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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,716 | OWR-14298007-011 | Simplicial-Polytope Reconstruction Overview | What partial information about a simplicial d-polytope P allows one to determine P up to certain equivalences? Stress spaces, reconstruction problems and lower bound problems Hailun Zheng (joint work with Satoshi Murai and Isabella Novik) Geometric, Algebraic and Topological Combinatorics 3303 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this broad question to introduce known results and two precise conjectures; the surviving open case is preserved in) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-011",
"literature-status:partially-solved",
"owr-year:2023"
] | Affine-stress and skeleton data determine polytopes in important cases, including the first nontrivial stress case and several restricted classes, but the general reconstruction question remains open. | [
{
"url": "https://arxiv.org/abs/2106.09284",
"label": "Novik--Zheng, reconstruction from graphs and stresses"
},
{
"url": "https://arxiv.org/abs/2208.06693",
"label": "Novik--Zheng, affine stresses and reconstruction"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "origi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | null | What partial information about a simplicial d-polytope P allows one to determine P up to certain equivalences? Stress spaces, reconstruction problems and lower bound problems Hailun Zheng (joint work with Satoshi Murai and Isabella Novik) Geometric, Algebraic and Topological Combinatorics 3303 | unrecoverable | The official report uses this broad question to introduce known results and two precise conjectures; the surviving open case is preserved in the following record. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,717 | OWR-14298007-012 | Even-Dimensional Stress-Space Reconstruction | Let $d=2k\geq 4$, and let $P$ be a simplicial $d$-polytope in its natural embedding with no missing faces of dimension at least $d-k+1$. Prove that the space of affine $k$-stresses determines $P$ up to affine equivalence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-012",
"literature-status:partially-solved",
"owr-year:2023"
] | The cited results settle the k=1 and k=\lfloor d/2\rfloor+1 boundary cases, while the even-dimensional d=2k\geq4 case is explicitly still open. | [
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2208.06693",
"label": "Novik--Zheng, affine stresses and reconstruction"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Let $d=2k\geq 4$, and let $P$ be a simplicial $d$-polytope in its natural embedding with no missing faces of dimension at least $d-k+1$. Prove that the space of affine $k$-stresses determines $P$ up to affine equivalence. | Hence these two results are precisely the k = ⌊d/2⌋ + 1 and k = 1 cases of the following conjecture of Kalai [4]. At the moment, the d = 2k \geq 4 case remains open. Geometric, Algebraic and Topological Combinatorics 3303 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,718 | OWR-14298007-013 | Ultra-Log-Concavity from a Matrix Recursion | For $n\geq 4$, define $(T_{n+1},Q_{n+1},C_{n+1})^T=M(T_n,Q_n,C_n)^T$, where $M=\begin{pmatrix}z&1+z&1+z\\0&1+z&z\\z+z^2&0&1+z\end{pmatrix}$ and $(T_4,Q_4,C_4)^T=(z^4+2z^3,z^4,2z^4+2z^3)^T$. Writing $V_n=T_n+Q_n+C_n=\sum_kv_{n,k}z^k$, prove that $(v_{n,k})_k$ is ultra-log-concave. More generally, develop criteria for un... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-013",
"literature-status:open",
"owr-year:2023"
] | The record poses the realizability and subspace-arrangement Pluecker-vector questions without a general definition or resolution; the primary report leaves both questions open. | [
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | For $n\geq 4$, define $(T_{n+1},Q_{n+1},C_{n+1})^T=M(T_n,Q_n,C_n)^T$, where $M=\begin{pmatrix}z&1+z&1+z\\0&1+z&z\\z+z^2&0&1+z\end{pmatrix}$ and $(T_4,Q_4,C_4)^T=(z^4+2z^3,z^4,2z^4+2z^3)^T$. Writing $V_n=T_n+Q_n+C_n=\sum_kv_{n,k}z^k$, prove that $(v_{n,k})_k$ is ultra-log-concave. More generally, develop criteria for un... | What is a ‘realizable’ M-convex function? What is a ‘Pluecker vector’ of a subspace arrangement? [1] L. PROBLEM 6 (Germain Poullot). Is log-concavity arising through ma- trix recursion? The problem presented here arises when studying the monotone path polytope of the hypersimplex ∆(n, 2). After numerous pages of tediou... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,719 | OWR-14298007-014 | Realizability of M-Convex Functions | Give a natural definition of a realizable $M$-convex function and of a Plucker vector for a subspace arrangement, extending the corresponding notions for valuated matroids and $M$-convex sets. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
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"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-014",
"literature-status:open",
"owr-year:2023"
] | The all-n ultra-log-concavity assertion for the recursive sequence is presented as a conjecture and was only computationally checked through n\leq300 in the report; no general proof was identified. | [
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Give a natural definition of a realizable $M$-convex function and of a Plucker vector for a subspace arrangement, extending the corresponding notions for valuated matroids and $M$-convex sets. | Is log-concavity arising through ma- trix recursion? of realizability for M-convex functions. Still, the notion does not seem clear com- pared to the nice picture for (valuated) matroids and M-convex sets, leaving the following questions open. What is a ‘realizable’ M-convex function? What is a ‘Pluecker vector’ of a s... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,720 | OWR-14298007-015 | Tensor Products of Matroids | Study the pairs of matroids that admit a tensor product: construct further examples, describe tensor products combinatorially for particular matroid classes, and characterize obstructions by forbidden minors. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-015",
"literature-status:partially-solved",
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] | Realizable matroids and some minor-closed tensor-product classes are understood, but the requested combinatorial descriptions and forbidden-minor theory remain incomplete. | [
{
"url": "https://arxiv.org/abs/2306.14771",
"label": "Anderson, Matroid Products in Tropical Geometry"
},
{
"url": "https://arxiv.org/abs/2411.02197",
"label": "Berczi et al., Matroid Products via Submodular Coupling"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "orig... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Study the pairs of matroids that admit a tensor product: construct further examples, describe tensor products combinatorially for particular matroid classes, and characterize obstructions by forbidden minors. | Can you describe tensor products combinatorially for particular classes of matroids? Can you say something about forbidden minors for the existence of tensor products (see [1])? Geometric, Algebraic and Topological Combinatorics 3311 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,721 | OWR-14298008-001 | Multiplication of Low-Regularity Functions | An important question is whether a pair of functions with low regularity can be multiplied. 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:** [Arbeitsgemeinschaft: QFT and Stochastic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/59, pp. 3319--3370](https://doi.org/10.4171/owr/2023/59)
## Literature review (checked 2026-0... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks this expository question and immediately answers it with Young's theorem, including the exact regularity criterion.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298008-001",
"literature-status:open",
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] | The extracted sentence does not specify the regularity spaces or the product notion; standard Young, paraproduct, and renormalization theories solve restricted formulations, not this unqualified question. | [
{
"url": "https://doi.org/10.4171/owr/2023/59",
"label": "Oberwolfach Report 59/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/59 | null | null | null | null | An important question is whether a pair of functions with low regularity can be multiplied. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report asks this expository question and immediately answers it with Young's theorem, including the exact regularity criterion. | null | null | null | null | null | Arbeitsgemeinschaft: QFT and Stochastic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/59, pp. 3319--3370 |
30,005,722 | OWR-14298008-002 | Equilibration from Log-Sobolev Inequalities | How fast does it equilibrate? Log-Sobolev Inequality Henri Elad Altman, Chunqiu Song The log-Sobolev inequality dνt 1 1 dνt Entν\infty = H (νt | ν\infty ) \leq I (νt | ν\infty ) = Iν\infty dν\infty 2\gamma 2\gamma dν\infty implies that te dynamics equilibrates exponentially fast with rate \gamma: kνt − ν\infty k2TV \le... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: QFT and Stochastic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/59, pp. 3319--3370](https://doi.org/10.4171/owr/2023/59)
## Literature review (checked 2026-0... | 3 | open | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this question to introduce log-Sobolev inequalities and then gives quantitative exponential equilibration bounds; i) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298008-002",
"literature-status:open",
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] | Log-Sobolev theory gives exponential equilibration under a stated inequality, but the extracted question does not specify a model or determine the sharp rate, so it remains open as written. | [
{
"url": "https://doi.org/10.4171/owr/2023/59",
"label": "Oberwolfach Report 59/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/59 | null | null | null | null | How fast does it equilibrate? Log-Sobolev Inequality Henri Elad Altman, Chunqiu Song The log-Sobolev inequality dνt 1 1 dνt Entν\infty = H (νt | ν\infty ) \leq I (νt | ν\infty ) = Iν\infty dν\infty 2\gamma 2\gamma dν\infty implies that te dynamics equilibrates exponentially fast with rate \gamma: kνt − ν\infty k2TV \le... | unrecoverable | The official report uses this question to introduce log-Sobolev inequalities and then gives quantitative exponential equilibration bounds; it is not a standalone unresolved problem. | null | null | null | null | null | Arbeitsgemeinschaft: QFT and Stochastic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/59, pp. 3319--3370 |
30,005,723 | OWR-14298009-001 | Modular Generators for Massive Double Cones | For a massive free scalar field localized in a double cone, determine whether the modular-generator component $M_-$ is independent of the mass and whether $M_-$ is a multiplication operator. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901](https://doi.org/10.4171/owr/2023/50... | 3 | open | null | 2,023 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298009-001",
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{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4092/OWR_2023_50.pdf?isAllowed=y&sequence=4",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/50 | null | null | null | For a massive free scalar field localized in a double cone, determine whether the modular-generator component $M_-$ is independent of the mass and whether $M_-$ is a multiplication operator. | Is M− a multiplication operator? Standard Subspaces in Quantum Field Theory and Representation Theory 2863 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901 |
30,005,724 | OWR-14298009-002 | Information Loss and an Intrinsic Arrow of Time | Is the hypothesis of an intrinsic arrow of time compatible with the success- ful theoretical treatment of time as a group? Are there uncertainties in the theoretical description of the past and how do they manifest themselves? How big is the loss of information on the properties of states over time that arises from the... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901](https://doi.org/10.4171/owr/2023/50... | 3 | open | null | 2,023 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. D. Buchholz (joint with K. Fredenhagen; OWR 50/2023, pp. 2871–2872) poses three questions about an intrinsic arrow of time, modelled by a semigroup of time translations acting on the observables in a future lightcone, and answers them th... | [
"owr",
"oberwolfach-reports",
"OWR-14298009-002",
"literature-status:open",
"owr-year:2023"
] | The arrow-of-time paper develops a model relating causal asymmetry to information loss, but the broad compatibility and uncertainty questions in the record are not settled as general theorems. | [
{
"url": "https://doi.org/10.1007/s10701-023-00728-4",
"label": "Arrow of Time and Quantum Physics"
},
{
"url": "https://doi.org/10.4171/owr/2023/50",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/50 | null | null | null | null | Is the hypothesis of an intrinsic arrow of time compatible with the success- ful theoretical treatment of time as a group? Are there uncertainties in the theoretical description of the past and how do they manifest themselves? How big is the loss of information on the properties of states over time that arises from the... | unrecoverable | The official report explicitly presents proposed answers and proved propositions for these expository questions, so the extraction is not a standalone open problem. | null | null | null | null | null | Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901 |
30,005,725 | OWR-14298009-003 | Quantum Operations from Temporal Asymmetry | Does the arrow of time enforce the quantum features of operations that are described by common language (classical terms), extracted from past information? Standard Subspaces in Quantum Field Theory and Representation Theory 2873 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901](https://doi.org/10.4171/owr/2023/50... | 3 | open | null | 2,023 | 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 | Answered in the source or not an open problem (solved (yes; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; answered in the source)**. In the same abstract (p. 2872, question 4), Buchholz asks whether the arrow of time enforces the quantum features of operations described in classical terms, and answers yes: for a free classical field, the group of operations defin... | [
"owr",
"oberwolfach-reports",
"OWR-14298009-003",
"literature-status:open",
"owr-year:2023"
] | The extracted question is a broad interpretive problem about quantum operations and classical language; existing arrow-of-time models do not provide a general theorem enforcing the claimed quantum features. | [
{
"url": "https://doi.org/10.1007/s10701-023-00728-4",
"label": "Arrow of Time and Quantum Physics"
},
{
"url": "https://doi.org/10.4171/owr/2023/50",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/50 | null | null | null | null | Does the arrow of time enforce the quantum features of operations that are described by common language (classical terms), extracted from past information? Standard Subspaces in Quantum Field Theory and Representation Theory 2873 | unrecoverable | The official report poses this as an organizing question and immediately develops the claimed answer; it is not presented as an unresolved mathematical problem. | null | null | null | null | null | Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901 |
30,005,726 | OWR-14298009-005 | Channel-Divergence Discussion | After presenting some results on channel divergences, we discuss briefly some open questions of relevance to the workshop. Standard Subspaces in Quantum Field Theory and Representation Theory 2893 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901](https://doi.org/10.4171/owr/2023/50... | 3 | open | null | 2,023 | 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 only says that open questions were discussed; it does not state any question that can be reconstructed as a standalone p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298009-005",
"literature-status:open",
"owr-year:2023"
] | The record is only a transition stating that open channel-divergence questions follow; it contains no standalone question whose resolution can be verified, so it remains open under the stated rule. | [
{
"url": "https://doi.org/10.1007/s00220-023-04855-x",
"label": "Hollands--Ranallo, Channel Divergences and Complexity in Algebraic QFT"
},
{
"url": "https://doi.org/10.4171/owr/2023/50",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/50 | null | null | null | null | After presenting some results on channel divergences, we discuss briefly some open questions of relevance to the workshop. Standard Subspaces in Quantum Field Theory and Representation Theory 2893 | unrecoverable | The official report only says that open questions were discussed; it does not state any question that can be reconstructed as a standalone problem. | null | null | null | null | null | Mini-Workshop: Standard Subspaces in Quantum Field Theory and Representation Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/50, pp. 2851--2901 |
30,005,727 | OWR-14298010-003 | Extremizers of Bézout Mixed-Volume Invariants | Characterize the convex bodies $K\subset\mathbb R^n$ satisfying $b(K)=n$. Is the $n$-simplex the only minimizer of the invariant $b_2$ among convex bodies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940](https://doi.org/10.4171/owr/2023/51)
## Lite... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298010-003",
"literature-status:partially-solved",
"owr-year:2023"
] | The simplex characterization is proved for polytopes and in dimension three, while the general convex-body minimizer and b(K)=n characterization remain open. | [
{
"url": "https://doi.org/10.1016/j.jmaa.2023.127461",
"label": "Extremizers in Soprunov--Zvavitch inequalities"
},
{
"url": "https://doi.org/10.1093/imrn/rnv390",
"label": "Soprunov--Zvavitch, Bezout inequality for mixed volumes"
