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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,816 | OWR-13498-004 | Linear Sum-of-Squares Representations on Grassmann Orbitopes | For every Grassmann orbitope $G_{k,n}$, is every calibration representable as a sum of squares of linear polynomials relative to the vanishing ideal $I_{k,n}$? Equivalently, if $\delta-\ell$ is the supporting nonnegative function on $G_{k,n}$, does there exist a representation $\delta-\ell(p)=\sum_i h_i(p)^2$ with all ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,015 | 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-13498-004",
"literature-status:open",
"owr-year:2015"
] | The all-Grassmann-orbitope conjecture, equivalent in the report to Harvey--Lawson Question 6.5, has no complete proof or disproof in the checked primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
},
{
"url": "https://arxiv.org/abs/0911.5436",
"label": "Sanyal--Sottile--Sturmfels"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | For every Grassmann orbitope $G_{k,n}$, is every calibration representable as a sum of squares of linear polynomials relative to the vanishing ideal $I_{k,n}$? Equivalently, if $\delta-\ell$ is the supporting nonnegative function on $G_{k,n}$, does there exist a representation $\delta-\ell(p)=\sum_i h_i(p)^2$ with all ... | For every Grassmann orbitope G_{k,n}, is every calibration representable as a sum of squares of linear polynomials relative to the vanishing ideal I_{k,n}? Equivalently, if \delta-\ell is the supporting nonnegative function on G_{k,n}, does there exist a representation \delta-\ell(p)=\sum_i h_i(p)^2 with all h_i linear... | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,817 | OWR-13498-006 | Commuting Billiard Maps and Confocal Ellipses | For two nested smooth convex plane domains with billiard maps $T_1,T_2$ acting on oriented lines meeting both domains, does $T_1\circ T_2=T_2\circ T_1$ imply that the two domains are bounded by confocal ellipses? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,015 | 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-13498-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The confocal-ellipse conclusion is proved for piecewise-analytic nested billiard domains, but the unrestricted smooth or general formulation in the extracted question remains unresolved. | [
{
"url": "https://arxiv.org/abs/1405.5990",
"label": "Glutsyuk, billiard ball maps"
},
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
},
{
"url": "https://arxiv.org/abs/2607.23853",
"label": "Recent billiard-map results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | For two nested smooth convex plane domains with billiard maps $T_1,T_2$ acting on oriented lines meeting both domains, does $T_1\circ T_2=T_2\circ T_1$ imply that the two domains are bounded by confocal ellipses? | For two nested smooth convex plane domains with billiard maps T_1,T_2 acting on oriented lines meeting both domains, does T_1\circ T_2=T_2\circ T_1 imply that the two domains are bounded by confocal ellipses? | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,818 | OWR-13498-008 | Reconstruction and Response Sets of AC Networks | For connected alternating-current networks with $b$ boundary vertices and complex response matrix $\Lambda$, give an algorithm to reconstruct a network and positive-real edge conductances from $\Lambda$; describe the response sets of series-parallel networks and of planar networks with all boundary vertices on the oute... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,015 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13498-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Rote solves reconstruction and realizability, but the series-parallel, planar, and variable conductance-classification questions in the extracted record are not all resolved. | [
{
"url": "https://arxiv.org/abs/1904.02031",
"label": "Rote, response maps of AC networks"
},
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | For connected alternating-current networks with $b$ boundary vertices and complex response matrix $\Lambda$, give an algorithm to reconstruct a network and positive-real edge conductances from $\Lambda$; describe the response sets of series-parallel networks and of planar networks with all boundary vertices on the oute... | For connected alternating-current networks with b boundary vertices and complex response matrix \Lambda, give an algorithm to reconstruct a network and positive-real edge conductances from \Lambda; describe the response sets of series-parallel networks and of planar networks with all boundary vertices on the outer face... | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,819 | OWR-13498-009 | Dihedral Rigidity and Offsets of Nonconvex Polytopes | For a polytope with fixed combinatorics, are all face angles determined by its dihedral angles in the nonconvex case? If $P$ is a nonconvex three-dimensional polytope with spherical boundary, does an offset polytope $P_\varepsilon$ exist for every sufficiently small $\varepsilon>0$, with each face translated outward by... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,015 | 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-13498-009",
"literature-status:partially-solved",
"owr-year:2015"
] | The offset-polytope existence question has a general treatment, and infinitesimal Stoker-type rigidity is known, but the full face-angle-from-dihedral-angle question for arbitrary non-convex polytopes remains open. | [
{
"url": "https://doi.org/10.1007/s00454-016-9811-5",
"label": "Straight skeletons and mitered offsets"
},
{
"url": "https://arxiv.org/abs/2209.13439",
"label": "Volume conjecture and Stoker rigidity"
},
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | For a polytope with fixed combinatorics, are all face angles determined by its dihedral angles in the nonconvex case? If $P$ is a nonconvex three-dimensional polytope with spherical boundary, does an offset polytope $P_\varepsilon$ exist for every sufficiently small $\varepsilon>0$, with each face translated outward by... | For a polytope with fixed combinatorics, are all face angles determined by its dihedral angles in the non-convex case? Also, if }P is a non-convex three-dimensional polytope with spherical boundary, does an offset polytope }P_\varepsilon always exist for sufficiently small }\varepsilon>0, with every face translated out... | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,820 | OWR-13498-010 | Discrete-Conformal Metric Subdivision Schemes | Let $T$ be a triangulated surface and let discrete conformally equivalent metrics $\lambda,\mu$ satisfy $\mu_{ij}=e^{(u_i+u_j)/2}\lambda_{ij}$. Does there exist a metric subdivision scheme producing subdivided metrics $\lambda',\mu'$ that remain discretely conformally equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,015 | 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-13498-010",
"literature-status:open",
"owr-year:2015"
] | No general metric subdivision scheme preserving the stated discrete conformal equivalence was found proved or disproved in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
},
{
"url": "https://arxiv.org/abs/1005.2698",
"label": "Discrete conformal maps and ideal hyperbolic polyhedra"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | Let $T$ be a triangulated surface and let discrete conformally equivalent metrics $\lambda,\mu$ satisfy $\mu_{ij}=e^{(u_i+u_j)/2}\lambda_{ij}$. Does there exist a metric subdivision scheme producing subdivided metrics $\lambda',\mu'$ that remain discretely conformally equivalent? | Let T be a triangulated surface and let discrete conformally equivalent metrics \lambda,\mu satisfy \mu_{ij}=e^{(u_i+u_j)/2}\lambda_{ij}. Does there exist a metric subdivision scheme producing subdivided metrics \lambda',\mu' that remain discretely conformally equivalent? | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,821 | OWR-13498-011 | Optimality of Greedy Circle Packings | Place infinitely many nonoverlapping disks tangent to the $x$-axis in the curvilinear triangular region bounded by the $x$-axis and two unit disks centered at $(\pm1,1)$, maximizing their total area. Does the greedy procedure that successively inserts a disk tangent to two previously placed disks attain the maximum are... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,015 | 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://zenodo.org/records/23049225",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] OWR-13498-011: a proof of Propp and Kenyon's Ford-circle maximum-area question is now public. (https://zenodo.org/records/23049225) | [
"owr",
"oberwolfach-reports",
"OWR-13498-011",
"literature-status:open",
"owr-year:2015"
