id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,116 | OWR-12005-009 | Round-Sphere Maximization of the First Boundary Eigenvalue | For every integer $m\geq3$, does the round sphere maximize $\lambda_1(\Sigma)|\Sigma|^{2/m}$ among convex hypersurfaces $\Sigma^m\subset\mathbb R^{m+1}$, where $\lambda_1(\Sigma)$ is the first nontrivial Laplace–Beltrami eigenvalue? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12005-009",
"literature-status:open",
"owr-year:2012"
] | The claim that the round sphere maximizes the normalized first eigenvalue for dimensions at least three is recorded as open; the report notes the two dimensional case but no higher dimensional resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For every integer $m\geq3$, does the round sphere maximize $\lambda_1(\Sigma)|\Sigma|^{2/m}$ among convex hypersurfaces $\Sigma^m\subset\mathbb R^{m+1}$, where $\lambda_1(\Sigma)$ is the first nontrivial Laplace–Beltrami eigenvalue? | For every integer m\geq 3, is the round sphere the maximizer among convex hypersurfaces \Sigma^m\subset\mathbb{R}^{m+1} of \lambda_1(\Sigma)|\Sigma|^{2/m}, where \lambda_1(\Sigma) is the first nontrivial Laplace--Beltrami eigenvalue? | corrected_verified | The official report states this round-sphere extremal question; mathematical typography was normalized. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,117 | OWR-12005-010 | Duplicate Round-Sphere Eigenvalue Question | For every integer m\geq 3, is the round sphere the maximizer among convex hypersurfaces \Sigma^m\subset\mathbb{R}^{m+1} of \lambda_1(\Sigma)|\Sigma|^{2/m}, where \lambda_1(\Sigma) is the first nontrivial Laplace--Beltrami eigenvalue? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report contains one round-sphere extremal question, and this extraction is textually identical in substance to the preceding re) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12005-010",
"literature-status:open",
"owr-year:2012"
] | The claim that the round sphere maximizes the normalized first eigenvalue for dimensions at least three is recorded as open; the report notes the two dimensional case but no higher dimensional resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | null | For every integer m\geq 3, is the round sphere the maximizer among convex hypersurfaces \Sigma^m\subset\mathbb{R}^{m+1} of \lambda_1(\Sigma)|\Sigma|^{2/m}, where \lambda_1(\Sigma) is the first nontrivial Laplace--Beltrami eigenvalue? | unrecoverable | The official report contains one round-sphere extremal question, and this extraction is textually identical in substance to the preceding record from the same report. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,118 | OWR-12005-011 | Fixed Volume Magnetic Eigenvalue Minimizers in Three Dimensions | For a real magnetic parameter $\beta$ and a bounded open set $\Omega\subset\mathbb{R}^3$, can one find a fixed-volume $\Omega$ that minimizes the first Dirichlet eigenvalue $E_1$ of $\left(i\nabla+\frac{\beta}{2}(-x_2,x_1,0)\right)^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12005-011",
"literature-status:partially-solved",
"owr-year:2012"
] | The three dimensional fixed volume magnetic problem remains unresolved; recent work proves non ball behavior and derives constraints in regimes, with numerical candidates, but does not identify a general minimizer. | [
{
"url": "https://arxiv.org/abs/2504.21597",
"label": "Baur"
},
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For a real magnetic parameter $\beta$ and a bounded open set $\Omega\subset\mathbb{R}^3$, can one find a fixed-volume $\Omega$ that minimizes the first Dirichlet eigenvalue $E_1$ of $\left(i\nabla+\frac{\beta}{2}(-x_2,x_1,0)\right)^2$? | For a real magnetic parameter \beta and a bounded open set \Omega\subset\mathbb{R}^3, can one find a fixed-volume \Omega that minimizes the first Dirichlet eigenvalue E_1 of \left(i\nabla+\frac{\beta}{2}(-x_2,x_1,0)\right)^2? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete statement was preserved while previously undelimited mathematical notation was normalized into readable prose. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,119 | OWR-12005-012 | Planar Steklov Isospectral Domains | Do there exist non-isometric planar domains that are isospectral for the Steklov eigenvalue problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12005-012",
"literature-status:open",
"owr-year:2012"
] | The extracted record contains only historical framing of Kac's question and omits the actual hypotheses or claim, so no precise literature status can be assigned. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | Do there exist non-isometric planar domains that are isospectral for the Steklov eigenvalue problem? | Do there exist non-isometric planar domains that are isospectral for the Steklov eigenvalue problem? | exact | The official report was checked and confirms the complete problem statement. The statement is internally readable; retained byte-for-byte. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,120 | OWR-12005-017 | Nodal Counts for Fractional Schrödinger Eigenfunctions | Let $0<s<1$, let $(-\Delta)^s+V$ be a lower-semibounded fractional Schrödinger operator on $L^2(\mathbb R^m)$ with real $V$, and let $\psi_k$ be a continuous real eigenfunction associated with the $k$th eigenvalue below the essential spectrum. Bound the number of connected components of $\{\psi_k\ne0\}$ in terms of $k$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12005-017",
"literature-status:open",
"owr-year:2012"
] | No general index versus nodal domain theorem is known for fractional Schrodinger eigenfunctions; available results give one dimensional and other partial oscillation bounds only. | [
{
"url": "https://doi.org/10.19086/da.2102",
"label": "Hur Johnson Martin"
},
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | Let $0<s<1$, let $(-\Delta)^s+V$ be a lower-semibounded fractional Schrödinger operator on $L^2(\mathbb R^m)$ with real $V$, and let $\psi_k$ be a continuous real eigenfunction associated with the $k$th eigenvalue below the essential spectrum. Bound the number of connected components of $\{\psi_k\ne0\}$ in terms of $k$... | For eigenfunctions \psi_k of a Dirichlet Laplacian or comparable elliptic operator, what can be said about the number of nodal domains in terms of the eigenvalue index k? | corrected_verified | The official report gives this fractional Schrödinger setting and asks for the analogue of nodal-domain bounds. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,121 | OWR-12006-001 | Projectively Unique Polytopes in Intermediate Dimensions | For which dimensions $4\leq d\leq80$ are there infinitely many combinatorial types of projectively unique $d$-polytopes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137](https://doi.org/10.4171/owr/2012/34)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,012 | 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-12006-001",
"literature-status:partially-solved",
"owr-year:2012"
] | The finiteness question is positive in dimensions two and three and negative in sufficiently high fixed dimensions, explicitly dimension sixty nine in the primary construction; intermediate dimensions and the full growth question remain unresolved. | [
{
"url": "https://arxiv.org/abs/1212.5812",
"label": "Adiprasito Ziegler"
},
{
"url": "https://ems.press/content/serial-article-files/46402",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/34 | null | null | null | For which dimensions $4\leq d\leq80$ are there infinitely many combinatorial types of projectively unique $d$-polytopes? | For fixed dimension d, is the number of combinatorial types of projectively unique d-polytopes finite, and how does the dimension of the realization space of a d-dimensional polytope grow with its size? | corrected_verified | The report’s second realization-space problem is answered in the same article, and its first problem is answered negatively for every dimension at least 81. The clean statement isolates the unresolved intermediate-dimensional range left by those results. | null | null | null | null | null | Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137 |
30,002,122 | OWR-12006-003 | Derived Schläfli Formula for Spherical Cone Metrics | For a spherical cone metric on a 2-sphere with k cone points of angles \alpha_i, let A=2\pi(2-k)+\sum_i\alpha_i and let its Hopf lift to S^3 have volume V=A^2/8. Determine how V changes when the cone angles vary; equivalently, establish the Schlaefli relation 2 dV=(A/2)\sum_i d\alpha_i. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137](https://doi.org/10.4171/owr/2012/34)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,012 | 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 | Answered in the source or not an open problem (solved (a completed calculation, not an open problem)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (a completed calculation, not an open problem)**. The record recasts as a task a step of J. M. Sullivan's abstract (OWR 34/2012, pp. 2118–2121): from V = A²/8 for the Hopf lift of a spherical cone metric, with A = 2π(2−k) + Σα_i, varying the cone angles gives 2dV =... | [
"owr",
"oberwolfach-reports",
"OWR-12006-003",
"literature-status:open",
"owr-year:2012"
] | The extracted record begins with the word conjecture but is truncated before stating the conjectural claim, so current literature cannot verify a precise proposition. | [
{
"url": "https://doi.org/10.4171/owr/2012/34",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/34 | null | null | null | null | For a spherical cone metric on a 2-sphere with k cone points of angles \alpha_i, let A=2\pi(2-k)+\sum_i\alpha_i and let its Hopf lift to S^3 have volume V=A^2/8. Determine how V changes when the cone angles vary; equivalently, establish the Schlaefli relation 2 dV=(A/2)\sum_i d\alpha_i. | unrecoverable | The source derives $2\,dV=(A/2)\sum_i d\alpha_i$ directly from $V=A^2/8$ and identifies it as the well-known Schläfli formula. This is a completed calculation, not an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137 |
30,002,123 | OWR-12006-004 | Shellability of Barycentric Subdivisions of Convex Complexes | If $C$ is a convex simplicial complex, is its barycentric subdivision shellable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137](https://doi.org/10.4171/owr/2012/34)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,012 | 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-12006-004",
"literature-status:open",
"owr-year:2012"
] | General shellability of the first barycentric subdivision remains unresolved; Adiprasito and Benedetti prove shellability after a bounded further subdivision and related collapsibility results, not the stated general first subdivision claim. | [
{
"url": "https://arxiv.org/abs/1709.07930",
"label": "Adiprasito Benedetti"
},
{
"url": "https://www.ihes.fr/~fguenth/files/OWR_2012_34.pdf",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/34 | null | null | null | If $C$ is a convex simplicial complex, is its barycentric subdivision shellable? | If C is a convex simplicial complex, is its barycentric subdivision shellable? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137 |
30,002,124 | OWR-12006-005 | Discrete Green Kernels, Escaping Geodesics, and Random Triangulations | Three independent questions are considered. First, under mild regularity assumptions on orthogonal dual planar graphs $\Gamma$ and $\Gamma^*$, can one prove the uniform asymptotics
$$G(u;u_0)=\frac{1}{2\pi}\log|u-u_0|+O(1),\qquad K(v;z_0)=O(|v-z_0|^{-1})?$$
Second, from every point of a metrically complete noncompact... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137](https://doi.org/10.4171/owr/2012/34)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,012 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12006-005",
"literature-status:open",
"owr-year:2012"
] | The record conflates a geodesic ray avoidance question with a random triangulation diameter question and is incomplete; related results are partial, so the combined extracted claim remains unresolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/76ac1159-94b4-4a15-9fc6-21b50a98dcc0/content",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/34 | null | null | null | Three independent questions are considered. First, under mild regularity assumptions on orthogonal dual planar graphs $\Gamma$ and $\Gamma^*$, can one prove the uniform asymptotics
$$G(u;u_0)=\frac{1}{2\pi}\log|u-u_0|+O(1),\qquad K(v;z_0)=O(|v-z_0|^{-1})?$$
Second, from every point of a metrically complete noncompact... | Under mild regularity assumptions on orthogonal dual planar graphs \Gamma and \Gamma^*, can one prove the uniform asymptotics G(u;u_0)=\frac{1}{2\pi}\log|u-u_0|+O(1) and K(v;z_0)=O(|v-z_0|^{-1})? For every point of a metrically complete noncompact Euclidean cone surface with finitely many negatively curved cone singula... | corrected_verified | The bundled extraction was retained as three explicitly separated questions because all three occur as independent open problems in the same official report. | null | null | null | null | null | Discrete Differential Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/34, pp. 2077--2137 |
30,002,125 | OWR-12007-002 | $C^0$ Hamiltonian Dynamics and Continuous Symplectic Structures | Can one define $C^0$ counterparts of the classical smooth symplectic objects, in particular a meaningful $C^0$ Hamiltonian dynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-002",
"literature-status:open",
"owr-year:2012"
] | The record asks broadly for continuous counterparts of smooth symplectic objects without isolating a precise proposition; the C0 Hamiltonian framework has partial results but remains an active open area. | [
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1808.09790",
"label": "C0 Hamiltonian dynamics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Can one define $C^0$ counterparts of the classical smooth symplectic objects, in particular a meaningful $C^0$ Hamiltonian dynamics? | Can one define C^0 counterparts of the classical smooth symplectic objects, in particular a meaningful C^0 Hamiltonian dynamics? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,126 | OWR-12007-006 | Local Middle-Dimensional Symplectic Nonsqueezing | Let $P_k$ be orthogonal projection onto the standard $\mathbb R^{2k}\subset\mathbb R^{2n}$. Two local middle-dimensional nonsqueezing questions remain open. First, for every symplectomorphism $\phi:\mathbb R^{2n}\to\mathbb R^{2n}$ and every $x\in\mathbb R^{2n}$, is
$$\operatorname{vol}_{2k}\bigl(P_k\phi(B_r(x))\bigr)\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-006",
"literature-status:open",
"owr-year:2012"
] | The global smooth nonlinear analogue has counterexamples, but the local smooth projection inequalities asked in the record remain unresolved. | [
{
"url": "https://arxiv.org/abs/1105.2931",
"label": "Abbondandolo--Matveyev, middle-dimensional squeezing"
},
{
"url": "https://arxiv.org/abs/1508.04015",
"label": "Rigolli, local analytic non-squeezing"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Let $P_k$ be orthogonal projection onto the standard $\mathbb R^{2k}\subset\mathbb R^{2n}$. Two local middle-dimensional nonsqueezing questions remain open. First, for every symplectomorphism $\phi:\mathbb R^{2n}\to\mathbb R^{2n}$ and every $x\in\mathbb R^{2n}$, is
$$\operatorname{vol}_{2k}\bigl(P_k\phi(B_r(x))\bigr)\... | Let P_k be orthogonal projection onto the standard \mathbb{R}^{2k}\subset\mathbb{R}^{2n}. Is it true that \operatorname{vol}_{2k}(P_k\phi(B_r))\geq\omega_{2k}r^{2k} for every symplectomorphism \phi, every r>0, and, locally, for sufficiently small r? If \{\phi_t\} is a smooth symplectic path with \phi_0 linear, is \oper... | corrected_verified | The official report disproves the global nonlinear inequality before posing exactly these two surviving local formulations. The clean statement removes the already-refuted global claim and restores the center point in the local-in-space version. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,127 | OWR-12007-007 | Parallel-Axiom Rigidity of Complete Riemannian Planes | If a complete Riemannian plane $P$ satisfies the parallel axiom that every geodesic and every point off it determine a unique disjoint geodesic through that point, must $P$ be isometric to the Euclidean plane? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-007",
"literature-status:open",
"owr-year:2012"
] | The parallel-axiom rigidity question for complete Riemannian planes is still identified as open in subsequent rigidity literature. | [
{
"url": "https://d-nb.info/1123477280/34",
"label": "Rigidity of complete manifolds without conjugate points"
},
{
"url": "https://archive.ymsc.tsinghua.edu.cn/pacm_download/21/980-JDG-94-3-A1-Bangert.pdf",
"label": "Bangert--Emmerich, area growth and rigidity"
},
{
"url": "https://doi.... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | If a complete Riemannian plane $P$ satisfies the parallel axiom that every geodesic and every point off it determine a unique disjoint geodesic through that point, must $P$ be isometric to the Euclidean plane? | If a complete Riemannian plane P satisfies the parallel axiom that every geodesic and every point off it determine a unique disjoint geodesic through that point, must P be isometric to the Euclidean plane? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,128 | OWR-12007-008 | Rationality and Computation of Free-Group Rotation Suprema | Let $F$ be the rank-two free group, and let $R(w,r,s)$ be the supremum of the lifted rotation number of $\rho(w)$ over representations with rotation numbers $r$ and $s$ on the generators. Is $R(w,r,s)\in\mathbb Q$ for every $w\in F$ and $r,s\in\mathbb Q$, and can one give a practical method to compute or approximate it... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"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-12007-008",
"literature-status:open",
"owr-year:2012"
] | The source itself prints real parameters, but w=a gives R(a,r,s)=r and immediately defeats universal rationality. Its positive-word results instead assume rational parameters. The intended rationality question is recorded with r,s rational; the discrepancy in the original report is explicit.