},
{
"url": "https://doi.org/10.4171/owr/2023/51",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/51 | null | null | null | Characterize the convex bodies $K\subset\mathbb R^n$ satisfying $b(K)=n$. Is the $n$-simplex the only minimizer of the invariant $b_2$ among convex bodies? | the characterization of all K such that b2 (K) = 2 is known, that of all K such that b(K) = n remains open. Though this conjecture remains open, we will discuss recent progress on restricting the set of potential minimizers; namely we will present a necessary condition on the support of the surface area measure of K. T... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940 |
30,005,728 | OWR-14298010-004 | Hodge–Riemann Relations for Convex Valuations | Do the hard Lefschetz theorem and the Hodge–Riemann bilinear relations hold in the algebra $\operatorname{Val}^\infty$ with respect to every element of the cone $\mathcal K=\{V(C,\mathbin{\bullet}[n-1]):C\in\mathcal K_+^\infty\}$ of valuations associated with smooth strictly convex bodies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940](https://doi.org/10.4171/owr/2023/51)
## Lite... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298010-004",
"literature-status:partially-solved",
"owr-year:2023"
] | The valuation hard-Lefschetz and Hodge--Riemann conjecture is proved for the one-dimensional Euclidean-ball cone, but the full cone of smooth convex bodies is not resolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/51",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/51 | null | null | null | Do the hard Lefschetz theorem and the Hodge–Riemann bilinear relations hold in the algebra $\operatorname{Val}^\infty$ with respect to every element of the cone $\mathcal K=\{V(C,\mathbin{\bullet}[n-1]):C\in\mathcal K_+^\infty\}$ of valuations associated with smooth strictly convex bodies? | The conjecture is now known to hold for the one-dimensional cone \infty \{V (D, •[n − 1]) | D \in K+ is a Euclidean ball\}. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940 |
30,005,729 | OWR-14298010-005 | Positive Weighted $h^*$-Polynomials beyond Product Weights | For a lattice polytope $P$, characterize homogeneous polynomial weights beyond $R_P$, particularly weights in $S_P$, for which the weighted $h^*$-polynomial has nonnegative coefficients and is coefficientwise monotone under inclusions $P\subseteq Q$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940](https://doi.org/10.4171/owr/2023/51)
## Lite... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298010-005",
"literature-status:open",
"owr-year:2023"
] | The 2024 paper proves nonnegativity and monotonicity for the stated classes of weights, but the extracted record omits a complete characterization; the broader question therefore remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.109627",
"label": "Weighted Ehrhart theory, Advances in Mathematics 2024"
},
{
"url": "https://doi.org/10.4171/owr/2023/51",
"label": "Oberwolfach Report 51/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/51 | null | null | null | For a lattice polytope $P$, characterize homogeneous polynomial weights beyond $R_P$, particularly weights in $S_P$, for which the weighted $h^*$-polynomial has nonnegative coefficients and is coefficientwise monotone under inclusions $P\subseteq Q$. | A natural question to ask is for which classes of polynomial functions w the weighted h∗ -polynomial h∗P,w (t) satisfies nonnegativity and monotonicity of its coefficients. We consider two families of weights: sums of products of linear forms that are nonnegative on P , denoted RP , and nonnegative sums of products of ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/51, pp. 2903--2940 |
30,005,730 | OWR-14298011-001 | Multidimensional Null Controllability for Bilinear Evolution Equations | For bilinear evolution equations $\dot u+Au+p(t)Bu=0$, prove $j$-null controllability in two and three dimensions without the moment method. Establish controllability for the Fokker–Planck equation with perfectly reflecting boundary conditions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298011-001",
"literature-status:open",
"owr-year:2023"
] | The report leaves j-null controllability under other two- and three-dimensional boundary strategies open. Later work proves special one-dimensional degenerate cases, not the extracted general question. | [
{
"url": "https://doi.org/10.1007/s00245-025-10236-8",
"label": "Boundary controllability for degenerate or singular hyperbolic equations, 2025"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | For bilinear evolution equations $\dot u+Au+p(t)Bu=0$, prove $j$-null controllability in two and three dimensions without the moment method. Establish controllability for the Fokker–Planck equation with perfectly reflecting boundary conditions. | Some perspectives and open question Whenever the moment method is used, it reduces the scope to 1D or radial results. This raises the question of proving j−null controllability, by other strategies for 2D and 3D controllability results such that the ones relying on (3). It is an open question to treat such boundary con... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,731 | OWR-14298011-002 | Automatic Convexity of Optimal Spiral Strategies | Must every optimal spiral-like fire-containment strategy be locally convex and satisfy the initial-angle condition (A1)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298011-002",
"literature-status:open",
"owr-year:2023"
] | A 2025 preprint proves a sharp threshold and constructs an optimal spiral-like barrier, but it does not explicitly prove the extracted automatic local-convexity and A1 implication; that exact claim remains unresolved. | [
{
"url": "https://arxiv.org/abs/2508.05324",
"label": "Bianchini and Zizza, Existence of spiral strategies for blocking fire spreading"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | Must every optimal spiral-like fire-containment strategy be locally convex and satisfy the initial-angle condition (A1)? | We believe instead that the hypothesis of local convexity and the assumption (A1) are automatically satisfied by optimal spiral-like strategies, which is an open question. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,732 | OWR-14298011-003 | Well-Defined Trajectories in Controlled Set Motions | For an optimal planar set motion $t\mapsto\Omega(t)$ minimizing terminal area under a bounded boundary-control effort, what regularity do the sets $\Omega(t)$ have, and can trajectories orthogonal to $\partial\Omega(t)$ always be defined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298011-003",
"literature-status:open",
"owr-year:2023"
] | The report identifies well-definedness of the relevant trajectories as open, and the later spiral-barrier literature does not establish well-definedness for the general trajectories in the extract. | [
{
"url": "https://arxiv.org/abs/2508.05324",
"label": "Bianchini and Zizza, Existence of spiral strategies for blocking fire spreading"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | For an optimal planar set motion $t\mapsto\Omega(t)$ minimizing terminal area under a bounded boundary-control effort, what regularity do the sets $\Omega(t)$ have, and can trajectories orthogonal to $\partial\Omega(t)$ always be defined? | At the present time, several related questions remain open. Can these trajectories be always well defined? Possible choices for the function \phi in (1) are: ( s2 0 if s \leq M, \phi(s) = or \phi(s) = (4) 2 +\infty if s > M. Notice that, if the second definition applies, then the first term in (1) has the meaning of a ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,733 | OWR-14298011-004 | Optimal Set Motions from Nonconvex Initial Regions | For the optimal set-motion problem, characterize optimal strategies when the initial set $\Omega_0$ is nonconvex and determine when all $\Omega(t)$ remain connected. Which planar results extend to $\mathbb R^n$ or Riemannian manifolds, and in particular do optimal set motions remain convex in $\mathbb R^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298011-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Recent work establishes existence and optimality results for constrained motions, including three-dimensional finite-perimeter settings, but the extracted nonconvex connectivity and general manifold or Rn convexity questions are not fully settled. | [
{
"url": "https://doi.org/10.1007/s00032-025-00419-x",
"label": "Optimally Controlled Moving Sets with Geographical Constraints, 2025"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | For the optimal set-motion problem, characterize optimal strategies when the initial set $\Omega_0$ is nonconvex and determine when all $\Omega(t)$ remain connected. Which planar results extend to $\mathbb R^n$ or Riemannian manifolds, and in particular do optimal set motions remain convex in $\mathbb R^3$? | (Q2) If the initial set Ω0 is not convex, what can one say about the optimal strategy? Under what conditions is it true that the sets Ω(t) are connected, for all t \in [0, T ] ? (Q3) More generally, all the above problems can be formulated on Rn , or even on an n-dimensional Riemann manifold. How much of the theory rem... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,734 | OWR-14298011-005 | Occupational Measures for Tonelli Hamilton–Jacobi Equations | Extend the theory relating critical sets, singular sets, and limiting occupational measures from $\frac12|Du+c|^2+V(x)=\alpha[c]$ on $\mathbb T^d$ to general Tonelli Hamilton–Jacobi equations $H(x,Du+c)=\alpha[c]$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298011-005",
"literature-status:open",
"owr-year:2023"
] | The report identifies the problem as requiring new ideas for general Tonelli Hamilton--Jacobi equations; existing generalized-characteristic and Lax--Oleinik results cover narrower settings. | [
{
"url": "https://doi.org/10.1007/s00526-017-1219-4",
"label": "Cannarsa and Cheng, Generalized characteristics and Lax--Oleinik operators"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | Extend the theory relating critical sets, singular sets, and limiting occupational measures from $\frac12|Du+c|^2+V(x)=\alpha[c]$ on $\mathbb T^d$ to general Tonelli Hamilton–Jacobi equations $H(x,Du+c)=\alpha[c]$. | is a challenging open question that will definitely require new ides. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,735 | OWR-14298011-006 | Bounded-Variation Solutions for Continuum Traffic Models | Does the hysteretic traffic-flow model admit a canonical Riemann solver and solutions of the initial-value problem for general bounded-variation data, at least for sufficiently small initial data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298011-006",
"literature-status:open",
"owr-year:2023"
] | The 2024 HARZ paper solves the Riemann problem under monotonicity, but the general bounded-variation initial-value problem conjectured in the extract is not proved. | [
{
"url": "https://doi.org/10.1111/sapm.12769",
"label": "Corli and Fan, The hysteretic Aw--Rascle--Zhang model"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | Does the hysteretic traffic-flow model admit a canonical Riemann solver and solutions of the initial-value problem for general bounded-variation data, at least for sufficiently small initial data? | We propose a suitable notion of string stability for continuum models and show that the LWR and AWR models model are string stable for wide classes of perturbations. In this framework there are many open problems. Second, the analysis of the initial-value problem for general data with bounded variation is missing; we c... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,736 | OWR-14298011-007 | Time-Varying Traffic Control and Lyapunov Learning | For the coupled traffic PDE–ODE system with an automated-vehicle control, prove existence for time-varying controls and solve the stabilization problem. Develop reliable neural methods for constructing Lyapunov functions for nonlinear systems. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011](https://doi.org/10.4171/owr/2023/52)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
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"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298011-007",
"literature-status:partially-solved",
"owr-year:2023"
] | A WIAS preprint constructs neural networks with global linear error for the drift under the additional restriction M<\sqrt{2}m; this is partial progress and does not prove the claim for all strongly convex Lipschitz potentials. | [
{
"url": "https://www.wias-berlin.de/preprint/3077/wias_preprints_3077.pdf",
"label": "Eigel, Miranda, Schuette, and Sommer, WIAS Preprint 3077"
},
{
"url": "https://doi.org/10.4171/owr/2023/52",
"label": "Oberwolfach Report 52/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/52 | null | null | null | For the coupled traffic PDE–ODE system with an automated-vehicle control, prove existence for time-varying controls and solve the stabilization problem. Develop reliable neural methods for constructing Lyapunov functions for nonlinear systems. | We illustrate with two examples how this approach can assist mathematicians in solving open problems. The first one is a preliminary neural network trained to find Lyapunov functions for a nonlinear system, which is a general open question. where \alpha \in (0, 1). We present an existence result (in the class of BV sol... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Control Methods in Hyperbolic PDEs (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/52, pp. 2941--3011 |
30,005,737 | OWR-14298013-001 | Post-Lie Structures with Semisimple Target | Let $\mathfrak g$ be a perfect nonsemisimple complex Lie algebra and let $\mathfrak n$ be semisimple. Prove that there is no post-Lie algebra structure on $(\mathfrak g,\mathfrak n)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298013-001",
"literature-status:open",
"owr-year:2023"
] | The report states that only the sl3 case is proved and explicitly presents the extension to an arbitrary semisimple Lie algebra as a conjecture; no later proof resolving it was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | Let $\mathfrak g$ be a perfect nonsemisimple complex Lie algebra and let $\mathfrak n$ be semisimple. Prove that there is no post-Lie algebra structure on $(\mathfrak g,\mathfrak n)$. | A further question is about the case where g is perfect and n is simple or semisim- ple. We conjecture that the same conclusion holds for any semisimple Lie algebra n, and not only for sl3 (C). Mini-Workshop: Poisson and Poisson-type algebras 2689 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,738 | OWR-14298013-002 | Jordan Brackets and Simple Transposed Poisson Algebras | Characterize the Jordan brackets that arise from transposed Poisson algebras and determine whether their associated Jordan algebras are special. Also determine whether a finite-dimensional simple transposed Poisson algebra can have both multiplications simple. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | partially_solved | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **partially_solved**, or **split the record**. It merges two questions of A. Fernández Ouaridi (OWR 46/2023, p. 2696) on transposed Poisson algebras (TPAs): (a) which Jordan brackets come from TPAs, and are their Kantor doubles special? (b) is there a finite-dimensional sim... | [
"owr",
"oberwolfach-reports",
"OWR-14298013-002",
"literature-status:open",
"owr-year:2023"
] | Known results rule out complex simple finite-dimensional TPAs in relevant cases and give formal-series examples, but the finite-dimensional example with both multiplications simple remains posed as an open question. | [
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | Characterize the Jordan brackets that arise from transposed Poisson algebras and determine whether their associated Jordan algebras are special. Also determine whether a finite-dimensional simple transposed Poisson algebra can have both multiplications simple. | This motivates the following open question. Are these Jordan algebras special? Is there any finite-dimensional simple TPA with both multiplications being simple? Mini-Workshop: Poisson and Poisson-type algebras 2697 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,739 | OWR-14298013-003 | Algebraic Structures for Transposed Bi-Hamiltonian Systems | Develop the theory of transposed bi-Hamiltonian algebras. More generally, identify the algebraic structures obtained by replacing the Poisson bracket with compatible Lie brackets in Poisson and transposed Poisson algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298013-003",
"literature-status:open",
"owr-year:2023"
] | The report presents these as natural research questions; the cited compatible-bracket literature does not supply a general theory of the transpose bi-Hamiltonian and transposed Poisson constructions. | [
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | Develop the theory of transposed bi-Hamiltonian algebras. More generally, identify the algebraic structures obtained by replacing the Poisson bracket with compatible Lie brackets in Poisson and transposed Poisson algebras. | Back to the Poisson algebra origin of this study, natural questions arise, such as (1) Study the transpose bi-Hamiltonian algebra? (2) What should be the algebraic structure when the Poisson bracket in a Poisson algebra is replaced by any of the compatible Lie algebras, with the bi-Hamiltonian system or a bi-Hamiltonia... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,740 | OWR-14298013-004 | BV Structures with Nonsemisimple Nakayama Automorphisms | Let $A_h$ be a twisted Calabi-Yau algebra whose Nakayama automorphism is not semisimple. Determine whether $HH^\bullet(A_h)$ admits a Batalin-Vilkovisky structure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298013-004",
"literature-status:open",
"owr-year:2023"