] | The greedy two-neighbor circle-insertion rule is still not established as globally area-maximizing, and no authoritative counterexample was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | Place infinitely many nonoverlapping disks tangent to the $x$-axis in the curvilinear triangular region bounded by the $x$-axis and two unit disks centered at $(\pm1,1)$, maximizing their total area. Does the greedy procedure that successively inserts a disk tangent to two previously placed disks attain the maximum are... | Place infinitely many non-overlapping disks tangent to the x-axis in the curvilinear triangular region bounded by the x-axis and two unit disks centered at (\pm1,1), maximizing their total area. Does the greedy procedure that successively inserts a disk tangent to two previously placed disks attain the maximum area? | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,822 | OWR-13498-012 | Self-Stress Identities for Sparse Graphs | For a planar wheel graph $G$ with $n$ vertices and $2n-2$ edges, suppose a self-stress $\omega$ and edge function $f_{ij}$ satisfy $\sum_{ij\in E(G)}\omega_{ij}f_{ij}=1$. Are there other graphs with $n$ vertices and $2n-2$ edges admitting such a self-stress? What general homological or cohomological phenomenon explains... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729](https://doi.org/10.4171/owr/2015/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,015 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13498-012",
"literature-status:open",
"owr-year:2015"
] | The wheel self-stress identity is known, but the requested classification of other graphs and its homological or cohomological meaning remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/13",
"label": "OWR Report 13/2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/13 | null | null | null | For a planar wheel graph $G$ with $n$ vertices and $2n-2$ edges, suppose a self-stress $\omega$ and edge function $f_{ij}$ satisfy $\sum_{ij\in E(G)}\omega_{ij}f_{ij}=1$. Are there other graphs with $n$ vertices and $2n-2$ edges admitting such a self-stress? What general homological or cohomological phenomenon explains... | For the planar wheel graph with n vertices and 2n-2 edges, the stated self-stress \omega and edge function f_{ij} satisfy \sum_{ij\in E(G)}\omega_{ij}f_{ij}=1. Are there other graphs with n vertices and 2n-2 edges admitting such a self-stress, and what general phenomenon or homological/cohomological meaning explains th... | 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 | Discrete Differential Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/13, pp. 661--729 |
30,002,823 | OWR-13499-001 | Duplicate Chromatic-Splitting Extraction | Chromatic splitting conjecture: for the p-local sphere spectrum, with chromatic layers L_nS and common fiber F_n\simeq F(L_{n-1}S,L_nS), the map L_{n-1}S\to L_{n-1}L_{K(n)}S should include a wedge summand, so that L_{n-1}L_{K(n)}S\simeq L_{n-1}S\vee\Sigma F_n, together with the predicted wedge decomposition of \Sigma F... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781](https://doi.org/10.4171/owr/2015/14)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,015 | 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/merged OWR extraction (The passage duplicates the chromatic splitting conjecture recorded in OWR-13499-002 and does not state a distinct problem. No separate clean) | [
"OWR-13499-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13499-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Chromatic splitting is established in several low-height cases and rationally at all heights, while the integral bad-prime picture remains unresolved; the naive height-two prime-two wedge description is known to fail. | [
{
"url": "https://doi.org/10.4171/owr/2015/14",
"label": "OWR Report 14/2015"
},
{
"url": "https://doi.org/10.1007/s00222-019-00943-9",
"label": "Chromatic splitting at height two"
},
{
"url": "https://arxiv.org/abs/2402.00960",
"label": "Rational chromatic splitting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/14 | null | null | null | null | Chromatic splitting conjecture: for the p-local sphere spectrum, with chromatic layers L_nS and common fiber F_n\simeq F(L_{n-1}S,L_nS), the map L_{n-1}S\to L_{n-1}L_{K(n)}S should include a wedge summand, so that L_{n-1}L_{K(n)}S\simeq L_{n-1}S\vee\Sigma F_n, together with the predicted wedge decomposition of \Sigma F... | unrecoverable | The passage duplicates the chromatic splitting conjecture recorded in OWR-13499-002 and does not state a distinct problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781 |
30,002,824 | OWR-13499-002 | Chromatic Splitting of the Local Sphere | For the $p$-local sphere spectrum, let $L_nS$ denote its chromatic localizations and let $F_n$ be the common fiber in the chromatic fracture square. Does $L_{n-1}L_{K(n)}S\simeq L_{n-1}S\vee\Sigma F_n$, with $\Sigma F_n$ admitting the predicted wedge decomposition into lower chromatic layers? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781](https://doi.org/10.4171/owr/2015/14)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,015 | 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... | [
"OWR-13499-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13499-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The conjecture holds in the reported low-height cases and has a rational all-height proof, but its full integral form at bad primes and higher heights is not known. | [
{
"url": "https://doi.org/10.4171/owr/2015/14",
"label": "OWR Report 14/2015"
},
{
"url": "https://doi.org/10.1007/s00222-019-00943-9",
"label": "Chromatic splitting at height two"
},
{
"url": "https://arxiv.org/abs/2402.00960",
"label": "Rational chromatic splitting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/14 | null | null | null | For the $p$-local sphere spectrum, let $L_nS$ denote its chromatic localizations and let $F_n$ be the common fiber in the chromatic fracture square. Does $L_{n-1}L_{K(n)}S\simeq L_{n-1}S\vee\Sigma F_n$, with $\Sigma F_n$ admitting the predicted wedge decomposition into lower chromatic layers? | Hopkins' chromatic splitting conjecture asks for a systematic description of how the localized chromatic layers L_nS of the p-local sphere glue together, including the wedge-summand decomposition L_{n-1}L_{K(n)}S\simeq L_{n-1}S\vee\Sigma F_n and the predicted homotopy type of \Sigma F_n. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781 |
30,002,825 | OWR-13499-003 | Chromatic Fiber Structure at Bad Primes | At primes p that are bad relative to chromatic level n, give a plausible systematic description of the homotopy type of $\Sigma F_n$, where $F_n$ is the common fiber in the chromatic splitting square for the p-local sphere. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781](https://doi.org/10.4171/owr/2015/14)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,015 | 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-13499-003",
"literature-status:open",
"owr-year:2015"
] | A plausible integral description of the suspension of the chromatic fiber at bad primes is still unavailable; rational results do not settle this problem. | [
{
"url": "https://doi.org/10.4171/owr/2015/14",
"label": "OWR Report 14/2015"
},
{
"url": "https://arxiv.org/abs/2402.00960",
"label": "Rational chromatic splitting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/14 | null | null | null | At primes p that are bad relative to chromatic level n, give a plausible systematic description of the homotopy type of $\Sigma F_n$, where $F_n$ is the common fiber in the chromatic splitting square for the p-local sphere. | At primes p that are bad relative to chromatic level n, give a plausible systematic description of the homotopy type of \Sigma F_n, where F_n is the common fiber in the chromatic splitting square for the p-local sphere. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Homotopy Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/14, pp. 731--781 |
30,002,826 | OWR-13500-003 | Bogomolov–Gieseker Inequality for Tilt-Semistable Threefold Complexes | BG inequality conjecture: let $X$ be a smooth projective threefold over $\mathbb C$, let $B,\omega\in\operatorname{NS}(X)_\mathbb Q$ with $\omega$ ample, and let $E$ be tilt-semistable with $\nu_{\omega,B}(E)=0$. Then $\operatorname{ch}^{B}_{3}(E)\leq\frac{1}{18}\operatorname{ch}^{B}_{1}(E)\cdot\omega^{2}$. The conject... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | solved | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1093/imrn/rnw122",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no, false in general)**. Y. Toda (joint with D. Piyaratne; OWR 15/2015, pp. 792–794, Conjecture 1) states the Bayer–Macrì–Toda inequality ch₃^B ≤ ch₁^B·ω²/18 for tilt-semistable E with ν = 0, on every smooth projective threefold. B. Schmidt, [IMRN 2017](https://do... | [
"owr",
"oberwolfach-reports",
"OWR-13500-003",
"literature-status:partially-solved",
"owr-year:2015"
] | The strong BMT inequality with coefficient one eighteenth is proved for important threefold classes, while recent work proves only a weaker coefficient one half in general; the extracted strong conjecture remains open. | [
{
"url": "https://arxiv.org/abs/1103.5010",
"label": "Bayer--Macri--Toda, BMT conjecture"
},
{
"url": "https://arxiv.org/abs/2607.04788",
"label": "Recent weak BMT theorem"
},
{
"url": "https://arxiv.org/abs/1410.1585",
