Source-Algebra Classification of Cyclic Blocks | For a cyclic block $B$ of a finite group $G$, determine whether $W(B)$ is recoverable from the character table of $G$; determine $W(B)$ for every nonuniserial cyclic block and every cyclic block of a finite quasisimple group; and reduce the general classification to the quasisimple case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 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-13750328-006",
"literature-status:partially-solved",
"owr-year:2023"
] | Hiss--Lassueur determine W(B) from character-table signs for odd primes and classify many quasisimple cases, with a 2025 continuation handling special-linear and unitary families; the four questions are not settled in full generality. | [
{
"url": "https://www.math.rwth-aachen.de/homes/Gerhard.Hiss/Preprints/sourcealgebraI.pdf",
"label": "Hiss--Lassueur, source algebra equivalence I"
},
{
"url": "https://www.math.rwth-aachen.de/~Gerhard.Hiss/Preprints/sourcealgebraIII.pdf",
"label": "Hiss--Lassueur, source algebra equivalence III... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For a cyclic block $B$ of a finite group $G$, determine whether $W(B)$ is recoverable from the character table of $G$; determine $W(B)$ for every nonuniserial cyclic block and every cyclic block of a finite quasisimple group; and reduce the general classification to the quasisimple case. | Question B. (1) Can W (B) be read off from the character table of G? (2) Can we determine W (B) for all (non-uniserial) cyclic blocks B of finite groups? (3) Can we determine W (B) for all cyclic blocks B of finite quasi-simple groups? (4) Can (b) be reduced to (c)? The report passage is retained verbatim as the releva... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,504 | OWR-13750328-007 | Optimal Character-Ratio Bounds for Almost Quasisimple Groups | For a finite almost quasisimple group $G$ and $g\in G\setminus Z(G)$, find the smallest explicit $\gamma(g)\in(0,1)$ satisfying $|\chi(g)|/\chi(1)\leq\gamma(g)$ for every nonlinear $\chi\in\operatorname{Irr}(G)$, and the smallest explicit $\alpha(g)\in(0,1)$ satisfying $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for every $\chi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-007",
"literature-status:open",
"owr-year:2023"
] | The requested optimal uniform character bounds for all finite almost quasisimple groups remain unresolved; modern uniform bounds solve important families and applications but do not give the full explicit optimum sought here. | [
{
"url": "https://annals.math.princeton.edu/2024/200-1/p01",
"label": "Larsen--Tiep, Uniform character bounds for finite classical groups"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberwolfach Report 19/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For a finite almost quasisimple group $G$ and $g\in G\setminus Z(G)$, find the smallest explicit $\gamma(g)\in(0,1)$ satisfying $|\chi(g)|/\chi(1)\leq\gamma(g)$ for every nonlinear $\chi\in\operatorname{Irr}(G)$, and the smallest explicit $\alpha(g)\in(0,1)$ satisfying $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for every $\chi... | Problem 1. Let G be a finite almost quasisimple group, g \in G r Z(G). (A) Find an explicit, and as small as possible, 0 < \gamma = \gamma(g) < 1, such that |χ(g)| \leq \gamma, \forall χ \in Irr(G) with χ(1) > 1. χ(1) (B) Find an explicit, and as small as possible, 0 < \alpha = \alpha(g) < 1, such that |χ(g)| \leq χ(1)... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,505 | OWR-13750328-009 | Alperin–McKay Conjecture | Let $b$ be an $\ell$-block of a finite group $G$ with defect group $D$, and let $B$ be its Brauer correspondent in $N_G(D)$. Prove $|\operatorname{Irr}_0(b)|=|\operatorname{Irr}_0(B)|$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-009",
"literature-status:open",
"owr-year:2023"
] | The Alperin--McKay equality is reduced to inductive conditions and proved in many families, but the general finite-group conjecture remains unresolved as of the check date. | [
{
"url": "https://arxiv.org/abs/2103.06394",
"label": "Ruhstorfer, Quasi-isolated blocks and the Alperin--McKay conjecture"
},
{
"url": "https://annals.math.princeton.edu/2025/201-2/p02",
"label": "Ruhstorfer, Alperin--McKay for the prime two"
},
{
"url": "https://doi.org/10.4171/owr/202... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Let $b$ be an $\ell$-block of a finite group $G$ with defect group $D$, and let $B$ be its Brauer correspondent in $N_G(D)$. Prove $|\operatorname{Irr}_0(b)|=|\operatorname{Irr}_0(B)|$. | In the representation theory of finite groups some of the most important conjec- tures relate the representation theory of a finite group G to the ones of its ℓ-local subgroups for a prime ℓ dividing the order of G. One of these conjectures is the Alperin–McKay conjecture, which forms a blockwise generalization of the Mc... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,506 | OWR-13750328-010 | Inductive Alperin–McKay Condition for Isolated Blocks | For finite simple groups of Lie type $B$ or $C$ and primes $\ell\geq 5$ outside the defining characteristic, verify the inductive Alperin–McKay condition for every isolated $\ell$-block by constructing the required equivariant height-zero-character bijection. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 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-13750328-010",