**What remains.** Rational... | [
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedM... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Let $F$ be the rank-two free group, and let $R(w,r,s)$ be the supremum of the lifted rotation number of $\rho(w)$ over representations with rotation numbers $r$ and $s$ on the generators. Is $R(w,r,s)\in\mathbb Q$ for every $w\in F$ and $r,s\in\mathbb Q$, and can one give a practical method to compute or approximate it... | Let F be the rank-two free group and let R(w,r,s) be the supremum of the lifted rotation number of \rho(w) over representations with rotation numbers r and s on the generators. Is R(w,r,s)\in\mathbb{Q} for every w\in F and r,s\in\mathbb{R}, and can one give a practical method to compute or approximate it? | corrected_verified | Corrected an apparent source-level parameter typo in OWR 35/2012, p. 2173: rationality can only be asked for rational r,s. The original real-parameter wording is retained for comparison. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,129 | OWR-12007-009 | Refined Slippery Bounds for Positive-Word Rotation Numbers | For a positive word $w=a^{\alpha_1}b^{\beta_1}\cdots b^{\beta_m}$ with $R(w,r,s)=p/q$, does
$$R(w,r,s)-h_a(w)r-h_b(w)s\leq \frac mq$$
hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-009",
"literature-status:open",
"owr-year:2012"
] | The refined slippery inequality is established only in restricted settings and remains an unresolved conjecture in the stated generality. | [
{
"url": "https://arxiv.org/abs/1110.0080",
"label": "Calegari--Walker, Ziggurats and rotation numbers"
},
{
"url": "https://e.math.cornell.edu/people/mann/papers/rigflexA.pdf",
"label": "Mann, rigidity and flexibility of circle actions"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | For a positive word $w=a^{\alpha_1}b^{\beta_1}\cdots b^{\beta_m}$ with $R(w,r,s)=p/q$, does
$$R(w,r,s)-h_a(w)r-h_b(w)s\leq \frac mq$$
hold? | For a positive word w=a^{\alpha_1}b^{\beta_1}\cdots b^{\beta_m}, if R(w,r,s)=p/q, is it true that R(w,r,s)-h_a(w)r-h_b(w)s\leq m/q? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,130 | OWR-12007-010 | Universal Rotation-Zero Words and Analytic Extremizers | Does there exist a nontrivial word $w$ in the rank-two free group such that the lifted rotation number of $\rho(w)$ is zero for every representation $\rho$ into the universal cover of $\operatorname{Homeo}^+(S^1)$? For arbitrary $w$, does there exist a real-analytic representation $\rho$ with $\operatorname{rot}(\rho(w... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-010",
"literature-status:open",
"owr-year:2012"
] | Both representation questions in the record remain open; no primary source located by the cutoff resolves either the universal vanishing question or the analytic realization question. | [
{
"url": "https://arxiv.org/abs/1110.0080",
"label": "Calegari--Walker, Ziggurats and rotation numbers"
},
{
"url": "https://e.math.cornell.edu/people/mann/papers/rigflexA.pdf",
"label": "Mann, rigidity and flexibility of circle actions"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Does there exist a nontrivial word $w$ in the rank-two free group such that the lifted rotation number of $\rho(w)$ is zero for every representation $\rho$ into the universal cover of $\operatorname{Homeo}^+(S^1)$? For arbitrary $w$, does there exist a real-analytic representation $\rho$ with $\operatorname{rot}(\rho(w... | Does there exist a nontrivial word w in the rank-two free group such that the lifted rotation number of \rho(w) is zero for every representation \rho into the universal cover of \operatorname{Homeo}^+(S^1)? For arbitrary w, does there exist a real-analytic representation \rho with \operatorname{rot}(\rho(w))=R(w,r,s)? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,131 | OWR-12007-011 | Hyperbolic Orbifold Realizations of Compact PL Manifolds | For every compact PL $n$-manifold $M$ without boundary, does there exist a cocompact lattice $\Gamma\subset O(n,1)$ such that $\mathbb H^n/\Gamma$ is PL-isomorphic to $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-011",
"literature-status:open",
"owr-year:2012"
] | Telescopic actions realize selected three- and four-dimensional cases, but the requested realization for arbitrary compact PL manifolds remains unresolved. | [
{
"url": "https://arxiv.org/abs/1104.4814",
"label": "Panov--Petrunin, telescopic actions"
},
{
"url": "https://arxiv.org/abs/1402.4503",
"label": "Panov--Petrunin, telescopic actions survey"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | For every compact PL $n$-manifold $M$ without boundary, does there exist a cocompact lattice $\Gamma\subset O(n,1)$ such that $\mathbb H^n/\Gamma$ is PL-isomorphic to $M$? | For every compact PL n-manifold M without boundary, does there exist a cocompact lattice \Gamma\subset O(n,1) such that \mathbb{H}^n/\Gamma is PL-isomorphic to M? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,132 | OWR-12007-012 | Translated-Point Bounds for Small Contact Isotopies | For a $C^0$-small contact isotopy $\{\phi_t\}$ on a contact manifold $(M,\xi)$, does every $\phi_t$ have at least as many translated points as the minimum number of critical points of a smooth function on $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-012",
"literature-status:partially-solved",
"owr-year:2012"
] | Morse-type lower bounds are proved for small and several structured contactomorphisms, while explicit contactomorphisms of the standard sphere without translated points disprove the unrestricted general conjecture. | [
{
"url": "https://arxiv.org/abs/1110.0691",
"label": "Sandon, Morse estimates for translated points"
},
{
"url": "https://arxiv.org/abs/2210.11002",
"label": "Contactomorphisms of the sphere without translated points"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberw... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | For a $C^0$-small contact isotopy $\{\phi_t\}$ on a contact manifold $(M,\xi)$, does every $\phi_t$ have at least as many translated points as the minimum number of critical points of a smooth function on $M$? | For a C^0-small contact isotopy \{\phi_t\} on a contact manifold (M,\xi), does every \phi_t have at least as many translated points as the minimum number of critical points of a smooth function on M? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,133 | OWR-12007-013 | Answered Survey of Zero-Entropy Disk Dynamics | How mixing or otherwise complex can a C^\infty area-preserving diffeomorphism of the closed 2-disk be when its topological entropy is zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | partially_solved | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The source uses this broad prompt to survey several notions of complexity, then records positive constructions for dense orbits, ergodicity,) | [
"OWR-12007-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-013",
"literature-status:partially-solved",
"owr-year:2012"
] | Zero-entropy area-preserving disk maps can exhibit dense or weakly mixing behavior, but the strongest mixing question remains unresolved. | [
{
"url": "https://arxiv.org/abs/1205.6243",
"label": "Bramham, pseudo-rotations and zero entropy"
},
{
"url": "https://annals.math.princeton.edu/2015/181-3/p04",
"label": "Bramham, periodic approximations"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Repor... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | null | How mixing or otherwise complex can a C^\infty area-preserving diffeomorphism of the closed 2-disk be when its topological entropy is zero? | unrecoverable | The source uses this broad prompt to survey several notions of complexity, then records positive constructions for dense orbits, ergodicity, and weak mixing. Its one explicit unresolved existence question is represented separately by OWR-12007-014. No separate clean statement is promoted; the original record remains pu... | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,134 | OWR-12007-014 | Mixing Zero-Entropy Area-Preserving Disk Diffeomorphisms | Does there exist a mixing area-preserving $C^\infty$-diffeomorphism of the closed $2$-disk with zero topological entropy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12007-013",
"OWR-12007-015"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-014",
"literature-status:open",
"owr-year:2012"
] | No mixing examples with the stated smooth area-preserving and zero-entropy properties have been established, and their existence remains unresolved. | [
{
"url": "https://arxiv.org/abs/1205.6243",
"label": "Bramham, pseudo-rotations and zero entropy"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Does there exist a mixing area-preserving $C^\infty$-diffeomorphism of the closed $2$-disk with zero topological entropy? | Does there exist a mixing area-preserving C^\infty-diffeomorphism of the closed 2-disk with zero topological entropy? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,135 | OWR-12007-015 | Duplicate Mixing Zero-Entropy Disk Question | Does there exist a mixing area-preserving C^\infty-diffeomorphism of the closed 2-disk with zero topological entropy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record exactly repeats the same-report mixing question represented canonically by OWR-12007-014. No separate clean statement is promote) | [
"OWR-12007-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-015",
"literature-status:open",
"owr-year:2012"
] | The existence of a mixing smooth area-preserving disk diffeomorphism with zero topological entropy remains an open problem. | [
{
"url": "https://arxiv.org/abs/1205.6243",
"label": "Bramham, pseudo-rotations and zero entropy"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | null | Does there exist a mixing area-preserving C^\infty-diffeomorphism of the closed 2-disk with zero topological entropy? | unrecoverable | This record exactly repeats the same-report mixing question represented canonically by OWR-12007-014. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,136 | OWR-12007-016 | Nonconjugate $\operatorname{SL}_3$-Character-Equivalent Free-Group Words | Do there exist elements $g,g'\in F_2$ that are $\operatorname{SL}_3(\mathbb C)$-character equivalent, meaning that all corresponding representation traces agree, but are not conjugate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-016",
"literature-status:open",
"owr-year:2012"
] | The primary literature reports the analogous trace characterization for two generators but leaves the existence of an SL3-character-equivalent nonconjugate pair in the free group unresolved. | [
{
"url": "https://arxiv.org/abs/1312.1261",
"label": "Lawton--Louder--McReynolds, traces and representations"
},
{
"url": "https://doi.org/10.4171/GGD/393",
"label": "Published traces and representations paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Do there exist elements $g,g'\in F_2$ that are $\operatorname{SL}_3(\mathbb C)$-character equivalent, meaning that all corresponding representation traces agree, but are not conjugate? | Do there exist elements g,g'\in F_2 that are SL_3(\mathbb{C})-character equivalent, meaning all corresponding representation traces agree, but are not conjugate? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,137 | OWR-12007-017 | Hofer Norms on Fundamental Groups of Symplectic Manifolds | For a symplectic manifold $(M,\omega)$, a ball $B$, and the induced Hofer norm $\lVert\gamma\rVert_B$ on $\pi_1(M)$, what can be said about this conjugation-invariant norm? Is it bounded, and is it equivalent to word length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-017",
"literature-status:partially-solved",
"owr-year:2012"
] | The norm is bounded on the two-torus and unbounded on an annulus when the fixed ball is sufficiently large, but its general boundedness and word-length equivalence remain unresolved. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/2d68ade4-b554-459d-9f08-bb2793165aa0/download",
"label": "Khanevsky, Oberwolfach lecture report"
},
{
"url": "https://arxiv.org/abs/1111.1923",
"label": "Khanevsky, Hofer norm and disk translations"
},
{
"url": "https://doi.org/10.4171/owr/20... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | For a symplectic manifold $(M,\omega)$, a ball $B$, and the induced Hofer norm $\lVert\gamma\rVert_B$ on $\pi_1(M)$, what can be said about this conjugation-invariant norm? Is it bounded, and is it equivalent to word length? | For a symplectic manifold (M,\omega), a ball B, and the induced Hofer norm \|\gamma\|_B on \pi_1(M), what can be said about this conjugation-invariant norm: is it bounded, and is it equivalent to word length? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,138 | OWR-12007-018 | Quasi-Isometry of Horospheres in Negative Curvature | If $(X^{n+1},g)$ is closed with negative sectional curvature, are all horospheres $(H,\widetilde g|_H)$ in its universal cover quasi-isometric to one another, and if so uniformly quasi-isometric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-018",
"literature-status:open",
"owr-year:2012"
] | Recent horospherical rigidity results impose additional hypotheses and prove special rigidity statements, but quasi-isometry of all horospheres in every closed negatively curved manifold is not established. | [
{
"url": "https://arxiv.org/abs/2411.15093",
"label": "Besson--Courtois--Hersonsky, horospherical rigidity"
},
{
"url": "https://doi.org/10.1017/etds.2024.58",
"label": "Rigidity of flat holonomies"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | If $(X^{n+1},g)$ is closed with negative sectional curvature, are all horospheres $(H,\widetilde g|_H)$ in its universal cover quasi-isometric to one another, and if so uniformly quasi-isometric? | If (X^{n+1},g) is closed with negative sectional curvature, are all horospheres (H,\widetilde g|_H) in its universal cover quasi-isometric to one another, and if so uniformly quasi-isometric? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,139 | OWR-12007-019 | Horosphere Geometry Under Quasi-Isometries of Universal Covers | In dimension $3$, are the horospheres for the lifted hyperbolic metric $\widetilde g_0$ and another negatively curved metric $\widetilde g$ quasi-isometric? More generally, what does a quasi-isometry between the universal covers say about their horospheres, and under what conditions do the lower and upper polynomial vo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-019",
"literature-status:open",
"owr-year:2012"
] | The dimension-three comparison with the hyperbolic metric and its proposed higher-dimensional generalization remain unresolved in the stated generality. | [
{
"url": "https://arxiv.org/abs/2411.15093",
"label": "Besson--Courtois--Hersonsky, horospherical rigidity"
},
{
"url": "https://doi.org/10.1017/etds.2024.58",
"label": "Rigidity of flat holonomies"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | In dimension $3$, are the horospheres for the lifted hyperbolic metric $\widetilde g_0$ and another negatively curved metric $\widetilde g$ quasi-isometric? More generally, what does a quasi-isometry between the universal covers say about their horospheres, and under what conditions do the lower and upper polynomial vo... | In dimension 3, are the horospheres for the lifted hyperbolic metric \widetilde g_0 and another negatively curved metric \widetilde g quasi-isometric? More generally, what does a quasi-isometry between the universal covers say about their horospheres, and under what conditions do the lower and upper polynomial volume-g... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,140 | OWR-12007-020 | Cocompact Hyperbolic Actions on CAT Spaces | Can one classify the $\operatorname{CAT}(0)$ or $\operatorname{CAT}(-1)$ spaces on which $\operatorname{Isom}(\mathbb H^n)$ acts cocompactly? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 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-12007-020",
"literature-status:open",
"owr-year:2012"
] | Exotic CAT-negative deformations and classifications under additional hypotheses are known, but no classification of all CAT0 or CAT-negative spaces with cocompact hyperbolic isometry action is available. | [
{
"url": "https://arxiv.org/abs/1201.0606",
"label": "Monod--Py, exotic hyperbolic deformations"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | Can one classify the $\operatorname{CAT}(0)$ or $\operatorname{CAT}(-1)$ spaces on which $\operatorname{Isom}(\mathbb H^n)$ acts cocompactly? | Can one classify the CAT(0) or CAT(-1) spaces on which Isom(H^n) acts cocompactly? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,141 | OWR-12007-021 | Lipschitz Realization of Surface Homotopy Equivalences | For compact negatively curved surfaces $M_1$ and $M_2$, does Thurston's length-spectrum criterion imply that every homotopy equivalence $f:M_1\to M_2$ is homotopic to an $L$-Lipschitz homeomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | partially_solved | null | 2,012 | 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-12007-021",
"literature-status:partially-solved",
"owr-year:2012"
] | Quantitative local marked-length-spectrum rigidity is proved for negatively curved surfaces and related locally symmetric cases, but the full extension of Thurston's global theorem remains unresolved. | [
{
"url": "https://arxiv.org/abs/2203.12128",
"label": "Butt, quantitative marked length spectrum rigidity"
},
{
"url": "https://arxiv.org/abs/math/9801039",
"label": "Thurston, minimal stretch maps"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | For compact negatively curved surfaces $M_1$ and $M_2$, does Thurston's length-spectrum criterion imply that every homotopy equivalence $f:M_1\to M_2$ is homotopic to an $L$-Lipschitz homeomorphism? | For compact negatively curved surfaces M_1 and M_2, does Thurston's length-spectrum criterion imply that every homotopy equivalence f:M_1\to M_2 is homotopic to an L-Lipschitz homeomorphism? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,142 | OWR-12007-022 | Topology of Strict-to-General Contactomorphism Inclusions | What is the topology of the natural inclusion
$$j:\operatorname{Cont}_0(M,\alpha)\hookrightarrow\operatorname{Cont}_0(M,\xi)$$
for a contact manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-022",
"literature-status:partially-solved",
"owr-year:2012"
] | The standard three-sphere case has a strong homotopy-theoretic description of the strict-contact subgroup inclusion, while the topology of the inclusion for general regular contact manifolds remains unresolved. | [
{
"url": "https://arxiv.org/abs/1409.1913",
"label": "Chern--Weil theory and strict contactomorphisms"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | What is the topology of the natural inclusion
$$j:\operatorname{Cont}_0(M,\alpha)\hookrightarrow\operatorname{Cont}_0(M,\xi)$$
for a contact manifold? | What is the topology of the natural inclusion j:Cont_0(M,alpha)\hookrightarrow Cont_0(M,xi) for a contact manifold? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,143 | OWR-12007-023 | Geometry and Quasimorphism Extension Along Contactomorphism Inclusions | What can be said about the geometry of