"label": "Bayer--Macri--Stellari, abelian threefolds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | BG inequality conjecture: let $X$ be a smooth projective threefold over $\mathbb C$, let $B,\omega\in\operatorname{NS}(X)_\mathbb Q$ with $\omega$ ample, and let $E$ be tilt-semistable with $\nu_{\omega,B}(E)=0$. Then $\operatorname{ch}^{B}_{3}(E)\leq\frac{1}{18}\operatorname{ch}^{B}_{1}(E)\cdot\omega^{2}$. The conject... | BG inequality conjecture: let X be a smooth projective threefold over \mathbb C, B,\omega\in\operatorname{NS}(X)_{\mathbb Q} with \omega ample, and let E be tilt-semistable with \nu_{\omega,B}(E)=0. Then \operatorname{ch}^{B}_{3}(E)\leq\frac{1}{18}\operatorname{ch}^{B}_{1}(E)\cdot\omega^{2}. The conjecture is known for... | 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 | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,827 | OWR-13500-007 | Exceptional Collections and Twisted Cubics on Fano Varieties | Let $X$ be a Küchle fourfold of type $(c5)$, realized as a half-anticanonical section of the associated fivefold $Y$. Does $Y$ have a full exceptional collection of length $12$ with a rectangular Lefschetz structure? Is the Hilbert scheme of rational twisted cubic curves on $X$ birational to a hyperkähler fourfold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,015 | 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-13500-007",
"literature-status:partially-solved",
"owr-year:2015"
] | Later work supplies birational and motivic information for the relevant Fano fourfold, but the asserted rectangular length-twelve exceptional collection and twisted-cubic Hilbert-scheme birationality remain conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2015/15",
"label": "OWR Report 15/2015"
},
{
"url": "https://arxiv.org/abs/1603.03161",
"label": "Kuznetsov, Kuechle fivefolds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | Let $X$ be a Küchle fourfold of type $(c5)$, realized as a half-anticanonical section of the associated fivefold $Y$. Does $Y$ have a full exceptional collection of length $12$ with a rectangular Lefschetz structure? Is the Hilbert scheme of rational twisted cubic curves on $X$ birational to a hyperkähler fourfold? | For the fivefold Y and associated fourfold X in the report, conjecturally Y has a full exceptional collection of length 12 with a rectangular Lefschetz structure, and the Hilbert scheme of rational twisted cubic curves in X is birational to a hyperk\ddot{a}hler fourfold. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,828 | OWR-13500-009 | Mirror Conifold Transitions and Analytic Smoothings | For a maximally degenerating projective conifold $Y$ with mirror $\check Y$ and conifold-point sets $S$ and $\check S$, are the following conditions equivalent: $Y$ has an analytic smoothing; some $\alpha\in H^1(Y\setminus S,\Omega^2)$ maps nontrivially to every summand of $H^2_S(Y,\Omega^2)\cong\mathbb C^S$; an analog... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,015 | 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-13500-009",
"literature-status:partially-solved",
"owr-year:2015"
] | The formal Gross--Siebert setting proves the stated equivalences and mirror conifold transition, but lifting the families to analytic families was explicitly still ongoing in the source. | [
{
"url": "https://doi.org/10.4171/owr/2015/15",
"label": "OWR Report 15/2015"
},
{
"url": "https://arxiv.org/abs/math/0309070",
"label": "Gross--Siebert, affine geometry and mirror symmetry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | For a maximally degenerating projective conifold $Y$ with mirror $\check Y$ and conifold-point sets $S$ and $\check S$, are the following conditions equivalent: $Y$ has an analytic smoothing; some $\alpha\in H^1(Y\setminus S,\Omega^2)$ maps nontrivially to every summand of $H^2_S(Y,\Omega^2)\cong\mathbb C^S$; an analog... | For a maximally degenerating projective conifold Y with mirror \check Y and conifold-point sets S,\check S, the following are equivalent: Y has an analytic smoothing; there exists \alpha\in H^1(Y\setminus S,\Omega^2) mapping nontrivially to every summand of H^2_S(Y,\Omega^2)\cong\mathbb C^S; the mirror has an analogous... | 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 | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,829 | OWR-13500-010 | Rationality of Ueno-Type Varieties | Let $E_4$ and $E_6$ be the anharmonic and equianharmonic elliptic curves with their standard automorphisms $g_4$ and $g_6$, and let $X_{n,m}$ be the minimal resolution of $E_m^n/\langle g_m\rangle$ for the diagonal action. Is $X_{4,6}$ rational? Is $X_{5,6}$ unirational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,015 | 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-13500-010",
"literature-status:partially-solved",
"owr-year:2015"
] | The varieties in the extracted Ueno-type rationality questions have substantial unirationality and invariant-theoretic results, but rationality of X four comma six and unirationality of X five comma six remain unanswered. | [
{
"url": "https://arxiv.org/abs/1506.01925",
"label": "Catanese--Oguiso--Verra"
},
{
"url": "https://doi.org/10.1080/10586458.2019.1691088",
"label": "Mellit, Ueno-type manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2015/15",
"label": "OWR Report 15/2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | Let $E_4$ and $E_6$ be the anharmonic and equianharmonic elliptic curves with their standard automorphisms $g_4$ and $g_6$, and let $X_{n,m}$ be the minimal resolution of $E_m^n/\langle g_m\rangle$ for the diagonal action. Is $X_{4,6}$ rational? Is $X_{5,6}$ unirational? | Determine whether X_{4,6} is rational and whether X_{5,6} is unirational. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,830 | OWR-13500-011 | Birational Modifications Proving Rationality of a Ueno Variety | The Ueno-type variety $X_{4,6}$ is birational to a diagonal cubic surface over $k(t_1,t_2)$. Can that cubic surface be modified birationally, analogously to the conic-bundle treatment of $X_{3,4}$, to prove that $X_{4,6}$ is rational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,015 | 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-13500-011",
"literature-status:open",
"owr-year:2015"
] | Catanese--Oguiso--Verra prove unirationality of X_{4,6}, while Mellit's later rationality argument is explicitly conditional on heuristic curve-counting conjectures; rationality therefore remains unresolved. | [
{
"url": "https://arxiv.org/abs/1506.01925",
"label": "Catanese--Oguiso--Verra, unirationality"
},
{
"url": "https://doi.org/10.1080/10586458.2019.1691088",
"label": "Mellit, rationality by curve counting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | The Ueno-type variety $X_{4,6}$ is birational to a diagonal cubic surface over $k(t_1,t_2)$. Can that cubic surface be modified birationally, analogously to the conic-bundle treatment of $X_{3,4}$, to prove that $X_{4,6}$ is rational? | Can the cubic surface in the birational description of X_{4,6} be modified birationally, as in the conic-bundle case, to prove that X_{4,6} is rational? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,831 | OWR-13500-013 | Mirror Classification of Orbifold Del Pezzo Surfaces | Are mutation-equivalence classes of Fano polygons in bijection with $\mathbb Q$-Gorenstein-deformation-equivalence classes of locally $\mathbb Q$-Gorenstein-rigid class-TG del Pezzo surfaces with cyclic quotient singularities, with a polygon $P$ corresponding to a generic $\mathbb Q$-Gorenstein deformation of its toric... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,015 | 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-13500-013",
"literature-status:partially-solved",
"owr-year:2015"
] | The four mirror-symmetry conjectures are proved in smooth and several simplest singular cases, but the general mutation, period, and qG-deformation classification assertions remain conjectural. | [
{
"url": "https://kasprzyk.work/research/pdf/mirror_symmetry_del_pezzo.pdf",
"label": "Akhtar--Coates--Galkin--Kasprzyk, original conjectures"
},
{
"url": "https://www.jstage.jst.go.jp/article/jmath/72/2/72_465/_pdf",
"label": "Cavey--Prince, verified cases"
},
{
"url": "https://pmc.ncbi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | Are mutation-equivalence classes of Fano polygons in bijection with $\mathbb Q$-Gorenstein-deformation-equivalence classes of locally $\mathbb Q$-Gorenstein-rigid class-TG del Pezzo surfaces with cyclic quotient singularities, with a polygon $P$ corresponding to a generic $\mathbb Q$-Gorenstein deformation of its toric... | Conjectures for orbifold del Pezzo surfaces: mutation-equivalence classes of Fano polygons are in one-to-one correspondence with qG-deformation-equivalence classes of locally qG-rigid class-TG del Pezzo surfaces with cyclic quotient singularities; for a Fano polygon P and a generic qG-deformation X of its toric surface... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,832 | OWR-13500-014 | Period Conjectures for Fano Polygons and Del Pezzo Surfaces | Let $P$ be a Fano polygon and $X$ a generic $\mathbb Q$-Gorenstein deformation of its toric surface. Is there an affine-linear mirror map $\phi:L_P^T\to H_X^{\mathrm{ts}}$ satisfying $\widehat G_X\circ\phi=\pi_P$? For Fano polygons with the same singularity content, does equality of classical periods under such an iden... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836](https://doi.org/10.4171/owr/2015/15)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,015 | 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-13500-014",
"literature-status:partially-solved",
"owr-year:2015"
] | The excerpt states the period and deformation conjectures B--D; special baskets and smooth cases are established, but no general theorem proves the remaining assertions. | [
{
"url": "https://kasprzyk.work/research/pdf/mirror_symmetry_del_pezzo.pdf",
"label": "Akhtar--Coates--Galkin--Kasprzyk, conjectures B--D"