] | BV structures are established for twisted Calabi--Yau or Frobenius algebras with semisimple Nakayama automorphism; the nonsemisimple Ah case in the extract remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | Let $A_h$ be a twisted Calabi-Yau algebra whose Nakayama automorphism is not semisimple. Determine whether $HH^\bullet(A_h)$ admits a Batalin-Vilkovisky structure. | Are there BV structures in HH• (Ah ) when the Nakayama automorphism of Ah is not semisimple? The Hochschild cohomology HH• (A) of an associative algebra A encodes many non- trivial properties and features of the algebra, including crucial information about its deformations. In [2], Gerstenhaber constructed two operatio... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,741 | OWR-14298013-005 | Poisson Nilpotency and Solvability in Small Characteristics | Let $L$ be a Lie algebra over a field of characteristic $p>0$. If $s(L)$ is Lie nilpotent, do its Lie nilpotency class and strong Lie nilpotency class coincide for $p=2$ or $3$? If $p>2$ and $s(L)$ is solvable, do its derived length and strong derived length coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298013-005",
"literature-status:open",
"owr-year:2023"
] | The 2017 theorem gives equality of Lie and strong Lie nilpotence classes only for p\geq5, and the 2023 report explicitly leaves p=2,3 as Problem 1. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2017.05.035",
"label": "Monteiro Alves and Petrogradsky, Lie structure of truncated symmetric Poisson algebras"
},
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | Let $L$ be a Lie algebra over a field of characteristic $p>0$. If $s(L)$ is Lie nilpotent, do its Lie nilpotency class and strong Lie nilpotency class coincide for $p=2$ or $3$? If $p>2$ and $s(L)$ is solvable, do its derived length and strong derived length coincide? | Some open questions on these topics are the following: Problem 1. Is this true also in characteristics p = 2, 3? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,742 | OWR-14298013-006 | Poisson Ideals of the Virasoro Algebra | Can we parame- terise them in a reasonable fashion, ideally in a way which gives us further information about the ideal? How does one distinguish Poisson primitive ideals from other prime Poisson ideals? • It is known, see [4, Corollary 5.1], that S(Vir) satisfies the ascending chain condition on prime Poisson ideals. ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715](https://doi.org/10.4171/owr/2023/46)
## Literature review (checked 20... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report lists these questions as motivation and then states that the authors answer all of them; the extraction is not an unreso) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298013-006",
"literature-status:open",
"owr-year:2023"
] | The report poses parametrization and classification of Poisson primitive ideals as open questions; the cited ascending-chain result for the Virasoro symmetric algebra does not settle the general problem. | [
{
"url": "https://doi.org/10.4171/owr/2023/46",
"label": "Oberwolfach Report 46/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/46 | null | null | null | null | Can we parame- terise them in a reasonable fashion, ideally in a way which gives us further information about the ideal? How does one distinguish Poisson primitive ideals from other prime Poisson ideals? • It is known, see [4, Corollary 5.1], that S(Vir) satisfies the ascending chain condition on prime Poisson ideals. ... | unrecoverable | The official report lists these questions as motivation and then states that the authors answer all of them; the extraction is not an unresolved problem. | null | null | null | null | null | Mini-Workshop: Poisson and Poisson-type algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/46, pp. 2681--2715 |
30,005,743 | OWR-14298014-001 | Reduced-Density-Matrix and RPA Discussion Fragment | Potential links between the P-Q-G-T1-T2 conditions and the random phase approximation were suggested, leading to interesting open problems to be investigated in the upcoming years. Two key open problems were identified. Mini-Workshop: Mathematics of Many-body Fermionic Systems 2811 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849](https://doi.org/10.4171/owr/2023/49)
## Literature review (c... | 3 | open | null | 2,023 | 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 mentions possible links between reduced-density-matrix conditions and random-phase approximation as a broad research dir) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298014-001",
"literature-status:open",
"owr-year:2023"
] | The report records links between the P-Q-G-T1-T2 conditions and the random phase approximation as prospective open problems; the current RDM and RPA literature does not provide the requested general connection. | [
{
"url": "https://doi.org/10.4171/owr/2023/49",
"label": "Oberwolfach Report 49/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/49 | null | null | null | null | Potential links between the P-Q-G-T1-T2 conditions and the random phase approximation were suggested, leading to interesting open problems to be investigated in the upcoming years. Two key open problems were identified. Mini-Workshop: Mathematics of Many-body Fermionic Systems 2811 | unrecoverable | The official report mentions possible links between reduced-density-matrix conditions and random-phase approximation as a broad research direction but gives no definite mathematical question in this record. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849 |
30,005,744 | OWR-14298014-003 | Local Density Approximation for the Canonical Functional | Can the local-density approximation be rigorously justified for the canonical density functional $F(\rho)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849](https://doi.org/10.4171/owr/2023/49)
## Literature review (c... | 3 | open | null | 2,023 | 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-14298014-003",
"literature-status:open",
"owr-year:2023"
] | The report still calls canonical LDA justification open; existing rigorous LDA results address different or more restricted functionals and do not settle the canonical F(rho) claim. | [
{
"url": "https://doi.org/10.4171/owr/2023/49",
"label": "Oberwolfach Report 49/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/49 | null | null | null | Can the local-density approximation be rigorously justified for the canonical density functional $F(\rho)$? | It is an open problem to justify the LDA for the canonical functional F (ρ). The most famous is the Local Density Approximation (LDA), where it is as- sumed that ρ is locally flat and the local energy is taken to be that of an infinite gas of constant density, per unit volume: ZZ Z 1 ρ(x)ρ(y) F (ρ) \approx FLDA (ρ) := ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849 |
30,005,745 | OWR-14298014-004 | Higher-Dimensional Semiclassical Kinetic-Energy Corrections | In dimensions $d\geq2$, can one justify the predicted next-order semiclassical correction to the kinetic energy, proportional to $\int_{\mathbb{R}^d}|\nabla\sqrt{\rho(x)}|^2\,dx$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849](https://doi.org/10.4171/owr/2023/49)
## Literature review (c... | 3 | open | null | 2,023 | 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-14298014-004",
"literature-status:open",
"owr-year:2023"
] | Semi-classical estimates approach the conjectured kinetic-energy bound, but the report states that the inequality and its next-order correction remain open for d\geq2. | [
{
"url": "https://doi.org/10.4171/owr/2023/49",
"label": "Oberwolfach Report 49/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/49 | null | null | null | In dimensions $d\geq2$, can one justify the predicted next-order semiclassical correction to the kinetic energy, proportional to $\int_{\mathbb{R}^d}|\nabla\sqrt{\rho(x)}|^2\,dx$? | 2 \sqrt{ } (5) T (ρ) \leq cTF ρ(x)1+ d dx + C |∇ ρ(x)|2 dx, Rd Rd This conjecture is still open in dimension d \geq 2, but recent works came arbitrarily close to the result in the following sense. Rd An interesting open problem is to justify the next order, which is predicted to be Z d − 2 −d+2 \sqrt{ } \textasciitilde... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849 |
30,005,746 | OWR-14298014-006 | Fermionic Character of Low-Lying Excitations | Do the low-lying excitations of a weakly interacting fermionic system have the character of fermionic quasiparticles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849](https://doi.org/10.4171/owr/2023/49)
## Literature review (c... | 3 | open | null | 2,023 | 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-14298014-006",
"literature-status:open",
"owr-year:2023"
] | Rigorous work derives ground-state and correlation-energy asymptotics in weak regimes, but no first-principles theorem establishes the general low-lying fermionic-quasiparticle characterization stated in the extract. | [
{
"url": "https://doi.org/10.1007/s00222-021-01041-5",
"label": "Correlation Energy of a Weakly Interacting Fermi Gas"
},
{
"url": "https://doi.org/10.4171/owr/2023/49",
"label": "Oberwolfach Report 49/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/49 | null | null | null | Do the low-lying excitations of a weakly interacting fermionic system have the character of fermionic quasiparticles? | It is a fundamental question whether the low-lying excitations of the weakly in- teracting system, i.e. the states energetically just above the ground state, have the character of fermionic quasiparticles, which very loosely speaking means that the states in Hilbert space correspond to wave packets with a small damping... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Mathematics of Many-body Fermionic Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/49, pp. 2809--2849 |
30,005,747 | OWR-14298015-001 | Neural Approximation of Strongly Convex Drifts with Linear Error | If $V$ is strongly convex with Lipschitz gradient, does there exist a neural network approximating $-\nabla V$ with error growing only linearly? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nonlinear Approximation of High-dimensional Functions in Scientific Computing (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/48, pp. 2771--2808](https://doi.org/10.4171/ow... | 3 | partially_solved | null | 2,023 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298015-001",
"literature-status:partially-solved",
"owr-year:2023"
] | A WIAS preprint constructs neural networks with global linear error under the additional restriction M<\sqrt{2}m; this is partial progress and does not prove the claim for all strongly convex Lipschitz potentials. | [
{
"url": "https://www.wias-berlin.de/preprint/3077/wias_preprints_3077.pdf",
"label": "Eigel, Miranda, Schuette, and Sommer, WIAS Preprint 3077"
},
{
"url": "https://doi.org/10.4171/owr/2023/48",
"label": "Oberwolfach Report 48/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/48 | null | null | null | If $V$ is strongly convex with Lipschitz gradient, does there exist a neural network approximating $-\nabla V$ with error growing only linearly? | We conjecture that due to the strong convexity of V and the Lipschitz continuity of ∇V , there exists a neural network capable of approximating −∇V with a linear error growth. Euler-Maruyama discretisation of the stochastic differential equation \sqrt{ } dXt = −∇V (Xt )dt + 2dWt through ResNet-like neural network struc... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Nonlinear Approximation of High-dimensional Functions in Scientific Computing (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/48, pp. 2771--2808 |
30,005,748 | OWR-14298016-003 | Jump Property of Implication Proof Systems | For an implicit propositional proof system $P$, is the system $\operatorname{imp}(P)=[P,P]$ a jump in proof strength? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061](https://doi.org/10.4171/owr/2023/53)
## Literature review (... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298016-003",
"literature-status:open",
"owr-year:2023"
] | The report states imp(P)=[P,P] as a conjecture. A 2026 study still describes jump existence for TAUT as an open problem, so no resolution of the extracted conjecture is available. | [
{
"url": "https://doi.org/10.4230/LIPIcs.ICALP.2026.88",
"label": "Egidy, Recursive Jump Operators and Optimal Proof Systems"
},
{
"url": "https://doi.org/10.4171/owr/2023/53",
"label": "Oberwolfach Report 53/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/53 | null | null | null | For an implicit propositional proof system $P$, is the system $\operatorname{imp}(P)=[P,P]$ a jump in proof strength? | We conjecture that imp(P ) := [P, P ] is a jump. Consistency, implicit proofs, and cut-elimination Pavel Pudlák Mathematical Logic: Proof Theory, Constructive Mathematics 3023 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061 |
30,005,749 | OWR-14298016-004 | Abstract Formalization of Proof-Theoretic Arguments | A much broader open question is how to formalise the underlying proofs in a suitable abstract system. New applications of proof theory: Greedy algorithms, probability, and proof assistants Thomas Powell. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061](https://doi.org/10.4171/owr/2023/53)
## Literature review (... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298016-004",
"literature-status:open",
"owr-year:2023"
] | The workshop report explicitly presents this as a broad open question, and no later primary formalisation resolving it was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/53",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/53 | null | null | null | A much broader open question is how to formalise the underlying proofs in a suitable abstract system. New applications of proof theory: Greedy algorithms, probability, and proof assistants Thomas Powell. | A much broader open question is how to formalise the underlying proofs in a suitable abstract system. New applications of proof theory: Greedy algorithms, probability, and proof assistants Thomas Powell | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061 |
30,005,750 | OWR-14298016-006 | Supremum Computation for Weakly Continuous Functions | For functions satisfying any of the weak continuity notions occurring in decompositions of ordinary continuity, how difficult is it to compute the supremum on a compact interval? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061](https://doi.org/10.4171/owr/2023/53)
## Literature review (... | 3 | partially_solved | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298016-006",
"literature-status:partially-solved",
"owr-year:2023"
] | A primary reverse-mathematics paper classifies supremum principles for many weak-continuity notions, but the broader taxonomy question in the excerpt is not exhausted. | [
{
"url": "https://doi.org/10.4171/owr/2023/53",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2405.06420",
"label": "weak-continuity paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/53 | null | null | null | For functions satisfying any of the weak continuity notions occurring in decompositions of ordinary continuity, how difficult is it to compute the supremum on a compact interval? | Now, there are dozens (hundreds?) of decompositions of continuity, where continuity is shown to be equivalent to the combination of two or more weak continuity3 notions, going back to Baire, as follows: continuity \leftrightarrow weak continuity notion A plus weak continuity notion B. (D) It is then a natural question ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061 |
30,005,751 | OWR-14298016-007 | Finite Axiomatizability of TEIP over Open Induction | Is the first-order theory TEIP of exponential integer parts of real-closed exponential fields finitely axiomatizable over open induction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061](https://doi.org/10.4171/owr/2023/53)
## Literature review (... | 3 | partially_solved | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298016-007",
"literature-status:partially-solved",
"owr-year:2023"
] | The 2026 primary paper still states finite axiomatizability over IOpen as open, while proving a strict hierarchy and related partial results. | [
{
"url": "https://users.math.cas.cz/~jerabek/papers/teip.pdf",
"label": "current TEIP paper"
},
{
"url": "https://doi.org/10.4171/owr/2023/53",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/53 | null | null | null | Is the first-order theory TEIP of exponential integer parts of real-closed exponential fields finitely axiomatizable over open induction? | Is TEIP finitely axiomatizable over IOpen? where \thetan1 (u0 ) denotes ^ ^ \forallx1 \existsu1 . . . \forallxn−1 \existsun−1 (xi > 0 \to ui \leq xi < 2ui ) ∧ ¬(ui uj < uk < 2ui uj ) . 1\leqi<n i,j,k<n | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Logic: Proof Theory, Constructive Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/53, pp. 3013--3061 |
30,005,752 | OWR-14298157-001 | Positivity Criterion for Quantum Greedy Bases | For the quantum greedy basis, is positivity preserved whenever $\delta_1\mid\delta_2$ or $\delta_2\mid\delta_1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136](https://doi.org/10.4171/owr/2024/2)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,024 | 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-14298157-001",
"literature-status:partially-solved",
"owr-year:2024"
] | The quantum greedy basis exists and positivity fails in general; positive cases are known, but the stated divisibility criterion remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2024/2",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.03.022",
"label": "quantum greedy-basis paper"
},
{
"url": "https://arxiv.org/abs/2202.01588",
"label": "quantum scattering-diagram paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/2 | null | null | null | For the quantum greedy basis, is positivity preserved whenever $\delta_1\mid\delta_2$ or $\delta_2\mid\delta_1$? | Conjecture ([3]). The positive is preserved if \delta1 |\delta2 or \delta2 |\delta1 . In this talk we explain how the same condition naturally emerges in view of the pentagon relation in the cluster scattering diagram method [1]. Here, we describe the quantum case. (The classical case is obtained in the limit q \to 1.)... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136 |
