id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,216 | OWR-14299089-003 | Realizability of Blade-Induced Matroid Subdivisions | Characterize when a subdivision induced by an arrangement of blades is realizable, equivalently when it is induced by a realizable tropical Plücker vector. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558](https://doi.org/10.4171/owr/2025/12)
## Literature review (... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299089-003",
"literature-status:open",
"owr-year:2025"
] | Compatible blade arrangements and explicit non-realizable examples are known, but no general characterization of when the induced subdivisions are realizable is established. | [
{
"url": "https://doi.org/10.4171/owr/2025/12",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2501.17249",
"label": "When alcoved polytopes add"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/12 | null | null | null | Characterize when a subdivision induced by an arrangement of blades is realizable, equivalently when it is induced by a realizable tropical Plücker vector. | Question 1. When are the induced subdivisions realizable, i.e., when are they induced by a realizable tropical Plücker vector? Clearly, any single blade induces a regular matroid subdivision. But this is not the case in general. For an example of a blade arrangement which induces a non-realizable tropical Plücker vec... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558 |
30,006,217 | OWR-14299089-005 | Minimal Convex Difference Decompositions of CPWL Functions | Given a continuous piecewise-linear function $f$, decompose it as $f=g-h$ with $g$ and $h$ convex continuous piecewise-linear functions having as few linear pieces as possible. Construct a finite procedure that finds a globally minimal decomposition in arbitrary dimension. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558](https://doi.org/10.4171/owr/2025/12)
## Literature review (... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299089-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299089-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Finite procedures solve the problem after fixing a compatible polyhedral complex, and special two-dimensional cases are solved, but a globally minimal decomposition in general dimensions remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/12",
"label": "OWR report"
},
{
"url": "https://openreview.net/forum?id=vVCHWVBsLH",
"label": "Decomposition polyhedra of CPWL functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/12 | null | null | null | Given a continuous piecewise-linear function $f$, decompose it as $f=g-h$ with $g$ and $h$ convex continuous piecewise-linear functions having as few linear pieces as possible. Construct a finite procedure that finds a globally minimal decomposition in arbitrary dimension. | How to decompose a CPWL function f into a difference f = g − h of two convex CPWL functions with as few pieces as possible? We propose a novel perspective on Problem 1 making use of polyhedral geome- try. The last statement implies a finite procedure to find a minimal decomposition among those decompositions that are c... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558 |
30,006,218 | OWR-14299089-006 | Duplicate Minimal Convex-Difference Decomposition Problem | It remains an open question to construct a minimal decomposition in general dimensions, or to describe a finite procedure to compute it. CWPL function f : Rn \to R can be written as the difference f = g − h of two convex CPWL functions [2, 4]. Consequently, a natural idea to circumvent the challenges induced by nonconv... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558](https://doi.org/10.4171/owr/2025/12)
## Literature review (... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this overlapping extraction repeats the minimal convex-difference decomposition problem represented canoni) | [
"OWR-14299089-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299089-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The 2024--2025 work proves a polyhedral characterization of decompositions, a vertex criterion for minimality, and special cases, but fixes the underlying polyhedral complex and does not supply a general-dimensional minimal decomposition or finite procedure. | [
{
"url": "https://arxiv.org/abs/2410.04907",
"label": "Brandenburg--Grillo--Hertrich, Decomposition Polyhedra"
},
{
"url": "https://doi.org/10.4171/owr/2025/12",
"label": "Oberwolfach Report 12/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/12 | null | null | null | null | It remains an open question to construct a minimal decomposition in general dimensions, or to describe a finite procedure to compute it. CWPL function f : Rn \to R can be written as the difference f = g − h of two convex CPWL functions [2, 4]. Consequently, a natural idea to circumvent the challenges induced by nonconv... | unrecoverable | The official report confirms that this overlapping extraction repeats the minimal convex-difference decomposition problem represented canonically by OWR-14299089-005. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558 |
30,006,219 | OWR-14299089-007 | Log-Concavity under Hadamard Products | For a polynomial p, define $W(p)$ by $\sum_{n\ge0}p(n)x^n=W(p)(x)/(1-x)^{\deg p+1}$. If $W(p)$ and $W(q)$ have nonnegative, log-concave coefficient sequences with no internal zeros, must $W(pq)$ have the same property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558](https://doi.org/10.4171/owr/2025/12)
## Literature review (... | 3 | solved | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes)**. The record now states Brändén–Ferroni–Jochemko's Question 6.1 (K. Jochemko, OWR 12/2025, p. 555), as Follow-up 6 suggested, and that question has since been answered. | [
"owr",
"oberwolfach-reports",
"OWR-14299089-007",
"literature-status:open",
"owr-year:2025"
] | The previous extraction asked about pointwise products of log-concave sequences, an immediate inequality. The source instead asks whether log-concavity of the numerator polynomials W(p) and W(q) is preserved by multiplying their interpolating polynomials p and q (Question 6.1).
**What remains.** The corrected numerato... | [
{
"url": "https://doi.org/10.1090/tran/9683",
"label": "Brändén–Ferroni–Jochemko, Hadamard products and log-concavity (2026)"
},
{
"url": "https://arxiv.org/abs/2408.12386",
"label": "Brändén–Ferroni–Jochemko — Question 6.1"
},
{
"url": "https://doi.org/10.4171/owr/2025/12",
"label":... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2025/12 | null | null | null | For a polynomial p, define $W(p)$ by $\sum_{n\ge0}p(n)x^n=W(p)(x)/(1-x)^{\deg p+1}$. If $W(p)$ and $W(q)$ have nonnegative, log-concave coefficient sequences with no internal zeros, must $W(pq)$ have the same property? | Whether the Hadamard products preserves log-concavity remains an open question at this point [1, Question 6.1]. In many instances, in combinatorics and otherwise, the coefficients agree with evaluations of a polynomial function, i.e., there is a polynomial p such that an = p(n) for all n \geq 0. It is a well-known fact... | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558 |
30,006,220 | OWR-14299090-001 | Improvements to the Signed Heat Method | Improve the Signed Heat Method for computing signed distance, with particular attention to output-sensitive formulations, accuracy guarantees, robustness, and computational complexity across meshes, point clouds, voxels, and nonmanifold geometry. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/5, pp. 209--274](https://doi.org/10.4171/owr/2025/5)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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-14299090-001",
"literature-status:open",
"owr-year:2025"
] | The Signed Heat Method is established and broadly applicable, but the report states that output-sensitive formulations and further improvements remain unclear; no general improvement theorem resolving the question was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/5",
"label": "Feng--Gkioulekas--Crane, Signed Heat Method report"
},
{
"url": "https://doi.org/10.1145/3657615",
"label": "Feng--Crane, Generalized signed distance"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/5 | null | null | null | Improve the Signed Heat Method for computing signed distance, with particular attention to output-sensitive formulations, accuracy guarantees, robustness, and computational complexity across meshes, point clouds, voxels, and nonmanifold geometry. | Can we improve upon the Signed Heat Method? Given how well the SHM works, a natural question is how to extend the method even further. The algorithm ends up amounting to solving two sparse linear systems. In addition to its simplicity, the SHM offers the following advantages: ‚ The method is based purely on intrinsic P... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/5, pp. 209--274 |
30,006,221 | OWR-14299090-002 | Feasible High-Performance Plasma Flows for Stellarators | Does there exist a stellarator plasma-flow configuration that is simultaneously highly efficient, dynamically stable, and physically buildable? Develop methods for exploring the configuration space while excluding self-intersections and other nonphysical deformations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/5, pp. 209--274](https://doi.org/10.4171/owr/2025/5)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299090-002",
"literature-status:open",
"owr-year:2025"
] | The report identifies the existence of a stellarator configuration that is simultaneously efficient, stable, and buildable under reactor engineering constraints as completely open; current designs demonstrate trade-offs rather than a resolution of this existence question. | [
{
"url": "https://doi.org/10.4171/owr/2025/5",
"label": "Lahner, Geometric Optimization for Plasma Fusion"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/5 | null | null | null | Does there exist a stellarator plasma-flow configuration that is simultaneously highly efficient, dynamically stable, and physically buildable? Develop methods for exploring the configuration space while excluding self-intersections and other nonphysical deformations. | The question whether a highly efficient and stable but at the same buildable plasma flow for stellarators exist remains completely open. Apart from several open questions on the engineering side, there are aspects in which machine learning might make important contributions in the exploration of the huge plasma flow co... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/5, pp. 209--274 |
30,006,222 | OWR-14299091-002 | Generalized Fried Conjecture for Anosov Flows | Identify the dynamical counterpart of the Ray–Singer metric, formulate the corresponding generalized Fried conjecture, and prove the predicted equality between the Ray–Singer norm and the dynamical invariant for general Anosov flows. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Results on Loop Spaces (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/13, pp. 559--578](https://doi.org/10.4171/owr/2025/13)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,025 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299091-002",
"literature-status:partially-solved",
"owr-year:2025"
] | Bismut and Shen construct the canonical Fried section and formulate the generalized Fried conjecture, answering the first two questions, but the asserted Ray--Singer norm identity remains conjectural in general despite special cases. | [
{
"url": "https://doi.org/10.1007/s00220-025-05400-8",
"label": "Bismut--Shen, Anosov vector fields and Fried sections"
},
{
"url": "https://doi.org/10.4171/owr/2025/13",
"label": "Oberwolfach Report 13/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/13 | null | null | null | Identify the dynamical counterpart of the Ray–Singer metric, formulate the corresponding generalized Fried conjecture, and prove the predicted equality between the Ray–Singer norm and the dynamical invariant for general Anosov flows. | This leads to the following questions: (1) What is the dynamical counterpart of the Ray-Singer metric ? (2) How can one formulate a generalized version of Fried’s conjecture ? (3) How can the generalized Fried conjecture be established ? Analytic torsion and Anosov flow Shu Shen (joint work with Jean-Michel Bismut) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Recent Results on Loop Spaces (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/13, pp. 559--578 |
30,006,223 | OWR-14299092-002 | Expander Degree Under Boundary Connected Sums | How are $\deg_{\mathrm{exp}}(X_1)$, $\deg_{\mathrm{exp}}(X_2)$, and $\deg_{\mathrm{exp}}(X_1\mathbin{\#_\partial}X_2)$ related? In particular, what is $\deg_{\mathrm{exp}}(D^3\times S^1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530](https://doi.org/10.4171/owr/2025/11)
## Literature r... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299092-002",
"literature-status:open",
"owr-year:2025"
] | The expander-degree paper proves the degree for D^4 and several orbifolds but lists computing the degree of S^1 times D^3 and its boundary-connected-sum behavior as open questions; the requested D^3 times S^1 value remains unresolved. | [
{
"url": "https://doi.org/10.1002/cpa.70024",
"label": "Bamler--Chen, Expander degree theory"
},
{
"url": "https://doi.org/10.4171/owr/2025/11",
"label": "Oberwolfach Report 11/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/11 | null | null | null | How are $\deg_{\mathrm{exp}}(X_1)$, $\deg_{\mathrm{exp}}(X_2)$, and $\deg_{\mathrm{exp}}(X_1\mathbin{\#_\partial}X_2)$ related? In particular, what is $\deg_{\mathrm{exp}}(D^3\times S^1)$? | Is there any relation between the degrees degexp (X1 ), degexp (X2 ), and degexp (X1 \#\partial X2 )? What is degexp (D3 \times S 1 )? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530 |
30,006,224 | OWR-14299092-005 | Mean-Curvature Blowup at Intermediate-Dimensional Singularities | At every finite-time singularity of mean-curvature flow in dimensions $3<n<7$, must the mean curvature become unbounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530](https://doi.org/10.4171/owr/2025/11)
## Literature r... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299092-005",
"literature-status:open",
"owr-year:2025"
] | Examples with bounded mean curvature are known in dimensions at least 7, while the 2026 literature still states that in dimensions 3 through 6 neither such examples nor an impossibility theorem are known. | [
{
"url": "https://doi.org/10.2140/apde.2026.19.857",
"label": "Angenent--Daskalopoulos--Sesum, Type-II smoothing"
},
{
"url": "https://doi.org/10.4171/owr/2025/11",
"label": "Oberwolfach Report 11/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/11 | null | null | null | At every finite-time singularity of mean-curvature flow in dimensions $3<n<7$, must the mean curvature become unbounded? | It therefore remains an open question whether the mean curvature always blows up at a finite-time mean curvature flow singularity in dimensions 3 < n < 7. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530 |
30,006,225 | OWR-14299092-006 | Isoperimetric Inequalities Between Total Q-Curvatures | For $0<\ell<k<n/2$, establish the sharp isoperimetric comparison between the total $k$-th and $\ell$-th $Q$-curvatures of metrics $g=u^{4/(n-2k)}g_{S^n}$ with positive $k$-th $Q$-curvature, and prove that equality holds exactly when $u(\xi)=a(1+b\cdot\xi)^{-(n-2k)/2}$ with $a\in\mathbb{R}$ and $b\in B^{n+1}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530](https://doi.org/10.4171/owr/2025/11)
## Literature r... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299092-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The proposed total-Q-curvature inequality is proved for k=2 and l=1 under a weaker scalar-curvature hypothesis, but the general range 0<l<k<n/2 remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2025/11",
"label": "Oberwolfach Report 11/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/11 | null | null | null | For $0<\ell<k<n/2$, establish the sharp isoperimetric comparison between the total $k$-th and $\ell$-th $Q$-curvatures of metrics $g=u^{4/(n-2k)}g_{S^n}$ with positive $k$-th $Q$-curvature, and prove that equality holds exactly when $u(\xi)=a(1+b\cdot\xi)^{-(n-2k)/2}$ with $a\in\mathbb{R}$ and $b\in B^{n+1}$. | Is there an isoperimetric inequality between the total k-th Q curvature and the total l-th Q curvature for 0 < l < k \leq n/2? We propose the following conjecture Conjecture. Let 0 < l < k < n/2. The following inequality (10) − n−2k ˆ n−2k Γ(n/2 + k) Γ(n/2 + l) 2(k−l) ˆ n−2l n−2l n−2l n−2l n−2l uL2k u \geq \omegan u n−... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530 |
30,006,226 | OWR-14299092-007 | The General Total-Q-Curvature Inequality | Does a sharp isoperimetric inequality relate total $k$th and $\ell$th $Q$-curvatures whenever $0<\ell<k\leq n/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530](https://doi.org/10.4171/owr/2025/11)
## Literature r... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299092-007",
"literature-status:partially-solved",
"owr-year:2025"
] | This duplicate extraction of the total-Q-curvature conjecture has the same status: the k=2,l=1 case is established under weaker assumptions, while the stated general inequality is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/11",
"label": "Oberwolfach Report 11/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/11 | null | null | null | Does a sharp isoperimetric inequality relate total $k$th and $\ell$th $Q$-curvatures whenever $0<\ell<k\leq n/2$? | We propose the following conjecture Conjecture. We prove that the Conjecture is true for k = 2 and l = 1 under a weaker condition. Is there an isoperimetric inequality between the total k-th Q curvature and the total l-th Q curvature for 0 < l < k \leq n/2? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/11, pp. 485--530 |
30,006,227 | OWR-14299093-001 | Landis-Conjecture Table-of-Contents Fragment | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Baptiste Devyver (joint with Louis Dupaigne, Pierre-Damien Thizy) Sharp Hardy-Poincaré-Sobolev inequalities in the Caffarelli-Kohn- Nirenberg hyperbolic space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614](https://doi.org/10.4171/owr/2025/14)