$$j:\operatorname{Cont}_0(M,\alpha)\hookrightarrow\operatorname{Cont}_0(M,\xi),$$
and can quasimorphisms from $\operatorname{Ham}(X,\omega)$ extend along $j$ in the prequantization case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203](https://doi.org/10.4171/owr/2012/35)
## Literature... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12007-023",
"literature-status:open",
"owr-year:2012"
] | The extracted record is a context-only follow-up and does not state a determinate geometric claim whose resolution can be verified; under the required rule it is open. | [
{
"url": "https://arxiv.org/abs/1409.1913",
"label": "Chern--Weil theory and strict contactomorphisms"
},
{
"url": "https://doi.org/10.4171/owr/2012/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/35 | null | null | null | What can be said about the geometry of
$$j:\operatorname{Cont}_0(M,\alpha)\hookrightarrow\operatorname{Cont}_0(M,\xi),$$
and can quasimorphisms from $\operatorname{Ham}(X,\omega)$ extend along $j$ in the prequantization case? | What can be said about the geometry of j:Cont_0(M,alpha)\hookrightarrow Cont_0(M,xi), and can quasi-morphisms from Ham(X,omega) extend along j in the prequantization case? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Geometric Group Theory, Hyperbolic Dynamics and Symplectic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/35, pp. 2139--2203 |
30,002,144 | OWR-12008-004 | De Giorgi Conjecture for Allen–Cahn | If a bounded solution of
$$\Delta u+(1-u^2)u=0\quad\text{in }\mathbb R^N$$
satisfies $\partial_{x_N}u>0$, must all level sets of $u$ be hyperplanes when $N\leq8$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/36, pp. 2205--2268](https://doi.org/10.4171/owr/2012/36)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,012 | 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-12008-004",
"literature-status:open",
"owr-year:2012"
] | The conjecture is proved in dimensions two and three and under extra assumptions through dimension eight, while the unrestricted cases four through eight remain open; dimensions nine and higher have counterexamples. | [
{
"url": "https://doi.org/10.1090/S0894-0347-00-00345-3",
"label": "Ambrosio--Cabré, De Giorgi conjecture in dimension three"
},
{
"url": "https://annals.math.princeton.edu/2009/169-1/p02",
"label": "Savin, regularity of flat level sets"
},
{
"url": "https://arxiv.org/abs/0806.3141",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/36 | null | null | null | If a bounded solution of
$$\Delta u+(1-u^2)u=0\quad\text{in }\mathbb R^N$$
satisfies $\partial_{x_N}u>0$, must all level sets of $u$ be hyperplanes when $N\leq8$? | For a bounded solution of Delta u+(1-u^2)u=0 in R^N with partial_{x_N}u>0, are all level sets of u hyperplanes for N<=8? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Calculus of Variations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/36, pp. 2205--2268 |
30,002,145 | OWR-12008-005 | Rigidity of Symmetric-Gradient Differential Inclusions | What structure can be proved for sufficiently regular $u$ satisfying the differential inclusion $Eu\in\{\lambda(a\mathbin{\odot}b):\lambda\in\mathbb R\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/36, pp. 2205--2268](https://doi.org/10.4171/owr/2012/36)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,012 | 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-12008-005",
"literature-status:partially-solved",
"owr-year:2012"
] | BD structure theorems and good blow-up results give substantial one-directional rigidity for the symmetric-gradient inclusion, but they do not provide a complete classification in the generality asked. | [
{
"url": "https://arxiv.org/abs/1601.06543",
"label": "De Philippis--Rindler, structure of A-free measures"
},
{
"url": "https://arxiv.org/abs/1604.04097",
"label": "De Philippis--Rindler, symmetric-gradient Young measures"
},
{
"url": "https://arxiv.org/abs/1911.01356",
"label": "De... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/36 | null | null | null | What structure can be proved for sufficiently regular $u$ satisfying the differential inclusion $Eu\in\{\lambda(a\mathbin{\odot}b):\lambda\in\mathbb R\}$? | What structure can be proved for sufficiently regular u satisfying the differential inclusion Eu in {lambda(a\mathbin{\odot}b):lambda in R}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Calculus of Variations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/36, pp. 2205--2268 |
30,002,146 | OWR-12009-002 | Nonaxisymmetric Stability of Extremal Kerr Waves | For sufficiently regular solutions $\psi$ of the scalar wave equation on extremal Kerr, does the pointwise decay estimate up to and including the event horizon that is known for axisymmetric solutions remain valid without assuming axisymmetry? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333](https://doi.org/10.4171/owr/2012/37)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 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-12009-002",
"literature-status:open",
"owr-year:2012"
] | Axisymmetric extremal-Kerr decay and non-extremal non-axisymmetric stability are known, but the full non-axisymmetric extremal-Kerr stability problem identified in the record remains unresolved. | [
{
"url": "https://arxiv.org/abs/1110.2006",
"label": "Aretakis, axisymmetric waves on extreme Kerr"
},
{
"url": "https://arxiv.org/abs/1402.7034",
"label": "Dafermos--Rodnianski--Shlapentokh-Rothman, subextremal Kerr stability"
},
{
"url": "https://doi.org/10.4171/owr/2012/37",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/37 | null | null | null | For sufficiently regular solutions $\psi$ of the scalar wave equation on extremal Kerr, does the pointwise decay estimate up to and including the event horizon that is known for axisymmetric solutions remain valid without assuming axisymmetry? | Can the stability result for waves on extremal Kerr be proved without the axisymmetry assumption? | corrected_verified | The official report proves pointwise decay for axisymmetric extremal-Kerr waves and explicitly leaves removal of axisymmetry open. | null | null | null | null | null | Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333 |
30,002,147 | OWR-12009-003 | Critical Ultrarelativistic Black-Hole Collision Solutions | For equal-mass nonspinning ultrarelativistic black-hole collisions near critical impact parameter, does a unique critical solution exist, and can its high-energy behavior be described by an adiabatic, helical-Killing, or colliding-impulsive-wave approximation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333](https://doi.org/10.4171/owr/2012/37)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 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-12009-003",
"literature-status:open",
"owr-year:2012"
] | No primary result located that constructs or classifies the proposed equal-mass ultrarelativistic circular binary; existing work treats helical-Killing approximations or high-energy encounters, so the extracted proposal remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/gr-qc/0410095",
"label": "Klein, helical binary spacetimes"
},
{
"url": "https://doi.org/10.1103/PhysRevD.111.084077",
"label": "Healy--Ciarfella--Lousto, high-speed colli... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/37 | null | null | null | For equal-mass nonspinning ultrarelativistic black-hole collisions near critical impact parameter, does a unique critical solution exist, and can its high-energy behavior be described by an adiabatic, helical-Killing, or colliding-impulsive-wave approximation? | For equal-mass nonspinning ultrarelativistic black-hole collisions near critical impact parameter, does a unique critical solution exist, and can its high-energy behavior be described by an adiabatic, helical-Killing, or colliding-impulsive-wave approximation? | exact | The official report explicitly raises uniqueness and the three proposed high-energy approximations for the equal-mass critical solution. | null | null | null | null | null | Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333 |
30,002,148 | OWR-12009-005 | Regular Conformal Equations for Matter with Nonzero Trace | For matter with a nonzero-trace energy-momentum tensor, does there exist a choice of conformal variables yielding a regular conformal field-equation system with matter? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333](https://doi.org/10.4171/owr/2012/37)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 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-12009-005",
"literature-status:open",
"owr-year:2012"
] | Later conformal work handles trace-free matter and selected non-trace-free sources, but no general regular conformal system for arbitrary nonzero-trace stress tensors has been established. | [
{
"url": "https://doi.org/10.4171/owr/2012/37",
"label": "Oberwolfach report"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC10788156/",
"label": "Friedrich et al., conformal methods review"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/37 | null | null | null | For matter with a nonzero-trace energy-momentum tensor, does there exist a choice of conformal variables yielding a regular conformal field-equation system with matter? | For matter with a nonzero-trace energy-momentum tensor, does there exist a choice of conformal variables yielding a regular conformal field-equation system with matter? | exact | The official report explicitly asks whether suitable conformal variables can regularize the matter system when the energy-momentum trace is nonzero. | null | null | null | null | null | Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333 |
30,002,149 | OWR-12009-006 | Non-Disappearance of Nonnegative Scalar-Curvature Limits | Do sequences of manifolds with nonnegative scalar curvature and no closed interior minimal surfaces other than their boundaries avoid disappearing in the limit unless their volumes tend to zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333](https://doi.org/10.4171/owr/2012/37)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 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-12009-006",
"literature-status:open",
"owr-year:2012"
] | The no-disappearance statement remains a conjecture; intrinsic-flat no-cancellation is proved only under extra hypotheses such as Ricci lower bounds or uniform contractibility. | [
{
"url": "https://doi.org/10.4171/owr/2012/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1606.08949",
"label": "Sormani, scalar curvature and intrinsic-flat convergence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/37 | null | null | null | Do sequences of manifolds with nonnegative scalar curvature and no closed interior minimal surfaces other than their boundaries avoid disappearing in the limit unless their volumes tend to zero? | Do sequences of manifolds with nonnegative scalar curvature and no closed interior minimal surfaces other than their boundaries avoid disappearing in the limit unless their volumes tend to zero? | exact | The official report states this non-disappearance assertion as a conjecture with the minimal-surface and volume qualifications intact. | null | null | null | null | null | Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333 |
30,002,150 | OWR-12009-007 | Resonant Mode Mixing in Anti-de-Sitter Instability | Is the instability of anti-de-Sitter space caused by resonant mode mixing that transfers energy from low to high frequencies until an apparent horizon forms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333](https://doi.org/10.4171/owr/2012/37)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,012 | 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-12009-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Resonant dynamics and turbulent transfer are derived or numerically supported in important AdS models, but a general theorem establishing the proposed mechanism together with eventual horizon formation is still absent. | [
{
"url": "https://doi.org/10.1103/PhysRevLett.107.031102",
"label": "Bizon--Rostworowski, weak turbulence"
},
{
"url": "https://doi.org/10.1103/PhysRevLett.115.081103",
"label": "Bizon--Maliborski--Rostworowski, resonant dynamics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/37 | null | null | null | Is the instability of anti-de-Sitter space caused by resonant mode mixing that transfers energy from low to high frequencies until an apparent horizon forms? | Is the instability of anti-de Sitter space caused by resonant mode mixing that transfers energy from low to high frequencies until an apparent horizon forms? | corrected_verified | The official report states this resonant-transfer mechanism as the proposed explanation of anti-de-Sitter instability. | null | null | null | null | null | Mathematical Aspects of General Relativity (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/37, pp. 2269--2333 |
30,002,151 | OWR-12010-003 | Grothendieck Section Conjecture for Hyperbolic Curves | For a number field $k$ and a smooth, geometrically connected curve $X$ over $k$ with nonabelian geometric fundamental group, is the map from $X(k)$ to conjugacy classes of sections of the fundamental-group exact sequence a bijection onto the noncuspidal sections? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 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-12010-003",
"literature-status:open",
"owr-year:2012"
] | The Grothendieck section conjecture for hyperbolic curves remains wide open; the literature contains special cases and local or conditional results, not a general proof. | [
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
},
{
"url": "https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1362/",
"label": "Stix, section conjecture for curves of index one"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | For a number field $k$ and a smooth, geometrically connected curve $X$ over $k$ with nonabelian geometric fundamental group, is the map from $X(k)$ to conjugacy classes of sections of the fundamental-group exact sequence a bijection onto the noncuspidal sections? | For a number field k and a smooth geometrically connected curve X/k with nonabelian geometric fundamental group, is the map from X(k) to conjugacy classes of sections of pi_1(X)\to G_k a bijection onto the noncuspidal sections? | corrected_verified | The official report states this form of Grothendieck’s section conjecture and all of its curve hypotheses. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,152 | OWR-12010-005 | Modular Construction of Prescribed $\mathbb Z_p$-Extensions | Let $F_\infty/F$ be the cyclotomic $\mathbb Z_p$-extension. Can modular methods construct a $\mathbb Z_p$-extension $L_Q/F_\infty$ that is Galois over $F$, on which $\operatorname{Gal}(F_\infty/F)$ acts cyclotomically, and that is unramified outside prescribed auxiliary primes $Q$ but ramified at $Q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-005",
"literature-status:open",
"owr-year:2012"
] | The record is a fragment about constructing L_Q and states an equivalence with a Leopoldt-type finiteness condition; the reciprocity input is proved, but the omitted hypotheses prevent a resolved classification of the extracted existence claim. | [
{
"url": "https://arxiv.org/abs/1205.3226",
"label": "Sharifi, reciprocity conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | Let $F_\infty/F$ be the cyclotomic $\mathbb Z_p$-extension. Can modular methods construct a $\mathbb Z_p$-extension $L_Q/F_\infty$ that is Galois over $F$, on which $\operatorname{Gal}(F_\infty/F)$ acts cyclotomically, and that is unramified outside prescribed auxiliary primes $Q$ but ramified at $Q$? | Can the required Z_p-extension L_Q of the cyclotomic extension be constructed by modular methods, with the prescribed Galois action and ramification? | corrected_verified | The official report supplies the base cyclotomic extension, Galois action, and ramification conditions omitted from the extraction. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,153 | OWR-12010-006 | Congruent Numbers in Three Residue Classes | Is every squarefree positive integer congruent to $5$, $6$, or $7$ modulo $8$ a congruent number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-006",
"literature-status:open",
"owr-year:2012"
] | The universal congruent-number assertion remains open; primary work proves infinitely many examples in each residue class, not every square-free integer in the three classes. | [
{
"url": "https://doi.org/10.1073/pnas.1216991109",
"label": "Tian, congruent numbers with many prime factors"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | Is every squarefree positive integer congruent to $5$, $6$, or $7$ modulo $8$ a congruent number? | Is every square-free positive integer congruent to 5, 6, or 7 modulo 8 a congruent number? | corrected_verified | The official report was checked and confirms the complete problem statement. The residue classes and modulus were placed in math delimiters without changing the question. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,154 | OWR-12010-010 | Classification and Specialization of p-Divisible Groups | Classify all $p$-divisible groups $D$ with fixed dimension and codimension, including their specialization relations, finite-level $\operatorname{Hom}$ groups, and useful specialization-monotone invariants. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-010",
"literature-status:open",
"owr-year:2012"
] | Classifying all D is posed as an explicit research objective; existing work classifies rank-one modules and develops families, not all objects. | [
{
"url": "https://arxiv.org/abs/2102.04820",
"label": "Bellovin, cohomology of phi-Gamma modules"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | Classify all $p$-divisible groups $D$ with fixed dimension and codimension, including their specialization relations, finite-level $\operatorname{Hom}$ groups, and useful specialization-monotone invariants. | Classify all p-divisible groups D with fixed dimension and codimension, including their specialization relations, finite-level Hom groups, and useful specialization-monotone invariants. | corrected_verified | The official report was checked and confirms the complete problem statement. The prime, group, and Hom-functor notation were restored without changing the classification problem. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,155 | OWR-12010-012 | Breuil–Mézard Multiplicity Formula | For a residual representation $\bar\rho:G_K\to\operatorname{GL}_2(\mathbb F)$, do there exist nonnegative integers $\mu_a(\bar\rho)$, independent of the regular $p$-adic Hodge type $\lambda$ and inertial type $\tau$, such that $e(R_{\lambda,\tau}/\pi_E R_{\lambda,\tau})=\sum_a n(a)\mu_a(\bar\rho)$ for every $\lambda$ a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** partia... | 3 | partially_solved | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-012",
"literature-status:partially-solved",
"owr-year:2012"