"literature-status:partially-solved",
"owr-year:2023"
] | The inductive Alperin--McKay condition is proved for the stated B and C cases with odd defining characteristic and ell\geq5, but the all-groups and all-primes conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Ruhstorfer--Brough, inductive Alperin--McKay condition"
},
{
"url": "https://annals.math.princeton.edu/2025/201-2/p02",
"label": "Ruhstorfer, Alperin--McKay for the prime two"
},
{
"url": "https://arxiv.org/abs/2103.06394",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For finite simple groups of Lie type $B$ or $C$ and primes $\ell\geq 5$ outside the defining characteristic, verify the inductive Alperin–McKay condition for every isolated $\ell$-block by constructing the required equivariant height-zero-character bijection. | Conjecture (Alperin–McKay). Let b be an ℓ-block of G with defect group D and B its Brauer correspondent in NG (D). Then |Irr0 (b)| = |Irr0 (B)|. In [Spä13], the Alperin–McKay conjecture was reduced to the verification of the so-called inductive Alperin–McKay condition (iAM) for all finite simple groups and primes ℓ. For... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,507 | OWR-13750328-012 | Frobenius–Schur Indicators in Real Nilpotent Blocks | Let $B$ be a real nilpotent nonprincipal $2$-block with defect pair $(D,E)$. Prove that there is a height-preserving bijection $\Gamma:\operatorname{Irr}(D)\to\operatorname{Irr}(B)$ such that $\epsilon(\Gamma(\lambda))=|D|^{-1}\sum_{e\in E\setminus D}\lambda(e^2)$ for every $\lambda\in\operatorname{Irr}(D)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 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-13750328-012",
"literature-status:partially-solved",
"owr-year:2023"
] | Sambale's bijection and indicator formula hold when the defect is abelian or dihedral and for solvable or quasisimple groups, while the stated general real-block conjecture is not proved. | [
{
"url": "https://doi.org/10.1007/s10013-023-00623-5",
"label": "Sambale, Real characters in nilpotent blocks"
},
{
"url": "https://arxiv.org/abs/2301.13440",
"label": "Sambale, primary preprint"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberwolfach Report 19/2023"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Let $B$ be a real nilpotent nonprincipal $2$-block with defect pair $(D,E)$. Prove that there is a height-preserving bijection $\Gamma:\operatorname{Irr}(D)\to\operatorname{Irr}(B)$ such that $\epsilon(\Gamma(\lambda))=|D|^{-1}\sum_{e\in E\setminus D}\lambda(e^2)$ for every $\lambda\in\operatorname{Irr}(D)$. | Conjecture 2. Let B be a real, nilpotent, non-principal 2-block of a finite group G with defect pair (D, E). Then there exists a height preserving bijection Γ : Irr(D) \to Irr(B) such that 1 X ǫ(Γ(\lambda)) = \lambda(e2 ) |D| e\inE\D It is a difficult problem to decide whether a real-valued character χ of a finite group G... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,508 | OWR-13750328-013 | Projective Characters and Square Roots in Real Blocks | Let $B$ be a real nonprincipal $2$-block with defect pair $(D,E)$, and let $(x,b)$ be a $B$-subsection whose defect pair is $(C_D(x),C_E(x))$ and whose block $b$ has unique projective indecomposable character $\Phi$. Prove that every $y\in G$ with $y^2=x$ satisfies $[\Phi_{C_G(y)},1_{C_G(y)}]=|y^{C_G(x)}\cap(E\setminus... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-013",
"literature-status:open",
"owr-year:2023"
] | The local Conjecture 4 is presented as a sufficient route to the general indicator formula, but the report gives no proof and current literature does not establish it in general. | [
{
"url": "https://doi.org/10.1007/s10013-023-00623-5",
"label": "Sambale, Real characters in nilpotent blocks"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberwolfach Report 19/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Let $B$ be a real nonprincipal $2$-block with defect pair $(D,E)$, and let $(x,b)$ be a $B$-subsection whose defect pair is $(C_D(x),C_E(x))$ and whose block $b$ has unique projective indecomposable character $\Phi$. Prove that every $y\in G$ with $y^2=x$ satisfies $[\Phi_{C_G(y)},1_{C_G(y)}]=|y^{C_G(x)}\cap(E\setminus... | Theorem 3. Conjecture 2 holds in each of the following cases: (i) D is abelian or a dihedral group. (ii) G is solvable or quasisimple. In general, Conjecture 2 is implied by the following local conjecture: Conjecture 4. Let B be a real, non-principal 2-block with defect pair (D, E). Let (x, b) be a B-subsection with de... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,509 | OWR-13750328-014 | Finitely Generated Cohomology in Stable Module Categories | For a finite group $G$ and a field $k$ of characteristic $p$, prove that the thick subcategory of $\operatorname{StMod}(kG)$ consisting of modules with finitely generated cohomology is generated by the thick subcategories of finitely generated modules and modules with no cohomology. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-014",