30,005,753 | OWR-14298157-002 | Belavin–Drinfeld Cluster Correspondence | Do Poisson–Lie and Poisson-homogeneous structures arising from Belavin–Drinfeld quasitriangular solutions of the classical Yang–Baxter equation admit compatible cluster structures? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136](https://doi.org/10.4171/owr/2024/2)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,024 | 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-14298157-002",
"literature-status:partially-solved",
"owr-year:2024"
] | The Belavin--Drinfeld cluster correspondence has been established for substantial families, but current primary literature still describes the general program as incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2024/2",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2308.16701",
"label": "unified exotic-structure paper"
},
{
"url": "https://arxiv.org/abs/2603.12486",
"label": "generalized GLn paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/2 | null | null | null | Do Poisson–Lie and Poisson-homogeneous structures arising from Belavin–Drinfeld quasitriangular solutions of the classical Yang–Baxter equation admit compatible cluster structures? | Although the answer to this question is negative in general - an example to that effect was constructed in [9] in the case of SL2 - we conjectured that the answer is affirmative in the case of Poisson-Lie structures corresponding to quasi-triangular solutions of the classical Yang–Baxter equation classified by Belavin ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136 |
30,005,754 | OWR-14298157-003 | Dual Canonical Basis Analogues for General Cluster Algebras | What are analogues of the dual canonical basis $B^*$ for other cluster algebras $k[A]$, and can the Fomin–Zelevinsky conjecture be generalized when $A$ is not contained in $N$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136](https://doi.org/10.4171/owr/2024/2)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,024 | 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-14298157-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Qin constructs dual-canonical or triangular analogs in broad Lie-theoretic families, but analogs for arbitrary cluster algebras remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/2",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2407.02480",
"label": "Lie-theoretic analogs paper"
},
{
"url": "https://arxiv.org/abs/2003.13674",
"label": "quantum-cluster basis paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/2 | null | null | null | What are analogues of the dual canonical basis $B^*$ for other cluster algebras $k[A]$, and can the Fomin–Zelevinsky conjecture be generalized when $A$ is not contained in $N$? | What are analogs of B∗ for other cluster algebras k[A]? Can we generalize FZ-conjecture to general A, which are not contained in N ? Analogs of dual canonical bases for cluster algebras from Lie theory Fan Qin | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136 |
30,005,755 | OWR-14298157-005 | Canonical Decomposition Cones and TF Equivalence | For every finite-dimensional algebra $A$ and $\theta\in K_0(\operatorname{proj}A)$, is the TF-equivalence class $[\theta]_{\mathrm{TF}}$ equal to the relative interior of the cone generated by $\operatorname{ind}(\mathbb{N}\theta)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136](https://doi.org/10.4171/owr/2024/2)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,024 | 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-14298157-005",
"literature-status:partially-solved",
"owr-year:2024"
] | The conjectured equality is proved for hereditary and E-tame algebras, while the general finite-dimensional-algebra case remains unresolved. | [
{
"url": "https://doi.org/10.1112/plms.12639",
"label": "published primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2024/2",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/2 | null | null | null | For every finite-dimensional algebra $A$ and $\theta\in K_0(\operatorname{proj}A)$, is the TF-equivalence class $[\theta]_{\mathrm{TF}}$ equal to the relative interior of the cone generated by $\operatorname{ind}(\mathbb{N}\theta)$? | Our first main result shows that all elements in the cone given by a canonical decomposition are TF equivalent. Theorem 1. Let A be a finite dimensional algebra over an algebraically closed field k. For each \theta \in K0 (projA), we have [\theta]TF ⊇ cone◦ (ind \theta). Notice that cone(ind ℕ\theta) ⊇ cone(ind \theta)... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Cluster Algebras and Its Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/2, pp. 69--136 |
30,005,756 | OWR-14298158-001 | Permutation-Patterns Table-of-Contents Fragment | 282 Justin Troyka (reporter) Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mini-Workshop: Permutation Patterns Table of Contents | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"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": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Unrecoverable OWR statement (The official report confirms that this record is a table-of-contents and heading fragment rather than a mathematical question. No separate c) | [] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-001",
"literature-status:open",
"owr-year:2024"
] | Table-of-contents entry, not an open problem.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, s... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | null | 282 Justin Troyka (reporter) Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mini-Workshop: Permutation Patterns Table of Contents | unrecoverable | The official report confirms that this record is a table-of-contents and heading fragment rather than a mathematical question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,757 | OWR-14298158-002 | Rationality of Separable Permutation Subclasses | If a subclass of the separable permutations contains all of $\operatorname{Av}(231)$ or one of its symmetries, must its generating function be nonrational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14298158-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-002",
"literature-status:partially-solved",
"owr-year:2024"
] | The exact rationality question remains unresolved; the known theorem proves the opposite implication, while the nearby strong-algebraicity conjecture is a separate disproved claim. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1007.1014",
"label": "separable-subclass theorem"
},
{
"url": "https://arxiv.org/abs/2211.12397",
"label": "wqo counterexample paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | If a subclass of the separable permutations contains all of $\operatorname{Av}(231)$ or one of its symmetries, must its generating function be nonrational? | Question 4. If a subclass of the separable permutations does contain all of Av(231) or one of its symmetries, must it have a nonrational generating function? By an elementary counting argument, such classes cannot contain infinite an- tichains, and thus they are well-quasi-ordered (wqo). Indeed, if a permutation class ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,758 | OWR-14298158-003 | Algebraicity of Labelled Well-Quasi-Ordered Permutation Classes | Does every labelled well-quasi-ordered permutation class have an algebraic generating function? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-003",
"literature-status:open",
"owr-year:2024"
] | The primary literature explicitly leaves algebraicity for labelled well-quasi-ordered classes as a future question; later counterexamples for ordinary wqo do not settle the stronger labelled case. | [
{
"url": "https://arxiv.org/abs/2211.12397",
"label": "primary wqo-enumeration paper"
},
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Does every labelled well-quasi-ordered permutation class have an algebraic generating function? | It is possible that one direction of False Conjecture 1 could be rescued by strengthening the hypotheses to require labelled well-quasi-ordering; see Brignall and Vatter [7], where the following question is stated. Does every labelled well-quasi-ordered permutation class have an algebraic generating function? The repor... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,759 | OWR-14298158-004 | Inversion Monotonicity for 1324-Avoiding Permutations | Let $\operatorname{Av}_{n,k}(\tau)$ denote length-n permutations avoiding $\tau$ with exactly k inversions. For every n and k, is $|\operatorname{Av}_{n,k}(1324)|\le |\operatorname{Av}_{n+1,k}(1324)|$? Does the analogous inequality hold for $\operatorname{Av}_{n,k}(1324,231)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 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"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-004",
"literature-status:partially-solved",
"owr-year:2024"
] | Claesson’s conjecture fixes the inversion count k and increases the permutation length n. The previous transcription instead increased k at fixed n, which is already false at n=2. The analogous two-pattern question is corrected in the same way.
**What remains.** The monotonicity questions with n increasing retain thei... | [
{
"url": "https://doi.org/10.1016/j.jcta.2012.05.006",
"label": "Claesson–Jelínek–Steingrímsson, Upper bounds for the Stanley–Wilf limit of 1324 (2012)"
},
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/20... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Let $\operatorname{Av}_{n,k}(\tau)$ denote length-n permutations avoiding $\tau$ with exactly k inversions. For every n and k, is $|\operatorname{Av}_{n,k}(1324)|\le |\operatorname{Av}_{n+1,k}(1324)|$? Does the analogous inequality hold for $\operatorname{Av}_{n,k}(1324,231)$? | 1. Anders Claesson Growth rate of Av(1324). The current bounds are 10.27 \leq gr(Av(1324)) \leq 13.5. Consider Avkn (1324), the set of permutations of size n with k inversions. Conjecture: |Avkn (1324)| \leq |Avkn+1 (1324)|. \sqrt{ } If true, we would have gr(Av(1324)) \leq e\pi 2/3 \approx 13.002 (2012). Another conje... | 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: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,760 | OWR-14298158-005 | Inversion Monotonicity in the Domino Subclass | Can the inversion-monotonicity conjecture for $1324$-avoiding permutations be proved on the domino subclass $[\operatorname{Av}(132)\mid\operatorname{Av}(231)]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "combinatorics",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-005",
"literature-status:partially-solved",
"owr-year:2024"
] | The domino class has an exact structural and enumerative treatment and related inversion-monotonicity progress, but no proof of the requested domino conjecture was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2604.01143",
"label": "2026 inversion-monotonicity paper"
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{
"url": "https://arxiv.org/abs/1711.10325",
"label": "1324 structural paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Can the inversion-monotonicity conjecture for $1324$-avoiding permutations be proved on the domino subclass $[\operatorname{Av}(132)\mid\operatorname{Av}(231)]$? | Can we prove the inversion conjecture on the domino subclass? Theorem (Claesson–Ulfarsson): |Avkn (1324, 231, 4321)| \leq |Avkn+1 (1324, 231, 4321)|. 2. Miklós Bóna Consider patterns of size 6. Look at these three principal classes: A = Av(132456), B = Av(124356), C = Av(123546). All three have the same growth rate, ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,761 | OWR-14298158-006 | Counting-Sequence Ratios for Length-Six Principal Classes | Let $A=\operatorname{Av}(132456)$ and $B=\operatorname{Av}(124356)$. How different are their counting sequences? Is their ratio constant or polynomial, and how close can the counting sequences of distinct principal permutation classes be? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "combinatorics",
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-006",
"literature-status:open",
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] | The report records the counting-sequence and ratio questions for the two principal classes, and no primary resolution of those comparisons was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Let $A=\operatorname{Av}(132456)$ and $B=\operatorname{Av}(124356)$. How different are their counting sequences? Is their ratio constant or polynomial, and how close can the counting sequences of distinct principal permutation classes be? | The question is: how different are the counting sequences of A and B? Is their ratio a constant? Is their ratio a polynomial? What is that polynomial? How close can they be? How different can they be? The domino subclass [Av(132) | Av(231)] (where we also require the whole thing to avoid 1324) is one of the main things... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,762 | OWR-14298158-007 | Rationality Below Growth Rate Four | Is every finitely based permutation class of growth rate less than $4$ rational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "combinatorics",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-007",
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] | Moment representations are proved for several principal classes and substantial pattern families, but the conjecture for every principal class remains open. | [
{
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{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i4p20",
"label": "moment-sequence paper"
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{
"url": "https://arxiv.org/abs/2109.13485",
"label": "length-five pattern paper"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Is every finitely based permutation class of growth rate less than $4$ rational? | 6. Robert Brignall Conjecture: Every finitely based class with growth rate < 4 is rational. Evidence: • If C is contained in the separable permutations and C does not contain Av(132) or its symmetries, then C is strongly rational (every subclass is rational). 5. Natasha Blitvić What do the permutons of consecutive-pat... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,763 | OWR-14298158-008 | Permuton Limits for Consecutive Avoiders and Uniquely Sorted Permutations | What are the permuton limits of consecutive-pattern avoiders? What are the permuton limits of uniquely sorted permutations, and of uniquely sorted permutations that avoid a fixed pattern? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-008",
"literature-status:partially-solved",
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] | Current work proves rationality for finitely based classes below 1 plus the golden ratio and explicitly reports that the conjectured threshold 4 remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
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{
"url": "https://sites.cs.st-andrews.ac.uk/pp25/program/booklet-pp25.pdf",
"label": "2025 primary-work summary"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | What are the permuton limits of consecutive-pattern avoiders? What are the permuton limits of uniquely sorted permutations, and of uniquely sorted permutations that avoid a fixed pattern? | What happens in other contexts, like graphons? • Every finitely based subclass of Av(123) is rational (Albert, Brignall, Rusku’vc, Vatter). 8. Colin Defant A uniquely-sorted permutation is a permutation that has one pre-image under the West stack-sorting map. We can also look at uniquely-sorted permutations avoiding ce... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,764 | OWR-14298158-009 | Universal Permuton Convergence and Algebraic Functional Equations | For a permutation class $C$, does a uniformly random permutation of size $n$ in $C$ always converge to a limiting permuton, and what is the analogue of this question for graphons? Also, which polynomial functional equations of the form $$P\bigl(F(t,u),F(t,0),\partial_uF(t,0),t,u\bigr)=0$$ force the formal power series ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-009",
"literature-status:open",
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] | The report poses the graphon extension as an open direction; related graphon and permuton theory exists, but no general answer to this question was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1307.2444",
"label": "graphon--permuton paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For a permutation class $C$, does a uniformly random permutation of size $n$ in $C$ always converge to a limiting permuton, and what is the analogue of this question for graphons? Also, which polynomial functional equations of the form $$P\bigl(F(t,u),F(t,0),\partial_uF(t,0),t,u\bigr)=0$$ force the formal power series ... | What does the permuton of the set of uniquely-sorted permutations look like? What about the permuton of the set of uniquely-sorted permutations that avoid a given pattern? 7. Mireille Bousquet-Mélou Does \sigman,C (uniformly random size-n permutation in C) converge to something for every class C? What happens in other... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,765 | OWR-14298158-010 | Separable-Permutation Enumeration Introduction | This talk reports on discussions and findings made by various combinations of M. Bóna (University of Florida), R. Brignall (Open University), C. Defant (Har- vard University), M. Opler (Czech Technical University) and V. Vatter (University of Florida) during the “Permutation Patterns” mini-workshop, held at Mathema- t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the rationality question already represented by OWR-14298158-002 and otherwise con) | [
"OWR-14298158-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-010",
"literature-status:open",
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] | Primary papers enumerate and structurally characterize uniquely sorted classes, but no permuton limit for the full family or its avoidance subclasses was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1908.04025",