] | The full Breuil--Mezard formula for arbitrary regular Hodge and inertial types over an arbitrary finite extension is not settled as one theorem; potentially Barsotti--Tate and other geometric or special cases are proved. | [
{
"url": "https://arxiv.org/abs/1208.3179",
"label": "Gee--Kisin, potentially Barsotti--Tate Breuil--Mezard"
},
{
"url": "https://msp.org/ant/2025/19-2/ant-v19-n2-p03-p.pdf",
"label": "Caraiani--Emerton--Gee--Savitt, geometric Breuil--Mezard"
},
{
"url": "https://doi.org/10.4171/owr/2012... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | For a residual representation $\bar\rho:G_K\to\operatorname{GL}_2(\mathbb F)$, do there exist nonnegative integers $\mu_a(\bar\rho)$, independent of the regular $p$-adic Hodge type $\lambda$ and inertial type $\tau$, such that $e(R_{\lambda,\tau}/\pi_E R_{\lambda,\tau})=\sum_a n(a)\mu_a(\bar\rho)$ for every $\lambda$ a... | For a residual representation rho-bar, do there exist nonnegative integers mu_a(rho-bar), independent of p-adic Hodge type lambda and inertial type tau, such that e(R_{lambda,tau}/pi_E)=sum_a n(a)mu_a(rho-bar) for all lambda and tau? | corrected_verified | The official report states the Breuil–Mézard conjecture with the residual representation and quotient-ring multiplicity shown here. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,156 | OWR-12010-014 | Serre-Weight Modularity Theorem | Does a residual representation r-bar occur modularly for a Serre weight sigma exactly when sigma is one of the weights predicted by the Buzzard-Diamond-Jarvis conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** partia... | 3 | partially_solved | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official contribution states and proves the claimed modularity criterion under its hypotheses; the extraction strips those hypotheses an) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-014",
"literature-status:partially-solved",
"owr-year:2012"
] | The BDJ weight recipe is proved in major unitary and GL2 settings under standard residual, local, and automorphy hypotheses, but the record's unqualified formulation is broader than those theorems. | [
{
"url": "https://doi.org/10.1090/S0894-0347-2013-00775-4",
"label": "Gee--Liu--Savitt, BDJ conjecture for unitary groups"
},
{
"url": "https://arxiv.org/abs/1309.0527",
"label": "Gee--Liu--Savitt, weight part of Serre"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | null | Does a residual representation r-bar occur modularly for a Serre weight sigma exactly when sigma is one of the weights predicted by the Buzzard-Diamond-Jarvis conjecture? | unrecoverable | The official contribution states and proves the claimed modularity criterion under its hypotheses; the extraction strips those hypotheses and incorrectly presents the theorem as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,157 | OWR-12010-016 | Arithmetic Fundamental Lemma in All Dimensions | For an unramified quadratic extension $E/F$ of $p$-adic fields, let $Y=\mathcal N_n$ embed diagonally in $\mathcal N_n\times\mathcal N_{n+1}$. For $\delta\in U(n+1)$ and $\gamma\in\operatorname{GL}_{n+1}(E)$ matching under $\operatorname{GL}_n(E)$, does the arithmetic fundamental lemma identity $\langle Y,(1\times\delt... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** partia... | 3 | partially_solved | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-016",
"literature-status:partially-solved",
"owr-year:2012"
] | The arithmetic fundamental lemma is proved in important minuscule, dimension, and p-adic cases, but the refined arithmetic Gan--Gross--Prasad formula and the full general AFL remain unresolved. | [
{
"url": "https://annals.math.princeton.edu/2021/193-3/p05",
"label": "Zhang, Weil representation and AFL"
},
{
"url": "https://arxiv.org/abs/2104.02779",
"label": "Mihatsch--Zhang, AFL over a general p-adic field"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolf... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | For an unramified quadratic extension $E/F$ of $p$-adic fields, let $Y=\mathcal N_n$ embed diagonally in $\mathcal N_n\times\mathcal N_{n+1}$. For $\delta\in U(n+1)$ and $\gamma\in\operatorname{GL}_{n+1}(E)$ matching under $\operatorname{GL}_n(E)$, does the arithmetic fundamental lemma identity $\langle Y,(1\times\delt... | Does the arithmetic fundamental lemma identity relating the intersection number (Y,(1 times delta)^*Y) to the derivative orbital integral orb-prime(gamma,1_{S_{n+1}}(O_F)) hold for all n and matching elements delta and gamma? | corrected_verified | The official report states the all-dimensional arithmetic fundamental lemma after recording the proved low-dimensional and special cases. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,158 | OWR-12010-017 | Distribution of Elliptic-Curve Selmer Exact Sequences | Given an abstract short exact sequence $S$ of $\mathbb Z_p$-modules, what is the density of elliptic curves $E$ over $k$ for which $0\to E(k)\otimes\mathbb Q_p/\mathbb Z_p\to\operatorname{Sel}_{p^\infty}(E)\to\operatorname{Sha}(E)[p^\infty]\to0$ is isomorphic to $S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-017",
"literature-status:open",
"owr-year:2012"
] | The density of isomorphism classes of the elliptic-curve Selmer exact sequence remains an open distribution problem; the literature constructs a model distribution and states the arithmetic identification as a conjecture. | [
{
"url": "https://doi.org/10.4310/CJM.2015.v3.n3.a1",
"label": "Bhargava--Kane--Lenstra--Poonen--Rains, distribution model"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | Given an abstract short exact sequence $S$ of $\mathbb Z_p$-modules, what is the density of elliptic curves $E$ over $k$ for which $0\to E(k)\otimes\mathbb Q_p/\mathbb Z_p\to\operatorname{Sel}_{p^\infty}(E)\to\operatorname{Sha}(E)[p^\infty]\to0$ is isomorphic to $S$? | Given an abstract short exact sequence S of Z_p-modules, what is the density of elliptic curves E over k for which 0 to E(k) tensor Q_p/Z_p to Sel_{p^infinity}(E) to X(E)[p^infinity] to 0 is isomorphic to S? | corrected_verified | The official report poses this as Question 1.1 with the Mordell–Weil, Selmer, and Tate–Shafarevich terms shown here. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,159 | OWR-12010-018 | Random Isotropic Model for Selmer Exact Sequences | For $V=\mathbb Z_p^{2n}$, $W=\mathbb Z_p^n\times\{0\}$, and random $Z\in\operatorname{OGr}_n(\mathbb Z_p)$, let $R=(Z\cap W)\otimes\mathbb Q_p/\mathbb Z_p$, $S=(Z\otimes\mathbb Q_p/\mathbb Z_p)\cap(W\otimes\mathbb Q_p/\mathbb Z_p)$, and $T=S/R$. Does the limiting distribution as $n\to\infty$ of $0\to R\to S\to T\to0$ e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-018",
"literature-status:open",
"owr-year:2012"
] | The Poonen--Rains-type identification of the limiting random-isotropic distribution with elliptic-curve Selmer data remains conjectural over number fields, despite substantial average-size and family results. | [
{
"url": "https://doi.org/10.4310/CJM.2015.v3.n3.a1",
"label": "Bhargava--Kane--Lenstra--Poonen--Rains, distribution model"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | For $V=\mathbb Z_p^{2n}$, $W=\mathbb Z_p^n\times\{0\}$, and random $Z\in\operatorname{OGr}_n(\mathbb Z_p)$, let $R=(Z\cap W)\otimes\mathbb Q_p/\mathbb Z_p$, $S=(Z\otimes\mathbb Q_p/\mathbb Z_p)\cap(W\otimes\mathbb Q_p/\mathbb Z_p)$, and $T=S/R$. Does the limiting distribution as $n\to\infty$ of $0\to R\to S\to T\to0$ e... | For V=\mathbb{Z}_p^{2n}, W=\mathbb{Z}_p^n\times\{0\}, and random Z\in OGr_n(\mathbb{Z}_p), let R=(Z\cap W)\otimes_{\mathbb{Z}_p}\mathbb{Q}_p, S=(Z\otimes\mathbb{Q}_p)\cap(W\otimes\mathbb{Q}_p), and T=S/R. Does the limiting distribution as n\to\infty of the exact sequences 0\to R\to S\to T\to0 equal the distribution of ... | corrected_verified | The official report states this random maximal-isotropic model, including the divisible-group quotients that were corrupted in the extraction. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,160 | OWR-12010-020 | Finite-Level Selmer Distributions from Isotropic Intersections | For fixed $e\geq1$, does the distribution of $\operatorname{Sel}_{p^e}(E)$ over elliptic curves $E$ equal, in the limit $n\to\infty$, the distribution of $Z\cap W$ for independently chosen random maximal isotropic direct summands $Z,W\in\operatorname{OGr}_n(\mathbb Z/p^e\mathbb Z)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-020",
"literature-status:open",
"owr-year:2012"
] | The extracted statement is incomplete after the first parts of an auxiliary theorem, and the underlying Selmer-distribution conjecture remains unresolved; it is therefore classified as open. | [
{
"url": "https://doi.org/10.4310/CJM.2015.v3.n3.a1",
"label": "Bhargava--Kane--Lenstra--Poonen--Rains, distribution model"
},
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | For fixed $e\geq1$, does the distribution of $\operatorname{Sel}_{p^e}(E)$ over elliptic curves $E$ equal, in the limit $n\to\infty$, the distribution of $Z\cap W$ for independently chosen random maximal isotropic direct summands $Z,W\in\operatorname{OGr}_n(\mathbb Z/p^e\mathbb Z)$? | Does the distribution of the e-torsion Selmer groups Sel_{p^e}(E) for elliptic curves E equal, in the limit n\to\infty, the distribution of Z\cap W for random maximal isotropic subspaces Z,W\in OGr_n(\mathbb{Z}/p^e\mathbb{Z})? | corrected_verified | The official report records this finite-level consequence as an explicit distributional prediction. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,161 | OWR-12010-021 | Direct-Summand Property for Selmer Restriction Images | Let $\beta:H^1(k,E[n])\to H^1(A,E[n])$ be the restriction map in the Selmer model. Is $\operatorname{im}\beta$ a direct summand for $100\%$ of elliptic curves $E$ over $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388](https://doi.org/10.4171/owr/2012/38)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12010-021",
"literature-status:open",
"owr-year:2012"
] | The source asks whether im beta is a direct summand for asymptotically almost all elliptic curves; the known rational-torsion case and the Poonen--Rains model do not settle the general question. | [
{
"url": "https://doi.org/10.4171/owr/2012/38",
"label": "OWR report 38"
},
{
"url": "https://doi.org/10.1090/S0894-0347-2012-00709-9",
"label": "Poonen--Rains"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/38 | null | null | null | Let $\beta:H^1(k,E[n])\to H^1(A,E[n])$ be the restriction map in the Selmer model. Is $\operatorname{im}\beta$ a direct summand for $100\%$ of elliptic curves $E$ over $k$? | Let \beta:H^1(k,E[n])\to H^1(A,E[n]) be the map in the Selmer model. Is im \beta a direct summand for 100\% of elliptic curves E over k? | corrected_verified | The official report poses this direct-summand question with the same density-one quantifier. | null | null | null | null | null | Arithmetic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/38, pp. 2335--2388 |
30,002,162 | OWR-12011-001 | Borderline Sobolev Blowup Criteria for Hyperdissipative Flow | For a possible finite-time blowup of the $d$-dimensional hyperdissipative flow, does the borderline conjecture
$$\lVert u(t)\rVert_{H^{(d+2)/6}(\mathbb R^d)}^2\to\infty\quad\text{as }t\to t_*$$
hold? Equivalently, is finiteness of this norm on $[0,T]$ sufficient for regularity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/39, pp. 2389--2427](https://doi.org/10.4171/owr/2012/39)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,012 | 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-12011-001",
"literature-status:open",
"owr-year:2012"
] | The extracted claim is the endpoint lower-branch regularity criterion for hyperdissipative Navier--Stokes; stronger dissipation regimes and special cases are known, but the endpoint criterion remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/39",
"label": "OWR report 39"
},
{
"url": "https://doi.org/10.1070/RM2003v058n02ABEH000610",
"label": "Escauriaza--Seregin--Sverak"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/39 | null | null | null | For a possible finite-time blowup of the $d$-dimensional hyperdissipative flow, does the borderline conjecture
$$\lVert u(t)\rVert_{H^{(d+2)/6}(\mathbb R^d)}^2\to\infty\quad\text{as }t\to t_*$$
hold? Equivalently, is finiteness of this norm on $[0,T]$ sufficient for regularity? | For a possible finite-time blowup of the d-dimensional hyperdissipative flow, does the borderline conjecture hold that \|u(t)\|_{H^{(d+2)/6}(\mathbb{R}^d)}^2\to\infty as t\to t_*? Equivalently, is finiteness of this norm on [0,T] sufficient for regularity? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/39, pp. 2389--2427 |
30,002,163 | OWR-12012-001 | Minimum Distance in Spherical Fibonacci Lattices | For the spherical Fibonacci point set $Z_{F_n}$, is $|z_0-z_1|=2/\sqrt{F_n}$ the least pairwise distance among its $F_n$ points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | open | null | 2,012 | 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-12012-001",
"literature-status:open",
"owr-year:2012"
] | The least-distance formula is still a conjecture; later work gives discrepancy and distribution results for spherical Fibonacci points but does not prove this exact minimum-distance identity. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://arxiv.org/abs/1109.3265",
"label": "Spherical Fibonacci points"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | For the spherical Fibonacci point set $Z_{F_n}$, is $|z_0-z_1|=2/\sqrt{F_n}$ the least pairwise distance among its $F_n$ points? | For the spherical Fibonacci point set Z_{F_n}, is |z_0-z_1|=2/\sqrt{F_n} the least pairwise distance in the F_n-point spherical Fibonacci lattice? | corrected_verified | The official report states this minimum-distance conjecture for the spherical Fibonacci construction. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,164 | OWR-12012-005 | Laplacians on Nonsymmetric Self-Similar Sets | Does a Laplacian exist on every connected nonsymmetric self-similar set? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12012-005",
"literature-status:open",
"owr-year:2012"
] | Laplacians are constructed for important classes such as pcf self-similar sets, but no general existence theorem covers arbitrary connected non-symmetric self-similar sets. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://doi.org/10.1016/j.chaos.2011.05.003",
"label": "Kigami--Strichartz"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | Does a Laplacian exist on every connected nonsymmetric self-similar set? | Does a Laplacian exist on every general connected non-symmetric self-similar set? | corrected_verified | The official report explicitly asks whether the Laplacian construction extends to every connected nonsymmetric self-similar set. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,165 | OWR-12012-007 | Weighted Condenser-Energy Minimizers | Let $\mathbf A=(A_i)_{i\in I}$ be a countable condenser of pairwise disjoint nonempty closed subsets of $\mathbb R^n$, let $\mathbf f=(f_i)$ be an admissible external field, let $\mathbf a=(a_i)$ satisfy $a_i>0$ and $\sum_i a_i<\infty$, and let $g\in C(\mathbb R^n)$ satisfy $0<c_1<g<c_2<\infty$. If $G_{\mathbf f}(\math... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | partially_solved | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12012-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Existence of the condenser minimizer is established under substantial hypotheses, including perfect-kernel settings with solvability criteria, but the broad infinite-dimensional question is not universally affirmative. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://doi.org/10.1007/s11118-012-9279-8",
"label": "Zorii"
},
{
"url": "https://arxiv.org/abs/1207.0604",
"label": "Zorii solvability criteria"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | Let $\mathbf A=(A_i)_{i\in I}$ be a countable condenser of pairwise disjoint nonempty closed subsets of $\mathbb R^n$, let $\mathbf f=(f_i)$ be an admissible external field, let $\mathbf a=(a_i)$ satisfy $a_i>0$ and $\sum_i a_i<\infty$, and let $g\in C(\mathbb R^n)$ satisfy $0<c_1<g<c_2<\infty$. If $G_{\mathbf f}(\math... | Under the stated condenser, external-field, and mass constraints, does there exist \lambda\in E_f^+(A,a,g) attaining the infimum, so that G_f(\lambda)=G_f(A,a,g)? | corrected_verified | The official report supplies the condenser, field, mass, weight, and finite-energy hypotheses and asks whether the constrained minimum is attained. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,166 | OWR-12012-008 | Density and Kissing Numbers for Binary Sphere Packings | For packings of Euclidean balls of radii $r_1$ and $r_2$ occurring in a prescribed proportion, what are the maximal packing density and mean kissing numbers $k_{11},k_{12},k_{21},k_{22}$? When $r_1$ and $r_2$ are close, does the density equal that for congruent balls, so that the two sizes do not mix? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | open | null | 2,012 | 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-12012-008",
"literature-status:open",
"owr-year:2012"
] | Bounds, exact results for selected radius ratios, and candidate phase diagrams are known, but there is no general maximal-density or kissing-number classification and no general no-mixing theorem for close radii. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://arxiv.org/abs/1206.2608",
"label": "de Laat--de Oliveira Filho--Vallentin"
},
{
"url": "https://doi.org/10.1103/PhysRevLett.107.125501",
"label": "Hopkins--Jiao--Stillinger--Torquato"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | For packings of Euclidean balls of radii $r_1$ and $r_2$ occurring in a prescribed proportion, what are the maximal packing density and mean kissing numbers $k_{11},k_{12},k_{21},k_{22}$? When $r_1$ and $r_2$ are close, does the density equal that for congruent balls, so that the two sizes do not mix? | For packings of Euclidean balls of radii r_1 and r_2 occurring in a prescribed proportion, what are the maximal packing density and mean kissing numbers k_{11},k_{12},k_{21},k_{22}? When r_1 and r_2 are close, does the density equal that for congruent balls, so that the two sizes do not mix? | corrected_verified | The official open-problem session states both the density and mean-kissing-number questions and the near-equal-radii subquestion. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,167 | OWR-12012-009 | Short Hamiltonian Cycles and Matchings in Convex Bodies | If $B$ is the unit disk and $P$ is a finite point set in $B$, must $P$ admit a Hamiltonian cycle whose sum of squared edge lengths is at most $8$? If $|P|$ is even, must it admit a perfect matching with sum of squared edge lengths at most $4$? What analogues hold for other convex bodies $C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | open | null | 2,012 | 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-12012-009",
"literature-status:open",
"owr-year:2012"
] | The unit-disk Hamiltonian-cycle and matching questions remain listed as open in later discrete-geometry surveys; the exact constants and extensions to other convex figures are not settled. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://www.researchgate.net/publication/328301196_Current_Open_Problems_in_Discrete_and_Computational_Geometry",