## Literature ... | 3 | open | null | 2,025 | 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"
} | {
"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 table-of-contents debris, not the statement of a conjecture.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299093-001",
"literature-status:open",
"owr-year:2025"
] | The extracted statement is truncated to the word Conjecture and does not identify a mathematical assertion that can be matched to a proof or counterexample; under the required normalization, its status is therefore open. | [
{
"url": "https://doi.org/10.4171/owr/2025/14",
"label": "Oberwolfach Report 14/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/14 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Baptiste Devyver (joint with Louis Dupaigne, Pierre-Damien Thizy) Sharp Hardy-Poincaré-Sobolev inequalities in the Caffarelli-Kohn- Nirenberg hyperbolic space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | unrecoverable | The official report confirms that this extraction is table-of-contents debris, not the statement of a conjecture. | null | null | null | null | null | Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614 |
30,006,228 | OWR-14299093-002 | Landis Unique-Continuation Conjecture | Let $V\in L^\infty(\mathbb R^N)$ satisfy $\|V\|_\infty\leq 1$, and let $u$ solve $(-\Delta+V)u=0$ on $\mathbb R^N$. If $u$ decays at least as fast as $e^{-k|x|}$ for some $k>1$, must $u\equiv 0$ without assuming positivity of the Schrödinger operator? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614](https://doi.org/10.4171/owr/2025/14)
## Literature ... | 3 | partially_solved | null | 2,025 | 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"
} | {
"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-14299093-002",
"literature-status:partially-solved",
"owr-year:2025"
] | The 2024 Das--Pinchover work proves a sharp decay criterion for nonnegative Schrödinger operators, but only under positivity and related hypotheses; the general real-valued Landis conjecture remains open outside such regimes. | [
{
"url": "https://arxiv.org/abs/2405.11695",
"label": "Das--Pinchover, Landis via criticality theory"
},
{
"url": "https://doi.org/10.1512/iumj.2021.70.8218",
"label": "Rossi, Landis with sharp decay"
},
{
"url": "https://doi.org/10.4171/owr/2025/14",
"label": "Oberwolfach Report 14/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/14 | null | null | null | Let $V\in L^\infty(\mathbb R^N)$ satisfy $\|V\|_\infty\leq 1$, and let $u$ solve $(-\Delta+V)u=0$ on $\mathbb R^N$. If $u$ decays at least as fast as $e^{-k|x|}$ for some $k>1$, must $u\equiv 0$ without assuming positivity of the Schrödinger operator? | decays as fast as e−k|x| with k > 1, then Landis claimed that u ≡ 0 in RN . Under a positivity assumption on the operator H, we provide a sharp decay criterion that ensures when a solution of the above equation in RN is trivial. It turns out that our decay criterion is in fact weaker than what Landis has proposed in th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614 |
30,006,229 | OWR-14299093-004 | Uniqueness and Fundamental Solutions for Fractional Diffusion | Let $M$ be a complete connected noncompact $N$-dimensional Riemannian manifold with $\operatorname{Ric}(M)\geq-(N-1)k$ and $\lambda_1(\Omega)\geq c\,m(\Omega)^{-2/N}$ for every relatively compact open $\Omega$. For $u_t=-(-\Delta_M)^s(u^m)$, where $s\in(0,1)$ and $m>1$, prove uniqueness of weak dual solutions, construc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614](https://doi.org/10.4171/owr/2025/14)
## Literature ... | 3 | open | null | 2,025 | 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"
} | {
"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-14299093-004",
"literature-status:open",
"owr-year:2025"
] | The report explicitly states that uniqueness, fundamental solutions with Dirac initial data, and pointwise bounds for general solutions remain open; no later source located resolves these claims in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2025/14",
"label": "Oberwolfach Report 14/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/14 | null | null | null | Let $M$ be a complete connected noncompact $N$-dimensional Riemannian manifold with $\operatorname{Ric}(M)\geq-(N-1)k$ and $\lambda_1(\Omega)\geq c\,m(\Omega)^{-2/N}$ for every relatively compact open $\Omega$. For $u_t=-(-\Delta_M)^s(u^m)$, where $s\in(0,1)$ and $m>1$, prove uniqueness of weak dual solutions, construc... | Uniqueness issues are not dealt with, and remain an open problem. Among several other open problems, we mention the proof of existence of fundamental solutions, i.e. solutions taking a Dirac delta as initial datum, as well as the proof of pointwise bounds for general solutions. • Existence of a WDS for data in L1Gs (M ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614 |
30,006,230 | OWR-14299093-005 | Converse Bessel-Pair Criterion for Grushin Operators | For Grushin vector fields, prove or disprove the converse Bessel-pair criterion: if the associated abstract Hardy or Hardy-Rellich inequalities hold for a pair of weights $(V,W)$, must $(V,W)$ be a Bessel pair? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614](https://doi.org/10.4171/owr/2025/14)
## Literature ... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299093-005",
"literature-status:open",
"owr-year:2025"
] | The Grushin work derives Hardy and Rellich inequalities from the Bessel-pair condition, but explicitly leaves the converse characterization as an open problem; the 2025 general framework does not resolve this Grushin converse. | [
{
"url": "https://arxiv.org/abs/2404.05510",
"label": "Ganguly--Kaur--Roychowdhury, Grushin Bessel pairs"
},
{
"url": "https://doi.org/10.4171/owr/2025/14",
"label": "Oberwolfach Report 14/2025"
},
{
"url": "https://arxiv.org/abs/2511.10039",
"label": "Cossetti--D'Arca, unified Besse... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/14 | null | null | null | For Grushin vector fields, prove or disprove the converse Bessel-pair criterion: if the associated abstract Hardy or Hardy-Rellich inequalities hold for a pair of weights $(V,W)$, must $(V,W)$ be a Bessel pair? | How- ever, we can ask the converse: if these types of inequalities hold, can we conclude that (V, W ) is a Bessel pair? Hardy and Rellich identities for Grushin operators Prasun Roychowdhury (joint work with Debdip Ganguly, Jotsaroop Kaur) Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings 607 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Hardy Inequalities in Discrete and Continuum Settings (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/14, pp. 579--614 |
30,006,231 | OWR-14299094-001 | Unique Ground-State Representability under Linear Constraints | For a constrained-search problem with observables $B_1,\ldots,B_m$, characterize when a prescribed expectation vector has a unique representing parameter $\beta\in\mathbb{R}^m$ and a unique ground-state representation, including critical values and degenerate ground spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Chemistry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/15, pp. 615--688](https://doi.org/10.4171/owr/2025/15)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299094-001",
"literature-status:partially-solved",
"owr-year:2025"
] | For the finite-dimensional constrained-search framework, uniqueness of the representing parameters is proved at regular values, while critical values can exhibit degeneracy and counterexamples; the broad regular-or-critical question is not completely settled by that result. | [
{
"url": "https://doi.org/10.1103/PhysRevA.112.032815",
"label": "Penz--van Leeuwen, Constrained search in imaginary time"
},
{
"url": "https://doi.org/10.4171/owr/2025/15",
"label": "Oberwolfach Report 15/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/15 | null | null | null | For a constrained-search problem with observables $B_1,\ldots,B_m$, characterize when a prescribed expectation vector has a unique representing parameter $\beta\in\mathbb{R}^m$ and a unique ground-state representation, including critical values and degenerate ground spaces. | Unique representability (regular and critical values, Hohenberg–Kohn (HK) theorem): Finally, we ask if, or when, the above form of ground-state representability with a \beta \in Rm is unique. that maps to b might be an ensemble state itself. In exceptional situations linked to degeneracies [4], the representability by ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Methods in Quantum Chemistry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/15, pp. 615--688 |
30,006,232 | OWR-14299094-002 | Multitask Hamiltonian Learning across Levels of Theory | Develop and analyze a multitask learning framework for Hamiltonians trained on data generated at different levels of electronic-structure theory. Determine how information should be shared across tasks and when transfer improves accuracy and sample efficiency. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Chemistry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/15, pp. 615--688](https://doi.org/10.4171/owr/2025/15)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299094-002",
"literature-status:open",
"owr-year:2025"
] | The report presents multitask Gaussian-process gains for heterogeneous electronic-structure data but identifies Hamiltonian learning across different theory levels as an open question; no primary study found provides a general solution. | [
{
"url": "https://doi.org/10.4171/owr/2025/15",
"label": "Oberwolfach Report 15/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/15 | null | null | null | Develop and analyze a multitask learning framework for Hamiltonians trained on data generated at different levels of electronic-structure theory. Determine how information should be shared across tasks and when transfer improves accuracy and sample efficiency. | In discussions spurred by this talk, seminar participants considered the open question of how the multitask framework may be applied to Hamiltonian learning from data generated with different levels of theory. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Methods in Quantum Chemistry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/15, pp. 615--688 |
30,006,233 | OWR-14299095-001 | Ensemble Necessity in Data Assimilation | Are ensemble-based data assimilation methods really necessary for accurate filtering? We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Data Assimilation: From Mathematical and Statistical Foundations to Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/10, pp. 451--484](https://doi.org/10.4171/owr/2025/10)
##... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report poses this question as a talk title and then gives a negative experimental answer in its studied setting: a learned sing) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299095-001",
"literature-status:partially-solved",
"owr-year:2025"
] | A learned analysis step matched a tuned ensemble Kalman filter while propagating a single forecast state in low-order chaotic experiments, demonstrating that ensembles are not universally necessary, but this does not establish general accuracy guarantees. | [
{
"url": "https://doi.org/10.4171/owr/2025/10",
"label": "Bocquet, Ensemble-free filtering report"
},
{
"url": "https://www.data-assimilation.riken.jp/en/events/isda_2021/abstracts/isda2025_03.pdf",
"label": "Bocquet et al., ISDA 2025 abstract"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/10 | null | null | null | null | Are ensemble-based data assimilation methods really necessary for accurate filtering? We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a ... | unrecoverable | The official report poses this question as a talk title and then gives a negative experimental answer in its studied setting: a learned single-state forecast attains ensemble-filter accuracy. | null | null | null | null | null | Data Assimilation: From Mathematical and Statistical Foundations to Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/10, pp. 451--484 |
30,006,234 | OWR-14299095-002 | Joint Design of Bridging Schedules and Transport Maps | Combine an optimized schedule of bridging densities, minimizing successive $\alpha$-divergences, with a class of bridging densities and a parametrized transport map $T$ for which the contraction factor $\omega<1$ is guaranteed at every step. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Data Assimilation: From Mathematical and Statistical Foundations to Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/10, pp. 451--484](https://doi.org/10.4171/owr/2025/10)
##... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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-14299095-002",
"literature-status:open",
"owr-year:2025"
] | The primary transport-map paper supplies convergence analyses and several intermediate-density choices, but explicitly leaves combining a scheduler with a parametrization that guarantees omega<1 as an open problem. | [
{
"url": "https://arxiv.org/abs/2402.17943",
"label": "Zanger--Zahm--Cui--Schreiber, Sequential transport maps"
},
{
"url": "https://doi.org/10.4171/owr/2025/10",
"label": "Oberwolfach Report 10/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/10 | null | null | null | Combine an optimized schedule of bridging densities, minimizing successive $\alpha$-divergences, with a class of bridging densities and a parametrized transport map $T$ for which the contraction factor $\omega<1$ is guaranteed at every step. | Combining our result, which is mainly focused on the design of schedulers of bridging densi- ties so that D\alpha \pi (ℓ) ||\pi (ℓ−1) is minimized, with a class of bridging densities and parametrization of T which has guarantees to achieve \omega < 1 for the given bridging density, is an open problem. for some arbitrar... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Data Assimilation: From Mathematical and Statistical Foundations to Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/10, pp. 451--484 |
30,006,235 | OWR-14299097-001 | Finite-Group-Theory Contents Fragment | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . 711 Justin Lynd (joint with Philip Hackney) Partial groups and higher Segal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Lucia Morotti (joint with Alexander Kleshchev, Pham Huu Tiep) Irreducible restrictions of spin representations of sy... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 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 a table-of-contents fragment, not a mathematical conjecture. No separate clean statemen) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-001",
"literature-status:open",
"owr-year:2025"
] | The extracted record is only a truncated table-of-contents fragment ending in `Conjecture`; it does not state an identifiable mathematical claim, so no stronger classification is justified. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . 711 Justin Lynd (joint with Philip Hackney) Partial groups and higher Segal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 713 Lucia Morotti (joint with Alexander Kleshchev, Pham Huu Tiep) Irreducible restrictions of spin representations of sy... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment, not a mathematical conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,236 | OWR-14299097-002 | Finite-Group-Theory Contents Continuation | Jakob Schneider (joint with Henry Bradford and Andreas Thom) The length of mixed identities for finite groups . . . . . . . . . . . . . . . . . . . . . . 730 Patrick Serwene Applications of Fusion Systems in Block Theory . . . . . . . . . . . . . . . . . . . . . 733 Bernd Stellmacher My thoughts on the Meierfrankenfeld... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 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 a continuation of the table of contents, not a mathematical problem. No separate clean ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-002",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a truncated table-of-contents fragment and contains no identifiable conjecture or problem statement; under the triage rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | null | Jakob Schneider (joint with Henry Bradford and Andreas Thom) The length of mixed identities for finite groups . . . . . . . . . . . . . . . . . . . . . . 730 Patrick Serwene Applications of Fusion Systems in Block Theory . . . . . . . . . . . . . . . . . . . . . 733 Bernd Stellmacher My thoughts on the Meierfrankenfeld... | unrecoverable | The official report confirms that this extraction is a continuation of the table of contents, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,237 | OWR-14299097-003 | Constant-Dimension Framings of Simple Locally Finite Localities | Let $\mathcal{L}$ be a simple locally finite locality at a prime $p$. Prove that $\mathcal{L}$ admits a framing by injective homomorphisms of finite localities $\mathcal{L}_n\to\mathcal{L}_{n+1}$ such that every $\mathcal{L}_n$ is simple and $\dim_p(\mathcal{L}_n)$ is independent of $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-003",
"literature-status:open",
"owr-year:2025"
] | The record ends immediately after `we conjecture` and omits the conjecture itself, so its truth cannot be assessed without inventing a claim. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Let $\mathcal{L}$ be a simple locally finite locality at a prime $p$. Prove that $\mathcal{L}$ admits a framing by injective homomorphisms of finite localities $\mathcal{L}_n\to\mathcal{L}_{n+1}$ such that every $\mathcal{L}_n$ is simple and $\dim_p(\mathcal{L}_n)$ is independent of $n$. | The category of finite localities (like the category of finite saturated fusion systems) provides a framework in which to carry out elementary finite-group-theoretic ar- guments, and for that reason we conjecture: Theorem (Gonzales). Let L be a compact locality at the prime p. Then there exists a sequence \gamma = (Ln ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,238 | OWR-14299097-004 | Non-Locally-Finite Simple Proper Localities | Does there exist a simple proper locality that is not locally finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-004",