"label": "uniquely-sorted permutations paper"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | null | This talk reports on discussions and findings made by various combinations of M. Bóna (University of Florida), R. Brignall (Open University), C. Defant (Har- vard University), M. Opler (Czech Technical University) and V. Vatter (University of Florida) during the “Permutation Patterns” mini-workshop, held at Mathema- t... | unrecoverable | The official report confirms that this extraction repeats the rationality question already represented by OWR-14298158-002 and otherwise contains introductory exposition. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,766 | OWR-14298158-011 | Structural Decomposition of Separable Permutation Subclasses | For a subclass $C$ of the separable permutations, must $C$ be closed under direct sums or skew sums, a finite union of such classes, or contained in an inflation $X[U]$ by a proper subclass $U$ as conjectured? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-011",
"literature-status:partially-solved",
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] | Known theorems give rationality when every Av(231) symmetry is excluded, but the converse question is unresolved and the proposed structural conjecture remains incomplete. | [
{
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"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1007.1014",
"label": "separable-subclass theorem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For a subclass $C$ of the separable permutations, must $C$ be closed under direct sums or skew sums, a finite union of such classes, or contained in an inflation $X[U]$ by a proper subclass $U$ as conjectured? | Conjecture 3. Let C be a subclass of the separable permutations. Then either C is sum or skew closed (or the finite union of such classes), or C \subseteq X [U] where X = Av(2413, 3142, 2143, 3412) and U is a proper subclass of C. The reason this would help us is due to the following result, which is a slight reinterpr... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,767 | OWR-14298158-012 | Generating-Function Field for Separable Permutation Subclasses | Does every proper subclass of the separable permutations have a generating function in $$\mathbb Q\!\left(z,\sqrt{1-4z},\sqrt{1-6z+5z^2}\right)?$$ Determine whether this field contains all such generating functions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "combinatorics",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14298158-012",
"literature-status:open",
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] | A concrete proper subclass refutes the smaller one-radical field, but the enlarged two-radical universality question in the excerpt remains unresolved. | [
{
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"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1510.06328",
"label": "explicit generating-function paper"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Does every proper subclass of the separable permutations have a generating function in $$\mathbb Q\!\left(z,\sqrt{1-4z},\sqrt{1-6z+5z^2}\right)?$$ Determine whether this field contains all such generating functions. | Is it the case that every proper subclass \sqrt{ } of the \sqrt{ } separable permutations has a generating function that belongs to Q(z, 1 − 4z, 1 − 6z + 5z 2 )? paper authored by three participants of this mini-workshop [5]. Specifically, the class Av(2143, 2413, 3142) has an enumeration sequence given by OEIS sequenc... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,768 | OWR-14298158-013 | Positivity Under Pattern Avoidance in Matchings | For which matching patterns does avoidance preserve positivity, and what can be deduced for general avoided patterns? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "combinatorics",
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"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-14298158-013",
"literature-status:partially-solved",
"owr-year:2024"
] | Exact enumerations and moment representations are known for several matching patterns, but the question for more general matching patterns remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1211.3442",
"label": "matching-avoidance paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For which matching patterns does avoidance preserve positivity, and what can be deduced for general avoided patterns? | We are therefore interested in studying pattern avoidance in matchings, as a potentially more natural setting in which to consider the question of when the avoidance of a specific sub-diagram (aka pattern) preserves positivity. What can can be deduced for more general patterns in matchings? where ρq is the q-Gaussian l... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,769 | OWR-14298158-014 | Moment Sequences from Matching Pattern Avoidance | For which matchings $\tau$ is $(M_n(\tau))_{n\geq0}$ a Hamburger moment sequence, equivalently $(M_{2n}(\tau))_{n\geq0}$ a Stieltjes moment sequence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-014",
"literature-status:partially-solved",
"owr-year:2024"
] | Several exact matching-avoidance sequences have integral moment representations supporting the conjecture, but no proof for every matching was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://link.springer.com/article/10.1007/s00026-022-00596-1",
"label": "matching-enumeration paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For which matchings $\tau$ is $(M_n(\tau))_{n\geq0}$ a Hamburger moment sequence, equivalently $(M_{2n}(\tau))_{n\geq0}$ a Stieltjes moment sequence? | 1. Statement of the problem Definition 1. We say that a matching \pi contains a matching \tau (as a pattern) if some subset of the pairs of \pi has elements in the same relative order as the elements of \tau . For example the matching \{(1, 3), (2, 6), (4, 5)\} contains \{(1, 3), (2, 4)\} as a pat- tern as the elements... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,770 | OWR-14298158-015 | Diagonal Permuton Limits for Skew-Sum Avoidance | For every nonempty permutation $\alpha$, is the permuton limit of $\operatorname{Av}(\alpha\ominus1)$ the diagonal permuton? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14298158-016"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-015",
"literature-status:partially-solved",
"owr-year:2024"
] | Rare-region theorems give partial geometric constraints for patterns of the form alpha minus 1, but Bevan's full diagonal-permuton conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i4p13",
"label": "rare-region paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For every nonempty permutation $\alpha$, is the permuton limit of $\operatorname{Av}(\alpha\ominus1)$ the diagonal permuton? | Conjecture. The permuton limit of Av(\alpha ⊖ 1) is the diagonal permuton, for any non-empty permutation \alpha. In trying to prove this conjecture, we have revisited work by Atapour and Madras [1] and Madras and Yıldırım [2] on exponentially rare regions of permuta- tion classes. For a pattern \tau \in Sk , they defin... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,771 | OWR-14298158-016 | Point-Probability Criterion Commentary | conjecture. The condition is consistent with what we know about the uniformly random permutation (chosen from the set of all size-n permutations), since in that case the probability of \pi(i) = j is exactly 1/n (rather than o(1/n)) for all i and j. The report passage is retained verbatim as the relevant context for thi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Unrecoverable OWR statement (The official report confirms that this fragment comments on a proved point-probability criterion and does not state an additional conjecture) | [
"OWR-14298158-015"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-016",
"literature-status:open",
"owr-year:2024"
] | Closing remark on Bevan’s conjecture, which is retained separately.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, s... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | null | conjecture. The condition is consistent with what we know about the uniformly random permutation (chosen from the set of all size-n permutations), since in that case the probability of \pi(i) = j is exactly 1/n (rather than o(1/n)) for all i and j. The report passage is retained verbatim as the relevant context for thi... | unrecoverable | The official report confirms that this fragment comments on a proved point-probability criterion and does not state an additional conjecture or open question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,772 | OWR-14298158-017 | Combinatorial Interpretations of Negative k-Arrangements | Let $A(n,k)$ denote the number of permutations of $[n]$ whose fixed points are colored with one of $k$ colors, extended polynomially from nonnegative integers $k$. Does $A(n,k)$ have a combinatorial interpretation for every negative integer $k$? More generally, does $A(2n,k)$ have a combinatorial interpretation for eve... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-017",
"literature-status:open",
"owr-year:2024"
] | The report explicitly poses both negative-integer and all-integer combinatorial-interpretation questions for A(n,k); the cited literature records them as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2001.00280",
"label": "Blitvić--Steingrímsson, Permutations, moments, measures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | Let $A(n,k)$ denote the number of permutations of $[n]$ whose fixed points are colored with one of $k$ colors, extended polynomially from nonnegative integers $k$. Does $A(n,k)$ have a combinatorial interpretation for every negative integer $k$? More generally, does $A(2n,k)$ have a combinatorial interpretation for eve... | Does A(n, k) have a combinatorial interpretation when k is an arbitrary negative integer? Furthermore, it follows by (2) that for n even, A(n, k) \geq 0 for any k \in R. (We are integrating x2 against a non-negative function over R.) A potentially easier question is therefore: Question′. Does A(2n, k) have a combinator... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,773 | OWR-14298158-018 | Monotone k-Shuffles in Long Permutations | For each fixed $k\in\mathbb{N}$, does every sufficiently long permutation contain a consecutive factor that is a $k$-shuffle of $12$ or $21$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308](https://doi.org/10.4171/owr/2024/6)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298158-018",
"literature-status:open",
"owr-year:2024"
] | The k-shuffle conjecture was explicitly unproved, with only finite verification and structural progress reported; no later proof of the stated general conjecture was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/6",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/6 | null | null | null | For each fixed $k\in\mathbb{N}$, does every sufficiently long permutation contain a consecutive factor that is a $k$-shuffle of $12$ or $21$? | Conjecture 1. For a fixed k \in N, any sufficiently long permutation contains a factor which is a k-shuffle of 12 or 21. Although we did not prove this conjecture, we made progress in a number of directions. First, we reinterpreted the conjecture as a question about the existence of a cycle in the following graph: Defi... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Permutation Patterns (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/6, pp. 273--308 |
30,005,774 | OWR-14298159-001 | Cocycle-Twist Classification of Pointed Hopf Algebras | Let $H$ be a finite-dimensional pointed Hopf algebra with group of group-like elements $G$ and infinitesimal braiding $V$. Prove that $H$ is a cocycle twist of $\mathcal B(V)\#\mathbb CG$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-001",
"literature-status:open",
"owr-year:2024"
] | The cocycle-twist classification conjecture remains general and unresolved; it is established for abelian groups and several known Nichols-algebra families, not for all finite-dimensional pointed Hopf algebras. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1212.5279",
"label": "Andruskiewitsch--Angiono--García Iglesias--Masuoka--Vay, Lifting via cocycle deformation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Let $H$ be a finite-dimensional pointed Hopf algebra with group of group-like elements $G$ and infinitesimal braiding $V$. Prove that $H$ is a cocycle twist of $\mathcal B(V)\#\mathbb CG$. | Conjecture 1. A finite-dimensional pointed Hopf algebra H is a cocycle twist of the bosonization of the Nichols algebra B(V ) by the group algebra of G: H ≃ (B(V )\#CG)\sigma , where \sigma : B(V )\#CG ⊗ B(V )\#CG \to C is an invertible 2-cocycle. This conjecture contains two important subproblems. Consider a group G a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,775 | OWR-14298159-002 | Uniqueness of Finite-Dimensional Post-Nichols Algebras | Let $G$ be a group and let $V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$ satisfy $\dim\mathcal B(V)<\infty$. Is $\mathcal B(V)$ the only finite-dimensional post-Nichols algebra of $V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-002",
"literature-status:open",
"owr-year:2024"
] | Generation in degree one is known for abelian groups and documented cases, but the question for arbitrary finite groups and finite-dimensional Nichols algebras remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1212.5279",
"label": "Lifting via cocycle deformation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Let $G$ be a group and let $V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$ satisfy $\dim\mathcal B(V)<\infty$. Is $\mathcal B(V)$ the only finite-dimensional post-Nichols algebra of $V$? | Is B(V ) the only finite-dimensional post-Nichols algebra of V ? (gen- eration in degree one). 1. Finite-dimensional Hopf algebras The base field is C. The classification of the finite-dimensional Hopf algebras is a wild problem since the classification of the finite groups is a wild problem; see [12]. Indeed the class... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,776 | OWR-14298159-003 | Finite-Dimensional Nichols Algebras over Finite Groups | Classify the pairs $(G,V)$ for which $G$ is finite, $V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$, and $\dim\mathcal B(V)<\infty$, and compute defining relations for every such Nichols algebra. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-003",
"literature-status:open",
"owr-year:2024"
] | The report states the classification of finite-dimensional Nichols algebras over arbitrary finite groups and the computation of their relations as an open problem; substantial rank and rack-specific classifications do not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1412.0857",
"label": "Heckenberger--Vendramin, classification over non-abelian groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Classify the pairs $(G,V)$ for which $G$ is finite, $V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$, and $\dim\mathcal B(V)<\infty$, and compute defining relations for every such Nichols algebra. | 2. Racks We do not know whether the following Question could be answered. Question 3. Classify the pairs (G, V ) where G is a finite group and V \in CG CG YD satisfies dim B(V ) < \infty and compute the relations of B(V ). If G is abelian, then both problems are solved by Heckenberger and Angiono respectively, see the ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,777 | OWR-14298159-004 | Fomin-Kirillov Algebras as Nichols Algebras | Determine whether the quadratic Fomin-Kirillov algebra associated with the symmetric group is a Nichols algebra in every rank, extending the known small-rank cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-004",
"literature-status:open",
"owr-year:2024"
] | The source itself identifies the general case as open, and the current literature supplies only special-case results rather than a general solution. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Determine whether the quadratic Fomin-Kirillov algebra associated with the symmetric group is a Nichols algebra in every rank, extending the known small-rank cases. | The general case is an open problem. Geometric problems related to approximations of Nichols algebras Francesco Esposito (joint work with Giovanna Carnovale, Lleonard Rubio y Degrassi) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,778 | OWR-14298159-005 | Simplicity of Twisted Hopf Algebras | Let $G=\prod_{i=1}^n(D_i\rtimes_{\varphi_i}M_i)$, where every $D_i\rtimes_{\varphi_i}M_i$ is a Frobenius group, every $M_i$ is an abelian group of prime-power order, $M=\prod_iM_i$ has square order, and $J$ arises from a $2$-cocycle on $\widehat M$. For $n\geq3$, determine whether the twisted Hopf algebra $(KG)^J$ is s... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-005",
"literature-status:open",
"owr-year:2024"
] | Finite-dimensional pointed Hopf algebras with Hopf orders satisfy the referenced conjectural conclusion, but the statement does not hold as a general theorem and the remaining cases are unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1212.5279",
"label": "Lifting via cocycle deformation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Let $G=\prod_{i=1}^n(D_i\rtimes_{\varphi_i}M_i)$, where every $D_i\rtimes_{\varphi_i}M_i$ is a Frobenius group, every $M_i$ is an abelian group of prime-power order, $M=\prod_iM_i$ has square order, and $J$ arises from a $2$-cocycle on $\widehat M$. For $n\geq3$, determine whether the twisted Hopf algebra $(KG)^J$ is s... | conjecture. Specifically, he proved that if the Hopf algebra admits a Hopf order over a number ring, then the conjecture holds. It is also worth to mention that the property of admitting a Hopf order could be useful for classifying semisimple Hopf algebras. Let H be a finite-dimensional Hopf algebra over a field K and ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,779 | OWR-14298159-006 | Balmer-Spectrum Motivation | If one accepts that line of approach to understanding the representation category of A, then a natural question to ask is how to compute the spectrum? Effectively, we kill projective A-modules, taking out injectives on the way since projectives and injectives are the same by the self-injectivity of A. We study these tr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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 uses this broad question to motivate the three precise tensor-triangular questions preserved in the following record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298159-006",