"label": "Current open problems survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | If $B$ is the unit disk and $P$ is a finite point set in $B$, must $P$ admit a Hamiltonian cycle whose sum of squared edge lengths is at most $8$? If $|P|$ is even, must it admit a perfect matching with sum of squared edge lengths at most $4$? What analogues hold for other convex bodies $C$? | If B is the unit disk and P is a finite point set in B, must P admit a Hamiltonian cycle whose sum of squared edge lengths is at most 8? If P has even cardinality, must it admit a perfect matching with sum of squared edge lengths at most 4? What analogues hold for other convex figures C instead of B or the unit square? | corrected_verified | The official open-problem session gives the constants, parity condition, and requested convex-body generalization. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,168 | OWR-12012-010 | Orthogonality-Avoiding Sets and Coulomb Local Minima | For a measurable set $A\subset S^2$ with $\langle x,y\rangle\ne0$ for all $x,y\in A$, what is the largest possible measure of $A$, and can the upper bound $1/3$ be improved? Separately, if $L_n$ is the number of local minima of the Coulomb potential for $n$ points on $S^2$, is $L_n>1$ for every sufficiently large $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492](https://doi.org/10.4171/owr/2012/40)
## Literature r... | 3 | partially_solved | null | 2,012 | 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 | {
"source_url": "https://doi.org/10.1093/imrn/rnv319",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (one of three questions answered). The record merges two problems of the problem session (OWR 40/2012, p. 2489). F. Vallentin asks for the largest measure of a subset of S² with no orthogonal pair (conjectured 1 − 1/√2 ≈ 0.293, two opposite caps) and wh... | [
"owr",
"oberwolfach-reports",
"OWR-12012-010",
"literature-status:open",
"owr-year:2012"
] | The extracted text conflates the spherical orthogonality-avoiding-set problem with a Coulomb local-minima question; neither the exact extremal value nor the stated eventual inequality is established. | [
{
"url": "https://doi.org/10.4171/owr/2012/40",
"label": "OWR report 40"
},
{
"url": "https://doi.org/10.1080/10586458.2009.10129052",
"label": "Cohn--Kumar--Schuermann"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/40 | null | null | null | For a measurable set $A\subset S^2$ with $\langle x,y\rangle\ne0$ for all $x,y\in A$, what is the largest possible measure of $A$, and can the upper bound $1/3$ be improved? Separately, if $L_n$ is the number of local minima of the Coulomb potential for $n$ points on $S^2$, is $L_n>1$ for every sufficiently large $n$? | For a measurable A\subset S^2 with (x,y)\ne0 for all x,y\in A, what is the largest possible measure of A, and can one improve the known upper bound 1/3? Also, if L_n denotes the number of local minima of the Coulomb potential for n points on S^2, is L_n>1 for all sufficiently large n? | corrected_verified | The official open-problem session places these two distinct questions consecutively; both are preserved and their separation is made explicit. | null | null | null | null | null | Optimal and Near Optimal Configurations on Lattices and Manifolds (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/40, pp. 2429--2492 |
30,002,169 | OWR-12013-001 | Intrinsic Viscosity Solutions for Rough Hamilton–Jacobi Equations | For rough Hamilton–Jacobi–Bellman equations driven by a rough path, can solutions defined as limits of viscosity solutions for smooth approximations be characterized intrinsically, for example by touching test functions as in classical viscosity theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Rough Paths and PDEs (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/41, pp. 2493--2540](https://doi.org/10.4171/owr/2012/41)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 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-12013-001",
"literature-status:open",
"owr-year:2012"
] | Pathwise viscosity and controlled-test-function theories now handle important rough and stochastic PDE classes, but a general intrinsic touching-test characterization of such solutions remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/41",
"label": "OWR report 41"
},
{
"url": "https://doi.org/10.1186/s41546-020-00049-8",
"label": "Rough PDE viscosity theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/41 | null | null | null | For rough Hamilton–Jacobi–Bellman equations driven by a rough path, can solutions defined as limits of viscosity solutions for smooth approximations be characterized intrinsically, for example by touching test functions as in classical viscosity theory? | For rough Hamilton--Jacobi--Bellman equations driven by a rough path, can solutions defined as limits of viscosity solutions for smooth approximations be characterized intrinsically, for example by touching test functions as in classical viscosity theory? | corrected_verified | The official report explicitly asks for an intrinsic characterization of the pathwise viscosity solution. | null | null | null | null | null | Rough Paths and PDEs (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/41, pp. 2493--2540 |
30,002,170 | OWR-12013-003 | Lower Bounds for Fractional Lévy-Area Approximation | For fractional Brownian Lévy area with Hurst parameter $H\in(1/4,1)$, sampled at $n$ equally spaced times on $[0,T]$, is the $L^2$ error of the conditional-expectation approximation bounded below by $c_H T^{2H}n^{-2H+1/2}$ for some $c_H>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Rough Paths and PDEs (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/41, pp. 2493--2540](https://doi.org/10.4171/owr/2012/41)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12013-003",
"literature-status:open",
"owr-year:2012"
] | The cited work proves the matching upper approximation rate for fractional Levy area, but the conjectured lower bound remains unproved in general outside special cases such as Brownian motion. | [
{
"url": "https://doi.org/10.4171/owr/2012/41",
"label": "OWR report 41"
},
{
"url": "https://doi.org/10.1016/j.spa.2010.06.002",
"label": "Neuenkirch--Tindel--Unterberger"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/41 | null | null | null | For fractional Brownian Lévy area with Hurst parameter $H\in(1/4,1)$, sampled at $n$ equally spaced times on $[0,T]$, is the $L^2$ error of the conditional-expectation approximation bounded below by $c_H T^{2H}n^{-2H+1/2}$ for some $c_H>0$? | For the fractional Brownian Levy area with Hurst parameter H\in(1/4,1), sampled at n equally spaced times, does the conditional-expectation approximation satisfy a matching lower bound c_H T^{2H}n^{-2H+1/2} for some constant c_H>0, matching the known upper rate? | corrected_verified | The official report states this lower-bound question, including the sampling interval and the approximation error that the extraction left implicit. | null | null | null | null | null | Rough Paths and PDEs (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/41, pp. 2493--2540 |
30,002,171 | OWR-12014-003 | Hirota Equations and Knot Meaning of Spectral Curves | For the spectral-curve partition function $\widetilde Z$, does it formally satisfy Hirota equations in infinitely many deformation parameters? What is the knot-theoretic meaning of the genus-zero property of the quotient of the $A$-polynomial curve by its involution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-003",
"literature-status:open",
"owr-year:2012"
] | The record includes a nonperturbative topological-recursion conjecture and explicitly leaves the knot-theoretic meaning of the vanishing invariant open; no general interpretation has since been established. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "OWR report 42"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | For the spectral-curve partition function $\widetilde Z$, does it formally satisfy Hirota equations in infinitely many deformation parameters? What is the knot-theoretic meaning of the genus-zero property of the quotient of the $A$-polynomial curve by its involution? | For the spectral-curve partition function \widetilde Z, does it formally satisfy Hirota equations in infinitely many deformation parameters? In addition, what is the knot-theoretic meaning of the observed genus-zero condition for the quotient of the A-polynomial curve by its involution? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,172 | OWR-12014-005 | L-Space Conjecture | For every closed, connected, orientable, prime $3$-manifold $W$, is $\pi_1(W)$ left-orderable if and only if $W$ is not a Heegaard–Floer $L$-space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate of canonical problem KP-3.48 | [
"KP-3.48"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-005",
"literature-status:partially-solved",
"owr-year:2012"
] | The L-space conjecture is proved for broad classes including graph manifolds and many surgery families, but the equivalence between non-L-space and left-orderability is not known for all prime orientable 3-manifolds. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "OWR report 42"
},
{
"url": "https://arxiv.org/abs/1107.5018",
"label": "Boyer--Gordon--Watson"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | For every closed, connected, orientable, prime $3$-manifold $W$, is $\pi_1(W)$ left-orderable if and only if $W$ is not a Heegaard–Floer $L$-space? | For every closed, connected, orientable, prime 3-manifold W, is the fundamental group \pi_1(W) left-orderable if and only if W is not a Heegaard--Floer L-space? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,173 | OWR-12014-006 | Positivity of Hyperbolic and Seifert Representation Volumes | For which closed oriented $3$-manifolds $M$ is the hyperbolic volume $HV(M)$, or the Seifert volume $SV(M)$, defined as the maximal representation volume for $\operatorname{PSL}(2,\mathbb{C})$ or $\operatorname{Isom}\widetilde{\operatorname{SL}}_2(\mathbb{R})$, respectively, positive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-006",
"literature-status:partially-solved",
"owr-year:2012"
] | Geometric cases and broad virtual-positivity theorems are known, including results relating positive simplicial volume to virtual Seifert volume, but a complete classification of positive hyperbolic and Seifert volumes is still absent. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "OWR report 42"
},
{
"url": "https://msp.org/gt/2017/21-5/gt-v21-n5-p13-s.pdf",
"label": "Derbez--Liu--Sun--Wang"
},
{
"url": "https://arxiv.org/abs/1111.6153",
"label": "Derbez--Wang"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | For which closed oriented $3$-manifolds $M$ is the hyperbolic volume $HV(M)$, or the Seifert volume $SV(M)$, defined as the maximal representation volume for $\operatorname{PSL}(2,\mathbb{C})$ or $\operatorname{Isom}\widetilde{\operatorname{SL}}_2(\mathbb{R})$, respectively, positive? | For which closed oriented 3-manifolds M is the hyperbolic volume HV(M), or the Seifert volume SV(M), defined as the maximal representation volume for PSL(2,\mathbb{C}) or Isom~SL_2(\mathbb{R}), respectively, positive? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,174 | OWR-12014-008 | Categorification of the Quantum Volume Conjecture | Does the generalized or quantum volume conjecture for the colored Jones polynomial admit a natural categorification, yielding a two-parameter super-A-polynomial governing the color behavior of HOMFLY homology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-008",
"literature-status:open",
"owr-year:2012"
] | The extracted record is a talk heading and broad categorification description rather than a precise proposition; the generalized volume-categorification program remains conjectural and the claim is not checkable as stated. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "OWR report 42"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | Does the generalized or quantum volume conjecture for the colored Jones polynomial admit a natural categorification, yielding a two-parameter super-A-polynomial governing the color behavior of HOMFLY homology? | Does the generalized or quantum volume conjecture for the colored Jones polynomial admit a natural categorification, yielding a two-parameter super-A-polynomial governing the color behavior of HOMFLY homology? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,175 | OWR-12014-009 | Minimal Pseudo-Anosov Dilatations | What is the behavior of the minimum pseudo-Anosov dilatation $\delta(S_{g,n})$ as a function of genus $g$ and punctures $n$? Is there an accumulation point of normalized dilatations smaller than $\ell_0=((3+\sqrt 5)/2)^2$, and what do small-dilatation mapping classes look like? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-009",
"literature-status:partially-solved",
"owr-year:2012"
] | There are sharp asymptotic bounds and explicit small-dilatation families, with further results for restricted classes, but the full dependence on genus and punctures, the smallest accumulation point, and the structure of all minimizers remain open. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "OWR report 42"
},
{
"url": "https://arxiv.org/abs/1403.2987",
"label": "Hironaka"
},
{
"url": "https://nyjm.albany.edu/j/2012/18-32v.pdf",
"label": "Valdivia"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | What is the behavior of the minimum pseudo-Anosov dilatation $\delta(S_{g,n})$ as a function of genus $g$ and punctures $n$? Is there an accumulation point of normalized dilatations smaller than $\ell_0=((3+\sqrt 5)/2)^2$, and what do small-dilatation mapping classes look like? | What is the behavior of the minimum pseudo-Anosov dilatation \delta(S_{g,n}) as a function of genus g and punctures n? Is there an accumulation point of normalized dilatations smaller than \ell_0=((3+\sqrt5)/2)^2, and what do small-dilatation mapping classes look like? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,176 | OWR-12014-011 | Torsion Growth and Hyperbolic Volume in Finite Covers | Let $X$ be an irreducible orientable $3$-manifold with empty or torus boundary, let $\operatorname{Vol}(X)$ be the sum of hyperbolic-piece volumes, and let $t(X,G)=|\operatorname{Tor}H_1(X_G,\mathbb Z)|$ for finite-index normal subgroups $G\triangleleft\pi_1(X)$. Is $\limsup_{G\to\infty}t(X,G)^{1/[\pi_1(X):G]}=\exp(\op... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-011",
"literature-status:open",
"owr-year:2012"
] | The extracted claim is the Bergeron--Venkatesh/Luck torsion-growth equality for finite covers of a hyperbolic 3-manifold. General towers remain conjectural; later work establishes upper bounds and special cases but not the stated equality. | [
{
"url": "https://www.numdam.org/item/10.5802/aif.3173/",
"label": "Raimbault, torsion growth and hyperbolic volume"
},
{
"url": "https://arxiv.org/abs/1004.1083",
"label": "Bergeron--Venkatesh, torsion growth"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | Let $X$ be an irreducible orientable $3$-manifold with empty or torus boundary, let $\operatorname{Vol}(X)$ be the sum of hyperbolic-piece volumes, and let $t(X,G)=|\operatorname{Tor}H_1(X_G,\mathbb Z)|$ for finite-index normal subgroups $G\triangleleft\pi_1(X)$. Is $\limsup_{G\to\infty}t(X,G)^{1/[\pi_1(X):G]}=\exp(\op... | Let X be an irreducible orientable 3-manifold with empty or torus boundary, let Vol(X) be the sum of hyperbolic-piece volumes, and let t(X,G)=|Tor H_1(X_G,\mathbb{Z})| over finite-index normal G\triangleleft\pi_1(X). Is limsup_{G\to\infty} t(X,G)^{1/[\pi:G]}=\exp(Vol(X)/(6\pi))? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,177 | OWR-12014-012 | Polynomial Separation at Roots of Unity | For every $f\in\mathbb Z[t_1,\ldots,t_n]$, does there exist $E>0$ such that for all roots of unity $z_1,\ldots,z_n$ of order at most $d$, either $f(z_1,\ldots,z_n)=0$ or $|f(z_1,\ldots,z_n)|>d^{-E}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-012",
"literature-status:open",
"owr-year:2012"
] | This is the polynomial lower-bound conjecture for nonzero values of an integer polynomial at bounded-order roots of unity. The reduction to sums of roots of unity is known, but no general polynomial separation bound has been proved. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "Oberwolfach Report 42, Conjecture 6"
},
{
"url": "https://doi.org/10.1112/blms.12826",
"label": "Barber, small sums of five roots of unity"
},
{
"url": "https://arxiv.org/abs/2607.06098",
"label": "Kalogirou, small sums of roo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | For every $f\in\mathbb Z[t_1,\ldots,t_n]$, does there exist $E>0$ such that for all roots of unity $z_1,\ldots,z_n$ of order at most $d$, either $f(z_1,\ldots,z_n)=0$ or $|f(z_1,\ldots,z_n)|>d^{-E}$? | For every f\in\mathbb{Z}[t_1,\ldots,t_n], does there exist E>0 such that for all roots of unity z_1,\ldots,z_n of order at most d, either f(z_1,\ldots,z_n)=0 or |f(z_1,\ldots,z_n)|>d^{-E}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,178 | OWR-12014-013 | Lower Bounds for Sums of Roots of Unity | Let $C_d=\{e^{2\pi i k/d}:k\in\mathbb Z\}$, and let $mC_d$ denote its $m$-fold Minkowski sum. For a set $A\subset\mathbb C$, write $\min_0(A)=\min\{|x|:x\in A\setminus\{0\}\}$. For every fixed positive integer $m$, does there exist $E=E(m)>0$ such that
$$\min_0(mC_d)>d^{-E}$$
for all $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-013",
"literature-status:open",
"owr-year:2012"
] | The equivalent fixed-m lower-bound problem for nonzero sums of roots of unity remains unresolved in general. Recent work gives increasingly strong constructions of small sums and solves isolated fixed-conductor cases, not the conjectured uniform lower bound. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "Oberwolfach Report 42, Conjecture 7"
},
{
"url": "https://doi.org/10.1112/blms.12826",
"label": "Barber, small sums of five roots of unity"
},
{
"url": "https://arxiv.org/abs/2607.06098",
"label": "Kalogirou, small sums of roo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | Let $C_d=\{e^{2\pi i k/d}:k\in\mathbb Z\}$, and let $mC_d$ denote its $m$-fold Minkowski sum. For a set $A\subset\mathbb C$, write $\min_0(A)=\min\{|x|:x\in A\setminus\{0\}\}$. For every fixed positive integer $m$, does there exist $E=E(m)>0$ such that
$$\min_0(mC_d)>d^{-E}$$
for all $d$? | For each fixed positive integer m, does there exist E=E(m)>0 such that, as d\to\infty, min_{0}((C_d)^{\# m})>d^{-E}, where C_d is the set of d-th roots of unity and (C_d)^{\# m} is its m-fold Minkowski sum? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,179 | OWR-12014-014 | Chain-Independent Homology Growth in Finite Covers | Let $G$ be finitely presented. For every field $K$ and every inverse system of finite-index normal subgroups $(G_i)_{i\in I}$ with $\bigcap_iG_i=\{1\}$, does the limit $\lim_{i\in I}b_1(G_i;K)/[G:G_i]$ exist and remain independent of the choices of $(G_i)$ and $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596](https://doi.org/10.4171/owr/2012/42)