},
{
"url": "https://www.jstage.jst.go.jp/article/jmath/72/2/72_465/_pdf",
"label": "Cavey--Prince, verified cases"
},
{
"url": "https://pmc.ncbi.nlm... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/15 | null | null | null | Let $P$ be a Fano polygon and $X$ a generic $\mathbb Q$-Gorenstein deformation of its toric surface. Is there an affine-linear mirror map $\phi:L_P^T\to H_X^{\mathrm{ts}}$ satisfying $\widehat G_X\circ\phi=\pi_P$? For Fano polygons with the same singularity content, does equality of classical periods under such an iden... | Let P be a Fano polygon and X a generic qG-deformation of its toric surface. Conjecturally there is an affine-linear mirror map \phi:L^T_P\to H_X^{ts} with \widehat G_X\circ\phi=\pi_P; if Fano polygons P_1,P_2 have the same singularity content and their classical periods agree after an affine-linear identification of L... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2015/15, pp. 783--836 |
30,002,833 | OWR-13673-001 | Conformal Field Theory Realizations of Subfactors | Does every subfactor arise in conformal field theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-001",
"literature-status:open",
"owr-year:2015"
] | Finite-depth subfactors and several broad families have CFT or quantum-double realizations, but the universal claim that every finite-depth subfactor arises from CFT still has no general construction. | [
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Oberwolfach report on subfactors and CFT"
},
{
"url": "https://arxiv.org/abs/1506.02606",
"label": "Bischoff--Davydov--Kawahigashi--Longo, index below four"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Does every subfactor arise in conformal field theory? | Does every subfactor arise in conformal field theory? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,834 | OWR-13673-002 | Four-Dimensional Standard-Subspace Nets with Minimal Length | Does there exist a natural local net of standard subspaces on double cones in Minkowski spacetime $\mathbb R^4$ with positive minimal length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-002",
"literature-status:open",
"owr-year:2015"
] | Minimal localization length is constructed for standard-subspace nets in one and two dimensions, but the requested natural four-dimensional double-cone net with positive minimal length is not established. | [
{
"url": "https://arxiv.org/abs/1403.1226",
"label": "Lechner--Longo, localization in standard spaces"
},
{
"url": "https://doi.org/10.1007/s00220-014-2199-2",
"label": "published localization results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Does there exist a natural local net of standard subspaces on double cones in Minkowski spacetime $\mathbb R^4$ with positive minimal length? | Does there exist a natural local net of standard subspaces on double cones in Minkowski spacetime \mathbb R^4 with positive minimal length? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,835 | OWR-13673-003 | Bisognano–Wichmann Covariance for Standard-Subspace Nets | Given a local net of standard subspaces $H(O)$ on double cones $O\subset\mathbb R^4$, covariant under a positive-energy unitary Poincaré representation $U$, does another positive-energy representation $U'$ on the same Hilbert space make $H$ covariant and satisfy the Bisognano–Wichmann property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-003",
"literature-status:open",
"owr-year:2015"
] | There are sufficient representation-theoretic conditions guaranteeing Bisognano--Wichmann and duality, and counterexamples without them; the general reconstruction of a suitable U' from the stated net remains unresolved. | [
{
"url": "https://arxiv.org/abs/1703.06831",
"label": "Morinelli, sufficient conditions"
},
{
"url": "https://doi.org/10.1007/s00220-021-04046-6",
"label": "Covariant homogeneous standard-subspace nets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Given a local net of standard subspaces $H(O)$ on double cones $O\subset\mathbb R^4$, covariant under a positive-energy unitary Poincaré representation $U$, does another positive-energy representation $U'$ on the same Hilbert space make $H$ covariant and satisfy the Bisognano–Wichmann property? | Given a local net of standard subspaces H(O) on double cones O\subset\mathbb R^4, covariant under a positive-energy unitary Poincare representation U, does there exist another positive-energy representation U' on the same Hilbert space making H covariant and satisfying the Bisognano--Wichmann property? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,836 | OWR-13673-004 | Strong Locality and Reconstruction of Vertex Operator Algebras | Is every unitary vertex operator algebra strongly local? Does every irreducible conformal net arise from a unitary vertex operator algebra through the conformal-net construction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 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-13673-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Every conformal net now has an associated unitary VOA, resolving that direction, while the converse assertion that every unitary VOA is strongly local remains explicitly conjectural. | [
{
"url": "https://arxiv.org/abs/2507.20735",
"label": "Henriques--Tener, conformal net to VOA"
},
{
"url": "https://arxiv.org/abs/1503.01260",
"label": "Carpi--Kawahigashi--Longo--Weiner, VOA/net correspondence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Is every unitary vertex operator algebra strongly local? Does every irreducible conformal net arise from a unitary vertex operator algebra through the conformal-net construction? | Every unitary vertex operator algebra is conjectured to be strongly local, and every irreducible conformal net is conjectured to arise from a unitary vertex operator algebra via the stated VOA-to-net construction. | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,837 | OWR-13673-005 | Conformal Field Theories Representing TMF Classes | Under the Stolz–Teichner identification of the moduli space of $\operatorname{Fer}(n)$-twisted extended two-dimensional field theories with $\mathrm{TMF}^{-n}$, how much of the field-theory side can conformal field theories detect, and can they produce interesting classes in $\pi_n(\mathrm{TMF})$? Here $\operatorname{F... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-005",
"literature-status:open",
"owr-year:2015"
] | Conformal-net and Stolz--Teichner constructions give candidates and low-degree evidence, but no general theorem realizes the requested nontrivial classes in pi_n(TMF) by conformal field theories. | [
{
"url": "https://arxiv.org/abs/1103.4187",
"label": "Douglas--Henriques, conformal nets and TMF"
},
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Henriques--Douglas, Stolz--Teichner cocycles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Under the Stolz–Teichner identification of the moduli space of $\operatorname{Fer}(n)$-twisted extended two-dimensional field theories with $\mathrm{TMF}^{-n}$, how much of the field-theory side can conformal field theories detect, and can they produce interesting classes in $\pi_n(\mathrm{TMF})$? Here $\operatorname{F... | Under the Stolz--Teichner identification of the moduli space of \operatorname{Fer}(n)-twisted extended two-dimensional field theories with TMF^{-n}, how much of the field-theory side can be detected using conformal field theories alone, and can this produce interesting classes in \pi_n(TMF)? Here \operatorname{Fer}(n) ... | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,838 | OWR-13673-006 | Lie-Algebraic Parametrization of TMF Classes | Are elements of $\pi_n(\mathrm{TMF})$ naturally parametrized by $n$-dimensional semisimple compact-type Lie algebras through the Stolz–Teichner cocycle construction? Does the Stolz–Teichner cocycle construction hit exactly the classes represented by compact Lie groups with left-invariant framings? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-006",
"literature-status:open",
"owr-year:2015"
] | Compact Lie algebras yield a proposed family of Stolz--Teichner cocycles, but the claim that this construction hits exactly the TMF classes represented by framed compact Lie groups remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Henriques--Douglas, proposed construction"
},
{
"url": "https://arxiv.org/abs/1103.4187",
"label": "Douglas--Henriques, TMF via conformal nets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Are elements of $\pi_n(\mathrm{TMF})$ naturally parametrized by $n$-dimensional semisimple compact-type Lie algebras through the Stolz–Teichner cocycle construction? Does the Stolz–Teichner cocycle construction hit exactly the classes represented by compact Lie groups with left-invariant framings? | Are there elements of \pi_n(TMF) naturally parametrized by n-dimensional semisimple compact-type Lie algebras and plausibly obtained from the Stolz--Teichner cocycle construction? Conjecturally, that construction hits exactly the classes represented by compact Lie groups with their left-invariant framings. | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,839 | OWR-13673-008 | Local Conformal Field Theories from Non-Semisimple Tensor Categories | For a nonsemisimple finite tensor category $\mathcal C$, do full local conformal field theories with chiral data $\mathcal C$ exist, and how can their bulk objects and sewing-compatible, mapping-class-group-invariant correlators be constructed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 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-13673-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Explicit local non-semisimple logarithmic CFTs exist, and general correlator constructions are available for finite ribbon categories, but a uniform existence theory for arbitrary non-semisimple C remains open. | [