"literature-status:open",
"owr-year:2025"
] | The question whether a simple proper locality can fail to be locally finite remains explicitly posed as an open question; the report gives local finiteness for compact localities but not this general case. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "Gonzales locality results and the stated open question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Does there exist a simple proper locality that is not locally finite? | We end with a question: Does there exist a simple, proper locality which is not locally finite ? CFSF2. Let e be a natural number and let Fe be the set of isomorphism classes of simple saturated fusion systems F over a finite 2-group, such that the locality associated with F has dimension e. Let Le be the set of all F ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,239 | OWR-14299097-005 | Cameron Greedy Base-Size Conjecture | Prove that there is an absolute constant $c$ such that every finite primitive permutation group $G$ has greedy base size $G(G)\leq c\,b(G)$, where $b(G)$ is its minimum base size. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Cameron’s Greedy Conjecture remains open for arbitrary finite primitive groups, while sporadic, odd-order, alternating, and diagonal-type families have substantial recent results. | [
{
"url": "https://arxiv.org/abs/2503.23964",
"label": "del Valle--Roney-Dougal, 2025"
},
{
"url": "https://arxiv.org/abs/2605.16032",
"label": "del Valle--Roney-Dougal, diagonal type"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "workshop status report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Prove that there is an absolute constant $c$ such that every finite primitive permutation group $G$ has greedy base size $G(G)\leq c\,b(G)$, where $b(G)$ is its minimum base size. | Recently, a program has begun to settle Cameron’s Greedy Conjecture. Thus far, the focus has been primarily on the almost simple primitive groups. The greedy base sizes for primitive G with sporadic socle have been determined in a recent paper [8], showing that for such groups the greedy base size coincides with the ba... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,240 | OWR-14299097-006 | Greedy Base Sizes for Uniform-Subset Actions | Determine the greedy base size for the standard action of a primitive permutation group on $r$-element subsets when the ground-set size is less than $4r^2$, completing the remaining uniform-subset cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-006",
"literature-status:open",
"owr-year:2025"
] | The exact conjecture is missing from the extraction, but the source states that the standard uniform-subset case remains open when the ground-set size is below the displayed 4r-squared threshold. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "del Valle workshop report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Determine the greedy base size for the standard action of a primitive permutation group on $r$-element subsets when the ground-set size is less than $4r^2$, completing the remaining uniform-subset cases. | A similar bound has also been determined in most cases for the standard actions of G on uniform subsets, but the problem remains open when the size of the ground set is less than 4r2 , where r is the subset size [9, Theorem 2.9]. Thus, given the situation for sporadic groups, and non-standard groups with alternating so... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,241 | OWR-14299097-007 | Transitive Binary Actions of Almost Simple Groups | Classify all transitive binary permutation actions of almost simple groups, extending the existing classification of primitive binary actions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-007",
"literature-status:open",
"owr-year:2025"
] | Primitive binary actions are classified, and alternating and symmetric cases have explicit partial classifications, but the source states that extending this to all transitive binary actions of almost simple groups remains a substantial open task. | [
{
"url": "https://arxiv.org/abs/2303.06003",
"label": "Gill--Guillot, alternating binary actions"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "current classification status"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Classify all transitive binary permutation actions of almost simple groups, extending the existing classification of primitive binary actions. | The following theorem was originally a conjecture of Cherlin and is now a theorem, thanks to the work of various authors including Cherlin, Dalla Volta, Gill, Hunt, Liebeck, Spiga and Wiscons [2, 3, 5, 6]. What are the transitive binary actions of the almost simple groups? The report passage is retained verbatim as the... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,242 | OWR-14299097-008 | Fusion Systems of Sectional Rank Three | Let $p$ be odd, let $S$ be a $p$-group of sectional rank three, and let $\mathcal{F}$ be a saturated fusion system on $S$ with $O_p(\mathcal{F})=1$ and $\mathcal{F}=O^p(\mathcal{F})$. Prove that either $S$ has maximal nilpotency class or $S$ has an abelian maximal subgroup. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The sectional-rank-three fusion-system dichotomy remains a conjecture in full generality, but maximal-class cases and several pearl and low-order families have been classified. | [
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "Grazian, conjecture and known cases"
},
{
"url": "https://etheses.bham.ac.uk/7670/1/Grazian17PhD.pdf",
"label": "Grazian, fusion systems on p-groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Let $p$ be odd, let $S$ be a $p$-group of sectional rank three, and let $\mathcal{F}$ be a saturated fusion system on $S$ with $O_p(\mathcal{F})=1$ and $\mathcal{F}=O^p(\mathcal{F})$. Prove that either $S$ has maximal nilpotency class or $S$ has an abelian maximal subgroup. | Conjecture 1. Let p be an odd prime, let S be a p-group of sectional rank 3 and let F be a saturated fusion system on S with Op (F ) = 1 and F = Op (F ). Then either S has maximal nilpotency class or S has a maximal subgroup that is abelian. The report passage is retained verbatim as the relevant context for this extra... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,243 | OWR-14299097-009 | Babai Polylogarithmic Diameter Conjecture for Finite Simple Groups | Prove that there is an absolute constant $C$ such that, for every finite simple group $G$ and every generating subset $A\subseteq G$, one has $A^\ell=G$ for some $\ell\leq(\log|G|)^C$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-009",
"literature-status:open",
"owr-year:2025"
] | Babai’s polylogarithmic diameter conjecture for arbitrary generating sets of finite simple groups is still open; bounded-rank, large-rank subcases, and special generating sets are known. | [
{
"url": "https://doi.org/10.1112/jlms.12018",
"label": "Biswas, large-rank diameter bounds"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "current workshop statement"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Prove that there is an absolute constant $C$ such that, for every finite simple group $G$ and every generating subset $A\subseteq G$, one has $A^\ell=G$ for some $\ell\leq(\log|G|)^C$. | The Liebeck–Nikolov–Conjecture is a stronger variant for sets that are not necessarily normal. It is worth noting that one of the central remaining open problems is Babai’s conjecture, which concerns showing that for every generating subset A of a finite simple group G we have Aℓ = G for ℓ \leq log |G|C for an absolute... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,244 | OWR-14299097-011 | Realizability and Tameness of Fusion Systems | Characterize when a saturated fusion system $\mathcal{F}$ on a Sylow $p$-subgroup $S$ is realized by a finite group: determine conditions guaranteeing a finite group $G$ with a normal subgroup $H\trianglelefteq G$, $S\in\operatorname{Syl}_p(G)$, and $\mathcal{F}=\mathcal{F}_S(G)$. Clarify the relation between realizabi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-011",
"literature-status:partially-solved",
"owr-year:2025"
] | Broto--Møller--Oliver--Ruiz prove realizability from realizable components and prove that realizable fusion systems are tame, but a full characterization of realizability and tameness remains open. | [
{
"url": "https://doi.org/10.1112/plms.12571",
"label": "Broto--Møller--Oliver--Ruiz, 2023"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "current workshop context"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Characterize when a saturated fusion system $\mathcal{F}$ on a Sylow $p$-subgroup $S$ is realized by a finite group: determine conditions guaranteeing a finite group $G$ with a normal subgroup $H\trianglelefteq G$, $S\in\operatorname{Syl}_p(G)$, and $\mathcal{F}=\mathcal{F}_S(G)$. Clarify the relation between realizabi... | In fact, tameness — the question of whether all realizable fusion systems are tame — was our original motivation for beginning this project. Under what conditions can one find G such that H E G, S \in Sylp (G), and F = FS (G)? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,245 | OWR-14299097-013 | Shortest Mixed Identities in Finite Groups | For a finite group $G$, determine the minimum length of a nontrivial mixed identity in the free product $G*F_r$, and obtain sharp values or asymptotic bounds across the principal families of finite groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-013",
"literature-status:partially-solved",
"owr-year:2025"
] | The shortest mixed-identity length is known for several families and completely for some low-rank cases, but the general finite-group question remains unresolved and recent work still records family-level gaps. | [
{
"url": "https://arxiv.org/abs/2306.14532",
"label": "Bradford--Schneider--Thom, finite mixed identities"
},
{
"url": "https://arxiv.org/abs/2608.14537",
"label": "Bradford--Ersoy--Schneider--Thom, 2026"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "source question an... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | For a finite group $G$, determine the minimum length of a nontrivial mixed identity in the free product $G*F_r$, and obtain sharp values or asymptotic bounds across the principal families of finite groups. | What is the length of a shortest mixed identity w \in G ∗ Fr for G? In contrast to the projective special linear groups, the projective symplectic and orthogonal groups do have short mixed identities. This observation is due to Tomanov [6]. Theorem 3 (Tomanov). The group PSp2m (q) for m \geq 2 satisfies a mixed identit... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,246 | OWR-14299097-014 | Mixed and Nonsingular Identities in Finite Lie-Type Groups | For the remaining families of finite groups of Lie type, determine the length of a shortest mixed identity and the length of a shortest nonsingular identity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-014",
"literature-status:partially-solved",
"owr-year:2025"
] | The remaining Lie-type families and shortest non-singular identities have substantial bounds and new 2026 structural results, but the source problem is not fully resolved for all families. | [
{
"url": "https://arxiv.org/abs/2306.14532",
"label": "Bradford--Schneider--Thom, finite mixed identities"
},
{
"url": "https://arxiv.org/abs/2608.14537",
"label": "Bradford--Ersoy--Schneider--Thom, 2026"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "explicit open ques... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | For the remaining families of finite groups of Lie type, determine the length of a shortest mixed identity and the length of a shortest nonsingular identity. | What about the remaining families of finite groups of Lie type: How long is a shortest mixed identity in this case? What about the shortest non-singular identities for these groups? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,247 | OWR-14299097-015 | Equivalence of Exotic and Block-Exotic Fusion Systems | Is a fusion system exotic if and only if it is block-exotic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-015",
"literature-status:partially-solved",
"owr-year:2025"
] | The exotic-versus-block-exotic equivalence is proved for important classes, including sectional-rank-three systems for primes at least 5, but remains conjectural in full generality. | [
{
"url": "https://arxiv.org/abs/2403.14265",
"label": "Serwene, exotic system on a subgroup of the Monster"
},
{
"url": "https://arxiv.org/abs/2302.05203",
"label": "Serwene, exceptional maximal-class families"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "conjecture s... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Is a fusion system exotic if and only if it is block-exotic? | We conjecture that the two mentioned ways for fusion systems to arise coincide: Conjecture 1. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,248 | OWR-14299097-016 | Optimal Character Bounds for Almost Quasisimple Groups | Let $G$ be a finite almost quasisimple group and $g\in G\setminus Z(G)$. Find an explicit exponent $0\leq\alpha(g)<1$, as small as possible, such that $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for every irreducible complex character $\chi$ of $G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752](https://doi.org/10.4171/owr/2025/16)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299097-016",
"literature-status:partially-solved",
"owr-year:2025"
] | Uniform exponential character bounds and sharp estimates for important classical-group regimes are proved, but finding the optimal explicit exponent for every almost quasisimple group and element remains open. | [
{
"url": "https://annals.math.princeton.edu/2024/200-1",
"label": "Larsen--Tiep, uniform character bounds"
},
{
"url": "https://arxiv.org/abs/2403.09047",
"label": "Larsen--Tiep, classical estimates"
},
{
"url": "https://doi.org/10.4171/owr/2025/16",
"label": "problem and current res... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/16 | null | null | null | Let $G$ be a finite almost quasisimple group and $g\in G\setminus Z(G)$. Find an explicit exponent $0\leq\alpha(g)<1$, as small as possible, such that $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for every irreducible complex character $\chi$ of $G$. | A finite group G is called almost quasisisimple if S ⊳ G/Z(G) \leq Aut(S) for some finite non-abelian simple group G. An important problem in complex representa- tion theory of finite almost quasisimple groups is the following Problem 1. Let G be a finite almost quasisimple group, g \in G \ Z(G). Find an explicit, and ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Finite Groups, Fusion Systems and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/16, pp. 689--752 |
30,006,249 | OWR-14299281-001 | Smooth Projective Realization of Connected Algebraic Groups | Let $G$ be a smooth connected algebraic group over a field $k$. Does there exist a smooth projective $k$-variety $X$ whose automorphism group is isomorphic to $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-001",
"literature-status:partially-solved",
"owr-year:2025"
] | The record is an incomplete lead-in, but the report identifies the inverse Galois problem for connected algebraic groups; the identity-component realization is proved for projective geometrically integral schemes, while the stronger smooth-projective full-automorphism formulation remains incomplete. | [
{
"url": "https://doi.org/10.1007/s00031-024-09865-0",
"label": "Brion--Schröer, inverse Galois problem"
},
{
"url": "https://doi.org/10.5802/afst.1746",
"label": "Blanc--Brion, smooth projective abelian cases"
},
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "source formu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Let $G$ be a smooth connected algebraic group over a field $k$. Does there exist a smooth projective $k$-variety $X$ whose automorphism group is isomorphic to $G$? | An important question is the following. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,250 | OWR-14299281-002 | Algebraic-Groups Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 Hanspeter Kraft Automorphism Groups of Varieties – A Survey . . . . . . . . . . . . . . . . . . . . . . 962 Shrawan Kumar Alternating sign behavior for the product structure in T -equivariant quantum K-theory of flag varieties . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment spanning unrelated talks and does not state a mathematical) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-002",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a truncated table-of-contents fragment ending in `conjecture` and does not identify the conjecture to be checked. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 Hanspeter Kraft Automorphism Groups of Varieties – A Survey . . . . . . . . . . . . . . . . . . . . . . 962 Shrawan Kumar Alternating sign behavior for the product structure in T -equivariant quantum K-theory of flag varieties . . . . . . . ... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment spanning unrelated talks and does not state a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,251 | OWR-14299281-003 | Truncated Algebraic-Group Conjecture | The conjecture below is a special case of a conjecture of N. 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:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extracted sentence omits both the conjecture and the name to which it refers, so a mathematical statem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-003",
"literature-status:open",
"owr-year:2025"
] | The record says only that a conjecture follows and omits both the conjecture and its mathematical subject, so the extracted claim cannot be assessed without speculation. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | null | The conjecture below is a special case of a conjecture of N. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that the extracted sentence omits both the conjecture and the name to which it refers, so a mathematical statement cannot be restored without speculation. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,252 | OWR-14299281-004 | Lie Algebras and Reconstruction from Variety Automorphisms | For an algebraic variety $X$, does $operatorname{Aut}(X)$ admit a natural Lie algebra that embeds into the algebraic vector fields on $X$? More generally, to what extent is $X$ determined by $operatorname{Aut}(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-004",