"literature-status:open",
"owr-year:2023"
] | The converse to finite generation of cohomology is formulated through Benson--Greenlees thick-subcategory conjectures; proofs cover the p-nilpotent-centralizer case and a few additional groups, not all finite groups. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.07.040",
"label": "Benson--Carlson, Modules with finitely generated cohomology"
},
{
"url": "https://arxiv.org/abs/2305.08580",
"label": "Benson--Greenlees, modules and singularities of C-star-BG"
},
{
"url": "https://doi.org/10.4171/owr/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For a finite group $G$ and a field $k$ of characteristic $p$, prove that the thick subcategory of $\operatorname{StMod}(kG)$ consisting of modules with finitely generated cohomology is generated by the thick subcategories of finitely generated modules and modules with no cohomology. | What about the converse? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,510 | OWR-13750328-015 | Singularity-Category Support and the Group-Theoretic Nucleus | For every finite group $G$, prove that the support of the singularity category $D_{\mathrm{sg}}(C^*BG)$ is exactly the group-theoretic nucleus $\Theta_G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-015",
"literature-status:open",
"owr-year:2023"
] | The conjectured equality between singularity-category support and the nucleus is proved in special cases, including the 2024 additional examples, but the general equality remains unproved. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.07.040",
"label": "Benson--Carlson, Modules with finitely generated cohomology"
},
{
"url": "https://arxiv.org/abs/2305.08580",
"label": "Benson--Greenlees, modules and singularities of C-star-BG"
},
{
"url": "https://doi.org/10.4171/owr/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For every finite group $G$, prove that the support of the singularity category $D_{\mathrm{sg}}(C^*BG)$ is exactly the group-theoretic nucleus $\Theta_G$. | We conjecture that this is the case in general. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,511 | OWR-13750328-016 | Character-Field Conjecture Introduction | We propose the following. 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:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report confirms that this extraction is only an incomplete setup; the following record preserves the full conjecture.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750328-016",
"literature-status:partially-solved",
"owr-year:2023"
] | For the fields-of-values Conjecture B, the if implication is proved and the only-if implication is reduced to height-zero characters in quasisimple blocks; the full equivalence remains open. | [
{
"url": "https://arxiv.org/abs/2304.12869",
"label": "Navarro--Ruhstorfer--Tiep--Vallejo, fields of values"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberwolfach Report 19/2023"
},
{
"url": "https://doi.org/10.1080/00927872.2025.2584406",
"label": "On a conjecture... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | null | We propose the following. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is only an incomplete setup; the following record preserves the full conjecture. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,512 | OWR-13750328-017 | Abelian Fields Generated by Height-Zero Characters | Let $p$ be prime and let $F$ be an abelian number field of conductor $n=p^am$ with $(m,p)=1$. Prove that $F=\mathbb Q(\chi)$ for some height-zero irreducible character $\chi$ in a $p$-block of a finite group if and only if $[\mathbb Q_n:\langle F,\mathbb Q_m\rangle]$ is coprime to $p$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 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-13750328-017",
"literature-status:partially-solved",
"owr-year:2023"
] | This continuation is the same fields-of-values Conjecture B: one direction is established and the converse is reduced to quasisimple blocks, but no general proof is available. | [
{
"url": "https://arxiv.org/abs/2304.12869",
"label": "Navarro--Ruhstorfer--Tiep--Vallejo, fields of values"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"label": "Oberwolfach Report 19/2023"
},
{
"url": "https://doi.org/10.1080/00927872.2025.2584406",