{
"url": "https://doi.org/10.1016/S0550-3213(98)00701-9",
"label": "Gaberdiel--Kausch, local logarithmic CFT"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.11.020",
"label": "Fuchs--Schweigert, non-semisimple correlators"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | For a nonsemisimple finite tensor category $\mathcal C$, do full local conformal field theories with chiral data $\mathcal C$ exist, and how can their bulk objects and sewing-compatible, mapping-class-group-invariant correlators be constructed? | For a non-semisimple finite tensor category C, do full local conformal field theories with chiral data C exist, and how can their bulk object and sewing-compatible mapping-class-group-invariant correlators be constructed? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,840 | OWR-13673-010 | Conformal Field Theory Realization of the Asaeda–Haagerup Subfactor | Does the Asaeda–Haagerup subfactor arise from a conformal field theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-010",
"literature-status:open",
"owr-year:2015"
] | The Asaeda--Haagerup fusion categories and their Drinfeld center are understood, but a conformal-field-theoretic realization of the Asaeda--Haagerup subfactor itself has not been established. | [
{
"url": "https://arxiv.org/abs/1501.07324",
"label": "Grossman--Izumi--Snyder, Asaeda--Haagerup categories"
},
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Snyder, Asaeda--Haagerup CFT question"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Does the Asaeda–Haagerup subfactor arise from a conformal field theory? | Does the Asaeda--Haagerup subfactor arise from a conformal field theory? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,841 | OWR-13673-011 | Weak Verlinde Formula beyond Rational Conformal Field Theory | Does the weak Verlinde formula hold beyond rational conformal field theory; specifically, do asymptotic quantum dimensions define a one-dimensional representation of the fusion ring for nonrational or logarithmic conformal field theories? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 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-13673-011",
"literature-status:partially-solved",
"owr-year:2015"
] | Huang proves the Verlinde formula under rationality and finiteness hypotheses, while logarithmic and non-rational examples have regularized or partial formulas; the stated weak formula is not known in full generality beyond rationality. | [
{
"url": "https://arxiv.org/abs/math/0406291",
"label": "Huang, Verlinde conjecture"
},
{
"url": "https://arxiv.org/abs/1411.3282",
"label": "Creutzig--Milas--Wood, regularized dimensions"
},
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Runkel, weak Verlinde question"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | Does the weak Verlinde formula hold beyond rational conformal field theory; specifically, do asymptotic quantum dimensions define a one-dimensional representation of the fusion ring for nonrational or logarithmic conformal field theories? | Does the weak Verlinde formula hold beyond rationality; namely, do asymptotic quantum dimensions define a one-dimensional representation of the fusion ring for the relevant non-rational or logarithmic conformal field theories? | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,842 | OWR-13673-012 | Finiteness of Automorphism Groups of Rational Vertex Operator Algebras | If $V$ is a rational, $C_2$-cofinite VOA of CFT type with $V_1=0$, then conjecturally $\operatorname{Aut}(V)$ is finite. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926](https://doi.org/10.4171/owr/2015/16)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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-13673-012",
"literature-status:open",
"owr-year:2015"
] | Finiteness of Aut(V) is proved for important subclasses such as framed VOAs, but the stated rational, C2-cofinite, V_1=0 conjecture remains recorded as open in current surveys and no general proof was found. | [
{
"url": "https://arxiv.org/abs/math/0106051",
"label": "Dong--Griess, automorphism groups"
},
{
"url": "https://doi.org/10.4171/owr/2015/16",
"label": "Lam, VOA automorphism conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/16 | null | null | null | If $V$ is a rational, $C_2$-cofinite VOA of CFT type with $V_1=0$, then conjecturally $\operatorname{Aut}(V)$ is finite. | If V is a rational, C_2-cofinite VOA of CFT type with V_1=0, then conjecturally \operatorname{Aut}(V) is finite. | 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 | Subfactors and Conformal Field Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/16, pp. 849--926 |
30,002,843 | OWR-13674-011 | Marcus–Spielman–Srivastava Theorem Extraction | Let \varepsilon>0 and let independent finite-support random vectors v_1,\ldots,v_m\in\mathbb C^d satisfy \sum_{i=1}^m\mathbb E(v_i v_i^*)=I_d and \mathbb E\|v_i\|^2\leq\varepsilon. Then \Pr\left(\left\|\sum_{i=1}^m v_i v_i^*\right\|\leq(1+\sqrt{\varepsilon})^2\right)>0. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (a proven theorem, not a question)) | null | null | [Discussion #4 literature review, 2026-09-29] **solved (a proven theorem, not a question)**. The record quotes Theorem 5 of T. Jörgens's talk (OWR 17/2015, p. 943), introduced there as proven: it is MSS Theorem 1.4 (see `OWR-4807-001`), with the same hypotheses and conclusion. | [
"owr",
"oberwolfach-reports",
"OWR-13674-011",
"literature-status:open",
"owr-year:2015"
] | The record ends after the hypotheses of a theorem and omits its conclusion, so no complete proposition is available for verification; under the queue rule this unresolved extraction is open. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | null | Let \varepsilon>0 and let independent finite-support random vectors v_1,\ldots,v_m\in\mathbb C^d satisfy \sum_{i=1}^m\mathbb E(v_i v_i^*)=I_d and \mathbb E\|v_i\|^2\leq\varepsilon. Then \Pr\left(\left\|\sum_{i=1}^m v_i v_i^*\right\|\leq(1+\sqrt{\varepsilon})^2\right)>0. | unrecoverable | The passage is a proved Marcus–Spielman–Srivastava theorem, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,844 | OWR-13674-012 | Kadison–Singer Paving Theorem Extraction | For r\in\mathbb N, \delta>0, and vectors u_1,\ldots,u_m\in\mathbb C^d with \sum_{i=1}^m u_i u_i^*=I_d and \|u_i\|^2\leq\delta, there exists a partition \{S_1,\ldots,S_r\} of \{1,\ldots,m\} such that \left\|\sum_{i\in S_j}u_i u_i^*\right\|\leq\left(\frac{1}{\sqrt r}+\sqrt\delta\right)^2 for every j. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 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 | Answered in the source or not an open problem (Suggest: solved for both, or flag both as not a problem.) | null | null | [Discussion #4 literature review, 2026-09-29] - The sibling `OWR-13674-012` (the talk's Corollary 6, MSS Corollary 1.5) is also open with a complete statement, so its note ("truncated before its conclusion") is wrong too. **Suggest: solved for both, or flag both as not a problem.** | [
"owr",
"oberwolfach-reports",
"OWR-13674-012",
"literature-status:open",
"owr-year:2015"
] | The displayed corollary is truncated before its conclusion, so the exact extracted claim cannot be checked despite the surrounding Kadison--Singer context; under the queue rule it is open. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | null | For r\in\mathbb N, \delta>0, and vectors u_1,\ldots,u_m\in\mathbb C^d with \sum_{i=1}^m u_i u_i^*=I_d and \|u_i\|^2\leq\delta, there exists a partition \{S_1,\ldots,S_r\} of \{1,\ldots,m\} such that \left\|\sum_{i\in S_j}u_i u_i^*\right\|\leq\left(\frac{1}{\sqrt r}+\sqrt\delta\right)^2 for every j. | unrecoverable | The passage is a proved paving theorem, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,845 | OWR-13674-015 | Constructive Selection for Bessel Sequences | Let $\{u_j\}_{j\in J}\subset\mathbb{C}^n$ be a finite Bessel sequence with bound $1$ and $\lVert u_j\rVert^2\leq\varepsilon$. Given scalars $t_j\in[0,1]$, design a constructive algorithm that finds $J^\prime\subset J$ satisfying $\left\lVert\sum_{j\in J^\prime}u_ju_j^*-\sum_{j\in J}t_ju_ju_j^*\right\rVert=O(\varepsilon... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13674-015",
"literature-status:open",
"owr-year:2015"
] | The requested constructive algorithm for the subset in the report's theorem remains an algorithmic strengthening not supplied by the existential Kadison--Singer proof; current literature does not establish this exact request. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
},
{
"url": "https://www.aimath.org/pastworkshops/beyondks.html",