"literature-status:open",
"owr-year:2024"
] | The spectrum question for stable representation categories of finite-dimensional Hopf algebras remains open in general; existing work gives comparison maps and computations under finiteness hypotheses or for special tensor categories. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2112.11170",
"label": "Nakano--Vashaw--Yakimov, spectrum and support theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | null | If one accepts that line of approach to understanding the representation category of A, then a natural question to ask is how to compute the spectrum? Effectively, we kill projective A-modules, taking out injectives on the way since projectives and injectives are the same by the self-injectivity of A. We study these tr... | unrecoverable | The official report uses this broad question to motivate the three precise tensor-triangular questions preserved in the following record. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,780 | OWR-14298159-007 | Cohomology and Balmer Spectra of Hopf Algebras | For a finite-dimensional, not necessarily cocommutative Hopf algebra $A$, determine when $H^*(A,k)$ is Noetherian, when the natural map $\Psi:\operatorname{Spec}(\operatorname{stab}A)\to\operatorname{Proj}H^*(A,k)$ is a homeomorphism, and how to compute $\operatorname{Proj}H^*(A,k)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | open | null | 2,024 | 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-14298159-007",
"literature-status:open",
"owr-year:2024"
] | Finite generation, comparison with the Balmer spectrum, and calculation of Proj H^*(A,k) are solved only in important special classes; the three questions as posed for general A remain open. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2112.11170",
"label": "Nakano--Vashaw--Yakimov, spectrum and support theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | For a finite-dimensional, not necessarily cocommutative Hopf algebra $A$, determine when $H^*(A,k)$ is Noetherian, when the natural map $\Psi:\operatorname{Spec}(\operatorname{stab}A)\to\operatorname{Proj}H^*(A,k)$ is a homeomorphism, and how to compute $\operatorname{Proj}H^*(A,k)$. | Andruskiewitsch’s talk: (1) When is Proj H ∗ (A, k) a scheme of finite type (when is H ∗ (A, k) Noether- ian)? (2) When is the map Ψ a homeomorphism? (3) Can we calculate Proj H ∗ (A, k)? supp : T \to subsets of Spec T. By a theorem of Balmer [1], Spec(stab A) (or of Db (A)) classifies A-modules up to “homological oper... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,781 | OWR-14298159-008 | Nichols Algebras over Nonabelian Simple Groups | Let $G$ be a finite nonabelian simple group and let $0\neq V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$. Must the Nichols algebra $\mathcal B(V)$ be infinite-dimensional? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272](https://doi.org/10.4171/owr/2024/5)
## Litera... | 3 | partially_solved | null | 2,024 | 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-14298159-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Finite-dimensionality is ruled out for many non-abelian simple groups and established in classified prime-dimensional cases, but no complete description for irreducible Yetter--Drinfeld modules is known. | [
{
"url": "https://doi.org/10.4171/owr/2024/5",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/plms.12559",
"label": "Angiono, pointed Hopf algebras over non-abelian groups"
},
{
"url": "https://arxiv.org/abs/1412.0857",
"label": "Heckenberger--Vendramin, classifi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/5 | null | null | null | Let $G$ be a finite nonabelian simple group and let $0\neq V\in{}_{\mathbb CG}^{\mathbb CG}\mathcal{YD}$. Must the Nichols algebra $\mathcal B(V)$ be infinite-dimensional? | What can be said about Nichols algebras over irreducible Yetter-Drinfeld mod- ules? Bridging Number Theory and Nichols Algebras via Deformations 263 The theorem suggests a challenging question: Are Nichols algebras over finite non-abelian simple groups infinite-dimensional? Theorem 3 (Andruskiewitsch–Carnovale–Garcı́a)... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/5, pp. 235--272 |
30,005,782 | OWR-14298160-001 | Artin-Group Workshop Introduction | Artin and Coxeter groups are ubiquitous in mathematics and have facilitated ap- plications in geometry and topology; such as Davis’ construction of a counterex- ample to the conjecture that all aspherical manifolds have Euclidean spaces as universal covers [Dav83] and Agol’s proof of the virtual Haken conjecture [Ago13... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | open | null | 2,024 | 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 is introductory workshop context duplicating the concrete Artin-group problems preserved below.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-001",
"literature-status:open",
"owr-year:2024"
] | Torsion-freeness and solvability of the word problem are established for substantial families of Artin groups, but remain open for general Artin groups as stated in the report. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | null | Artin and Coxeter groups are ubiquitous in mathematics and have facilitated ap- plications in geometry and topology; such as Davis’ construction of a counterex- ample to the conjecture that all aspherical manifolds have Euclidean spaces as universal covers [Dav83] and Agol’s proof of the virtual Haken conjecture [Ago13... | unrecoverable | The official report confirms that this is introductory workshop context duplicating the concrete Artin-group problems preserved below. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,783 | OWR-14298160-002 | Homological Motivation from Stability Conditions | A fundamental question is to understand these properties using pure homological algebra and generalise them to a broader class of categories. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | open | null | 2,024 | 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 states a broad research motivation rather than a mathematically delimited open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-002",
"literature-status:open",
"owr-year:2024"
] | This is an intentionally broad methodological question with no uniquely specified theorem to verify; the requested general homological-algebraic framework remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/math/0409360",
"label": "Balmer, spectrum of prime ideals in tensor triangulated categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | null | A fundamental question is to understand these properties using pure homological algebra and generalise them to a broader class of categories. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report states a broad research motivation rather than a mathematically delimited open problem. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,784 | OWR-14298160-003 | Stability Manifolds for Threefold Flops | For the category $\mathcal D$ associated with a threefold flopping contraction, determine whether its distinguished stability-manifold component regularly covering the associated hyperplane complement is the universal cover, whether the mutation action is faithful, whether $\operatorname{Stab}(\mathcal D)$ is connected... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | open | null | 2,024 | 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-14298160-003",
"literature-status:open",
"owr-year:2024"
] | A connected component covering the hyperplane complement is proved, but faithfulness, universal-cover status, global connectedness, and contractibility are posed as unresolved questions. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | For the category $\mathcal D$ associated with a threefold flopping contraction, determine whether its distinguished stability-manifold component regularly covering the associated hyperplane complement is the universal cover, whether the mutation action is faithful, whether $\operatorname{Stab}(\mathcal D)$ is connected... | The questions A few questions naturally emerge in the above setup. (1) Is the covering map in theorem 2 the universal cover, i.e. does ϕ describe a faithful action? (2) Is the stability manifold connected, i.e. are there no stability conditions outside the connected component appearing in theorem 2? (3) Is the connecte... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,785 | OWR-14298160-004 | Three Structural Problems for Artin Groups | Prove that every Artin group is torsion-free, has a solvable word problem, and satisfies the $K(\pi,1)$ conjecture, or determine precisely which Artin groups fail any of these properties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | open | null | 2,024 | 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-14298160-004",
"literature-status:open",
"owr-year:2024"
] | The statement is a general warning rather than a single theorem; the report documents several long-standing Artin-group problems that remain open outside special classes. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | Prove that every Artin group is torsion-free, has a solvable word problem, and satisfies the $K(\pi,1)$ conjecture, or determine precisely which Artin groups fail any of these properties. | There are many long-standing open questions about Artin groups. Let Γ be a finite simplicial graph with edges labeled by integers greater than or equal to 2. The Artin group AΓ is the group with presentation hs1 , . . . , sn | si sj si . . . = sj si sj . . .i | \{z \} | \{z \} mij mij Mini-Workshop: Artin Groups meet T... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,786 | OWR-14298160-006 | Definition of the Coxeter Galaxy | What is the Coxeter galaxy? This report is based on [1], which is dedicated to the memory of Jacques Tits for his influential work on Coxeter groups. It was him who, as an honorary Bourbaki, coined the terms Coxeter group and Coxeter diagram. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "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 uses this phrase as a section heading and then defines the Coxeter galaxy; it is not an open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-006",
"literature-status:partially-solved",
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] | The Coxeter galaxy is now rigorously defined and its local finiteness, infinite dimensionality, finite connected components, and low-rank structure are known, but its full global geometry and the associated isomorphism problem remain open. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
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{
"url": "https://doi.org/10.1016/j.jalgebra.2023.12.006",
"label": "Santos Rego--Schwer, The galaxy of Coxeter groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | null | What is the Coxeter galaxy? This report is based on [1], which is dedicated to the memory of Jacques Tits for his influential work on Coxeter groups. It was him who, as an honorary Bourbaki, coined the terms Coxeter group and Coxeter diagram. | unrecoverable | The official report uses this phrase as a section heading and then defines the Coxeter galaxy; it is not an open problem. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,787 | OWR-14298160-007 | Coxeter-Galaxy Structure Overview | How does the galaxy look like locally and globally? Figure 1. Four complete Coxeter graphs describing a same group. The graphs C1 , C2 and C3 may be obtained from C0 by (repeated) applications of blow-ups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | open | null | 2,024 | 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"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this phrase as a section heading and immediately states structural theorems; the remaining questions are preserved ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-007",
"literature-status:open",
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] | The published structural theorem settles several coarse properties, but the local and global layer-growth and intersection questions explicitly remain open. | [
{
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"label": "original OWR report"
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{
"url": "https://doi.org/10.1016/j.jalgebra.2023.12.006",
"label": "Santos Rego--Schwer, The galaxy of Coxeter groups"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | null | How does the galaxy look like locally and globally? Figure 1. Four complete Coxeter graphs describing a same group. The graphs C1 , C2 and C3 may be obtained from C0 by (repeated) applications of blow-ups. | unrecoverable | The official report uses this phrase as a section heading and immediately states structural theorems; the remaining questions are preserved in the following records. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,788 | OWR-14298160-008 | Layer Growth in the Coxeter Galaxy | Determine how the dimensions of the layers of the Coxeter galaxy grow with rank, and whether the defining Coxeter graph determines the number of vertices in the intersection of its connected component with a given layer. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Vertical navigation and several low-rank cases are known, while the general reachability and coloring problem, especially the horizontal part, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.12.006",
"label": "Santos Rego--Schwer, The galaxy of Coxeter groups"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | Determine how the dimensions of the layers of the Coxeter galaxy grow with rank, and whether the defining Coxeter graph determines the number of vertices in the intersection of its connected component with a given layer. | Many questions remain open: how does the dimension of the layers grow if rank grows? Can one tell from a graph how many vertices are contained in the in intersection of a component with a given layer? 3. How to navigate the galaxy? Classical approaches to the isomorphism problem involve a) reducing to a specific subcla... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,789 | OWR-14298160-009 | Finite Moves for Coxeter Presentations | Does there exist a finite list of vertical and horizontal moves such that any two vertices in one connected component of the Coxeter galaxy are joined by a finite sequence of those moves? Can an algorithm also specify the kinds of moves needed along such a path? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "group_theory",
"display_name": "Group Theory",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-009",
"literature-status:partially-solved",
"owr-year:2024"
] | Profinite rigidity is proved for the first three galaxy layers and helps decide the restricted isomorphism problem there, but its role and effectiveness in the full galaxy remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.12.006",
"label": "Santos Rego--Schwer, The galaxy of Coxeter groups"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | Does there exist a finite list of vertical and horizontal moves such that any two vertices in one connected component of the Coxeter galaxy are joined by a finite sequence of those moves? Can an algorithm also specify the kinds of moves needed along such a path? | How to navigate the galaxy? Although many preliminary results exist, several fundamental problems remain open: Question 3.1 (Reachability and Coloring Problem). Does there exist a finite list of vertical and horizontal moves such that, for any vertex in the Coxeter galaxy, any other vertex in its connected component ca... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,790 | OWR-14298160-010 | Profinite Rigidity in the Coxeter Galaxy | How does profinite rigidity come into play? 3. How to navigate the galaxy? Classical approaches to the isomorphism problem involve a) reducing to a specific subclass of Coxeter groups and to b) finding explicit moves, i.e. explicit manipu- lations, between defining graphs. These moves correspond to edges in the Coxeter... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234](https://doi.org/10.4171/owr/2024/4)
## Literature review (checke... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this phrase as a section heading and follows it with a proved profinite-rigidity theorem for ranks at most three, n) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298160-010",
"literature-status:partially-solved",
"owr-year:2024"
] | The profinite-rigidity theorem for Coxeter diagrams of rank at most three is established, while the general profinite-rigidity question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/4",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.12.006",
"label": "Santos Rego--Schwer, The galaxy of Coxeter groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/4 | null | null | null | null | How does profinite rigidity come into play? 3. How to navigate the galaxy? Classical approaches to the isomorphism problem involve a) reducing to a specific subclass of Coxeter groups and to b) finding explicit moves, i.e. explicit manipu- lations, between defining graphs. These moves correspond to edges in the Coxeter... | unrecoverable | The official report uses this phrase as a section heading and follows it with a proved profinite-rigidity theorem for ranks at most three, not an open problem. | null | null | null | null | null | Mini-Worskhop: Artin Groups meet Triangulated Categories (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/4, pp. 203--234 |