"literature-status:partially-solved",
"owr-year:2025"
] | The Lie algebra of Aut(X) naturally embeds in the algebraic vector fields, and determination by Aut(X) holds in important restricted settings, but no general reconstruction theorem exists and trivial-automorphism examples obstruct one. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "Kraft survey and stated questions"
},
{
"url": "https://doi.org/10.1112/jlms.12866",
"label": "Kraft--Zaidenberg, algebraically generated groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | For an algebraic variety $X$, does $operatorname{Aut}(X)$ admit a natural Lie algebra that embeds into the algebraic vector fields on $X$? More generally, to what extent is $X$ determined by $operatorname{Aut}(X)$? | Is it a subalgebra of the vector fields? Is X determined by Aut(X)? Some History Theorem 1 (Whittaker 1963, see [Whi63]). If X and Y are “nice” topological \sim spaces, then every isomorphism Autcont (X) − \to Autcont (Y ) between the groups of \sim continuous automorphisms is induced by a homeomorphism X − \to Y . Thus... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,253 | OWR-14299281-005 | Groups Realizable as Variety Automorphism Groups | Which groups occur as automorphism groups $operatorname{Aut}(X)$ of algebraic varieties $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Many classes of automorphism groups are realized, including every finite group on a smooth affine curve in characteristic zero, but the general classification of groups occurring as Aut(X) remains open. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "Kraft survey"
},
{
"url": "https://arxiv.org/abs/1501.06362",
"label": "Kraft, automorphism groups of affine varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Which groups occur as automorphism groups $operatorname{Aut}(X)$ of algebraic varieties $X$? | What Kind of Groups Appear as Aut(X)? • Aut(A1 \ \{a1 , . . . , ak \}) is trivial for k \geq 3 points in general position; • Ȧ := A1 \ \{0\}, Aut(Ȧ \times Ȧ \times \cdot \cdot \cdot \times Ȧ) ≃ GLm (Z) ⋉ (k∗ )m . | \{z \} m times | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,254 | OWR-14299281-007 | Simplicity of Special Automorphism Groups of Affine Space | For $n\geq3$, is the special automorphism group $operatorname{SAut}(\mathbb A^n)$ simple as an abstract group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-007",
"literature-status:partially-solved",
"owr-year:2025"
] | SAut(A2) is not simple abstractly, while Blanc proves topological simplicity in all dimensions; the higher-dimensional abstract simplicity problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "Blanc result as reported"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | For $n\geq3$, is the special automorphism group $operatorname{SAut}(\mathbb A^n)$ simple as an abstract group? | Is Aut(X) Simple? n n Let SAut(A ) \subseteq Aut(A ) denote the kernel of the Jacobian determinant \partialfi jac : Aut(An ) \to k∗ , (f1 , . . . , fn ) 7\to det( ). \partialxj It was shown in 1974 by Danilov that the group SAut(A2 ) is not simple as an abstract group [Dan74], cf. • If Aut(Dp )◦ ≃ Aut(Dq )◦ as ind-grou... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,255 | OWR-14299281-008 | Open Problems on Ind-Groups of Automorphisms | Let $X$ be an affine variety. Determine whether the following assertions hold. First, if $G\subseteq\operatorname{Aut}(X)$ is connected and closed and $N\triangleleft G$ is proper and closed, then $\operatorname{Lie}(N)\subsetneq\operatorname{Lie}(G)$. Second, if closed subgroups $H,G\subseteq\operatorname{Aut}(X)$ sat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-008",
"literature-status:open",
"owr-year:2025"
] | The five displayed questions about closed subgroups, algebraic elements, nestedness, non-discrete automorphism groups, and the tame-subgroup normalizer are explicitly presented as open problems; recent structural results do not settle them in general. | [
{
"url": "https://doi.org/10.4171/OWR/2025/20",
"label": "Kraft survey, open problems"
},
{
"url": "https://arxiv.org/abs/2312.08359",
"label": "Kraft--Zaidenberg, nested automorphism groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Let $X$ be an affine variety. Determine whether the following assertions hold. First, if $G\subseteq\operatorname{Aut}(X)$ is connected and closed and $N\triangleleft G$ is proper and closed, then $\operatorname{Lie}(N)\subsetneq\operatorname{Lie}(G)$. Second, if closed subgroups $H,G\subseteq\operatorname{Aut}(X)$ sat... | Some Open Problems (1) Let G \subseteq Aut(X) be a connected closed subgroup and N \$ G a proper normal and closed subgroup. Does it follow that Lie N \$ Lie G? (2) Let H, G \subseteq Aut(X) be closed subgroups. Does it follow that G \subseteq H? (3) Let G \subseteq Aut(X) be a closed subgroup consisting of algebraic e... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,256 | OWR-14299281-009 | Alternating Signs in Equivariant Quantum K-Theory | Do the structure constants of the Schubert-basis product in $T$-equivariant quantum $K$-theory $QK_T(G/P)$ satisfy the conjectured alternating-sign property? Equivalently, does the corresponding Pontryagin product in the localized equivariant $K$-theory of the affine Grassmannian have this alternating-sign behavior? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-009",
"literature-status:open",
"owr-year:2025"
] | The alternating-sign conjecture for the equivariant quantum K-theory Pontryagin product is known only in special cases; the general conjecture remains open. | [
{
"url": "https://ems.press/content/serial-article-files/51849",
"label": "OWR 2025 report"
},
{
"url": "https://borowiecki.dev/pdf/2510.07689",
"label": "Conjectural positivity preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Do the structure constants of the Schubert-basis product in $T$-equivariant quantum $K$-theory $QK_T(G/P)$ satisfy the conjectured alternating-sign property? Equivalently, does the corresponding Pontryagin product in the localized equivariant $K$-theory of the affine Grassmannian have this alternating-sign behavior? | conjecture. Alternating sign behavior for the product structure in T -equivariant quantum K-theory of flag varieties Shrawan Kumar Center of the small quantum group: towards a combinatorial model Anna Lachowska (joint work with Qi You, Nicolas Hemelsoet, Oskar Kivinen) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,257 | OWR-14299281-010 | Centers of Small Quantum Groups | Let $W_P\subseteq W$ be the stabilizer of a weight $\lambda$, and let $DR_W^{W_P}$ be the canonical quotient of the diagonal coinvariant algebra. Is the $G$-invariant part $z_\lambda^G$ of the corresponding block of the small-quantum-group center isomorphic to $DR_W^{W_P}$ as a bigraded vector space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-010",
"literature-status:partially-solved",
"owr-year:2025"
] | The stated center conjecture has a dimension equality and substantial type-A results, but the claimed bigraded isomorphism is not proved in general. | [
{
"url": "https://ems.press/content/serial-article-files/51849",
"label": "OWR 2025 report"
},
{
"url": "https://doi.org/10.1093/imrn/rnx062",
"label": "Lachowska--You, principal blocks"
},
{
"url": "https://doi.org/10.1112/plms.12193",
"label": "Lachowska--You, singular blocks"
}
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Let $W_P\subseteq W$ be the stabilizer of a weight $\lambda$, and let $DR_W^{W_P}$ be the canonical quotient of the diagonal coinvariant algebra. Is the $G$-invariant part $z_\lambda^G$ of the corresponding block of the small-quantum-group center isomorphic to $DR_W^{W_P}$ as a bigraded vector space? | In general the right-hand side of the isomorphism in 2 is hard to compute. A eP in several low careful study of the C∗ -equivariant cohomologies of the variety N rank cases allowed to formulate the combinatorial conjecture on the structure of the blocks of the center [6, 7] (with some restrictions on l): Conjecture 3. ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,258 | OWR-14299281-011 | Invariant Centers of Small Quantum Groups | For a small quantum group of type $A$, is the invariant center $z(u_q(\mathfrak g))^G$ isomorphic to the full center $z(u_q(\mathfrak g))$? More generally, determine the bigraded and multiplicative structure of the center and construct a natural Weyl-group action compatible with its diagonal-coinvariant model. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-011",
"literature-status:open",
"owr-year:2025"
] | The extracted record explicitly leaves important questions open; the nearby invariant-center conjecture is known only in small type-A rank and fails in several other types, so no general resolution is established. | [
{
"url": "https://ems.press/content/serial-article-files/51849",
"label": "OWR 2025 report"
},
{
"url": "https://doi.org/10.1112/plms.12193",
"label": "Lachowska--You, singular blocks"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | For a small quantum group of type $A$, is the invariant center $z(u_q(\mathfrak g))^G$ isomorphic to the full center $z(u_q(\mathfrak g))$? More generally, determine the bigraded and multiplicative structure of the center and construct a natural Weyl-group action compatible with its diagonal-coinvariant model. | Several important questions remain open. The next major advance is due to the work [3] where an isomorphism of algebras between the center z(uq (g)) and certain cohomology of an affine Springer fiber was conjectured and later proved. The paper [5] in combination [3] uses this new geometric model to prove the following res... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,259 | OWR-14299281-012 | Orbit Decompositions in Wonderful Group Schemes | Let $x$ lie in a chamber $C$ of the Bruhat–Tits building, let $G(k)_{C,0}$ be the associated Iwahori subgroup, and let $G_{x,f}$ be the corresponding wonderful group scheme. Classify the $G(k)_{C,0}\times G(k)_{C,0}$-orbits in $G_{x,f}(\mathfrak{o})$, and describe its diagonal-stable pieces, in analogy with the Bruhat ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-012",
"literature-status:open",
"owr-year:2025"
] | The wonderful group-scheme construction is available, but the requested Iwahori orbit classification and Diag-stable-piece description remain posed as open questions. | [
{
"url": "https://ems.press/content/serial-article-files/51849",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2505.12777",
"label": "Li, wonderful embeddings for group schemes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Let $x$ lie in a chamber $C$ of the Bruhat–Tits building, let $G(k)_{C,0}$ be the associated Iwahori subgroup, and let $G_{x,f}$ be the corresponding wonderful group scheme. Classify the $G(k)_{C,0}\times G(k)_{C,0}$-orbits in $G_{x,f}(\mathfrak{o})$, and describe its diagonal-stable pieces, in analogy with the Bruhat ... | Given such a parallel between G and Gx,f , we ask if there is a classification of (G(k)C,0 \times G(k)C,0 )-orbits in Gx,f (o), where C \subset B(G) is a chamber containing x and G(k)C,0 is thus an Iwahoric subgroup, as an analogue of the classification of (B \timesk B)-orbits in G [2, § 2.1]; if we have a description of... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,260 | OWR-14299281-013 | Acting Groups and Identity-Component Automorphisms | Let $X=G/P$, where $G$ is simple adjoint and $P$ is a nonreduced parabolic subgroup scheme. When is the natural homomorphism $G\hookrightarrow\operatorname{Aut}^0(X)$ an isomorphism, and what is the structure of $\operatorname{Aut}^0(X)$ when the inclusion is strict? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010](https://doi.org/10.4171/owr/2025/20)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299281-013",
"literature-status:open",
"owr-year:2025"
] | The extracted fragment asks when a particular equivariant homomorphism to the identity-component automorphism group is an isomorphism, but omits the required setup; the broad realization theorem does not settle this exact criterion, so it is classified open. | [
{
"url": "https://ems.press/content/serial-article-files/51849",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2205.08117",
"label": "Brion--Schroeer, inverse Galois problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/20 | null | null | null | Let $X=G/P$, where $G$ is simple adjoint and $P$ is a nonreduced parabolic subgroup scheme. When is the natural homomorphism $G\hookrightarrow\operatorname{Aut}^0(X)$ an isomorphism, and what is the structure of $\operatorname{Aut}^0(X)$ when the inclusion is strict? | A natural question is to determine exactly when ι : G ֒\to Aut0X is an isomorphism. any parabolic subgroup is an intersection of parabolics with maximal reduced part. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/20, pp. 941--1010 |
30,006,261 | OWR-14299282-001 | Climate Tipping Probabilities under Parameter Uncertainty | For a climate model with uncertain parameters, determine how parameter uncertainty changes the bifurcation structure, identify which parameters dominate the tipping dynamics, and compute the probability that the system tips. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078](https://doi.org/10.4171/owr/2025/21)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299282-001",
"literature-status:open",
"owr-year:2025"
] | Probabilistic bifurcation and tipping methods quantify uncertainty for important model classes, but no general theory determines tipping probabilities from uncertain parameters for the extracted climate-system question. | [
{
"url": "https://ems.press/content/serial-article-files/51850",
"label": "OWR 2025 report"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2657590/",
"label": "Imprecise probability of climate tipping"
},
{
"url": "https://arxiv.org/abs/2110.15859",
"label": "Parametric uncert... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/21 | null | null | null | For a climate model with uncertain parameters, determine how parameter uncertainty changes the bifurcation structure, identify which parameters dominate the tipping dynamics, and compute the probability that the system tips. | How do uncertain model parameters affect the bifurcation behaviour of the system and which parameters contribute most to the tipping dynamics? What is the probability of a system to tip? Climate Tipping Points under Uncertainty – A Bifurcation Theoretic Perspective Kerstin Lux-Gottschalk (joint work with Christian Kueh... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078 |
30,006,262 | OWR-14299282-002 | Modes and Maximum A Posteriori Estimators on Metric Spaces | For a probability measure $\mu$ on a metric space $(X,d)$, define and characterize what it means for a point to be a most likely outcome. Determine when competing notions of mode or maximum a posteriori estimator agree and when a unique canonical notion exists. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078](https://doi.org/10.4171/owr/2025/21)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299282-002",
"literature-status:partially-solved",
"owr-year:2025"
] | Axiomatic work classifies multiple small-ball modes and MAP notions and identifies well-behaved cases, but there is no unique universal meaning of most likely for arbitrary metric-space measures. | [
{
"url": "https://ems.press/content/serial-article-files/51850",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2306.16278",
"label": "Classification of small-ball modes"
},
{
"url": "https://doi.org/10.1137/22M154243X",
"label": "Lambley--Sullivan, MAP estimators"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/21 | null | null | null | For a probability measure $\mu$ on a metric space $(X,d)$, define and characterize what it means for a point to be a most likely outcome. Determine when competing notions of mode or maximum a posteriori estimator agree and when a unique canonical notion exists. | What does it mean to be the “most likely” outcome of a probability measure µ \in P(X) on a metric space (X, d)? Defining Modes and MAP Estimators: A Systematic Approach Ilja Klebanov (joint work with Hefin Lambley and T. J. Sullivan) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078 |
30,006,263 | OWR-14299282-003 | Score-Uncertainty Propagation in Reflected Generative Models | Quantify how uncertainty in an estimated score propagates through a reflected score-based generative diffusion. Derive finite-time and distributional error bounds that account for reflection at the domain boundary. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078](https://doi.org/10.4171/owr/2025/21)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299282-003",
"literature-status:open",
"owr-year:2025"
] | General score-based diffusion uncertainty bounds exist, and reflected diffusion models are constructed, but propagation of score-estimation uncertainty through the reflected process remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/51850",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2405.15754",
"label": "Score-model uncertainty quantification"
},
{
"url": "https://openreview.net/forum?id=QcKoLuEO3r",
"label": "Reflected diffusion models... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/21 | null | null | null | Quantify how uncertainty in an estimated score propagates through a reflected score-based generative diffusion. Derive finite-time and distributional error bounds that account for reflection at the domain boundary. | While the present work abstracts from numerical and implementation issues, it suggests further research directions, particularly with regard to uncer- tainty quantification in reflected generative models, where the propagation of score estimation uncertainty through the generative process remains an open question. p dX... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078 |