"label": "AIM Beyond Kadison--Singer workshop problems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | Let $\{u_j\}_{j\in J}\subset\mathbb{C}^n$ be a finite Bessel sequence with bound $1$ and $\lVert u_j\rVert^2\leq\varepsilon$. Given scalars $t_j\in[0,1]$, design a constructive algorithm that finds $J^\prime\subset J$ satisfying $\left\lVert\sum_{j\in J^\prime}u_ju_j^*-\sum_{j\in J}t_ju_ju_j^*\right\rVert=O(\varepsilon... | Find a constructive algorithm that produces the subset J'\subset J whose existence is guaranteed by Theorem 2. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,846 | OWR-13674-017 | Matrix Spencer Signing Conjecture | Given $n\times n$ matrices $A_1,\ldots,A_n$ with $\lVert A_i\rVert\leq 1$, does there exist a signing $s_i\in\{\pm1\}$ such that $\left\lVert\sum_{i=1}^n s_iA_i\right\rVert=O(\sqrt n)$? More generally, for $m>n$, is the bound $O\left(\sqrt{n\log(m/n)+1}\right)$ valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 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-13674-017",
"literature-status:open",
"owr-year:2015"
] | This is the square Matrix Spencer signing conjecture. It is proved for important restricted classes, including low-rank matrices, but the general O(\sqrt{n}) assertion remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1137/23M1592201",
"label": "Bansal--Jiang--Meka, Matrix Spencer up to poly-logarithmic rank"
},
{
"url": "https://arxiv.org/abs/2606.16005",
"label": "An Algebraic Matrix Sp... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | Given $n\times n$ matrices $A_1,\ldots,A_n$ with $\lVert A_i\rVert\leq 1$, does there exist a signing $s_i\in\{\pm1\}$ such that $\left\lVert\sum_{i=1}^n s_iA_i\right\rVert=O(\sqrt n)$? More generally, for $m>n$, is the bound $O\left(\sqrt{n\log(m/n)+1}\right)$ valid? | Given n\times n matrices A_1,\ldots,A_n with \|A_i\|\leq1, does there exist a signing s_i\in\{\pm1\} such that \left\|\sum_{i=1}^n s_iA_i\right\|=O(\sqrt n)? More generally, for m>n, is the bound O\left(\sqrt{n\log(m/n)+1}\right) valid? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,847 | OWR-13674-018 | Kadison–Singer Methods for Ihara Zeta Functions | For a connected $k$-regular graph $G$ with adjacency matrix $A$, the Ihara zeta function satisfies $\zeta(u,G)^{-1}=(1-u^2)^{|E|-|V|}\det(I-Au+(k-1)u^2I)$. Can Kadison–Singer and interlacing-polynomial methods yield new information about this zeta function? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13674-018",
"literature-status:open",
"owr-year:2015"
] | The extract asks broadly whether the workshop techniques yield further information about the Ihara zeta function, without specifying a proposition or a target theorem; no definite resolution is identified. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | For a connected $k$-regular graph $G$ with adjacency matrix $A$, the Ihara zeta function satisfies $\zeta(u,G)^{-1}=(1-u^2)^{|E|-|V|}\det(I-Au+(k-1)u^2I)$. Can Kadison–Singer and interlacing-polynomial methods yield new information about this zeta function? | Can techniques from the Kadison--Singer workshop give further information about the Ihara zeta function of a regular connected graph? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,848 | OWR-13674-019 | Quantitative Real-Rootedness and Two-Eigenvalue Interlacing | Can one define a quantitative distance from real-rootedness for which inequalities implied by real-rootedness persist with a distance-dependent penalty? Can interlacing-polynomial methods be extended to control two eigenvalues simultaneously? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | open | null | 2,015 | 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-13674-019",
"literature-status:open",
"owr-year:2015"
] | The extract poses an unspecific quantitative strengthening about controlling two eigenvalues and improving paving block counts; the stated research question is not resolved by the cited Kadison--Singer theorem. | [
{
"url": "https://doi.org/10.4171/owr/2015/17",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | Can one define a quantitative distance from real-rootedness for which inequalities implied by real-rootedness persist with a distance-dependent penalty? Can interlacing-polynomial methods be extended to control two eigenvalues simultaneously? | Can one define a quantitative distance from real-rootedness so that real-rooted inequalities extend with a distance-dependent penalty, and can the interlacing-polynomial method be extended to bound two eigenvalues simultaneously? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,849 | OWR-13674-020 | Two-Sided Paving Bounds | Can the reduction from partitioning to paving be improved so that a single partition controls both the top and bottom eigenvalues, reducing the known $O(\varepsilon^{-4})$ block bound toward the lower bound $\Omega(\varepsilon^{-2})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969](https://doi.org/10.4171/owr/2015/17)
## Literature review (checked 20... | 3 | solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1093/imrn/rnz111",
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} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. A. Marcus (problem session, OWR 17/2015, pp. 965–966, Problem 4(4)) notes that ε-paving is known with O(ε⁻⁴) blocks because the top and bottom eigenvalues are bounded with two separate partitions, against a lower bound Ω(ε⁻²), and asks whether one partitio... | [
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{
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/17 | null | null | null | Can the reduction from partitioning to paving be improved so that a single partition controls both the top and bottom eigenvalues, reducing the known $O(\varepsilon^{-4})$ block bound toward the lower bound $\Omega(\varepsilon^{-2})$? | Can the cheating used to obtain one-sided paving bounds be suspended so that both sides of the paving bound are obtained simultaneously? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Arbeitsgemeinschaft: The Kadison-Singer Conjecture (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/17, pp. 927--969 |
30,002,850 | OWR-13675-002 | Direct McKay Reduction for Self-Normalizing Sylow Two-Subgroups | For self-normalizing Sylow 2-subgroups, can the McKay conjecture be directly reduced to almost simple groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | For self-normalizing Sylow 2-subgroups, can the McKay conjecture be directly reduced to almost simple groups? | For self-normalizing Sylow 2-subgroups, can the McKay conjecture be directly reduced to almost simple groups? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,851 | OWR-13675-004 | Broué’s Abelian Defect Group Conjecture | If $B$ is a block of $\mathcal{O}G$ with abelian defect group $P$, then $B$ and its Brauer correspondent in $N_G(P)$ are derived equivalent. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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] | Brou\'e's abelian defect group conjecture remains open in general, although it is proved for important families such as symmetric groups and many specific Lie-type or sporadic cases. | [
{
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | If $B$ is a block of $\mathcal{O}G$ with abelian defect group $P$, then $B$ and its Brauer correspondent in $N_G(P)$ are derived equivalent. | If B is a block of \mathcal{O}G with abelian defect group P, then B and its Brauer correspondent in N_G(P) are derived equivalent. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,852 | OWR-13675-006 | Sharp Group-Order Bounds from Small Brauer Degrees | Let $G$ be a finite group with $O_p(G)=1$ such that $\beta(1)_p\leq p$ for every irreducible $p$-Brauer character $\beta$. Is $\lvert G\rvert_2\leq2^7$ when $p=2$? Is $\lvert G\rvert_p\leq p^2$ when $p\geq5$, or when $p=3$ and $A_7$ is not involved in $G$? Is $\lvert G\rvert_3\leq3^3$ when $p=3$ and $A_7$ is involved i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
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"label": "A note on p-parts of... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | Let $G$ be a finite group with $O_p(G)=1$ such that $\beta(1)_p\leq p$ for every irreducible $p$-Brauer character $\beta$. Is $\lvert G\rvert_2\leq2^7$ when $p=2$? Is $\lvert G\rvert_p\leq p^2$ when $p\geq5$, or when $p=3$ and $A_7$ is not involved in $G$? Is $\lvert G\rvert_3\leq3^3$ when $p=3$ and $A_7$ is involved i... | Assume O_p(G)=1 and every irreducible p-Brauer character \beta of G satisfies \beta(1)_p\le p. The conjectured sharp bounds are |G|_2\le 2^7 in case (i), |G|_p\le p^2 in case (ii), and |G|_3\le 3^3 in case (iii). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,853 | OWR-13675-009 | Structural Explanation of the McKay Conjecture | Why should the McKay conjecture hold, namely why should $|\operatorname{Irr}_{\ell'}(G)|=|\operatorname{Irr}_{\ell'}(N_G(P))|$ for a Sylow $\ell$-subgroup $P$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
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30,002,854 | OWR-13675-010 | Reduction of Torsion Endotrivial Modules to Trivial p-Prime Core | Can determination of the torsion subgroup $TT(G)$ of the endotrivial-module group $T(G)$ be reduced essentially to groups satisfying $O_{p'}(G)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