30,005,791 | OWR-14298161-001 | Optimal Eulerian Liftings of Second-Order Functionals | For the second-order functional $E(u)=\int_\Omega H(\nabla^2u(x))\,dx$, what is the largest convex, lower-semicontinuous, subadditive lifting of $E$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388](https://doi.org/10.4171/owr/2024/7)
## Literature review (checked 2026-08-22)
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"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298161-001",
"literature-status:open",
"owr-year:2024"
] | For second-order energies E(u)=\int H(\nabla^2u), the report and the subsequent primary lifting paper leave the optimal Eulerian lifting as an explicit open problem. | [
{
"url": "https://doi.org/10.4171/owr/2024/7",
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{
"url": "https://arxiv.org/abs/2309.02260",
"label": "Lavenant, Lifting functionals defined on maps to measure-valued maps"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/7 | null | null | null | For the second-order functional $E(u)=\int_\Omega H(\nabla^2u(x))\,dx$, what is the largest convex, lower-semicontinuous, subadditive lifting of $E$? | What is the largest convex, lower semi-continuous and subadditive functional which lifts E in this case? 3. An open question Consider a functional of second order for a map u : Ω \subset Rq \to Rd : Z E(u) = H(∇2 u(x)) dx, Ω | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388 |
30,005,792 | OWR-14298161-002 | Semigeostrophic Equations on the Whole Rotating Sphere | Can local well-posedness for the semigeostrophic equation on a closed spherical subdomain contained strictly in one hemisphere be extended to the whole rotating sphere, despite the degeneracy of the Coriolis parameter at the equator? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388](https://doi.org/10.4171/owr/2024/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,024 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "PDEs and their applications in physics and geometry.",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14298161-002",
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{
"url": "https://doi.org/10.4171/owr/2024/7",
"label": "original OWR report"
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{
"url": "https://doi.org/10.1137/22M1532846",
"label": "Silini, local existence on curved domains"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/7 | null | null | null | Can local well-posedness for the semigeostrophic equation on a closed spherical subdomain contained strictly in one hemisphere be extended to the whole rotating sphere, despite the degeneracy of the Coriolis parameter at the equator? | We finally present some questions and open problems that naturally arise from the previous part of the talk. This problem is interesting from a physical standpoint because it involves the well-posedness of the semigeostrophic equation in a more accurate context, which, to my knowledge, remains an open question even for... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388 |
30,005,793 | OWR-14298161-003 | Stability and Alternative Costs in Spherical Optimal Transport | Can stability of spherical semigeostrophic solutions be proved as the curvature $\kappa\to0$? Is there another cost $c(x,y)$ on $S^2$ for which the transport map $c\text{-}\exp_x(\nabla p_t(x))$ yields a continuity equation for the transported density that does not involve the velocity $u_t$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388](https://doi.org/10.4171/owr/2024/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,024 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298161-003",
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] | The report poses both small-κ stability and an alternative spherical transport cost as open questions; no primary result resolving either question in the stated setting was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/7",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/7 | null | null | null | Can stability of spherical semigeostrophic solutions be proved as the curvature $\kappa\to0$? Is there another cost $c(x,y)$ on $S^2$ for which the transport map $c\text{-}\exp_x(\nabla p_t(x))$ yields a continuity equation for the transported density that does not involve the velocity $u_t$? | Is it possible to prove stability properties of the solutions in terms of κ ≪ 1? Is there another cost function c = c(x, y) on S 2 for which the transport map c- expx (∇pt (x)) gives a continuity equation for the associated density that does not involve ut ? Quantum mechanics, density functional theory, optimal transpo... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Applications of Optimal Transportation (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/7, pp. 309--388 |
30,005,794 | OWR-14298162-001 | K-Stability Table-of-Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . 864 Workshop: K-Stability, Birational Geometry and Mirror Symmetry Table of Contents K-Stability, Birational Geometry and Mirror Symmetry 833 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870](https://doi.org/10.4171/owr/2024/14)
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"name": "algebraic_geometry",
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"description": "Geometric objects defined by polynomial equations.",
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] | The extracted record contains only the word `conjecture' and a table-of-contents page number, so no definite mathematical claim can be identified or shown resolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/14",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/14 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . 864 Workshop: K-Stability, Birational Geometry and Mirror Symmetry Table of Contents K-Stability, Birational Geometry and Mirror Symmetry 833 | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment ending in the word conjecture, not a mathematical problem. | null | null | null | null | null | K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870 |
30,005,795 | OWR-14298162-002 | Valuation Bounds When the Center Meets the Negative Part | Let $X$ be a smooth Fano threefold, let $P\in S\subset X$, and for $u\in[0,\tau]$ write the Zariski decomposition $-K_X-uS=P(u)+N(u)$. If $P\in\operatorname{Supp}N(u)$ for some $u$, find $K>0$ such that $\frac{3}{(-K_X)^3}\int_0^\tau P(u)^2\cdot S\cdot\operatorname{ord}_F(N(u)|_S)\,du\leq K A_S(F)$ for every prime divi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870](https://doi.org/10.4171/owr/2024/14)
## Literature review (checked ... | 3 | open | null | 2,024 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"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-14298162-002",
"literature-status:open",
"owr-year:2024"
] | The 2024 report explicitly poses the case P\inSupp(N(u)) as an unresolved technical question and asks for a uniform bound; no later proof resolving this exact case was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/14",
"label": "K-Stability, Birational Geometry and Mirror Symmetry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/14 | null | null | null | Let $X$ be a smooth Fano threefold, let $P\in S\subset X$, and for $u\in[0,\tau]$ write the Zariski decomposition $-K_X-uS=P(u)+N(u)$. If $P\in\operatorname{Supp}N(u)$ for some $u$, find $K>0$ such that $\frac{3}{(-K_X)^3}\int_0^\tau P(u)^2\cdot S\cdot\operatorname{ord}_F(N(u)|_S)\,du\leq K A_S(F)$ for every prime divi... | What if P \in Supp(N (u)) for some u \in [0, \tau ]? for every prime divisor F over S. Thus, if P 6\in Supp(N (u)) for u \in [0, \tau ], then S 1 \deltaP S, W•,• ⩾ R\tau D2 . 3 (−KX )3 q(u) du 0 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870 |
30,005,796 | OWR-14298162-003 | Duplicate Negative-Part Valuation Question | How to do this? What if P \in Supp(N (u)) for some u \in [0, \tau ]? In this case, we want to find a K > 0 such that Z\tau 3 3 P (u)2 \cdot S \cdot ordF N (u) S du ⩽ K \cdot AS (F ) (−KX ) 0 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870](https://doi.org/10.4171/owr/2024/14)
## Literature review (checked ... | 3 | open | null | 2,024 | 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 repeats the same negative-part valuation question preserved in the preceding record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298162-003",
"literature-status:open",
"owr-year:2024"
] | This extracted record is the literal request How to do this? for the preceding bound, with no independent formal statement; the cited report leaves that bound as an open question, so the unresolved claim is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/14",
"label": "K-Stability, Birational Geometry and Mirror Symmetry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/14 | null | null | null | null | How to do this? What if P \in Supp(N (u)) for some u \in [0, \tau ]? In this case, we want to find a K > 0 such that Z\tau 3 3 P (u)2 \cdot S \cdot ordF N (u) S du ⩽ K \cdot AS (F ) (−KX ) 0 | unrecoverable | The official report confirms that this extraction repeats the same negative-part valuation question preserved in the preceding record. | null | null | null | null | null | K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870 |
30,005,797 | OWR-14298162-004 | Algebro-Geometric Meaning of Noncommutative Volume Bounds | Find an algebro-geometric interpretation of the noncommutative volume term that replaces the Euler characteristic in the analogue of the non-symmetric Mahler inequality for singularities with noncommutative crepant resolutions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870](https://doi.org/10.4171/owr/2024/14)
## Literature review (checked ... | 3 | partially_solved | null | 2,024 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"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-14298162-004",
"literature-status:partially-solved",
"owr-year:2024"
] | The report records the Mahler-type inequality as conjectural, while the proposed noncommutative-crepant-resolution interpretation is verified for finite quotient singularities and several further examples; the general interpretation remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/14",
"label": "K-Stability, Birational Geometry and Mirror Symmetry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/14 | null | null | null | Find an algebro-geometric interpretation of the noncommutative volume term that replaces the Euler characteristic in the analogue of the non-symmetric Mahler inequality for singularities with noncommutative crepant resolutions. | conjecture. It is natural to ask whether there is a reasonable interpretation of this inequality in terms of algebraic geometry. Hence, we are looking for an interpretation of the volume of P in terms of algebraic geometry. But this volume is known to coincide with the Euler characteristic of a crepant resolution Xe of... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870 |
30,005,798 | OWR-14298162-005 | Higher Fano Manifolds as Higher Rational-Connectedness Conditions | For every $k$, prove that $k$-Fano manifolds are covered by rational $k$-folds and that a proper family over a $k$-dimensional base whose fibers are $k$-Fano admits a rational section, modulo the Brauer obstruction. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870](https://doi.org/10.4171/owr/2024/14)
## Literature review (checked ... | 3 | open | null | 2,024 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"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-14298162-005",
"literature-status:open",
"owr-year:2024"
] | The question whether the auxiliary condition F_k can be chosen as k-Fano is explicitly left as a question; the cited evidence proves only partial implications such as coverage by rational k-folds in low k. | [
{
"url": "https://doi.org/10.4171/owr/2024/14",
"label": "K-Stability, Birational Geometry and Mirror Symmetry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/14 | null | null | null | For every $k$, prove that $k$-Fano manifolds are covered by rational $k$-folds and that a proper family over a $k$-dimensional base whose fibers are $k$-Fano admits a rational section, modulo the Brauer obstruction. | Question. [1] Can one take the condition Fk to be “X is k-Fano”? K-Stability, Birational Geometry and Mirror Symmetry 849 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | K-Stability, Birational Geometry and Mirror Symmetry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/14, pp. 827--870 |
30,005,799 | OWR-14298163-001 | Discrete-Geometry Problems Table-of-Contents Entry | 189 Collected by Nikita Gladkov Open Problems in Discrete Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment, not a mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-001",
"literature-status:open",
"owr-year:2024"
] | The record is a section-heading fragment rather than a mathematical assertion, so no claim is identifiable whose truth could be established; under the queue rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | null | 189 Collected by Nikita Gladkov Open Problems in Discrete Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment, not a mathematical problem. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,800 | OWR-14298163-002 | Polynomial-Homology Families and the p-q Theorem | Fix constants $c$ and $t$. Let $\mathcal F$ be a family of subsets of $\mathbb R^d$ such that $\sum_{i=1}^{\lfloor d/2\rfloor}\widetilde\beta_i(\bigcap\mathcal G)\leq c|\mathcal G|^t$ for every finite $\mathcal G\subseteq\mathcal F$. Prove that $\mathcal F$ satisfies a $(p,q)$-theorem for every $p\geq q\geq d+1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-002",
"literature-status:open",
"owr-year:2024"
] | The 2024 report states this (p,q)-theorem as a conjecture for the indicated topological set systems; the cited fractional-Helly result supplies a special regime, not the full assertion. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Fix constants $c$ and $t$. Let $\mathcal F$ be a family of subsets of $\mathbb R^d$ such that $\sum_{i=1}^{\lfloor d/2\rfloor}\widetilde\beta_i(\bigcap\mathcal G)\leq c|\mathcal G|^t$ for every finite $\mathcal G\subseteq\mathcal F$. Prove that $\mathcal F$ satisfies a $(p,q)$-theorem for every $p\geq q\geq d+1$. | We conjecture that such families satisfy a (p, q)-theorem for all p \geq q \geq d + 1. to improve the bound on the fractional Helly number of topological set systems in Rd : Theorem 7 (Goaoc–Holmsen–Patáková, 2021). Let F be a family of sets in Rd . If HC⌊d/2⌋ (F ) \leq C, then F has fractional Helly number at most d... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,801 | OWR-14298163-004 | Chromatic Number of Overlapping Unit-Circle Constellations | Determine the maximum chromatic number of the tangency graph of a possibly overlapping constellation of unit circles. Equivalently, determine the chromatic number of the plane in the Hadwiger-Nelson problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-004",
"literature-status:open",
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] | The extracted record asks for the maximum chromatic number in the overlapping-unit-circle and general-circle cases, but gives no resolved value; the report retains these as open variants after the non-overlapping unit-circle result. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Determine the maximum chromatic number of the tangency graph of a possibly overlapping constellation of unit circles. Equivalently, determine the chromatic number of the plane in the Hadwiger-Nelson problem. | What is the maximum chromatic number of a (possibly overlapping) constellation of unit circles? (d) The circle problem. What is the maximum chromatic number of a general constellation of circles? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,802 | OWR-14298163-005 | Three Problems on Triangulations | Resolve the following triangulation problems: (1) do two triangulations with the same support always have a common iterated stellar subdivision; (2) are any two point configurations in $\mathbb R^3$ or $\mathbb R^4$ connected by bistellar flips; and (3) for every $d$, is there a constant $c_d$ such that $c_dP$ has a un... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-005",
"literature-status:open",
"owr-year:2024"
] | The record bundles three distinct open problems about stellar subdivisions, bistellar flips, and unimodular triangulations; no single theorem resolves all three, and the report presents them explicitly as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Resolve the following triangulation problems: (1) do two triangulations with the same support always have a common iterated stellar subdivision; (2) are any two point configurations in $\mathbb R^3$ or $\mathbb R^4$ connected by bistellar flips; and (3) for every $d$, is there a constant $c_d$ such that $c_dP$ has a un... | We give several open problems, including the following: (1) Oda’s factorization conjecture: Do any two triangulations with the same support have a common iterated stellar subdivision? (2) Are any two point sets in R3 and R4 connected by bistellar flips? (3) Is there a constant cd such that for any lattice polytope P in... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,803 | OWR-14298163-006 | Borsuk Partition Problem in Dimensions Four Through Sixty-Three | For each $4\leq d\leq 63$, determine whether every bounded set $S\subseteq\mathbb R^d$ can be partitioned into at most $d+1$ subsets of diameter strictly smaller than $\operatorname{diam}(S)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 6,
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"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "oberwolfach-reports-open... | null | {
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"literature-status:partially-solved",
"owr-year:2024"
] | Kahn–Kalai counterexamples disprove the universal Borsuk conjecture. They do not determine the answer separately in the dimensions 4–63 explicitly requested by this OWR record.