30,006,264 | OWR-14299282-004 | Posterior Sampling for Random-Tree Besov Priors | Develop general, provably convergent algorithms for sampling Bayesian inverse-problem posteriors arising from random-tree Besov priors, with quantitative mixing and complexity guarantees. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078](https://doi.org/10.4171/owr/2025/21)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299282-004",
"literature-status:partially-solved",
"owr-year:2025"
] | Independence Metropolis and multilevel MCMC methods provide effective posterior sampling for important elliptic inverse problems with random-tree Besov priors, but a general sampling solution is not established. | [
{
"url": "https://ems.press/content/serial-article-files/51850",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2302.00678",
"label": "Multilevel MCMC with random-tree Besov priors"
},
{
"url": "https://www.aimsciences.org/article/doi/10.3934/ipi.2022059",
"label": "Ra... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/21 | null | null | null | Develop general, provably convergent algorithms for sampling Bayesian inverse-problem posteriors arising from random-tree Besov priors, with quantitative mixing and complexity guarantees. | An interesting open question is how to sample from the posteriors arising from random tree Besov priors. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Uncertainty Quantification (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/21, pp. 1011--1078 |
30,006,265 | OWR-14299283-001 | Representation-Theoretic Meaning of Steinberg Quotient Characters | For each dominant weight $\lambda$, identify a natural representation-theoretic or geometric object whose character is the Steinberg quotient $t(\lambda)$. Determine in particular whether it is the character of a finite-dimensional module. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-001",
"literature-status:partially-solved",
"owr-year:2025"
] | Smith--Treumann localization now gives a geometric and categorical realization of the Steinberg quotient through parity-sheaf stalk data, but identification with the ordinary character of a finite-dimensional G-module is not established. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2606.21697",
"label": "Achar--Sobaje, Steinberg quotients and localization"
},
{
"url": "https://arxiv.org/abs/2301.11465",
"label": "Sobaje, Steinberg quoti... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | For each dominant weight $\lambda$, identify a natural representation-theoretic or geometric object whose character is the Steinberg quotient $t(\lambda)$. Determine in particular whether it is the character of a finite-dimensional module. | What is t(\lambda) the character of? Smith–Treumann localization and the Steinberg module Pramod N. Achar (joint work with Paul Sobaje) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,266 | OWR-14299283-002 | Information outside the Thin Affine Grassmannian | What representation-theoretic or geometric information is carried by the components of the fixed-point affine Grassmannian $\operatorname{Gr}^{\varpi}$ lying outside its thin part? Also determine how equivariant and Iwahori–Whittaker Smith–Treumann localization are related and compare the Leslie–Lonergan and Riche–Will... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299283-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-002",
"literature-status:open",
"owr-year:2025"
] | A later comparison relates the two Smith--Treumann localization constructions, but the extracted question about information on components outside the thin affine Grassmannian remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2606.21697",
"label": "Achar--Sobaje, Steinberg quotients and localization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | What representation-theoretic or geometric information is carried by the components of the fixed-point affine Grassmannian $\operatorname{Gr}^{\varpi}$ lying outside its thin part? Also determine how equivariant and Iwahori–Whittaker Smith–Treumann localization are related and compare the Leslie–Lonergan and Riche–Will... | What information lives on the components of Gr̟ outside of Grthin ? Finally, the third question is based on the insight of Riche–Williamson [6] that the Smith–Treumann localization functor and Smith parity sheaves make sense not only for Ǧ(C[[z]])-equivariant sheaves, but also for Iwahori–Whittaker (IW) sheaves, as co... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,267 | OWR-14299283-006 | Duplicate Thin-Affine-Grassmannian Question Continuation | We hope that these results lay the groundwork for future study of Question 2. where the multiplicities aµ,\lambda are the same integers appearing in the decomposition M T(\lambda) ⊗ St = T((p − 1)ρ + µ)⊕aµ,\lambda . µ\inX+ | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction is a concluding sentence pointing back to the question represented canonically by OWR-1429) | [
"OWR-14299283-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-006",
"literature-status:open",
"owr-year:2025"
] | The reported decomposition supplies groundwork, but the extracted Question 2 about the information carried by components outside the thin affine Grassmannian remains a stated direction for future work. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2606.21697",
"label": "Achar--Sobaje, Steinberg quotients and localization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | null | We hope that these results lay the groundwork for future study of Question 2. where the multiplicities aµ,\lambda are the same integers appearing in the decomposition M T(\lambda) ⊗ St = T((p − 1)ρ + µ)⊕aµ,\lambda . µ\inX+ | unrecoverable | The official report confirms that this extraction is a concluding sentence pointing back to the question represented canonically by OWR-14299283-002. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,268 | OWR-14299283-009 | Lagrangian p-Supports of Holonomic Quantization Modules | Let $X$ be a conical symplectic singularity, let $A_\lambda$ be a quantization, and let $M$ be a holonomic finite $A_\lambda$-module. Prove that for all sufficiently large primes $p$, the support of the reduction $M_p$ over the $p$-center is Lagrangian. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-009",
"literature-status:partially-solved",
"owr-year:2025"
] | Lagrangianity is proved for smooth D-modules and q-D-modules, but the broader conjecture for reductions of holonomic modules over quantizations of conical symplectic singularities remains open. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2504.19329",
"label": "Etingof, Lagrangianity of p-supports"
},
{
"url": "https://doi.org/10.1007/s00222-018-0837-6",
"label": "Bitoun, p-supports of holonom... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | Let $X$ be a conical symplectic singularity, let $A_\lambda$ be a quantization, and let $M$ be a holonomic finite $A_\lambda$-module. Prove that for all sufficiently large primes $p$, the support of the reduction $M_p$ over the $p$-center is Lagrangian. | 4. Potential Applications 1. Let X be a conical symplectic singularity. It has a family of quantizations At,\lambda defined by I. Losev, where \lambda \in HP 2 (X) = H 2 (X, e C), where X e is a Q-factorial terminalization of X. The family of varieties X\lambda := SpecA0,\lambda is the universal Poisson deformation of ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,269 | OWR-14299283-010 | Cluster Monomials as Simple Shifted Quantum Affine Modules | For the cluster algebra $\mathcal{A}_{\Gamma'_\infty}$ and category $\mathcal{O}$ of the associated shifted quantum affine algebra, prove that every cluster monomial is represented by a simple object under the cluster-algebra isomorphism relating these structures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-010",
"literature-status:partially-solved",
"owr-year:2025"
] | The cluster-monomial correspondence is proved for the sl2 case and formulated generally for simply-laced shifted quantum affine algebras; the general conjecture remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2401.04616",
"label": "Geiss--Hernandez--Leclerc, shifted quantum affine algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | For the cluster algebra $\mathcal{A}_{\Gamma'_\infty}$ and category $\mathcal{O}$ of the associated shifted quantum affine algebra, prove that every cluster monomial is represented by a simple object under the cluster-algebra isomorphism relating these structures. | In general, we conjecture the following, that we establish for g = sl2 in [GHL1]. Enveloping Algebras and Geometric Representation Theory 1301 Conjecture [GHL1] All cluster monomials in AΓ′\infty correspond to classes of simple objects in O through our isomorphism. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,270 | OWR-14299283-011 | Reported Quasi-BPS Construction | In [4] and [5], we propose using a noncommutative space: T(d)w , called a BPS category, as answer to Question 2. Enveloping Algebras and Geometric Representation Theory 1311 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | partially_solved | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents the quasi-BPS category as the authors’ proposed and partially established answer to a preceding geometric-reali) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-011",
"literature-status:partially-solved",
"owr-year:2025"
] | Quasi-BPS categories give theorem-level categorical realizations of relevant K-theory and BPS cohomology in broad symmetric-quiver settings, while the requested general geometric and Hall-categorical interpretation still has conjectural parts. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2309.08425",
"label": "Quasi-BPS categories"
},
{
"url": "https://arxiv.org/abs/2309.08432",
"label": "Topological K-theory of quasi-BPS categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | null | In [4] and [5], we propose using a noncommutative space: T(d)w , called a BPS category, as answer to Question 2. Enveloping Algebras and Geometric Representation Theory 1311 | unrecoverable | The official report presents the quasi-BPS category as the authors’ proposed and partially established answer to a preceding geometric-realization question; this extracted sentence does not state a separate open problem. No separate clean statement is promoted; the original record remains publicly visible and retained ... | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,271 | OWR-14299283-012 | K-Theory Equivalence of Hall and Quasi-BPS Categories | Prove that the algebraic or topological $K$-theory of $D\text{-}\operatorname{mod}_{\mathrm{coh}}(\mathcal{X}(d))_{w/d}$ is isomorphic, under the specialization map, to the $K$-theory of the quasi-BPS category $\mathbb{T}(d)_w$. Establish the corresponding slope-zero Hall-category equivalence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | open | null | 2,025 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-012",
"literature-status:open",
"owr-year:2025"
] | The K-theory isomorphisms and the proposed slope-zero Hall-category identification are stated as conjectures in the report; no general proof was located. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2309.08425",
"label": "Quasi-BPS categories"
},
{
"url": "https://arxiv.org/abs/2309.08432",
"label": "Topological K-theory of quasi-BPS categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | Prove that the algebraic or topological $K$-theory of $D\text{-}\operatorname{mod}_{\mathrm{coh}}(\mathcal{X}(d))_{w/d}$ is isomorphic, under the specialization map, to the $K$-theory of the quasi-BPS category $\mathbb{T}(d)_w$. Establish the corresponding slope-zero Hall-category equivalence. | We conjecture that the (algebraic or topological) K-theory of D-modcoh (X (d))w/d and T(d)w are isomorphic under a specialization map. In particular, if we consider a slope zero Hall category, namely the monoidal category: M D-HA(Q)0 := D-modcoh (X (d)), d\inNI then we conjecture the following: \sim Conjecture 1. The r... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,272 | OWR-14299283-013 | Catalan Formulas for Ekedahl-Oort Intersection Cohomology | Generalize the existing method to obtain explicit Catalan-combinatorial formulas for the local intersection cohomology of every Ekedahl–Oort space $\operatorname{EO}(r,h)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332](https://doi.org/10.4171/owr/2025/25)
## Literature review (che... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299283-013",
"literature-status:partially-solved",
"owr-year:2025"
] | Local intersection cohomology and irreducible-component formulas are established, but the proposed Catalan-combinatorics formula for all EO(r,h) cases remains conjectural. | [
{
"url": "https://ems.press/content/serial-article-files/51851",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2502.07688",
"label": "Fang--Reineke, local intersection cohomology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/25 | null | null | null | Generalize the existing method to obtain explicit Catalan-combinatorial formulas for the local intersection cohomology of every Ekedahl–Oort space $\operatorname{EO}(r,h)$. | We conjecture that our method can be generalized to provide explicit formulas for all EO(r,h) in terms of certain Catalan combinatorics. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/25, pp. 1271--1332 |
30,006,273 | OWR-14299284-001 | The Bondal–Orlov D-Equivalence Conjecture | Let $X$ and $X'$ be smooth projective complex Calabi–Yau varieties. If $X$ and $X'$ are birational, must their bounded derived categories $D^b(X)$ and $D^b(X')$ be equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-001",
"literature-status:partially-solved",
"owr-year:2025"
] | Derived equivalence is proved in substantial special cases, including K3 type, while the general Bondal--Orlov D-equivalence conjecture remains open; odd cohomology of A_g is now known in genera 5 and 7, but full cohomology for higher genus is not known. | [
{
"url": "https://ems.press/content/serial-article-files/51852",
"label": "OWR 2025 report"
},
{
"url": "https://arxiv.org/abs/2012.02892",
"label": "Odd cohomology of moduli of principally polarized abelian varieties"
},
{
"url": "https://doi.org/10.2140/gt.2024.28.497",
"label": "P... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Let $X$ and $X'$ be smooth projective complex Calabi–Yau varieties. If $X$ and $X'$ are birational, must their bounded derived categories $D^b(X)$ and $D^b(X')$ be equivalent? | The D- equivalence conjecture of Bondal-Orlov states that if X and X ′ are birational, then there is an equivalence of bounded derived categories Db (X) ≃ Db (X ′ ) . Moreover, a more general version of the D-equivalence conjecture is proven for bounded derived categories of twisted sheaves on X and X ′ . In spite of t... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,274 | OWR-14299284-002 | Atomic Categories and Stable Rationality | For a smooth projective surface $X$ over a field $k$, is $X$ rational if and only if every atom of $D^b(X)$ is equivalent to $D^b(L)$ for some finite field extension $L/k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-002",
"literature-status:partially-solved",
"owr-year:2025"
] | The atomic-category criterion gives a proved surface-level analogue of the Kuznetsov conjecture, but the proposed extension to three-dimensional and stable-rationality questions remains conjectural. | [
{
"url": "https://ems.press/content/serial-article-files/51852",
"label": "OWR 2025 report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | For a smooth projective surface $X$ over a field $k$, is $X$ rational if and only if every atom of $D^b(X)$ is equivalent to $D^b(L)$ for some finite field extension $L/k$? | This is the baby analog of Kuznetsov’s Conjecture 1. Proof. Given a birational map P2 99K X, atoms of X will come from blow up centers. Conversely, for the other direction we can assume X is minimal in which case the result follows by inspection. Example 3 (Châtelet surface). A Châtelet surface surface X \to P1 is a ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,275 | OWR-14299284-003 | Truncated Derived-Category Conjecture | We conjecture that this is the case. 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:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction contains only the phrase introducing a conjecture and omits the conjecture itself. No separ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-003",
"literature-status:open",
"owr-year:2025"
] | The record is only the sentence `We conjecture that this is the case' and does not identify the mathematical assertion; the unresolved or unclear claim is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | null | We conjecture that this is the case. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that the extraction contains only the phrase introducing a conjecture and omits the conjecture itself. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,276 | OWR-14299284-004 | Multiplicativity of Tautological Chow Projections | Is the tautological projection from the Chow ring to its tautological subspace a ring homomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-004",
"literature-status:partially-solved",
"owr-year:2025"
] | The general question whether the tautological projection on the Chow ring of \mathcal{A}_g is multiplicative remains unresolved, but Iribar López proves the homomorphism property in several cases and for a natural subring generated by Noether--Lefschetz data. | [
{
"url": "https://doi.org/10.1017/fmp.2025.10018",
"label": "Iribar López, Noether--Lefschetz cycles"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Is the tautological projection from the Chow ring to its tautological subspace a ring homomorphism? | The following basic question is introduced in [3]: Question 1. Is the tautological projection (1) a ring homomorphism? We report on joint work with R. Pandharipande and H.-H. Tseng on the enumer- ative geometry of the space of maps C \to E, when C is a genus g curve, E is an elliptic curve, and both curves move in modu... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,277 | OWR-14299284-005 | Higher-Genus Gromov–Witten Invariants of Elliptic Targets | How can the higher-genus descendant Gromov–Witten invariants $\langle\Lambda\tau_k(0)\rangle^{\pi,d}_{g,1}$ of the universal elliptic curve be computed when degeneration of the target to a rational curve is unavailable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-005",