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30,002,855 | OWR-13675-013 | Diagrammatic Actions on Principal Tilting Categories | For a semisimple simply connected group $G$ in characteristic $p$ greater than its Coxeter number, can the principal tilting category $\mathrm{Tilt}_0$ be given a right $\mathcal{D}$-module structure with $B_s$ acting as translation, together with an equivalence $\mathrm{AS}_{\mathrm{deg}}\simeq \mathrm{Tilt}_0$ of rig... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | For a semisimple simply connected group $G$ in characteristic $p$ greater than its Coxeter number, can the principal tilting category $\mathrm{Tilt}_0$ be given a right $\mathcal{D}$-module structure with $B_s$ acting as translation, together with an equivalence $\mathrm{AS}_{\mathrm{deg}}\simeq \mathrm{Tilt}_0$ of rig... | For a semisimple simply connected group G in characteristic p greater than its Coxeter number, can the principal tilting category Tilt_0 be given a right \mathcal{D}-module structure with B_s acting as translation, together with an equivalence AS_{\mathrm{deg}}\simeq Tilt_0 of right \mathcal{D}-module categories? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,856 | OWR-13675-014 | Character-Degree Rigidity of Nonabelian Simple Groups | If $H$ is a nonabelian simple group and $\operatorname{cd}(G)=\operatorname{cd}(H)$, then $G$ is isomorphic to $H\times A$ for some abelian group $A$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"label": "Tong-Viet, Journal of A... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | If $H$ is a nonabelian simple group and $\operatorname{cd}(G)=\operatorname{cd}(H)$, then $G$ is isomorphic to $H\times A$ for some abelian group $A$. | If H is a nonabelian simple group and cd(G)=cd(H), then G is isomorphic to H\times A for some abelian group A. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,857 | OWR-13675-015 | Uniform Polynomial Bases for Stabilizer Modules | Let $\lambda\vdash n$, let $U\leq\operatorname{GL}_n(q)$ be the lower unitriangular subgroup, and decompose the restricted permutation module $\operatorname{Res}^{\operatorname{GL}_n(q)}_U M(\lambda)$ into summands indexed by row-standard $\lambda$-tableaux. For a basis $B$ of the Specht module $S(\lambda)$ adapted to ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027](https://doi.org/10.4171/owr/2015/18)
## Literature review (checked 2026-08-21)
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"owr-year:2015"
] | The James--D conjecture and its nonnegative-coefficient refinement are established for partitions with at most two parts, but the record asks for the general partition case and no complete proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/18",
"label": "Oberwolfach Report 18"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/18 | null | null | null | Let $\lambda\vdash n$, let $U\leq\operatorname{GL}_n(q)$ be the lower unitriangular subgroup, and decompose the restricted permutation module $\operatorname{Res}^{\operatorname{GL}_n(q)}_U M(\lambda)$ into summands indexed by row-standard $\lambda$-tableaux. For a basis $B$ of the Specht module $S(\lambda)$ adapted to ... | For \lambda\vdash n, can a basis B be chosen independently of K so that for every s\in St(\lambda) there is p_s\in\mathbb{Z}[x] with p_s(1)=1 and |B_s|=p_s(q), possibly with the refinement p_s\in\mathbb{Z}_{\ge0}[x-1]? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Representations of Finite Groups (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/18, pp. 971--1027 |
30,002,858 | OWR-13677-001 | Copula Realizations and Centers of Complete Mixes | For an $n$-completely mixable distribution $F$, what copula can realize an $n$-complete mix with all margins equal to $F$? Can the uniqueness of the center of a joint mix be proved by a more elegant analytic argument? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copulae: On the Crossroads of Mathematics and Economics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/20, pp. 1085--1137](https://doi.org/10.4171/owr/2015/20)
## Literature review (che... | 3 | open | null | 2,015 | 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-13677-001",
"literature-status:open",
"owr-year:2015"
] | The queue record contains multiple complete-mixability questions; later work gives partial structural and nonuniqueness results, but the requested copula construction and the general uniqueness/analytic-proof issues are not settled together. | [
{
"url": "https://doi.org/10.4171/owr/2015/20",
"label": "Oberwolfach Report 20"
},
{
"url": "https://doi.org/10.1214/14-PS250",
"label": "Wang, Current Open Questions in Complete Mixability"
},
{
"url": "https://doi.org/10.1007/s10959-023-01277-2",
"label": "Komisarski--Labuschagne"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/20 | null | null | null | For an $n$-completely mixable distribution $F$, what copula can realize an $n$-complete mix with all margins equal to $F$? Can the uniqueness of the center of a joint mix be proved by a more elegant analytic argument? | For an n-completely mixable distribution F, what copula can realize an n-complete mix with all margins F, and can the uniqueness of the center of a joint mix be proved by a more elegant analytic argument? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Copulae: On the Crossroads of Mathematics and Economics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/20, pp. 1085--1137 |
30,002,859 | OWR-13677-003 | Baire Category of Purely Singular Copulas | Let $\mathcal C_d$ be the space of $d$-dimensional copulas equipped with the metric
$$D_1(C_1,C_2)=\int_{[0,1]^d}\lvert C_1(u)-C_2(u)\rvert\,du.$$
Is the subset of purely singular copulas nonmeager in $(\mathcal C_d,D_1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Copulae: On the Crossroads of Mathematics and Economics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/20, pp. 1085--1137](https://doi.org/10.4171/owr/2015/20)
## Literature review (che... | 3 | open | null | 2,015 | 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 | {
"source_url": "https://zenodo.org/records/23372815",
"checked_at": "2026-10-14",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-14] I have released an unrefereed preprint, **Purely Singular Copulas Are Typical for the Markov-Kernel Metric D1** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23372815) | [
"owr",
"oberwolfach-reports",
"OWR-13677-003",
"literature-status:open",
"owr-year:2015"
] | Purely singular copulas are known to be typical in a uniform metric, but the corresponding second-category question in the D1 metric remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/20",
"label": "Oberwolfach Report 20"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0022247X15004527",
"label": "A typical copula is singular"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/20 | null | null | null | Let $\mathcal C_d$ be the space of $d$-dimensional copulas equipped with the metric
$$D_1(C_1,C_2)=\int_{[0,1]^d}\lvert C_1(u)-C_2(u)\rvert\,du.$$
Is the subset of purely singular copulas nonmeager in $(\mathcal C_d,D_1)$? | Is the class of purely singular copulas of second category in (\mathcal{C}_d,D_1)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Copulae: On the Crossroads of Mathematics and Economics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/20, pp. 1085--1137 |
30,002,860 | OWR-13678-001 | Unbounded Sizes of Sensitive Triangulations | Are the sizes of sensitive triangulations unbounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 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-13678-001",
"literature-status:open",
"owr-year:2015"
] | The sensitive-triangulation size problem is explicitly recorded as a long-standing open problem; no theorem establishing a uniform bound or unboundedness for all dimensions was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | Are the sizes of sensitive triangulations unbounded? | Are the sizes of sensitive triangulations unbounded? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,861 | OWR-13678-002 | Cubic Spline Interpolation on General Triangulations | Given a planar triangulation, is arbitrary interpolation of function values at its vertices always possible by a spline in $S_3^1$? In the corresponding quartic $C^1$ setting, is simultaneous interpolation of function and gradient values at the vertices impossible for some triangulations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,015 | 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 | {
"source_url": null,
"checked_at": "2026-10-09",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-09] **partially_solved (item 16: no; item 18: open)**. Items 16 and 18 of P. Alfeld's abstract, Oberwolfach Rep. 12 (Report 21/2015), p. 1146. | [
"owr",
"oberwolfach-reports",
"OWR-13678-002",
"literature-status:open",
"owr-year:2015"
] | The record contains two unresolved spline-interpolation conjectures, one asserting universal interpolation and the other asserting failure in the general case; available results cover special triangulations or degree ranges only. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1016/S0377-0427(99)00350-7",
"label": "Interpolation by C1 splines of degree at least four"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | Given a planar triangulation, is arbitrary interpolation of function values at its vertices always possible by a spline in $S_3^1$? In the corresponding quartic $C^1$ setting, is simultaneous interpolation of function and gradient values at the vertices impossible for some triangulations? | Is interpolation of function values at triangulation vertices always possible with a spline in S^1_3, and is interpolation of both function and gradient values at the vertices always impossible in the general case? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,862 | OWR-13678-003 | Complementarity Form of the Schumaker Strang Conjecture | For every $q\in\mathbb{R}^n$, does there exist $x\in\mathbb{R}^n$ such that $x\geq 0$, $Mx+q\geq 0$, and $\langle Mx+q,x\rangle=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 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-13678-003",