**What remains.** The dimension-by-dimension classification asked here remains incomplete. | [
{
"url": "https://doi.org/10.1090/S0273-0979-1993-00398-7",
"label": "Kahn and Kalai, A counterexample to Borsuk’s conjecture"
},
{
"url": "https://teorth.github.io/optimizationproblems/constants/28a.html",
"label": "Maintained Borsuk minimum-dimension problem"
},
{
"url": "https://huggi... | 2026-09-27T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For each $4\leq d\leq 63$, determine whether every bounded set $S\subseteq\mathbb R^d$ can be partitioned into at most $d+1$ subsets of diameter strictly smaller than $\operatorname{diam}(S)$. | question (sometime known as the Borsuk conjecture): does every set S \subset Rd with finite diameter diam(S) is the union of at most d + 1 sets of diameter less than diam(S)? It is known to be true for d = 2 (see [1]) and for d = 3 (see [14], [4] and [6] for a simpler proof). Proved to be false for d > 63 see [19] for ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,804 | OWR-14298163-008 | Dolnikov’s Colorful Transversal Conjecture | Let $K\subseteq\mathbb R^2$ be compact and convex, and let $\mathcal F_1,\mathcal F_2,\mathcal F_3$ be finite families of translates of $K$. If $A\cap B\neq\varnothing$ whenever $A\in\mathcal F_i$, $B\in\mathcal F_j$, and $i\neq j$, prove that some $\mathcal F_j$ can be pierced by three points. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,024 | 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-14298163-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Dol'nikov's conjecture is proved for centrally symmetric bodies, triangles, disks, bodies of constant width, and bodies sufficiently close to a disk, but the full compact-convex-set statement remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://doi.org/10.1007/s00454-024-00669-3",
"label": "Transversals to Colorful Intersecting Convex Sets"
},
{
"url": "https://arxiv.org/abs/2307.07714",
"label": "On a colorful problem by... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $K\subseteq\mathbb R^2$ be compact and convex, and let $\mathcal F_1,\mathcal F_2,\mathcal F_3$ be finite families of translates of $K$. If $A\cap B\neq\varnothing$ whenever $A\in\mathcal F_i$, $B\in\mathcal F_j$, and $i\neq j$, prove that some $\mathcal F_j$ can be pierced by three points. | On Dol’nikov’s Conjecture. Edgardo Roldán-Pensado (joint work with Cuauhtémoc Gomez-Navarro, Leonardo Martı́nez-Sandoval) In the talk I talked about a recent result with Josh Zahl where we show how to use ideas from discrete geometry in order to prove results in projection theory. Specifically, we prove the following... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,805 | OWR-14298163-010 | Simultaneous Embeddings of Random Planar Graphs | Let $\mathcal T_n$ be the family of labeled stacked triangulations obtained by starting from $K_4$ on vertices $v_1,\ldots,v_4$ and, for each $i=4,\ldots,n-1$, inserting $v_{i+1}$ into one of the current $2i-4$ triangular faces and joining it to that face's three vertices. If $G_1,G_2$ are sampled independently and uni... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-010",
"literature-status:open",
"owr-year:2024"
] | The 2024 primary paper formulates this exact two-random-planar-graphs probability as Problem 6.1; it proves non-embeddability for about 3 log_2(n) independent stacked triangulations, not the requested two-graph limit. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://doi.org/10.1007/s00454-024-00665-7",
"label": "A Logarithmic Bound for Simultaneous Embeddings of Planar Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $\mathcal T_n$ be the family of labeled stacked triangulations obtained by starting from $K_4$ on vertices $v_1,\ldots,v_4$ and, for each $i=4,\ldots,n-1$, inserting $v_{i+1}$ into one of the current $2i-4$ triangular faces and joining it to that face's three vertices. If $G_1,G_2$ are sampled independently and uni... | Open problems. One open problem that would be very interesting to settle (in particular with regards to Problem 1) is the following: For large n, what is the probability that two independently sampled random planar graphs G1 , G2 from the probability distribution used in the proofs of Theorem 1 and 2 admit a simultaneo... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,806 | OWR-14298163-013 | No-Three-in-Line Problem | For every positive integer $n$, can one select $2n$ points from the grid $[n]^2$ such that no three selected points are collinear? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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 | Duplicate of canonical problem COMB-011 | [
"COMB-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-013",
"literature-status:open",
"owr-year:2024"
] | The no-three-in-line conjecture still has no proof for all n: current primary work gives constructions through finite ranges and improved bounds, but does not establish 2n points on every n by n grid. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://arxiv.org/abs/2602.07751",
"label": "Constraint Satisfaction Programming for the No-three-in-line Problem"
},
{
"url": "https://doi.org/10.1007/s10623-025-01632-w",
"label": "Permu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For every positive integer $n$, can one select $2n$ points from the grid $[n]^2$ such that no three selected points are collinear? | The famous no-three-in-line problem raised by Dudeney [6] in 1917: Is it true that one can select 2n points in [n]2 such that no three are collinear? Variation of no-three-in-line problem Ji Zeng (joint work with Andrew Suk, Yaobin Chen, Xizhi Liu, Jiaxi Nie) 188 Oberwolfach Report 3/2024 d showed that \alphad,k (n) \l... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,807 | OWR-14298163-014 | Asymptotics of Higher-Dimensional General-Position Sets | For fixed $d$ and $k$, determine the asymptotic order of $\alpha_{d,k}(n)$, the maximum size of a subset of $[n]^d$ containing no $k+2$ points in a $k$-dimensional affine subspace. In particular, determine $\alpha_{4,2}(n)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-014",
"literature-status:open",
"owr-year:2024"
] | For alpha_{4,2}(n) and general fixed d,k, the literature supplies upper and lower bounds but explicitly leaves the asymptotic magnitude undetermined; newer bounds do not close the gap. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/on-higher-dimensional-point-sets-in-general-position/6552A470A725144363409132B022837",
"label": "On higher dimen... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For fixed $d$ and $k$, determine the asymptotic order of $\alpha_{d,k}(n)$, the maximum size of a subset of $[n]^d$ containing no $k+2$ points in a $k$-dimensional affine subspace. In particular, determine $\alpha_{4,2}(n)$. | Problem 1. Determine the asymptotic magnitude of \alpha4,2 (n), and more generally, of \alphad,k (n) for all fixed d and k. As another variation of the no-three-in-line problem, we consider the quan- tity \alpha(F2q , p), defined as the maximum size of a collinear-triple-free subset S in a p-random set of F2q , that is... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,808 | OWR-14298163-015 | Collinear-Triple-Free Sets in Random Grids | Characterize $\alpha([n]^2,p)$, the maximum size of a collinear-triple-free subset of a random subset of $[n]^2$ in which each grid point is retained independently with probability $p$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-015",
"literature-status:open",
"owr-year:2024"
] | The report identifies characterization of alpha([n]^2,p) for a p-random grid as a future direction; the finite-field analogue is treated, but the grid problem has no cited complete characterization. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Characterize $\alpha([n]^2,p)$, the maximum size of a collinear-triple-free subset of a random subset of $[n]^2$ in which each grid point is retained independently with probability $p$. | To obtain the desired quantitative bounds of our containers, we apply the hy- pergraph container lemma together with a “balanced supersaturation” result of collinear triples in F2q . And we leverage the pseudorandomness of the point-line incidence bipartite graph of F2q to achieve such a “balanced supersaturation”. Thi... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,809 | OWR-14298163-016 | Point-to-Nonincident-Line Separation | Let $p_1,\ldots,p_n\in[0,1]^2$ and let each line $\ell_i$ pass through $p_i$. Determine the largest possible value of $\delta=\min_{i\neq j}d(p_i,\ell_j)$. In particular, prove or disprove that $\delta\leq n^{-1+\varepsilon}$ for every $\varepsilon>0$ and all sufficiently large $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-016",
"literature-status:open",
"owr-year:2024"
] | The extracted distance question lacks the normalization and hypotheses needed to identify a definite extremal theorem; the report presents it as an open incidence problem, and no authoritative resolution of this exact formulation was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $p_1,\ldots,p_n\in[0,1]^2$ and let each line $\ell_i$ pass through $p_i$. Determine the largest possible value of $\delta=\min_{i\neq j}d(p_i,\ell_j)$. In particular, prove or disprove that $\delta\leq n^{-1+\varepsilon}$ for every $\varepsilon>0$ and all sufficiently large $n$. | What is the smallest possible distance \delta = d(pi , ℓj ) between a point pi and a line ℓj for i 6= j? Lower bounds for incidences Dmitrii Zakharov (joint work with Alex Cohen, Cosmin Pohoata) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,810 | OWR-14298163-017 | Thick Drawings of Grid Graphs | Does there exist an absolute constant $C$ such that every grid graph with $n$ vertices admits a $1$-thick drawing in a square of side length $C\sqrt n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-017",
"literature-status:open",
"owr-year:2024"
] | The 1-thick grid-graph drawing problem is explicitly listed as open; existing thick-drawing results for special graph families do not establish a universal C for every grid graph. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Does there exist an absolute constant $C$ such that every grid graph with $n$ vertices admits a $1$-thick drawing in a square of side length $C\sqrt n$? | Is there a constant C such that for any n any \sqrt{ }grid graph with n vertices admits a 1–thick drawing in a square of side length C n? This question is based on the “Sponge problem”, see [1]. [1] Larry Guth, The Width-Volume Inequality Geometric and Functional Analysis 17 (2007), pp. Open Problems in Discrete Geomet... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,811 | OWR-14298163-018 | Face-Size Distribution in Random Pseudoline Arrangements | For a uniformly random simple pseudoline arrangement on $n$ pseudolines and a uniformly random face, prove that the limiting probabilities $p_k$ of having $k$ sides exist and determine them, beginning with the triangle probability $p_3$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-018",
"literature-status:open",
"owr-year:2024"
] | The report states that even convergence of the probabilities for random-face sizes in uniform simple pseudoline arrangements is unproved; consequently the limiting triangle probability p_3 remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For a uniformly random simple pseudoline arrangement on $n$ pseudolines and a uniformly random face, prove that the limiting probabilities $p_k$ of having $k$ sides exist and determine them, beginning with the triangle probability $p_3$. | What is the probability p3 that a random face in a random simple pseudoline arrangement is a triangle, in the limit as the number n of pseudolines goes to infinity? The answer is the same if we ask for the size of the convex hull in a random abstract order type. Problem 1 (Sergey Avvakumov). A grid graph is a graph dra... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,812 | OWR-14298163-019 | Finiteness of Generalized Moore Graphs | For a fixed constant $c>0$, are there only finitely many regular graphs satisfying $\operatorname{girth}(G)=(2-c)\operatorname{diam}(G)$, apart from the known complete and odd-cycle families? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-019",
"literature-status:open",
"owr-year:2024"
] | Known Moore-graph classification leaves the exceptional degree-57 diameter-two case unresolved, and the broader near-Moore formulation in this fragment is not settled by the classification theorems. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://arxiv.org/abs/2210.09577",
"label": "Existence of a Moore graph of degree 57 is still open"
},
{
"url": "https://www.combinatorics.org/files/Surveys/ds14/ds14v2-2013.pdf",
"label":... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For a fixed constant $c>0$, are there only finitely many regular graphs satisfying $\operatorname{girth}(G)=(2-c)\operatorname{diam}(G)$, apart from the known complete and odd-cycle families? | Is their number also finite? girth = 2 diam − 1 Except for Kn and C2n+1 there are just sporadic regular Moore graphs. What about regular Moore graphs satisfying | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,813 | OWR-14298163-020 | Topology Near the Systolic-Diameter Bound | For each $\varepsilon>0$, are there only finitely many topological types of Riemannian manifolds satisfying $\operatorname{systole}(M)/\operatorname{diam}(M)\geq 2-\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-020",
"literature-status:open",
"owr-year:2024"
] | The systole-to-diameter finiteness question is explicitly posed in the report; finiteness theorems are known under stronger curvature, entropy, or hyperbolicity hypotheses, but they do not settle the stated 2-epsilon question. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://arxiv.org/abs/2109.13025",
"label": "Finiteness Theorems for Gromov-Hyperbolic Spaces and Groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | For each $\varepsilon>0$, are there only finitely many topological types of Riemannian manifolds satisfying $\operatorname{systole}(M)/\operatorname{diam}(M)\geq 2-\varepsilon$? | What if I have a Riemanian manifold with systole \leq 2? diam Gromov showed that this bound is attained only at RPn . Is the number of topologies for 2 − \varepsilon finite? The question is the following: Question 1. For what values of k is Dk contractible for every point set P of size n? Note that D1 is just the conve... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,814 | OWR-14298163-021 | Bounded Pairwise Crossings in Hypercube Drawings | Does there exist an absolute constant $c\in\mathbb N$ such that every hypercube graph $Q_d$ has a topological drawing in the plane with no collection of $c$ pairwise crossing edges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-021",
"literature-status:open",
"owr-year:2024"
] | The hypercube drawing question is still open in the report's formulation; known k-quasi-planar results give edge bounds under drawing restrictions but do not provide an absolute crossing-clique bound for all hypercubes. | [
{
"url": "https://doi.org/10.4171/owr/2024/3",
"label": "Discrete Geometry (2024)"
},
{
"url": "https://doi.org/10.1137/110858586",
"label": "The Number of Edges in k-Quasi-planar Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Does there exist an absolute constant $c\in\mathbb N$ such that every hypercube graph $Q_d$ has a topological drawing in the plane with no collection of $c$ pairwise crossing edges? | The question is the following: Question 1. Does there exist an absolute constant c \in N such that for every d \in N the hypercube graph Qd admits a topological drawing in the plane such that there exists no collection of c pairwise crossing edges? This relates to another open question, namely whether the maximum numbe... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,815 | OWR-14298163-022 | Tverberg Regions and Random Great-Circle Cells | Resolve the following two questions. (1) For which $k$ is the region $D_k=\{q\in\mathbb R^d:\operatorname{TvD}(P,q)\geq k\}$ contractible for every $n$-point set $P\subseteq\mathbb R^d$? (2) For $n$ great circles in general position on $S^2$, choose a cell $c$ uniformly, remove the circles touching $c$, and let $x$ be ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-022",
"literature-status:open",
"owr-year:2024"
] | The extracted question is an incomplete fragment and does not specify the random variable or hypotheses; no verifiable resolution can be assigned, so it remains open. | [
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Resolve the following two questions. (1) For which $k$ is the region $D_k=\{q\in\mathbb R^d:\operatorname{TvD}(P,q)\geq k\}$ contractible for every $n$-point set $P\subseteq\mathbb R^d$? (2) For $n$ great circles in general position on $S^2$, choose a cell $c$ uniformly, remove the circles touching $c$, and let $x$ be ... | How large can the expectation of x be? The question is the following: Question 1. For what values of k is Dk contractible for every point set P of size n? Note that D1 is just the convex hull of P , which is of course contractible. On the other hand, the set of Tverberg points is in general not even connected, so Dk n ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
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