"literature-status:partially-solved",
"owr-year:2025"
] | The general all-genus computation of the displayed Gromov--Witten invariants is not known; relative moduli constructions, degree calculations, and selected low-genus or special cases provide substantial but incomplete progress. | [
{
"url": "https://doi.org/10.1017/fmp.2025.10018",
"label": "Iribar López, Noether--Lefschetz cycles"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | How can the higher-genus descendant Gromov–Witten invariants $\langle\Lambda\tau_k(0)\rangle^{\pi,d}_{g,1}$ of the universal elliptic curve be computed when degeneration of the target to a rational curve is unavailable? | Determining these invariants in general is an open question since degeneration of the target elliptic curve to a rational curve is not allowed. How to compute the Gromov-Witten invariants hΛ\tauk (0)i\pi,d g,1 ? Mg,1 Gromov-Witten invariants of \pi are defined by the above correspondence: Z (2) hΛ\tauk (0)i\pi,d g,1 :=... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,278 | OWR-14299284-006 | All-Genus Gromov–Witten Invariants of Hilbert Schemes | Give a method to compute, for every genus $g$, the equivariant Gromov–Witten invariants of $\operatorname{Hilb}^d(\mathbb C^2)$ in curve classes $\beta_n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The genus-zero theory is known and higher-genus theory has been related to local-curve theories, but no method computing all equivariant invariants in the stated generality for every genus is established. | [
{
"url": "https://people.math.ethz.ch/~rahul/HilbC2YY.pdf",
"label": "You, higher-genus theory of Hilbert schemes"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Give a method to compute, for every genus $g$, the equivariant Gromov–Witten invariants of $\operatorname{Hilb}^d(\mathbb C^2)$ in curve classes $\beta_n$. | Question 3. Provide a method to compute the invariants (3) for all g. For g = 0, this was carried out by R. Pandharipande and A. Okounkov [5]. In this case, the theory is governed by the operator of quantum multiplication by D: (4) MD = D ⋆ : HT∗ (Hilbd (C2 ))[[q]] −\to HT∗ (Hilbd (C2 ))[[q]] . The Deligne–Mumford stac... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,279 | OWR-14299284-007 | Universal-Cover Decomposition of Klt Pairs with Nef Anticanonical Class | Describe the universal-cover decomposition of a klt pair with nef anticanonical class. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-007",
"literature-status:open",
"owr-year:2025"
] | Structure theorems for projective klt pairs with nef anti-log-canonical divisor give locally constant fibrations and reduce part of the problem, but the requested Beauville--Bogomolov-type decomposition of the universal cover remains unresolved in the stated generality. | [
{
"url": "https://doi.org/10.1017/nmj.2024.21",
"label": "Matsumura--Wang, non-vanishing and structure"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Describe the universal-cover decomposition of a klt pair with nef anticanonical class. | Note that the decomposition of the universal cover of a klt pair with nef anti- canonical class is still an open problem; see [MW21, Conjecture 1.5]. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,280 | OWR-14299284-009 | Semiorthogonal Decompositions Along Extremal Contractions | Suppose a smooth Fano variety $X$ has extremal contractions to smooth Fano varieties $Y$ and $Z$. Do there exist semiorthogonal decompositions of $D^b(X)$ compatible with pullback from $Y$ and $Z$, with the two decompositions related by mutation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-009",
"literature-status:open",
"owr-year:2025"
] | The proposed compatibility of semiorthogonal decompositions with all extremal contractions of smooth Fano varieties is still stated as a conjecture; known examples and mutations do not establish the general assertion. | [
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Suppose a smooth Fano variety $X$ has extremal contractions to smooth Fano varieties $Y$ and $Z$. Do there exist semiorthogonal decompositions of $D^b(X)$ compatible with pullback from $Y$ and $Z$, with the two decompositions related by mutation? | Conjecture 3. Let (1) be the extremal contractions of smooth Fano varieties. Then there exist semiorthogonal decompositions of Db (X) that are compatible with pullbacks along these maps: Db (X) = hA1 , . . . , As , P1 , . . . , Pr i = hQ1 , . . . , Qu , B1 , . . . , Bt i, In our situation, X = M , Y = P3g−3 (resp. P3g−... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,281 | OWR-14299284-010 | Quantum-Monodromy Computation of Mutation Braids | Let a smooth Fano variety $X$ admit extremal contractions to smooth Fano varieties $Y$ and $Z$, and let the pullback-compatible semiorthogonal decompositions of $D^b(X)$ be related by a mutation braid. Is this braid equal to the monodromy braid of the eigenvalues of quantum multiplication by $c_1(X)$ as the complexifie... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-010",
"literature-status:open",
"owr-year:2025"
] | The identification of the mutation braid with monodromy of quantum multiplication by the first Chern class has only example-level evidence and remains explicitly conjectural in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Let a smooth Fano variety $X$ admit extremal contractions to smooth Fano varieties $Y$ and $Z$, and let the pullback-compatible semiorthogonal decompositions of $D^b(X)$ be related by a mutation braid. Is this braid equal to the monodromy braid of the eigenvalues of quantum multiplication by $c_1(X)$ as the complexifie... | Conjecture 4. The braid appearing in Conjecture 3 can be computed as the mon- odromy of the eigenvalues of c1 (X) acting on the small quantum cohomology ring QH∗ (X, C), as the quantum parameter \tau varies along a path in the ample cone of X (with a small B-field perturbation iB to avoid collisions of eigenvalues). As... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,282 | OWR-14299284-011 | Duplicate Atomic-Decomposition Extraction | and the eigenspace corresponding to 8\lambda is isomorphic to H ∗ (Sym g−1−|\lambda| (C), C). We therefore conjecture: We do not claim originality for these conjectures, which align with existing literature (see, e.g., [4–7, 13]). Currently, the only way to test Conjecture 4 is by computing and comparing the two braids... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction is an overlapping lead-in to the same atomic semiorthogonal-decomposition conjecture repre) | [
"OWR-14299284-012"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-011",
"literature-status:open",
"owr-year:2025"
] | The record points to the conjectural atomicity statement for the moduli space of rank-two bundles; the Sanda--Shamoto framework proves important special cases but not this asserted compatibility in the stated generality. | [
{
"url": "https://arxiv.org/abs/1705.05989",
"label": "Sanda--Shamoto, analogue of Dubrovin's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | null | and the eigenspace corresponding to 8\lambda is isomorphic to H ∗ (Sym g−1−|\lambda| (C), C). We therefore conjecture: We do not claim originality for these conjectures, which align with existing literature (see, e.g., [4–7, 13]). Currently, the only way to test Conjecture 4 is by computing and comparing the two braids... | unrecoverable | The official report confirms that this extraction is an overlapping lead-in to the same atomic semiorthogonal-decomposition conjecture represented canonically by OWR-14299284-012. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,283 | OWR-14299284-012 | Atomic Decomposition of Rank-Two Bundle Moduli | Is the proposed semiorthogonal decomposition of $SU_C(2,\Lambda)$ atomic, meaning that it is compatible with the decomposition of $H^*(SU_C(2,\Lambda),\mathbb C)$ into generalized eigenspaces of quantum multiplication by $c_1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516](https://doi.org/10.4171/owr/2025/28)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299284-011"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299284-012",
"literature-status:open",
"owr-year:2025"
] | The claimed atomic semiorthogonal decomposition compatible with generalized quantum-cohomology eigenspaces remains a conjecture for the stated moduli space; no general proof was found by the cutoff date. | [
{
"url": "https://arxiv.org/abs/1705.05989",
"label": "Sanda--Shamoto, analogue of Dubrovin's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2025/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/28 | null | null | null | Is the proposed semiorthogonal decomposition of $SU_C(2,\Lambda)$ atomic, meaning that it is compatible with the decomposition of $H^*(SU_C(2,\Lambda),\mathbb C)$ into generalized eigenspaces of quantum multiplication by $c_1$? | Conjecture 5. The semiorthogonal decomposition of SU C (2, Λ) from Theorem 1 is atomic, i.e., compatible with the orthogonal decomposition of H ∗ (SU C (2, Λ), C) into generalized eigenspaces of quantum multiplication by c1 . The precise notion of compatibility is as in the Sanda–Shamoto conjecture [13]. and the eigens... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/28, pp. 1451--1516 |
30,006,284 | OWR-14299285-002 | Resolved Directed-Landscape Converse Lead-In | Is the opposite true? Unlike the KPZ fixed point, there are not exact formulas for all statistics in the di- rected landscape. Instead, the construction proceeds by studying a scaling limit of the one aspect of the classical Robinson-Schensted-Knuth (RSK) correspondence. The connection between the directed landscape an... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388](https://doi.org/10.4171/owr/2025/26)
## ... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks this converse question only as a lead-in and immediately answers it with the stated theorem, so the extraction is n) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299285-002",
"literature-status:open",
"owr-year:2025"
] | The record contains only the isolated question `Is the opposite true?' and does not specify the proposition or its negation; the unresolved or unclear claim is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2025/26",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/26 | null | null | null | null | Is the opposite true? Unlike the KPZ fixed point, there are not exact formulas for all statistics in the di- rected landscape. Instead, the construction proceeds by studying a scaling limit of the one aspect of the classical Robinson-Schensted-Knuth (RSK) correspondence. The connection between the directed landscape an... | unrecoverable | The official report asks this converse question only as a lead-in and immediately answers it with the stated theorem, so the extraction is not an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388 |
30,006,285 | OWR-14299285-003 | Universal CLE Metrics as Chemical-Distance Limits | For every $\kappa$, does the $\operatorname{CLE}_\kappa$ metric arise as the scaling limit of the intrinsic, or chemical-distance, metric of every discrete model whose interfaces converge to $\operatorname{CLE}_\kappa$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388](https://doi.org/10.4171/owr/2025/26)
## ... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299285-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The universal CLE_\kappa metric conjecture remains open, but the 2026 primary work proves convergence of the intrinsic metric for critical planar percolation, the \kappa=6 case. | [
{
"url": "https://arxiv.org/abs/2604.14122",
"label": "Dankovic--Markering--Miller--Yuan, planar critical percolation"
},
{
"url": "https://doi.org/10.4171/owr/2025/26",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/26 | null | null | null | For every $\kappa$, does the $\operatorname{CLE}_\kappa$ metric arise as the scaling limit of the intrinsic, or chemical-distance, metric of every discrete model whose interfaces converge to $\operatorname{CLE}_\kappa$? | We conjecture that the CLEκ metric describes the scaling limit of the intrinsic (a.k.a. chemical distance) metric of any discrete model which converges to a CLEκ in the scaling limit. The scaling limit of simple random walk and the intrinsic metric on 2D critical percolation clusters Jason Miller (joint work with Valer... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388 |
30,006,286 | OWR-14299285-004 | Random Moduli of General Brownian Surfaces | Derive the random conformal moduli of Brownian surfaces of arbitrary topology, extending the known Brownian-annulus case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388](https://doi.org/10.4171/owr/2025/26)
## ... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299285-004",
"literature-status:open",
"owr-year:2025"
] | The random modulus of the Brownian annulus has been rigorously derived, but the record's extension to Brownian surfaces of general topology remains a stated conjectural direction rather than a completed theorem. | [
{
"url": "https://arxiv.org/abs/2203.12398",
"label": "Ang--Remy--Sun, moduli of annuli"
},
{
"url": "https://doi.org/10.4171/owr/2025/26",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/26 | null | null | null | Derive the random conformal moduli of Brownian surfaces of arbitrary topology, extending the known Brownian-annulus case. | We conclude our talk with a list of future directions and open questions. (1) So far we have only rigorously derived the random modulus for the Brown- ian annulus. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388 |
30,006,287 | OWR-14299285-005 | Symmetries of Open-Boundary Asymmetric Exclusion Processes | What role do the non-Abelian symmetries of the intensity matrix play for the asymmetric simple exclusion process with open boundaries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388](https://doi.org/10.4171/owr/2025/26)
## ... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299285-005",
"literature-status:open",
"owr-year:2025"
] | Symmetry and reverse-duality results are known for several ASEP-related systems, but the role of these symmetries for open-boundary ASEP is still explicitly posed as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2025/26",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/26 | null | null | null | What role do the non-Abelian symmetries of the intensity matrix play for the asymmetric simple exclusion process with open boundaries? | An intriguing open problem is the role of such symmetries for the ASEP with open boundaries. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Statistical Physics Out of Equilibrium: Quantitative Results and Universality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/26, pp. 1333--1388 |
30,006,288 | OWR-14299286-001 | Efficient Optimization of Neural-Network Weights | Given a fixed neural-network architecture, can globally optimal weights be found in reasonable computational time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Multiscale Methods (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/22, pp. 1079--1162](https://doi.org/10.4171/owr/2025/22)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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-14299286-001",
"literature-status:open",
"owr-year:2025"
] | There is no general efficient procedure for finding optimal weights even after fixing an architecture; primary complexity results show exact training hardness for simple networks, while practical guarantees require additional assumptions. | [
{
"url": "https://papers.nips.cc/paper_files/paper/2023/hash/71c31ebf577ffdad5f4a74156daad518-Abstract-Conference.html",
"label": "Abrahamsen--Bouritsas--Dughmi--Miltzow, training complexity"
},
{
"url": "https://doi.org/10.4171/owr/2025/22",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/22 | null | null | null | Given a fixed neural-network architecture, can globally optimal weights be found in reasonable computational time? | One of the most pressing problems in deep learning is the question of how to design good networks for a given task and how to train them efficiently. However, even if we know the optimal architecture, it is still an open question of how to find the optimal weights in reasonable compute time. Towards optimal hierarchica... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Multiscale Methods (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/22, pp. 1079--1162 |
30,006,289 | OWR-14299286-002 | Maximal Computable Dissipative Solutions of Euler Equations | If a numerical scheme for the Euler system converges to a weak solution, is its limit a maximal computable dissipative solution? If the same scheme is oscillatory, does a maximal computable dissipative solution fail to exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Multiscale Methods (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/22, pp. 1079--1162](https://doi.org/10.4171/owr/2025/22)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,025 | 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"
} | {
"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-14299286-002",
"literature-status:open",
"owr-year:2025"
] | The maximal-computable-dissipative-solution assertion is formulated as a recent conjecture; existing K-convergence and entropy-selection results do not prove the two-part statement for arbitrary Euler schemes. | [
{
"url": "https://arxiv.org/abs/2505.02070",
"label": "Feireisl--Lukacova-Medvidova--Yu, oscillatory approximations"
},
{
"url": "https://doi.org/10.4171/owr/2025/22",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/22 | null | null | null | If a numerical scheme for the Euler system converges to a weak solution, is its limit a maximal computable dissipative solution? If the same scheme is oscillatory, does a maximal computable dissipative solution fail to exist? | In the case that the strong solution to the above equations exists, the dissipative solutions coincide with the strong solution on its life span [1]. If the consistent approximations only converge weakly and not strongly, the limit is not a weak solution. This means the defects are nonzero. We can apply a newly develop... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Multiscale Methods (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/22, pp. 1079--1162 |