## Literature review (checked 2026-08-... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12014-014",
"literature-status:open",
"owr-year:2012"
] | The extracted open conjecture asks for existence and subgroup-chain independence of normalized first Betti-number limits for finitely presented residually finite groups. Positive-characteristic convergence and chain independence remain open in general. | [
{
"url": "https://doi.org/10.4171/owr/2012/42",
"label": "Oberwolfach Report 42, Betti-limit conjecture"
},
{
"url": "https://arxiv.org/abs/1003.0434",
"label": "Linnell--Lueck--Sauer, Fp-Betti limits"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/42 | null | null | null | Let $G$ be finitely presented. For every field $K$ and every inverse system of finite-index normal subgroups $(G_i)_{i\in I}$ with $\bigcap_iG_i=\{1\}$, does the limit $\lim_{i\in I}b_1(G_i;K)/[G:G_i]$ exist and remain independent of the choices of $(G_i)$ and $K$? | Let G be finitely presented. For every field K and every inverse system of finite-index normal subgroups (G_i)_{i\in I} with \bigcap_i G_i=\{1\}, does the limit \lim_{i\in I} b_1(G_i;K)/[G:G_i] exist and remain independent of the choices of (G_i) and K? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Low-Dimensional Topology and Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/42, pp. 2541--2596 |
30,002,180 | OWR-12015-001 | Jet Curvature and the First Chern Class | If a complex manifold $X$ has nondegenerate negative $k$-jet curvature, must its real first Chern class satisfy $c_1(X)_{\mathbb R}\ne0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656](https://doi.org/10.4171/owr/2012/43)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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-12015-001",
"literature-status:open",
"owr-year:2012"
] | The question whether non-degenerate negative k-jet curvature forces nonzero real first Chern class is still presented as an unresolved problem; later work retains the surrounding jet-curvature equivalence as a hard conjectural problem. | [
{
"url": "https://ems.press/content/serial-article-files/46414",
"label": "Oberwolfach Report 43, jet-curvature question"
},
{
"url": "https://www-fourier.univ-grenoble-alpes.fr/~demailly/source_files/takagi16/JJM1566_final_page_proof.pdf",
"label": "Demailly, jet metrics and curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/43 | null | null | null | If a complex manifold $X$ has nondegenerate negative $k$-jet curvature, must its real first Chern class satisfy $c_1(X)_{\mathbb R}\ne0$? | If a complex manifold X has non-degenerate negative k-jet curvature, must its real first Chern class satisfy c_1(X)_{\mathbb R}\ne 0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656 |
30,002,181 | OWR-12015-002 | Rational Curves on Calabi–Yau Threefolds with Nef Divisors | If a Calabi–Yau threefold $X$ has a nonzero nef, non-ample line bundle, must $X$ contain a rational curve? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656](https://doi.org/10.4171/owr/2012/43)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,012 | 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-12015-002",
"literature-status:partially-solved",
"owr-year:2012"
] | Oguiso's implication is proved when the Calabi--Yau threefold has second Betti number greater than four, with further special-case results, but the unrestricted statement remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/43344",
"label": "Diverio--Ferretti, Oguiso conjecture"
},
{
"url": "https://arxiv.org/abs/1601.01273",
"label": "Lazic--Oguiso--Peternell, nef line bundles"
},
{
"url": "https://arxiv.org/abs/2010.12233",
"label": "Rational cu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/43 | null | null | null | If a Calabi–Yau threefold $X$ has a nonzero nef, non-ample line bundle, must $X$ contain a rational curve? | If a Calabi--Yau threefold X has a nonzero nef non-ample line bundle, must X contain a rational curve? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656 |
30,002,182 | OWR-12015-004 | Log Abundance for Semi-Log-Canonical Pairs | Let $(X,\Delta)$ be a projective semi-log-canonical pair with $\Delta$ a $\mathbb Q$-divisor. If $K_X+\Delta$ is nef, must $K_X+\Delta$ be semi-ample? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656](https://doi.org/10.4171/owr/2012/43)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,012 | 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-12015-004",
"literature-status:partially-solved",
"owr-year:2012"
] | The extract combines proved finiteness results for log pluricanonical representations with the log abundance conjecture for projective semi-log-canonical pairs. Abundance is known in important lower-dimensional and numerically trivial cases, but the general conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/43",
"label": "Gongyo, log pluricanonical representations and abundance"
},
{
"url": "https://doi.org/10.1017/fms.2025.10092",
"label": "Hashizume, log canonical MMP"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/43 | null | null | null | Let $(X,\Delta)$ be a projective semi-log-canonical pair with $\Delta$ a $\mathbb Q$-divisor. If $K_X+\Delta$ is nef, must $K_X+\Delta$ be semi-ample? | Let (X,\Delta) be a projective semi-log-canonical pair with \Delta a Q-divisor. If K_X+\Delta is nef, must K_X+\Delta be semi-ample? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656 |
30,002,183 | OWR-12015-007 | Symplectic Moduli Spaces of Sheaves | Let $X$ be an irreducible holomorphic symplectic manifold and $M$ a moduli space of sheaves on $X$. Must $M$ also be an irreducible holomorphic symplectic manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656](https://doi.org/10.4171/owr/2012/43)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,012 | 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-12015-007",
"literature-status:open",
"owr-year:2012"
] | The general question whether a moduli space of sheaves on an IHS manifold is again IHS remains open. Known results establish many positive constructions on K3 and abelian surfaces, while moduli spaces on higher-dimensional IHS manifolds can be singular or require a symplectic resolution. | [
{
"url": "https://arxiv.org/abs/1308.4304",
"label": "Wandel, tautological sheaves and moduli"
},
{
"url": "https://doi.org/10.1007/s00229-020-01223-0",
"label": "Examples of smooth components of sheaf moduli"
},
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-sigm... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/43 | null | null | null | Let $X$ be an irreducible holomorphic symplectic manifold and $M$ a moduli space of sheaves on $X$. Must $M$ also be an irreducible holomorphic symplectic manifold? | Let X be an irreducible holomorphic symplectic manifold and M a moduli space of sheaves on X. Is M again an irreducible holomorphic symplectic manifold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Komplexe Analysis (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/43, pp. 2597--2656 |
30,002,184 | OWR-12016-001 | Persistence Times of Dynamical-Percolation Crossings | How long may it take for a crossing event to disappear in dynamical percolation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745](https://doi.org/10.4171/owr/2012/44)
## Literature review (checked 2... | 3 | partially_solved | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12016-001",
"literature-status:partially-solved",
"owr-year:2012"
] | For dynamical critical percolation, rigorous results give superpolynomial decay for the persistence of a box crossing and exponential tails for the first exceptional infinite-cluster time. These bounds answer part of the timing question, but do not determine a sharp general tail law. | [
{
"url": "https://doi.org/10.1214/EJP.v17-2229",
"label": "Hammond--Mossel--Pete, exit-time tails"
},
{
"url": "https://arxiv.org/abs/1208.3826",
"label": "Hammond--Pete--Schramm, exceptional-set local time"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/44 | null | null | null | How long may it take for a crossing event to disappear in dynamical percolation? | How long may it take for a crossing event to disappear in dynamical percolation? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745 |
30,002,185 | OWR-12016-002 | Sharp Tail Decay for Persistent Critical Crossings | For critical dynamical percolation and the left–right crossing event $C_Q$ of a square $Q$, is the tail probability bounded by
$$\mathbb P[\omega_s\in C_Q\text{ for all }s\in[0,t]]\leq\exp(-t^{2/3+o(1)})$$
as $t\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745](https://doi.org/10.4171/owr/2012/44)
## Literature review (checked 2... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12016-002",
"literature-status:open",
"owr-year:2012"
] | The stated exp(-t^{2/3+o(1)}) tail is explicitly presented as a conjectural possible sharp decay. The cited dynamical-percolation results establish exponential or superpolynomial bounds in related regimes, not this asymptotic. | [
{
"url": "https://doi.org/10.4171/owr/2012/44",
"label": "Oberwolfach Report 44, dynamical percolation"
},
{
"url": "https://doi.org/10.1214/EJP.v17-2229",
"label": "Hammond--Mossel--Pete, exit-time tails"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/44 | null | null | null | For critical dynamical percolation and the left–right crossing event $C_Q$ of a square $Q$, is the tail probability bounded by
$$\mathbb P[\omega_s\in C_Q\text{ for all }s\in[0,t]]\leq\exp(-t^{2/3+o(1)})$$
as $t\to\infty$? | For critical dynamical percolation and the left--right crossing event C_Q of a square Q, is the tail probability conjecturally bounded by \mathbb P[\omega_s\in C_Q for all s\in[0,t]]\leq\exp(-t^{2/3+o(1)}) as t\to\infty? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745 |
30,002,186 | OWR-12016-003 | Integrated Super-Brownian Scaling of High-Dimensional Incipient Clusters | What is the scaling limit of the entire high-dimensional incipient infinite cluster? The conjecture is that a properly rescaled cluster converges to integrated super-Brownian excursion (ISE). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745](https://doi.org/10.4171/owr/2012/44)
## Literature review (checked 2... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12016-003",
"literature-status:open",
"owr-year:2012"
] | The extracted statement ends after saying that it is an open problem to identify something, without retaining the object or claim to be identified. It is therefore unresolved and unclassifiable as solved under the queue rule. | [
{
"url": "https://doi.org/10.4171/owr/2012/44",
"label": "Oberwolfach Report 44, source extract"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/44 | null | null | null | What is the scaling limit of the entire high-dimensional incipient infinite cluster? The conjecture is that a properly rescaled cluster converges to integrated super-Brownian excursion (ISE). | What is the scaling limit of the entire high-dimensional incipient infinite cluster? The conjecture is that a properly rescaled cluster converges to integrated super-Brownian excursion (ISE). | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745 |
30,002,187 | OWR-12016-007 | Scaling Limits Across the Directed-Polymer Crossover | For $(1+1)$-dimensional directed polymers, does the scaling limit at the $\beta=\infty$ end of the convergence diagram exist; what are the properties of the intermediate-disorder crossover bridge; and, for environment scalings slower than $n^{-1/4}$, does the pair $(\omega_n,S_n)$ have a distributional limit, and if so... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745](https://doi.org/10.4171/owr/2012/44)
## Literature review (checked 2... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12016-007",
"literature-status:open",
"owr-year:2012"
] | The slower-than-n^{-1/4} disorder regime and its joint scaling limit with the polymer path remain open in the cited research line; the n^{-1/4} intermediate-disorder limit and faster-scaling Brownian regime are known, but the KPZ-side crossover is not fully established. | [
{
"url": "https://doi.org/10.4171/owr/2012/44",
"label": "Oberwolfach Report 44, convergence diagram"
},
{
"url": "https://doi.org/10.1103/PhysRevLett.105.090603",
"label": "Alberts--Khanin--Quastel, intermediate disorder"
},
{
"url": "https://arxiv.org/abs/1202.4403",
"label": "Albe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/44 | null | null | null | For $(1+1)$-dimensional directed polymers, does the scaling limit at the $\beta=\infty$ end of the convergence diagram exist; what are the properties of the intermediate-disorder crossover bridge; and, for environment scalings slower than $n^{-1/4}$, does the pair $(\omega_n,S_n)$ have a distributional limit, and if so... | For 1+1-dimensional directed polymers, does the scaling limit at the beta=infinity end of the convergence diagram exist; what are the properties of the intermediate-disorder crossover bridge; and for environment scalings slower than n^{-1/4}, does the pair (\omega_n,S_n) have a distributional limit, and if so is it the... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745 |
30,002,188 | OWR-12016-008 | Parameter Dependence of Directed-Polymer Endpoint Limits | In the $(1+1)$-dimensional directed-polymer convergence diagram, does the putative scaling limit at the right-hand end depend on the parameters $\beta$ and $\alpha$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745](https://doi.org/10.4171/owr/2012/44)
## Literature review (checked 2... | 3 | open | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12016-008",
"literature-status:open",
"owr-year:2012"
] | The extract is a diagrammatic question about dependence of the unresolved polymer scaling limit on beta and alpha. Known endpoint regimes do not determine the intermediate crossover requested here. | [
{
"url": "https://doi.org/10.4171/owr/2012/44",
"label": "Oberwolfach Report 44, polymer diagram"
},
{
"url": "https://doi.org/10.1103/PhysRevLett.105.090603",
"label": "Alberts--Khanin--Quastel, disorder regimes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/44 | null | null | null | In the $(1+1)$-dimensional directed-polymer convergence diagram, does the putative scaling limit at the right-hand end depend on the parameters $\beta$ and $\alpha$? | In the 1+1-dimensional directed-polymer convergence diagram, does the putative scaling limit at the right-hand end depend on the parameters beta and alpha? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/44, pp. 2657--2745 |
30,002,189 | OWR-12018-003 | HOMFLY Polynomials from Nested Hilbert Schemes | Let $C=\{E(x,y)=0\}$ be a planar curve singularity at $(0,0)$, with Milnor number
$$\mu=\dim_{\mathbb C}\frac{\mathbb C[[x,y]]}{(\partial E/\partial x,\partial E/\partial y)}.$$
Does the HOMFLY–PT polynomial of its algebraic link satisfy
$$\overline P(L_{C,(0,0)})=(a/q)^{\mu-1}\sum_{\ell,m}q^{2\ell}(-a^2)^m\chi\!\left(... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866](https://doi.org/10.4171/owr/2012/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12018-005"
] | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; duplicate of `OWR-12018-003`)**. It is titled a duplicate and states the same conjecture in words (OWR 46/2012, p. 2812), proved by Maulik as above. **Give it the same status as `-003`**; its note, which speaks of a cabling theorem, describes a different pass... | [
"owr",
"oberwolfach-reports",
"OWR-12018-003",
"literature-status:open",
"owr-year:2012"
] | The record preserves setup for the Hilbert-scheme/HOMFLY correspondence but not the conjectural formula itself; the missing assertion prevents a determinate literature verdict. | [
{
"url": "https://doi.org/10.4171/owr/2012/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/46 | null | null | null | Let $C=\{E(x,y)=0\}$ be a planar curve singularity at $(0,0)$, with Milnor number
$$\mu=\dim_{\mathbb C}\frac{\mathbb C[[x,y]]}{(\partial E/\partial x,\partial E/\partial y)}.$$
Does the HOMFLY–PT polynomial of its algebraic link satisfy
$$\overline P(L_{C,(0,0)})=(a/q)^{\mu-1}\sum_{\ell,m}q^{2\ell}(-a^2)^m\chi\!\left(... | For a planar curve singularity C=\{E(x,y)=0\} at (0,0), with Milnor number \mu=\dim \mathbb C[[x,y]]/(\partial E/\partial x,\partial E/\partial y), the HOMFLY--PT polynomial of its algebraic link is conjectured to satisfy \overline P(L_{C,(0,0)})=(a/q)^{\mu-1}\sum_{\ell,m}q^{2\ell}(-a^2)^m\chi(C_{(0,0)}^{[\ell,\ell+m]}... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866 |
30,002,190 | OWR-12018-005 | Duplicate: HOMFLY Polynomials from Nested Hilbert Schemes | For a planar curve singularity C at (0,0), the HOMFLY--PT polynomial of its algebraic link is conjectured to equal the weighted Euler-characteristic sum over the nested punctual Hilbert schemes C_{(0,0)}^{[\ell,\ell+m]}. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866](https://doi.org/10.4171/owr/2012/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | solved | null | 2,012 | 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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | Duplicate/merged OWR extraction (Comparison with the official report and OWR-12018-003 confirms that this is a shortened repeat of the same ordinary HOMFLY conjecture. No se) | [
"OWR-12018-003"
] | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; duplicate of `OWR-12018-003`)**. It is titled a duplicate and states the same conjecture in words (OWR 46/2012, p. 2812), proved by Maulik as above. **Give it the same status as `-003`**; its note, which speaks of a cabling theorem, describes a different pass... | [
"owr",
"oberwolfach-reports",
"OWR-12018-005",
"literature-status:open",
"owr-year:2012"
] | The extracted text states a cabling theorem and supplies no standalone conjecture or question whose truth value can be assessed. | [
{
"url": "https://doi.org/10.4171/owr/2012/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/46 | null | null | null | null | For a planar curve singularity C at (0,0), the HOMFLY--PT polynomial of its algebraic link is conjectured to equal the weighted Euler-characteristic sum over the nested punctual Hilbert schemes C_{(0,0)}^{[\ell,\ell+m]}. | unrecoverable | Comparison with the official report and OWR-12018-003 confirms that this is a shortened repeat of the same ordinary HOMFLY conjecture. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866 |
30,002,191 | OWR-12018-006 | Homological Hilbert-Scheme Conjecture for Algebraic Links | Let $C$ be a planar curve singularity at $(0,0)$ with Milnor number $\mu$. Does the triply graded HOMFLY homology of its algebraic link satisfy
$$\left(\frac aq\right)^{\mu-1}\sum_{\ell,m}q^{2\ell}a^{2m}t^{m^2}P_t^{\mathrm{vir}}\!\left(C_{(0,0)}^{[\ell,\ell+m]}\right)=P(L_{C,(0,0)})$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866](https://doi.org/10.4171/owr/2012/46)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12018-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12018-006",