"label": "On a conjecture... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Let $p$ be prime and let $F$ be an abelian number field of conductor $n=p^am$ with $(m,p)=1$. Prove that $F=\mathbb Q(\chi)$ for some height-zero irreducible character $\chi$ in a $p$-block of a finite group if and only if $[\mathbb Q_n:\langle F,\mathbb Q_m\rangle]$ is coprime to $p$. | character χ of a finite group G having height zero in its p-block with Q(χ) = F if, and only if, |Qn : hF, Qm i| is coprime to p. We show that Conjecture B is implied by the statement Alperin-McKay-Navarro conjecture. Moreover, we can prove “if” implication in Conjecture B and show that the “only if” implication holds i... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,513 | OWR-13750328-018 | Nonexoticity of Block Fusion Systems | Prove that the saturated fusion system determined by any $\ell$-block of a finite group is nonexotic. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-018",
"literature-status:open",
"owr-year:2023"
] | It remains open whether every fusion system of a finite-group block is nonexotic; block-exoticity is proved for several families, but no general realization theorem is known. | [
{
"url": "https://doi.org/10.1515/jgth-2019-0035",
"label": "Serwene, Block-exoticity of a family of exotic fusion systems"
},
{
"url": "https://arxiv.org/abs/2302.05203",
"label": "Serwene, proving a conjecture for fusion systems"
},
{
"url": "https://doi.org/10.4171/owr/2023/19",
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Prove that the saturated fusion system determined by any $\ell$-block of a finite group is nonexotic. | It is a theorem that any ℓ-block B of kG determines a saturated fusion system FD (B) on its defect group D and an open problem to show that FD (B) is never exotic. Spetses from the p-local perspective Jason Semeraro (joint work with Radha Kessar, Gunter Malle) where Irrd (Q) = \{µ \in Irr(Q) | vℓ (|Q|/µ(1)) = d\} is th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,514 | OWR-13750328-019 | Nonnegativity of Fusion-System Multiplicities | For every saturated fusion system $\mathcal F$ and every nonnegative integer $d$, prove $m(\mathcal F,d)\geq 0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-019",
"literature-status:open",
"owr-year:2023"
] | The inequality m(F,d)\geq0 is supported by calculations and proved in selected spets and fusion-system families, but no proof for every saturated fusion system and nonnegative d is established. | [
{
"url": "https://arxiv.org/abs/2003.07213",
"label": "Kessar--Malle--Semeraro, weight conjectures for ell-compact groups and spetses"
},
{
"url": "https://doi.org/10.1080/10586458.2021.1926004",
"label": "Semeraro, A 2-compact group as a spets"
},
{
"url": "https://doi.org/10.4171/owr/2... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For every saturated fusion system $\mathcal F$ and every nonnegative integer $d$, prove $m(\mathcal F,d)\geq 0$. | For example, we conjectured that m(F , d) \geq 0 for any saturated fusion system and non-negative integer d. • a set Uch(G) of “unipotent” characters, and for each \gamma \in Uch(G), a “de- gree” \gamma(1) \in QW [x], where QW is the character field of W ; • for a root of unity ζ, a partition of Uch(G) into ζ-Harish–Cha... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,515 | OWR-13750328-022 | Four Modular Isomorphism Problems | Determine whether the Modular Isomorphism Problem has a positive answer for groups of odd order and for groups of nilpotency class $2$; whether there are $p$-groups $G,H$ and a characteristic-$p$ field $k$ with $\mathbb F_pG\not\cong\mathbb F_pH$ but $kG\cong kH$; and which invariants of $G$ are determined by $kG$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 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-13750328-022",
"literature-status:open",
"owr-year:2023"
] | The general odd-order and class-two modular isomorphism questions remain open; substantial subclasses such as cyclic center and center index p^3 are solved. | [
{
"url": "https://doi.org/10.1365/s13291-022-00249-5",
"label": "modular isomorphism survey"
},
{
"url": "https://doi.org/10.1515/forum-2023-0237",
"label": "class-two cyclic-center result"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | Determine whether the Modular Isomorphism Problem has a positive answer for groups of odd order and for groups of nilpotency class $2$; whether there are $p$-groups $G,H$ and a characteristic-$p$ field $k$ with $\mathbb F_pG\not\cong\mathbb F_pH$ but $kG\cong kH$; and which invariants of $G$ are determined by $kG$. | Can we then find the isomorphism type of G as a group? Several natural questions remain open though, including: • Does the Modular Isomorphism Problem have a positive answer for groups of odd order? • Does it have a positive answer for groups of nilpotency class 2? • What is the role of the field in the problem: might th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
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