30,006,290 | OWR-14299287-001 | Solution Concepts for Fluid-Mechanics Equations | What solution concepts are appropriate for the partial differential equations of fluid mechanics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270](https://doi.org/10.4171/owr/2025/24)
## Literature review (checked... | 3 | open | null | 2,025 | 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"
} | {
"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-14299287-001",
"literature-status:open",
"owr-year:2025"
] | The record is a broad foundational question about suitable solution concepts for fluid-mechanics PDEs; multiple weak, dissipative, measure-valued, and selection concepts exist, but no generally accepted complete solution concept is known. | [
{
"url": "https://doi.org/10.4171/owr/2025/24",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/24 | null | null | null | What solution concepts are appropriate for the partial differential equations of fluid mechanics? | What are good solution concepts for the PDEs of fluid mechanics? Mathematical Advances in Geophysical Fluid Dynamics 1253 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270 |
30,006,291 | OWR-14299287-002 | Selecting Among Nonunique Fluid-Mechanics Solutions | Find a satisfactory solution concept for fluid-mechanics PDEs that resolves or selects among nonunique admissible weak solutions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270](https://doi.org/10.4171/owr/2025/24)
## Literature review (checked... | 3 | open | null | 2,025 | 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"
} | {
"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-14299287-002",
"literature-status:open",
"owr-year:2025"
] | Nonuniqueness of admissible weak solutions has motivated dissipative and selection frameworks, but the report correctly identifies the general search for a satisfactory solution concept as outstanding and unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/24",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/24 | null | null | null | Find a satisfactory solution concept for fluid-mechanics PDEs that resolves or selects among nonunique admissible weak solutions. | The quest for a good solution concept for the PDEs arising in mathematical fluid mechanics is an outstanding open problem. The main purpose of this talk is to address the question of how to deal with the fact that admissible weak solutions are not unique. What are good solution concepts for the PDEs of fluid mechanics?... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270 |
30,006,292 | OWR-14299287-003 | Inertial Manifolds for Navier–Stokes Equations | Do the two-dimensional Navier–Stokes equations admit an inertial manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270](https://doi.org/10.4171/owr/2025/24)
## Literature review (checked... | 3 | open | null | 2,025 | 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"
} | {
"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-14299287-003",
"literature-status:open",
"owr-year:2025"
] | Inertial manifolds are known for regularized or hyperviscous Navier--Stokes models, but existence for the usual two-dimensional Navier--Stokes equations remains a long-standing open problem. | [
{
"url": "https://www.mathnet.ru/eng/rm10095",
"label": "Zelik, attractors and inertial manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2025/24",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/24 | null | null | null | Do the two-dimensional Navier–Stokes equations admit an inertial manifold? | However, it remains an open question whether the Navier– Stokes equations (NSE) admit an inertial manifold. Inertial Manifolds for Regularized Navier-Stokes Equations Yanqiu Guo (joint work with Mohammad Abu Hamed, Ciprian G. Gal, Michael Ilyin, Edriss S. Titi) Mathematical Advances in Geophysical Fluid Dynamics 1255 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270 |
30,006,293 | OWR-14299287-004 | Selective Decay in Forced-Dissipative Flows | Can selective-decay variational principles be extended to forced-dissipative flows? Do their predictions remain valid for complex topography, what causes topographically pinned vortices, and can the strengths and locations of those vortices be predicted? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270](https://doi.org/10.4171/owr/2025/24)
## Literature review (checked... | 3 | partially_solved | null | 2,025 | 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"
} | {
"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-14299287-004",
"literature-status:partially-solved",
"owr-year:2025"
] | A primary study derives a perturbative selective-decay extension for weak forcing and damping and validates bifurcation predictions numerically, but a general forced-dissipative theory is not established. | [
{
"url": "https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/twodimensional-turbulence-above-topography-condensation-transition-and-selection-of-minimum-enstrophy-solutions/654AD74779542F674C5A51FE5F82F28",
"label": "Gallet, two-dimensional turbulence above topography"
},
{
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/24 | null | null | null | Can selective-decay variational principles be extended to forced-dissipative flows? Do their predictions remain valid for complex topography, what causes topographically pinned vortices, and can the strengths and locations of those vortices be predicted? | A second question of interest is whether such variational principles can be ex- tended to out-of-equilibrium systems. How to extend selective decay to the forced-dissipative situation? Mathematical Advances in Geophysical Fluid Dynamics 1261 • The present numerical simulations were performed with single-scale topog- ra... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270 |
30,006,294 | OWR-14299287-005 | Predicting Topographically Pinned Vortices | Extend selective-decay theory so that it predicts the strength and location of vortices pinned to topography. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270](https://doi.org/10.4171/owr/2025/24)
## Literature review (checked... | 3 | open | null | 2,025 | 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"
} | {
"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-14299287-005",
"literature-status:open",
"owr-year:2025"
] | The forced-dissipative topography theory reproduces condensates and identifies pinned vortices numerically, but a theory predicting their strength and location remains an explicit open question. | [
{
"url": "https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/twodimensional-turbulence-above-topography-condensation-transition-and-selection-of-minimum-enstrophy-solutions/654AD74779542F674C5A51FE5F82F28",
"label": "Gallet, two-dimensional turbulence above topography"
},
{
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/24 | null | null | null | Extend selective-decay theory so that it predicts the strength and location of vortices pinned to topography. | Can the theory be extended to predict their strength and location? topography is at a scale strictly smaller than the domain size, although no scale separation is required. We revisit selective decay for this setup and highlight a new branch of solutions to the variational problem, which corresponds to a large-scale ‘c... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/24, pp. 1215--1270 |
30,006,295 | OWR-14299288-001 | Toric-Geometry Contents Fragment | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900 Patience Ablett Gotzmann’s persistence theorem for smooth projective toric varieties . . . 903 Karim Adiprasito Oda’s strong factorization conjecture (and relatives) . . . . . . . . . . . . . . . . . 905 Klaus Altmann (joint with... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-001",
"literature-status:open",
"owr-year:2025"
] | The record is a truncated table-of-contents fragment ending in `Conjecture' and does not state a mathematical claim; the unresolved or unclear item is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900 Patience Ablett Gotzmann’s persistence theorem for smooth projective toric varieties . . . 903 Karim Adiprasito Oda’s strong factorization conjecture (and relatives) . . . . . . . . . . . . . . . . . 905 Klaus Altmann (joint with... | unrecoverable | The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,296 | OWR-14299288-002 | Matroids as Smooth Projective Toric Varieties | Develop a precise theory explaining the extent to which matroids behave like smooth projective toric varieties, including analogues for sheaf cohomology, vector bundles, intersection theory, and Hodge-theoretic structures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-002",
"literature-status:open",
"owr-year:2025"
] | Matroid Chow rings satisfy strong toric-like Hodge properties, but the record's broad question about sheaf cohomology, vector bundles, and a full toric analogue remains unresolved and is not a single settled claim. | [
{
"url": "https://ems.press/content/serial-article-files/51856",
"label": "Eur, matroids and projective toric varieties"
},
{
"url": "https://lsa.umich.edu/math/news-events/all-events.detail.html/125630-21855469.html",
"label": "Eur, conference abstract"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Develop a precise theory explaining the extent to which matroids behave like smooth projective toric varieties, including analogues for sheaf cohomology, vector bundles, intersection theory, and Hodge-theoretic structures. | How do matroids behave like a smooth projective toric variety? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,297 | OWR-14299288-003 | Vanishing Theorems for Divisors on Matroid Wonderful Varieties | Let $W_L$ be the wonderful variety of a realizable matroid and let $D$ be a nef divisor on the ambient permutohedral variety. Prove that $H^i(W_L,\mathcal{O}_{W_L}(D|_{W_L}))=0$ for every $i>0$; if $D|_{W_L}$ is also big, prove that $H^i(W_L,\mathcal{O}_{W_L}(K_{W_L}+D|_{W_L}))=0$ for every $i>0$. Also determine whethe... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2510.05207",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (unrefereed preprint)**. C. Eur (OWR 19/2025, p. 890) states M. Larson's conjecture: for D nef on the permutohedral variety, H^i(W_L, D|W_L) = 0 for i > 0, and H^i(W_L, K + D|W_L) = 0 for i > 0 when D|W_L is big; he calls the anti-log-canonical vanishing H^i(W_L, −... | [
"owr",
"oberwolfach-reports",
"OWR-14299288-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The 2025 report records substantial partial results for the nef-divisor vanishing conjecture, including a full-dimensional cone of nef divisors and the log-canonical case, while explicitly leaving the stronger anti-log-canonical vanishing open; Eur's 2024 paper proves the log-canonical vanishing in arbitrary characteri... | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-024-00979-7",
"label": "Eur, Cohomologies of tautological bundles of matroids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Let $W_L$ be the wonderful variety of a realizable matroid and let $D$ be a nef divisor on the ambient permutohedral variety. Prove that $H^i(W_L,\mathcal{O}_{W_L}(D|_{W_L}))=0$ for every $i>0$; if $D|_{W_L}$ is also big, prove that $H^i(W_L,\mathcal{O}_{W_L}(K_{W_L}+D|_{W_L}))=0$ for every $i>0$. Also determine whethe... | Conjecture 3. For any nef divisor D on Xn , we have H i (WL , OWL (D|WL )) = 0 for all i > 0, and if further D|WL is big then H i (WL , OWL (KWL + D|WL )) = 0 for all i > 0.1 We highlight three partial results towards the conjecture currently available. Theorem 4. [9] For a full-dimensional subcone C of the nef cone of... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,298 | OWR-14299288-004 | Nonpositively Curved Cusped Manifolds from Tropical Curves | Given a tropical curve represented by $\Sigma^{(1)}\subset\Sigma_{\mathbb{P}^n}$, construct a nonpositively curved cusped manifold $L_{\Sigma^{(1)}}$ whose boundary is a union of $n+1$ real tori of dimension $n-1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-004",
"literature-status:open",
"owr-year:2025"
] | The requested construction of a nonpositively curved cusped manifold for every stated tropical curve is not established by the located literature; Haney constructs a special one-vertex example, which is evidence rather than a general solution. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2402.03296",
"label": "Haney, Cusped hyperbolic Lagrangians as mirrors to lines in three-space"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Given a tropical curve represented by $\Sigma^{(1)}\subset\Sigma_{\mathbb{P}^n}$, construct a nonpositively curved cusped manifold $L_{\Sigma^{(1)}}$ whose boundary is a union of $n+1$ real tori of dimension $n-1$. | Can we associate to tropical curve given by Σ(1) \subset ΣPn a nonpos- itively curved cusped manifold LΣ(1) whose boundary is a union of (n + 1) real tori of dimension n − 1? Local and Global Realizability Problems in Tropical Geometry. Based on the work of [2], we may expect the following: Evidence from symplectic geo... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,299 | OWR-14299288-005 | Legendrian Augmentations and Matroid Realizations | For every matroid $M$, construct a Legendrian $\Lambda_M$ whose augmentations correspond naturally to realizations of $M$, or characterize precisely which matroids admit such a Legendrian model. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-005",
"literature-status:open",
"owr-year:2025"
] | The report poses the existence of a Legendrian whose augmentations recover matroid realizations as a general question, and no authoritative source located by the cutoff proves such a correspondence for arbitrary matroids. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | For every matroid $M$, construct a Legendrian $\Lambda_M$ whose augmentations correspond naturally to realizations of $M$, or characterize precisely which matroids admit such a Legendrian model. | For a matroid M , does there exist a Legendrian ΛM whose augmen- tations correspond to realizations of M ? Evidence from symplectic geometry suggests that P will only be defined after picking an augmentation for the Legendrian link of the cusp locus of LΣ(1) . This inspires the following more general question: The Donal... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,300 | OWR-14299288-006 | Categorical Noncommutative Neighborhoods of Toric Subvarieties | For a broad class of subvarieties $Y\subset X_\Sigma$, construct a deformation of categories whose generic fiber is $\operatorname{Coh}_{\mathrm{dg}}(X_\Sigma)$, an object in the special fiber deforming to $\mathcal{O}_Y$, a possibly singular nonpositively curved space $L_V$, and a noncommutative neighborhood described... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-006",
"literature-status:open",
"owr-year:2025"
] | The extracted record asks for a broad categorical, nonpositively curved, and noncommutative-neighborhood construction; its definitions and existence assertions remain programmatic and no general theorem resolving the question was located. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | For a broad class of subvarieties $Y\subset X_\Sigma$, construct a deformation of categories whose generic fiber is $\operatorname{Coh}_{\mathrm{dg}}(X_\Sigma)$, an object in the special fiber deforming to $\mathcal{O}_Y$, a possibly singular nonpositively curved space $L_V$, and a noncommutative neighborhood described... | Question 6. For a large class of subvarieties Y \subset XΣ can we find: • A deformation of categories Ct whose general fiber is isomorphic to Cohdg (XΣ ), • An object C0 \in Ob(C0 ) deforming to OY ; • A (possibly singular) nonpositively curved space space LV ; and • A noncommutative neighborhood of C0 given by C0 \to ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,301 | OWR-14299288-007 | Duplicate Zero-Mutable Log-Resolution Conjecture | We propose to construct smoothings by the following steps: (1) Let P \subset N be a 3-dimensional lattice polytope. We conjecture that these log structures admit log crepant log resolutions. What is a log structure, Alessio? Singular Log Structures and Smoothings of toric Fano 3-folds Alessio Corti (joint work with Tim... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this introductory extraction states the same zero-mutable log-resolution conjecture represented canonicall) | [
"OWR-14299288-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-007",
"literature-status:open",
"owr-year:2025"
] | The stated log-crepant-resolution assertion is still presented as a conjecture in the primary 2025 paper and report; later work supplies examples and families but not a proof for all the stated three-dimensional log structures. | [
{
"url": "https://arxiv.org/abs/2503.11610",
"label": "Corti, Graefnitz, and Ruddat, Singular Log Structures and Log Crepant Log Resolutions I"
},
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | null | We propose to construct smoothings by the following steps: (1) Let P \subset N be a 3-dimensional lattice polytope. We conjecture that these log structures admit log crepant log resolutions. What is a log structure, Alessio? Singular Log Structures and Smoothings of toric Fano 3-folds Alessio Corti (joint work with Tim... | unrecoverable | The official report confirms that this introductory extraction states the same zero-mutable log-resolution conjecture represented canonically by OWR-14299288-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,302 | OWR-14299288-008 | Resolutions of Zero-Mutable Log Structures | Prove that every zero-mutable log structure admits a log-crepant log resolution. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299288-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-008",
"literature-status:open",
"owr-year:2025"