"literature-status:partially-solved",
"owr-year:2012"
] | The homological Hilbert-scheme formula remains open in full generality, but it has been proved in substantial families and specializations, including torus-knot cases and related geometric realizations. | [
{
"url": "https://doi.org/10.4171/owr/2012/46",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1201.2115",
"label": "Oblomkov--Rasmussen--Shende, HOMFLY homology conjecture"
},
{
"url": "https://arxiv.org/abs/2407.18123",
"label": "Khovanov--Rozansky homology for C... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/46 | null | null | null | Let $C$ be a planar curve singularity at $(0,0)$ with Milnor number $\mu$. Does the triply graded HOMFLY homology of its algebraic link satisfy
$$\left(\frac aq\right)^{\mu-1}\sum_{\ell,m}q^{2\ell}a^{2m}t^{m^2}P_t^{\mathrm{vir}}\!\left(C_{(0,0)}^{[\ell,\ell+m]}\right)=P(L_{C,(0,0)})$$? | For a planar curve singularity C at (0,0), the homological conjecture asserts \sum_{\ell,m}(a/q)^{\mu-1}q^{2\ell}a^{2m}t^m P^{\mathrm{vir}}(C_{(0,0)}^{[\ell,\ell+m]})=P(L_{C,(0,0)}), relating nested Hilbert schemes to the triply graded HOMFLY homology of the algebraic link. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866 |
30,002,192 | OWR-12018-007 | Duplicate: Homological Hilbert-Scheme Conjecture | The homological Hilbert-scheme conjecture for algebraic links has been verified for T_{2,n}, T_{3,n}, and several other small torus knots, while its general validity remains open. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866](https://doi.org/10.4171/owr/2012/46)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report presents this passage as verification context for the conjecture already recorded in OWR-12018-006, not as a separate pr) | [
"OWR-12018-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12018-007",
"literature-status:partially-solved",
"owr-year:2012"
] | This is the same homological conjecture as the adjacent record: important torus-knot and geometric cases are known, while the full planar-curve statement is not established. | [
{
"url": "https://doi.org/10.4171/owr/2012/46",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1201.2115",
"label": "Oblomkov--Rasmussen--Shende, HOMFLY homology conjecture"
},
{
"url": "https://arxiv.org/abs/2407.18123",
"label": "Khovanov--Rozansky homology for C... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/46 | null | null | null | null | The homological Hilbert-scheme conjecture for algebraic links has been verified for T_{2,n}, T_{3,n}, and several other small torus knots, while its general validity remains open. | unrecoverable | The official report presents this passage as verification context for the conjecture already recorded in OWR-12018-006, not as a separate problem. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866 |
30,002,193 | OWR-12018-010 | Classification of Simple Normal Surface Singularities | What are the simple normal surface singularities? The conjecture is that they are exactly the rational singularities whose resolution graphs arise from graphs of rational double points and rational triple points by making some vertex weights more negative; in particular, rigid normal surface singularities do not exist. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866](https://doi.org/10.4171/owr/2012/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,012 | 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-12018-010",
"literature-status:open",
"owr-year:2012"
] | The proposed classification of simple normal surface singularities and the related nonexistence of rigid normal surface singularities remain conjectural; Stevens proved only one direction generally and special classes in the other direction. | [
{
"url": "https://doi.org/10.4171/owr/2012/46",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1303.0692",
"label": "Stevens, Simple surface singularities"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/46 | null | null | null | What are the simple normal surface singularities? The conjecture is that they are exactly the rational singularities whose resolution graphs arise from graphs of rational double points and rational triple points by making some vertex weights more negative; in particular, rigid normal surface singularities do not exist. | What are the simple normal surface singularities? The conjecture is that they are exactly the rational singularities whose resolution graphs arise from graphs of rational double points and rational triple points by making some vertex weights more negative; in particular, rigid normal surface singularities do not exist. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/46, pp. 2799--2866 |
30,002,194 | OWR-12170-001 | Classification Problems for Finite Weyl Groupoids | Are all finite Weyl groupoids invariants of Nichols algebras? Can simplicial arrangements be classified? How far does the connection between reflection groupoids and cluster algebras extend? What is the connection with toric varieties? How can sporadic finite Weyl groupoids be explained? Can the classification of finit... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905](https://doi.org/10.4171/owr/2012/47)
## Literature review (checked ... | 3 | partially_solved | null | 2,012 | 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-12170-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Finite Weyl groupoids and several Nichols-algebra classifications are known, but the six recorded problems include unresolved realization, simplicial-arrangement, cluster, toric, sporadic-structure, and deduction questions. | [
{
"url": "https://doi.org/10.4171/owr/2012/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1008.5291",
"label": "Cuntz--Heckenberger, Finite Weyl groupoids"
},
{
"url": "https://arxiv.org/abs/1503.08117",
"label": "Cuntz--Lentner, A simplicial complex of Nichol... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/47 | null | null | null | Are all finite Weyl groupoids invariants of Nichols algebras? Can simplicial arrangements be classified? How far does the connection between reflection groupoids and cluster algebras extend? What is the connection with toric varieties? How can sporadic finite Weyl groupoids be explained? Can the classification of finit... | Open problems are: whether all finite Weyl groupoids are invariants of Nichols algebras; classification of simplicial arrangements; extension of the connection between reflection groupoids and cluster algebras; clarification of the connection to toric varieties; understanding sporadic finite Weyl groupoids; and derivin... | corrected_verified | The official report lists these six questions together in its open-problems section. | null | null | null | null | null | Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905 |
30,002,195 | OWR-12170-002 | Cartan Schemes and Positive-Characteristic Lie Algebras | Are the objects in the classification of finite Cartan schemes that do not occur in the classification of arithmetic root systems related to Lie algebras in positive characteristic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905](https://doi.org/10.4171/owr/2012/47)
## Literature review (checked ... | 3 | open | null | 2,012 | 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-12170-002",
"literature-status:open",
"owr-year:2012"
] | Whether the relevant unidentified diagonal Nichols braidings are related to Lie algebras in positive characteristic is posed as an open question, and no complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2012/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/47 | null | null | null | Are the objects in the classification of finite Cartan schemes that do not occur in the classification of arithmetic root systems related to Lie algebras in positive characteristic? | For the remaining finite-dimensional Nichols algebras of diagonal type, are the unidentified objects in the Cartan-scheme classification related to Lie algebras in positive characteristic? | corrected_verified | The official report asks this question about the additional Cartan-scheme objects, not about unidentified Nichols algebras. | null | null | null | null | null | Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905 |
30,002,196 | OWR-12170-003 | Dimension and Quadraticity of Transposition Nichols Algebras | For $n\geq6$, determine the dimension of the Nichols algebra $\mathfrak B(\mathcal O_2^n,-1)$ associated with the conjugacy class of transpositions in $S_n$ and the constant cocycle $-1$. Is this algebra quadratic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905](https://doi.org/10.4171/owr/2012/47)
## Literature review (checked ... | 3 | open | null | 2,012 | 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-12170-003",
"literature-status:open",
"owr-year:2012"
] | For the Nichols algebra of the fixed-point-free involution rack O_{2n} with cocycle -1, n greater than or equal to 6, finite dimensionality and quadraticity remain unresolved; the infinite-dimensionality of its quadratic cover does not settle equality with the Nichols algebra. | [
{
"url": "https://doi.org/10.4171/owr/2012/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2001.04597",
"label": "Barligea, On the dimension of the Fomin--Kirillov algebra and related algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/47 | null | null | null | For $n\geq6$, determine the dimension of the Nichols algebra $\mathfrak B(\mathcal O_2^n,-1)$ associated with the conjugacy class of transpositions in $S_n$ and the constant cocycle $-1$. Is this algebra quadratic? | For the Nichols algebra of the Jordanian quantum plane, or more generally a Nichols algebra of triangular type in the stated finite-GK-dimension setting, is the algebra quadratic? | corrected_verified | The official report states this dimension and quadraticity problem; the extraction’s “triangular Nichols algebra” label was incorrect. | null | null | null | null | null | Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905 |
30,002,197 | OWR-12170-004 | Finite Generation of Cohomology for Finite Tensor Categories | Is the cohomology of every finite tensor category finitely generated; equivalently, can the Etingof–Ostrik conjecture be proved or disproved, first for further classes of finite-dimensional Hopf algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905](https://doi.org/10.4171/owr/2012/47)
## Literature review (checked ... | 3 | partially_solved | null | 2,012 | 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-12170-004",
"literature-status:partially-solved",
"owr-year:2012"
] | The Etingof--Ostrik finite-generation conjecture is proved for important classes, including complex pointed Hopf algebras with abelian group-likes and quasi-split finite-dimensional Hopf algebras, but remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2012/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2004.07149",
"label": "Mastnak--Pevtsova--Schauenburg--Witherspoon, cohomology of pointed Hopf algebras"
},
{
"url": "https://doi.org/10.4171/DM/1025",
"label": "Andruski... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/47 | null | null | null | Is the cohomology of every finite tensor category finitely generated; equivalently, can the Etingof–Ostrik conjecture be proved or disproved, first for further classes of finite-dimensional Hopf algebras? | Is the cohomology of every finite tensor category finitely generated; equivalently, can one prove or disprove the Etingof--Ostrik conjecture, first for further classes of finite-dimensional Hopf algebras? | corrected_verified | The official report presents this as the Etingof–Ostrik conjecture and suggests the stated Hopf-algebra cases. | null | null | null | null | null | Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905 |
30,002,198 | OWR-12170-005 | Hilbert-Series Factorization for Finite-Dimensional Nichols Algebras | Does every finite-dimensional Nichols algebra have a Hilbert series of the form $H_{\mathfrak B}(t)=(\alpha_1)_t\cdots(\alpha_n)_t(\beta_1)_{t^2}\cdots(\beta_m)_{t^2}$, where $(r)_t=1+t+\cdots+t^{r-1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905](https://doi.org/10.4171/owr/2012/47)
## Literature review (checked ... | 3 | open | null | 2,012 | 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-12170-005",
"literature-status:open",
"owr-year:2012"
] | The extracted conjecture is truncated after each finite-dimensional Nichols algebra; the associated Hilbert-series factorization conjecture and the non-abelian classification remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/47",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1503.08117",
"label": "Cuntz--Lentner, A simplicial complex of Nichols algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/47 | null | null | null | Does every finite-dimensional Nichols algebra have a Hilbert series of the form $H_{\mathfrak B}(t)=(\alpha_1)_t\cdots(\alpha_n)_t(\beta_1)_{t^2}\cdots(\beta_m)_{t^2}$, where $(r)_t=1+t+\cdots+t^{r-1}$? | Conjecture: every finite-dimensional Nichols algebra has Hilbert series H_B(t)=(\alpha_1)_t\cdots(\alpha_n)_t(\beta_1)_{t^2}\cdots(\beta_m)_{t^2}, where (r)_t=1+t+\cdots+t^{r-1}. | corrected_verified | The official report states this factorization as a conjectural property of every finite-dimensional Nichols algebra. | null | null | null | null | null | Mini-Workshop: Nichols Algebras and Weyl Groupoids (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/47, pp. 2879--2905 |
30,002,199 | OWR-12172-002 | Toric Orbits Meeting Subvariety Closures | Given a subvariety $Y$ of the algebraic torus $T=(\mathbb C^*)^n$ and a toric variety $X_\Sigma$ with dense torus $T$, which $T$-orbits of $X_\Sigma$ meet the closure of $Y$ in $X_\Sigma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | open | null | 2,012 | 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 | 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)**. M. A. Cueto (OWR 49/2012, p. 2949, Question 1) asks which torus orbits of a toric variety X_Σ meet the closure of a subvariety Y of the torus, and answers it with Tevelev's lemma: the orbit of σ ∈ Σ meets the closure iff the tropicalizat... | [
"owr",
"oberwolfach-reports",
"OWR-12172-002",
"literature-status:open",
"owr-year:2012"
] | The extracted tropicalization passage states background and a question about toric-orbit intersections but does not preserve a distinct conjecture or theorem to verify. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | Given a subvariety $Y$ of the algebraic torus $T=(\mathbb C^*)^n$ and a toric variety $X_\Sigma$ with dense torus $T$, which $T$-orbits of $X_\Sigma$ meet the closure of $Y$ in $X_\Sigma$? | Given a subvariety Y of the algebraic torus T=(\mathbb{C}^{*})^n and a toric variety X_\Sigma with dense torus T, which T-orbits of X_\Sigma meet the closure of Y in X_\Sigma? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,200 | OWR-12172-003 | Sharp Syzygy Bounds for Torus Actions | For a rational Poincaré duality space with torus rank $r$, if its equivariant cohomology is not free, the syzygy bound is at most $\lfloor(r-1)/2\rfloor$. Is this bound sharp for $r\geq5$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | solved | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1093/imrn/rnv090",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. M. Franz (joint with C. Allday and V. Puppe; OWR 49/2012, p. 2956) notes that for a rational Poincaré duality space with an action of T = (S¹)^r, equivariant cohomology that is not free is at most a syzygy of order ⌊(r − 1)/2⌋, and asks whether this is sha... | [
"owr",
"oberwolfach-reports",
"OWR-12172-003",
"literature-status:open",
"owr-year:2012"
] | The syzygy-order bound for equivariant cohomology is explicitly reported as sharp for r at most 4 and unresolved for r at least 5; no later complete construction or proof was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | For a rational Poincaré duality space with torus rank $r$, if its equivariant cohomology is not free, the syzygy bound is at most $\lfloor(r-1)/2\rfloor$. Is this bound sharp for $r\geq5$? | For a rational Poincare duality space with torus rank r, if its equivariant cohomology is not free, the syzygy bound is at most \lfloor(r-1)/2\rfloor; is this bound sharp for r\geq 5? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,201 | OWR-12172-004 | Effective Cones of Wonderful Arrangement Compactifications | For a wonderful compactification $Y$ of a hyperplane-arrangement complement, can the tropical iterative procedure determine its effective cone and provide a method to study the Castravet–Tevelev conjecture for $M_{0,n}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | open | null | 2,012 | 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-12172-004",
"literature-status:open",
"owr-year:2012"
] | The record only says that an iterative procedure may help study the Castravet--Tevelev effective-cone conjecture; it does not state that conjecture in full, and no determinate resolution follows from the extracted text. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | For a wonderful compactification $Y$ of a hyperplane-arrangement complement, can the tropical iterative procedure determine its effective cone and provide a method to study the Castravet–Tevelev conjecture for $M_{0,n}$? | For a wonderful compactification Y of a hyperplane-arrangement complement, can the tropical iterative procedure determine its effective cone and provide a method to study the Castravet--Tevelev conjecture for M_{0,n}? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,202 | OWR-12172-005 | Combinatorial Freeness of Piecewise-Polynomial Fan Modules | For the piecewise-polynomial module $C^0(\Sigma)$ associated with a polyhedral fan $\Sigma$, does there exist a simple combinatorial condition equivalent to its freeness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | open | null | 2,012 | 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-12172-005",
"literature-status:open",
"owr-year:2012"
] | The existence of a simple combinatorial criterion for freeness of the relevant nonsimplicial toric piecewise-polynomial module remains an open problem in the cited report. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | For the piecewise-polynomial module $C^0(\Sigma)$ associated with a polyhedral fan $\Sigma$, does there exist a simple combinatorial condition equivalent to its freeness? | For the piecewise-polynomial module C^0(\Sigma) associated with a polyhedral fan \Sigma, does there exist a simple combinatorial condition equivalent to its freeness? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,203 | OWR-12172-006 | Lifting Pentagon-Arrangement Symmetries to Homotopy Invariants | For the pentagon hyperplane arrangement whose combinatorial symmetry induces an automorphism of the complement homology, can this automorphism extend to an automorphism of the $E^\infty$-coalgebra, and can it extend to an automorphism of the fundamental group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | open | null | 2,012 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12172-006",
"literature-status:open",
"owr-year:2012"
] | The pentagon-arrangement automorphism questions about extension to an E-infinity coalgebra and to the fundamental group are posed as open problems, with no complete later resolution identified. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | For the pentagon hyperplane arrangement whose combinatorial symmetry induces an automorphism of the complement homology, can this automorphism extend to an automorphism of the $E^\infty$-coalgebra, and can it extend to an automorphism of the fundamental group? | For the pentagon hyperplane arrangement whose combinatorial symmetry induces an automorphism of the complement homology, can this automorphism extend to an automorphism of the E^\infty-coalgebra, and can it extend to an automorphism of the fundamental group? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,204 | OWR-12172-007 | Resolutions and Higher-Dimensional Structure of Orlik–Terao Algebras | For the Orlik–Terao algebra $R/I_A$ of a hyperplane arrangement $A$, what phenomena occur in higher dimensions and for reflection arrangements, and what is its minimal free resolution, even when $A\subseteq\mathbb P^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49... | 3 | partially_solved | null | 2,012 | 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-12172-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Cohen--Macaulayness, blowup descriptions, modular decompositions, and important special classes are known, but no general minimal free resolution or complete higher-dimensional and reflection-arrangement theory is established. | [
{
"url": "https://doi.org/10.4171/owr/2012/49",
"label": "original OWR problem"
},
{
"url": "https://arxiv.org/abs/1701.03470",
"label": "Orlik--Terao blowup algebra"
},
{
"url": "https://doi.org/10.1016/j.aam.2015.08.003",
"label": "Orlik--Terao ideal and relation space"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/49 | null | null | null | For the Orlik–Terao algebra $R/I_A$ of a hyperplane arrangement $A$, what phenomena occur in higher dimensions and for reflection arrangements, and what is its minimal free resolution, even when $A\subseteq\mathbb P^2$? | For the Orlik--Terao algebra R/I_A of a hyperplane arrangement A, what phenomena occur in higher dimensions and for reflection arrangements, and what is its minimal free resolution, even when A\subseteq\mathbb{P}^2? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Cohomology Rings and Fundamental Groups of Hyperplane Arrangements, Wonderful Compactifications, and Real Toric Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/49, pp. 2939--2983 |
30,002,205 | OWR-12173-001 | Euclidean Ramsey Configurations and Sphericity | Which finite point configurations $K\subset\mathbb R^n$ are Ramsey for Euclidean $r$-colorings? In particular, are the Ramsey configurations exactly the spherical configurations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | open | null | 2,012 | 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-12173-001",
"literature-status:open",
"owr-year:2012"
] | The record only says that a classification is open and does not identify the objects, equivalence relation, or theorem being classified; no precise claim can therefore be verified beyond retaining open status. | [
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | Which finite point configurations $K\subset\mathbb R^n$ are Ramsey for Euclidean $r$-colorings? In particular, are the Ramsey configurations exactly the spherical configurations? | Which finite point configurations K\subset\mathbb{R}^n are Ramsey for Euclidean r-colorings; in particular, are the Ramsey configurations exactly the spherical configurations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,206 | OWR-12173-002 | Convergence Criteria for Hardy-Field Multiple Ergodic Averages | Let $T$ be a measure-preserving transformation, let $f_1,\ldots,f_k\in L^\infty$, and let $a_1,\ldots,a_k$ be functions in a common Hardy field with polynomial growth. Consider
$$\frac1N\sum_{n=1}^N T^{\lfloor a_1(n)\rfloor}f_1\cdots T^{\lfloor a_k(n)\rfloor}f_k.$$
Do these averages converge if and only if every nonzer... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | partially_solved | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12173-002",
"literature-status:partially-solved",
"owr-year:2012"
] | The proposed criterion for multiple averages of several Hardy-field sequences has been proved under stronger hypotheses and in substantial general-position cases, but the full necessary-and-sufficient statement for arbitrary collections remains unresolved. | [
{
"url": "https://arxiv.org/abs/1103.3808",
"label": "Hardy-field open-problem survey"
},
{
"url": "https://arxiv.org/abs/2109.07941",
"label": "joint ergodicity for Hardy sequences"
},
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | Let $T$ be a measure-preserving transformation, let $f_1,\ldots,f_k\in L^\infty$, and let $a_1,\ldots,a_k$ be functions in a common Hardy field with polynomial growth. Consider
$$\frac1N\sum_{n=1}^N T^{\lfloor a_1(n)\rfloor}f_1\cdots T^{\lfloor a_k(n)\rfloor}f_k.$$
Do these averages converge if and only if every nonzer... | Let a_1,\ldots,a_k be Hardy-field functions of at most polynomial growth and let (2) be the corresponding multiple ergodic average with iterates \lfloor a_i(n)\rfloor. Do these averages converge if and only if every nontrivial a\in\operatorname{span}(a_1,\ldots,a_k) satisfies at least one of: |a(t)-cp(t)|\succ\log t fo... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,207 | OWR-12173-003 | Roth Recurrence in Groups of Intermediate Growth | Can there exist a positive-measure set $B$ in a measure-preserving action of a group of intermediate growth such that $\mu(g_1^nB\cap g_2^nB)=0$ for every $n\ne0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12173-003",
"literature-status:open",
"owr-year:2012"
] | Nilpotent groups satisfy the relevant Roth-type recurrence while solvable groups of exponential growth admit counterexamples; the existence of such counterexamples for groups of intermediate growth remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1017/S0143385703000427",
"label": "solvable exponential-growth counterexamples"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | Can there exist a positive-measure set $B$ in a measure-preserving action of a group of intermediate growth such that $\mu(g_1^nB\cap g_2^nB)=0$ for every $n\ne0$? | Can there exist a positive-measure set B in a measure-preserving action of a group of intermediate growth such that \mu(g_1^nB\cap g_2^nB)=0 for every n\ne 0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,208 | OWR-12173-004 | Additive Sets Preserving Piecewise Syndeticity | Let $A\subset\mathbb Z$ have the property that $A+B$ is piecewise syndetic, or alternatively piecewise Bohr, whenever $B\subset\mathbb Z$ has positive upper Banach density. What can be said about $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | open | null | 2,012 | 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-12173-004",
"literature-status:open",
"owr-year:2012"
] | The record is only the question `What can be said about A?' and does not define A or state a mathematical assertion, so the extracted problem is unresolved and cannot be classified more narrowly. | [
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | Let $A\subset\mathbb Z$ have the property that $A+B$ is piecewise syndetic, or alternatively piecewise Bohr, whenever $B\subset\mathbb Z$ has positive upper Banach density. What can be said about $A$? | Let A\subset\mathbb{Z} have the property that A+B is piecewise syndetic, or alternatively piecewise Bohr, whenever B\subset\mathbb{Z} has positive upper Banach density. What can be said about A? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,209 | OWR-12173-005 | Sarnak's Möbius Disjointness Conjecture | For every sequence $a_n=f(T^n x)$ generated by a zero-topological-entropy dynamical system, is
$$\sum_{n\leq N}\mu(n)a_n=o(N)$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12173-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12173-005",
"literature-status:open",
"owr-year:2012"
] | Sarnak's Mobius-disjointness conjecture remains open in its full zero-entropy generality, although it is proved for many structured systems and its logarithmically averaged variant has substantial progress. | [
{
"url": "https://arxiv.org/abs/1710.04039",
"label": "Sarnak conjecture survey"
},
{
"url": "https://doi.org/10.1016/j.jmaa.2024.128621",
"label": "recent logarithmic-average result"
},
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | For every sequence $a_n=f(T^n x)$ generated by a zero-topological-entropy dynamical system, is
$$\sum_{n\leq N}\mu(n)a_n=o(N)$$? | Sarnak conjecture: for every deterministic sequence a_n=f(T^n x) generated by a zero-topological-entropy dynamical system, does \sum_{n\leq N}\mu(n)a_n=o(N) hold? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,210 | OWR-12173-007 | Duplicate: Sarnak's Möbius Disjointness Conjecture | Can Sarnak's conjecture be proved for every deterministic sequence, namely that its correlation with the Mo\ddot{\mathrm{obius}} function is o(N); the conjecture is known in several special cases and is implied by Chowla's conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059](https://doi.org/10.4171/owr/2012/50)
## Literature... | 3 | open | null | 2,012 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (Comparison with the official report and OWR-12173-005 confirms that this is a second extraction of the same conjecture plus evidence about s) | [
"OWR-12173-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12173-007",
"literature-status:open",
"owr-year:2012"
] | The excerpt records evidence and known special cases for Sarnak's conjecture rather than a separate theorem; the general conjecture it invokes is still open, so the extracted claim is not solved. | [
{
"url": "https://arxiv.org/abs/1710.04039",
"label": "Sarnak conjecture survey"
},
{
"url": "https://doi.org/10.4171/owr/2012/50",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/50 | null | null | null | null | Can Sarnak's conjecture be proved for every deterministic sequence, namely that its correlation with the Mo\ddot{\mathrm{obius}} function is o(N); the conjecture is known in several special cases and is implied by Chowla's conjecture? | unrecoverable | Comparison with the official report and OWR-12173-005 confirms that this is a second extraction of the same conjecture plus evidence about special cases. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/50, pp. 2985--3059 |
30,002,211 | OWR-12174-001 | Detecting Genuine Modes in Density Deconvolution | In one-dimensional nonparametric density deconvolution, if regularization can introduce an apparent additional mode, can one statistically determine whether the mode is real and significant enough to reject the smooth reconstruction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/51, pp. 3061--3127](https://doi.org/10.4171/owr/2012/51)
## Literature... | 3 | partially_solved | null | 2,012 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12174-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Multiscale confidence procedures can test whether modes and qualitative features in one-dimensional deconvolution are genuine or artifacts, but a general interpretability and significance theory for arbitrary regularized inverse reconstructions is not available. | [
{
"url": "https://arxiv.org/abs/1107.1404",
"label": "multiscale shape inference in deconvolution"
},
{
"url": "https://doi.org/10.4171/owr/2012/51",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/51 | null | null | null | In one-dimensional nonparametric density deconvolution, if regularization can introduce an apparent additional mode, can one statistically determine whether the mode is real and significant enough to reject the smooth reconstruction? | In one-dimensional nonparametric density deconvolution, if regularization can introduce an apparent additional mode, can one statistically determine whether the mode is real and significant enough to reject the smooth reconstruction? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/51, pp. 3061--3127 |
30,002,212 | OWR-12174-003 | Noise Conditions for Quasioptimal Total-Variation Regularization | For total-variation regularization with generalized quasioptimality and Hanke–Raus parameter-choice rules, what noise-restriction set $N$ ensures convergence of the combined method? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/51, pp. 3061--3127](https://doi.org/10.4171/owr/2012/51)
## Literature... | 3 | partially_solved | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12174-003",
"literature-status:partially-solved",
"owr-year:2012"
] | Convergence results exist for quasioptimality and Hanke--Raus rules under deterministic-noise, source, or Banach-space hypotheses, but no general noise-restriction set ensuring convergence for total-variation regularization has been established. | [
{
"url": "https://doi.org/10.4171/owr/2012/51",
"label": "original OWR problem"
},
{
"url": "https://etna.ricam.oeaw.ac.at/volumes/2011-2020/vol38/abstract.php?pages=233-257",
"label": "noise-level-free convergence analysis"
},
{
"url": "https://arxiv.org/abs/1606.00115",
"label": "H... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/51 | null | null | null | For total-variation regularization with generalized quasioptimality and Hanke–Raus parameter-choice rules, what noise-restriction set $N$ ensures convergence of the combined method? | For total-variation regularization with generalized quasioptimality and Hanke--Raus parameter-choice rules, what noise-restriction set N ensures convergence of the combined method? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/51, pp. 3061--3127 |
30,002,213 | OWR-12175-001 | Toms–Winter Regularity Conjecture | For every unital, simple, separable, nuclear $C^*$-algebra $A$, are the following conditions equivalent: $A$ has finite nuclear dimension; $A\otimes\mathcal Z\cong A$; and $A$ has strict comparison? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12175-002"
] | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **partially solved**; the dataset currently labels both open. Toms–Winter conjecture, introduction of OWR 52/2012, p. 3130: for (infinite-dimensional) unital simple separable nuclear C∗-algebras, are (i) finite nuclear dimension, (ii) 𝒵-stability, (iii) strict comparison e... | [
"owr",
"oberwolfach-reports",
"OWR-12175-001",
"literature-status:open",
"owr-year:2012"
] | The fragment refers broadly to Elliott's classification program and supplies no precise conjecture; broad classes are classified, but there is no general classification theorem for all separable nuclear C-star algebras. | [
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1306.1049",
"label": "complexity of nuclear C-star isomorphism"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | For every unital, simple, separable, nuclear $C^*$-algebra $A$, are the following conditions equivalent: $A$ has finite nuclear dimension; $A\otimes\mathcal Z\cong A$; and $A$ has strict comparison? | Conjecture: for every unital simple separable nuclear C^{*}-algebra A, the following are equivalent: A has finite nuclear dimension; A\otimes\mathcal{Z}\cong A; and A has strict comparison. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,214 | OWR-12175-002 | Duplicate: Toms–Winter Regularity Conjecture | Is it true for every unital simple separable nuclear C^{*}-algebra A that finite nuclear dimension, \mathcal{Z}-stability, and strict comparison are equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (Comparison with the official report and OWR-12175-001 confirms that this is a restatement of the same three-way equivalence. No separate cle) | [
"OWR-12175-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12175-002",
"literature-status:partially-solved",
"owr-year:2012"
] | Finite nuclear dimension and Z-stability are now equivalent for simple separable nuclear non-elementary algebras, and Z-stability implies strict comparison; the converse from strict comparison to Z-stability remains open in full generality. | [
{
"url": "https://ems.press/content/serial-article-files/52386?nt=1",
"label": "2026 regularity survey"
},
{
"url": "https://arxiv.org/abs/1403.0747",
"label": "nuclear dimension and Z-stability"
},
{
"url": "https://arxiv.org/abs/1209.3292",
"label": "strict comparison in finite-dim... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | null | Is it true for every unital simple separable nuclear C^{*}-algebra A that finite nuclear dimension, \mathcal{Z}-stability, and strict comparison are equivalent? | unrecoverable | Comparison with the official report and OWR-12175-001 confirms that this is a restatement of the same three-way equivalence. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
30,002,215 | OWR-12175-003 | $\mathcal Z$-Stability and Regularity of Nuclear $C^*$-Algebras | Does $\mathcal Z$-stability imply finite nuclear dimension for all unital simple separable nuclear $C^*$-algebras? More broadly, does the equivalence between $\mathcal Z$-stability and strict comparison hold without the additional hypotheses currently known? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209](https://doi.org/10.4171/owr/2012/52)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **partially solved**; the dataset currently labels both open. Toms–Winter conjecture, introduction of OWR 52/2012, p. 3130: for (infinite-dimensional) unital simple separable nuclear C∗-algebras, are (i) finite nuclear dimension, (ii) 𝒵-stability, (iii) strict comparison e... | [
"owr",
"oberwolfach-reports",
"OWR-12175-003",
"literature-status:open",
"owr-year:2012"
] | This is a continuation of the preceding regularity conjecture and records only partial implications and promising classification results, not a separately stated theorem; the unresolved general implication keeps the extracted record open. | [
{
"url": "https://ems.press/content/serial-article-files/52386?nt=1",
"label": "current Toms--Winter status"
},
{
"url": "https://doi.org/10.4171/owr/2012/52",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/52 | null | null | null | Does $\mathcal Z$-stability imply finite nuclear dimension for all unital simple separable nuclear $C^*$-algebras? More broadly, does the equivalence between $\mathcal Z$-stability and strict comparison hold without the additional hypotheses currently known? | Does \mathcal{Z}-stability imply finite nuclear dimension for all unital simple separable nuclear C^{*}-algebras, and more broadly does the equivalence between \mathcal{Z}-stability and strict comparison hold without the additional hypotheses currently known? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | C*-Algebras, Dynamics, and Classification (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/52, pp. 3129--3209 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.