] | The primary paper and workshop report explicitly formulate the assertion that zero-mutable log structures admit log-crepant resolutions as a conjecture; subsequent constructions verify examples and infinite families, not the general statement. | [
{
"url": "https://arxiv.org/abs/2503.11610",
"label": "Corti, Graefnitz, and Ruddat, Singular Log Structures and Log Crepant Log Resolutions I"
},
{
"url": "https://arxiv.org/abs/2503.18661",
"label": "Graefnitz, Smoothings from zero mutable Laurent polynomials"
},
{
"url": "https://doi.... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Prove that every zero-mutable log structure admits a log-crepant log resolution. | We conjecture that zero-mutable log structures always have log resolutions. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,303 | OWR-14299288-009 | Combinatorics of Bondal-Thomsen Polytopes | Determine the combinatorial properties and significance of the Bondal–Thomsen polytopes, including their face structure, lattice points, adjacency, and relation to toric-arrangement strata and derived categories. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-009",
"literature-status:partially-solved",
"owr-year:2025"
] | The question is not settled in full: the 2025 report gives a definition and a combinatorial description through the Cox category, while Bauermeister et al. prove a bijection between relevant toric-arrangement strata and zonotope lattice points and relate dimensions, providing concrete combinatorial structure. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2507.14356",
"label": "Bauermeister et al., Strata of toric hyperplane arrangements"
},
{
"url": "https://arxiv.org/abs/2501.00130",
"label": "Ballard et al., Realizing Ki... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Determine the combinatorial properties and significance of the Bondal–Thomsen polytopes, including their face structure, lattice points, adjacency, and relation to toric-arrangement strata and derived categories. | What are the combinatorial properties and significance of the Bondal- Thomsen polytopes? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,304 | OWR-14299288-010 | Bondal-Thomsen Polytopes within Lattice-Polytope Theory | Place the finite collection of Bondal–Thomsen polytopes within the general theory of lattice polytopes: characterize their intrinsic combinatorial properties, denominator bounds, and relations to zonotopes and toric arrangements. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-010",
"literature-status:partially-solved",
"owr-year:2025"
] | The broad lattice-polytope question remains open, but the report records denominator bounds and the 2025 toric-arrangement paper gives further zonotope and lattice-point structure related to the Bondal-Thomsen collection. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2507.14356",
"label": "Bauermeister et al., Strata of toric hyperplane arrangements"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Place the finite collection of Bondal–Thomsen polytopes within the general theory of lattice polytopes: characterize their intrinsic combinatorial properties, denominator bounds, and relations to zonotopes and toric arrangements. | How does this finite set of polytopes fit more generally in the theory of lattice polytopes? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,305 | OWR-14299288-011 | Oda’s Strong Factorization Conjecture for Toric Varieties | Can any two smooth birational toric varieties be connected by a sequence of smooth blowups followed by a sequence of smooth blowdowns? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-011",
"literature-status:open",
"owr-year:2025"
] | The fragment refers to the relation between smooth toric birational models and the strong factorization conjecture; the classical smooth-center statement remains open, although a weighted or rationally smooth version was proved. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2404.05930",
"label": "Adiprasito and Pak, All triangulations have a common stellar subdivision"
},
{
"url": "https://doi.org/10.2748/tmj/1309952085",
"label": "Da Silva a... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Can any two smooth birational toric varieties be connected by a sequence of smooth blowups followed by a sequence of smooth blowdowns? | What can be said about their relation? Oda’s strong factorization conjecture (and relatives) Karim Adiprasito | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,306 | OWR-14299288-012 | Unimodular Placing Triangulations after Lattice Dilation | For every lattice polytope $P$, prove that there exist a positive integer $n$ and a total ordering of the lattice points of $nP$ for which the induced placing triangulation of $nP$ is unimodular. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-012",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a proposed sufficient conjecture for strong factorization; the report states it but supplies no proof, and the underlying smooth strong factorization problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2404.05930",
"label": "Adiprasito and Pak, All triangulations have a common stellar subdivision"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | For every lattice polytope $P$, prove that there exist a positive integer $n$ and a total ordering of the lattice points of $nP$ for which the induced placing triangulation of $nP$ is unimodular. | We proposed one possible route, that leads to a reasonable conjecture that, if true, would imply the strong factorization conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,307 | OWR-14299288-013 | Restrictions of Toric Vector Bundles to Embedded Varieties | Characterize the vector bundles $E$ on a variety $Y$ for which there exist a toric embedding $i:Y\to X_\Sigma$ and a toric vector bundle $F$ on $X_\Sigma$ with $E\cong i^*F$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-013",
"literature-status:open",
"owr-year:2025"
] | The record asks for a general criterion for a vector bundle on an arbitrary variety to be the restriction of a toric vector bundle after a suitable toric embedding; the cited toric-bundle classification does not resolve this extension problem. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Characterize the vector bundles $E$ on a variety $Y$ for which there exist a toric embedding $i:Y\to X_\Sigma$ and a toric vector bundle $F$ on $X_\Sigma$ with $E\cong i^*F$. | for circuits c \in Zs . Then F = Pe . Example 7. For the tangent bundle on P2 , we have an equivariant surjection coming from the Euler sequence: O(D0 ) ⊕ O(D1 ) ⊕ O(D2 ) ։ T P2 \to 0. The Cox ring of P2 is S = C[x0 , x1 , x2 ], and we have T P2 = Pe for P = S(D0 ) ⊕ S(D1 ) ⊕ S(D1 )/hx0 e0 + x1 e1 + x2 e2 i. Restrictio... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,308 | OWR-14299288-014 | Deformation Spaces of Smooth Complete Toric Varieties | Is the deformation space of a smooth complete toric variety determined by its tangent cone? Is the number of its irreducible components related to the number of distinct simplicial complexes representing first-order deformations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-014",
"literature-status:open",
"owr-year:2025"
] | The 2025 report poses both dependence on the tangent cone and a component-count relation as questions; recent work gives combinatorial descriptions of first-order and higher obstructions and examples, but no general answer to either question. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2409.02824",
"label": "Ilten and Robins, Locally Trivial Deformations of Toric Varieties"
},
{
"url": "https://msp.org/ant/2020/14-4/ant-v14-n4-p04-s.pdf",
"label": "Ilten... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Is the deformation space of a smooth complete toric variety determined by its tangent cone? Is the number of its irreducible components related to the number of distinct simplicial complexes representing first-order deformations? | Is the deformation space of a smooth complete toric variety deter- mined by the tangent cone? Is there any relation between the number of irreducible components of the deformation space and the number of distinct simplicial complexes that cor- respond to first-order deformations? The report passage is retained verbatim... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,309 | OWR-14299288-015 | Combinatorial Proof of Hurwitz and Discriminant Weight-Polytope Equality | Give a purely combinatorial proof that the weight polytope $W(\Delta_{X\times\mathbb{P}^{n-1}})$ of the discriminant coincides with the weight polytope $W(\operatorname{Hu}_A)$ of the Hurwitz form. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-015",
"literature-status:open",
"owr-year:2025"
] | The equality of the Hurwitz-form and discriminant weight polytopes is established, including by analytic and secondary-polytope methods, but the requested purely combinatorial reproof is explicitly left as a problem. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s42543-023-00079-z",
"label": "Sano, Weight Polytopes and Energy Functionals of Toric Varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Give a purely combinatorial proof that the weight polytope $W(\Delta_{X\times\mathbb{P}^{n-1}})$ of the discriminant coincides with the weight polytope $W(\operatorname{Hu}_A)$ of the Hurwitz form. | Can we (re)-prove the coincidence between W(∆X\timesPn−1 ) and W(HuA ) in a combinatorial way? P(N +1)n−1 . Hence, one can compute W(∆X\timesPn−1 ) instead of W(HuA ), follow- ing [3]. Acknowledgment. This work was supported by JSPS KAKENHI Grant Num- ber 22K03325. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,310 | OWR-14299288-016 | Projectivized Toric Vector Bundles as Toric Varieties | Characterize the ways in which the projectivization of a toric vector bundle behaves like a smooth projective toric variety. Determine which toric-geometric structures, invariants, and vanishing properties extend to such projectivizations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940](https://doi.org/10.4171/owr/2025/19)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299288-016",
"literature-status:open",
"owr-year:2025"
] | The extracted question seeks a general structural comparison between projectivized toric vector bundles and smooth projective toric varieties; existing work treats special bundles and related projectivization or endomorphism problems, not the stated general behavior. | [
{
"url": "https://doi.org/10.4171/owr/2025/19",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2605.25013",
"label": "Bakhtary, Canonical Projectivization of Smooth Complete Toric Varieties"
},
{
"url": "https://arxiv.org/abs/2510.26757",
"label": "Gonzalez-Anaya et... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/19 | null | null | null | Characterize the ways in which the projectivization of a toric vector bundle behaves like a smooth projective toric variety. Determine which toric-geometric structures, invariants, and vanishing properties extend to such projectivizations. | How does the projectivization of a (toric) vector bundle behave like a smooth pro- jective toric variety? TBD: Toric Bundles Duh! Gregory G. Smith (joint work with Michael Perlman) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Toric Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/19, pp. 883--940 |
30,006,311 | OWR-14299289-001 | Relative-Langlands Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Kalyani Kansal Spherical varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853 Dmitry Kubrak Hyperspherical varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment and does not contain the conjecture whose final word prece) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-001",
"literature-status:open",
"owr-year:2025"
] | The extracted text is a table-of-contents fragment ending in the word conjecture and does not state a mathematically identifiable claim; under the queue rule it is unresolved and therefore classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Kalyani Kansal Spherical varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853 Dmitry Kubrak Hyperspherical varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment and does not contain the conjecture whose final word precedes it. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,312 | OWR-14299289-003 | Arithmetic Topology over Rings of S-Integers | How does the arithmetic-topology correspondence change when the base ring is replaced by the ring of $S$-integers of a global field $F$, where $S$ contains all archimedean places when $F$ is a number field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-003",
"literature-status:open",
"owr-year:2025"
] | The extracted record asks for the corresponding arithmetic-topological treatment over rings of S-integers; no general theorem answering this extension was located, so the question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | How does the arithmetic-topology correspondence change when the base ring is replaced by the ring of $S$-integers of a global field $F$, where $S$ contains all archimedean places when $F$ is a number field? | What if we consider instead the ring of S-integers of F , for a finite set of places S of F , containing the archimedean places when K is a number field? Arbeitsgemeinschaft: Relative Langlands Duality 829 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,313 | OWR-14299289-004 | Period-Sheaf Expository Fragment | We can now consider the stack PicX Σ classifying pairs (L, \sigma), where L is a line bundle on Σ and \sigma is a section of L. Forgetting the section provides a morphism pX : PicX Σ \to PicΣ . The function ΘΦ is associated by the sheaf-to-functions correspondence to the sheaf (pX )! Q̄ℓ . This sheaf is called the ”per... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction consists of a definition of the period sheaf followed by the setup for a different period ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-004",
"literature-status:open",
"owr-year:2025"
] | The record is an expository fragment defining a period sheaf and describing its role in a global duality conjecture, not a resolved standalone theorem; the associated general global-duality framework remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2010.01906",
"label": "Arinkin et al., Geometric Langlands theory with nilpotent singular support"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | We can now consider the stack PicX Σ classifying pairs (L, \sigma), where L is a line bundle on Σ and \sigma is a section of L. Forgetting the section provides a morphism pX : PicX Σ \to PicΣ . The function ΘΦ is associated by the sheaf-to-functions correspondence to the sheaf (pX )! Q̄ℓ . This sheaf is called the ”per... | unrecoverable | The official report confirms that this extraction consists of a definition of the period sheaf followed by the setup for a different period problem; it does not state a separate open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,314 | OWR-14299289-005 | The Ichino–Ikeda Period Conjecture | Let $F$ be a global field and let $\pi=\pi_V\boxtimes\pi_{V\oplus F}$ be a multiplicity-one tempered cuspidal automorphic representation of $SO(V)\times SO(V\oplus F)$. Does the square of its global period equal the central Rankin–Selberg value divided by the adjoint value, multiplied by the normalized product of local... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-005",
"literature-status:partially-solved",
"owr-year:2025"
] | The extracted record concerns the Ichino--Ikeda period formula; it is proved for important unitary-group cases and many special cases, including stable and endoscopic cases, while the general orthogonal and broader formulation remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://pmihes.centre-mersenne.org/articles/10.1007/s10240-021-00129-1/",
"label": "Beuzart-Plessis, Chaudouard, and Zydor, Global Gan-Gross-Prasad for unitary groups"
},
{
"url": "https://doi.org/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Let $F$ be a global field and let $\pi=\pi_V\boxtimes\pi_{V\oplus F}$ be a multiplicity-one tempered cuspidal automorphic representation of $SO(V)\times SO(V\oplus F)$. Does the square of its global period equal the central Rankin–Selberg value divided by the adjoint value, multiplied by the normalized product of local... | 3.4. The Ichino–Ikeda conjecture. We now return to the setting of a global field F . We take a cuspidal automorphic representation \pi = \piV ⊠ \piV ⊕F of G = SO(V ) \times SO(V ⊕ F ). We assume for simplicity that it is tempered (Ichino– Ikeda state their conjecture without this assumption, but it is more complicated ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,315 | OWR-14299289-006 | Solved-Conjecture Tail for Spherical Varieties | This conjecture is known in many cases due to [3, 4], see also [1, §9] In the talk, we showed that the conjecture holds in the following three examples: (1) G = Gm and X = A1 , where Z = Gm and µ is as conjectured for ǦX = Gm and VX = T ∗ A1 . Arbeitsgemeinschaft: Relative Langlands Duality 841 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 the concluding sentence of an earlier conjecture, immediately saying that it is known in) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The extracted conjecture is explicitly described as known in many cases, and the report verifies three examples; the general relative-Langlands statement is not proved in the cited material. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi, Sakellaridis, and Venkatesh, Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | This conjecture is known in many cases due to [3, 4], see also [1, §9] In the talk, we showed that the conjecture holds in the following three examples: (1) G = Gm and X = A1 , where Z = Gm and µ is as conjectured for ǦX = Gm and VX = T ∗ A1 . Arbeitsgemeinschaft: Relative Langlands Duality 841 | unrecoverable | The official report confirms that the extraction is the concluding sentence of an earlier conjecture, immediately saying that it is known in many cases and verified in the examples that follow; it contains no standalone formulation. No separate clean statement is promoted; the original record remains publicly visible a... | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.