"literature-status:open",
"owr-year:2015"
] | The Schumaker--Strang lower-bound conjecture and its complementarity formulation remain active in the general case; recent work proves important degree and genericity cases but not the stated full conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i1p29/pdf",
"label": "Generalized Splines on Graphs, EJC 2024"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | For every $q\in\mathbb{R}^n$, does there exist $x\in\mathbb{R}^n$ such that $x\geq 0$, $Mx+q\geq 0$, and $\langle Mx+q,x\rangle=0$? | For every q\in\mathbb{R}^n, does there exist x\in\mathbb{R}^n such that x\ge0, Mx+q\ge0, and \langle Mx+q,x\rangle=0? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,863 | OWR-13678-004 | Linear Precision of Toric Bezier Patches and Volumes | Which toric Bezier patches have linear precision, which toric Bezier volumes have rational linear precision, and how can birational maps of projective 3-space be classified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,015 | 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-13678-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Linear-precision toric surface patches have been classified in important cases and higher-dimensional families with rational linear precision are known, but the requested general classification in dimension three is still incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1007/s10208-009-9052-6",
"label": "Linear Precision for Toric Surface Patches"
},
{
"url": "https://doi.org/10.1007/s10208-022-09583-7",
"label": "Families of Polytopes wi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | Which toric Bezier patches have linear precision, which toric Bezier volumes have rational linear precision, and how can birational maps of projective 3-space be classified? | Which toric Bezier patches have linear precision, which toric Bezier volumes have rational linear precision, and how can birational maps of projective 3-space be classified? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,864 | OWR-13678-005 | Characterization of Hermite Ideal Projectors | Which finite-dimensional ideal projectors are Hermite projectors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 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-13678-005",
"literature-status:open",
"owr-year:2015"
] | There are substantial structural results for finite-dimensional Hermite projectors, including complete-intersection and primary-decomposition criteria, but no general characterization of all finite-dimensional ideal projectors that are Hermite projectors. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1007/s00365-015-9311-5",
"label": "Shekhtman, On One Class of Hermite Projectors"
},
{
"url": "https://doi.org/10.3390/sym15091658",
"label": "Shekhtman--Tuesink, Symmetry... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | Which finite-dimensional ideal projectors are Hermite projectors? | Which finite-dimensional ideal projectors are Hermite projectors? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,865 | OWR-13678-006 | Complete-Intersection Kernels of Ideal Projectors | If an ideal projector $P$ has a zero-dimensional kernel generated by exactly $d$ polynomials in $\mathbb{C}[x_1,\ldots,x_d]$, must $P$ be a Hermite projector? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | solved | null | 2,015 | 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": "https://doi.org/10.1007/s00365-008-9016-0",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; our combination of known results)**. B. Shekhtman (OWR 21/2015, p. 1183, Conjecture 1) conjectures that an ideal projector P on C[x₁, …, x_d] whose kernel is generated by exactly d polynomials (and is zero-dimensional) is Hermite, i.e. a limit of Lagrange pro... | [
"owr",
"oberwolfach-reports",
"OWR-13678-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The complete-intersection-kernel conjecture is proved under the additional no-roots-at-infinity hypothesis, while the unrestricted conjecture remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1007/s00365-015-9311-5",
"label": "Shekhtman, On One Class of Hermite Projectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | If an ideal projector $P$ has a zero-dimensional kernel generated by exactly $d$ polynomials in $\mathbb{C}[x_1,\ldots,x_d]$, must $P$ be a Hermite projector? | If an ideal projector P has a kernel that is a complete intersection, then P is Hermite. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,866 | OWR-13678-007 | Hermite-Projector Theorem Extraction | If P is an ideal projector with ker P=\langle f_1,\ldots,f_d\rangle and f=(f_1,\ldots,f_d):\mathbb{C}^d\to\mathbb{C}^d has no roots at infinity, then P is Hermite. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,015 | 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 | Answered in the source or not an open problem (solved (a theorem, not a problem)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (a theorem, not a problem)**. The record is Theorem 6 of Shekhtman's abstract above (if ker P = ⟨f₁, …, f_d⟩ and f has no roots at infinity, P is Hermite), proved in his [Constr. Approx. 44 (2016)](https://doi.org/10.1007/s00365-015-9311-5) paper; its title already... | [
"owr",
"oberwolfach-reports",
"OWR-13678-007",
"literature-status:partially-solved",
"owr-year:2015"
] | The supplied theorem gives a proved partial result supporting the Hermite-projector conjecture, but it does not cover all finite-dimensional ideal projectors. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1007/s00365-015-9311-5",
"label": "Shekhtman, On One Class of Hermite Projectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | null | If P is an ideal projector with ker P=\langle f_1,\ldots,f_d\rangle and f=(f_1,\ldots,f_d):\mathbb{C}^d\to\mathbb{C}^d has no roots at infinity, then P is Hermite. | unrecoverable | The passage is a proved sufficient condition for an ideal projector to be Hermite, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,867 | OWR-13678-008 | Matrix Characterization of Complete Intersections | Let $P$ be an ideal projector and let $M_j$ be multiplication by $x_j$ on $\mathbb{C}[x_1,\ldots,x_d]/\ker P$. Characterize when $\ker P$ is a complete intersection in terms of the commuting matrices $M_1,\ldots,M_d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 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-13678-009"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13678-008",
"literature-status:open",
"owr-year:2015"
] | The record asks for a characterization of complete intersections through the associated commuting matrices; the cited projector theory supplies criteria and examples but no general characterization. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://eudml.org/doc/229343",
"label": "Shekhtman, Some Tidbits on Ideal Projectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | Let $P$ be an ideal projector and let $M_j$ be multiplication by $x_j$ on $\mathbb{C}[x_1,\ldots,x_d]/\ker P$. Characterize when $\ker P$ is a complete intersection in terms of the commuting matrices $M_1,\ldots,M_d$. | What is a characterization of complete intersections in terms of the commuting matrices defined by (1)? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,868 | OWR-13678-009 | Duplicate Complete-Intersection Extraction | What is a characterization of complete intersections in terms of the commuting matrices defined by (1)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The passage is a duplicate extraction of the commuting-matrix problem recorded in OWR-13678-008. No separate clean statement is promoted; th) | [
"OWR-13678-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13678-009",
"literature-status:open",
"owr-year:2015"
] | This is the same unresolved complete-intersection characterization problem stated in the record; current commuting-matrix criteria do not settle it in general. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://eudml.org/doc/229343",
"label": "Shekhtman, Some Tidbits on Ideal Projectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | null | What is a characterization of complete intersections in terms of the commuting matrices defined by (1)? | unrecoverable | The passage is a duplicate extraction of the commuting-matrix problem recorded in OWR-13678-008. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,869 | OWR-13678-010 | Exact Dimensions of Trivariate Spline Spaces | In the remaining cases where the upper and lower dimension bounds differ, does the dimension equal the upper bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200](https://doi.org/10.4171/owr/2015/21)
## Literature review (checked 2026-08... | 3 | open | null | 2,015 | 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 | {
"source_url": "https://zenodo.org/records/23057868",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **The Dimension of Trivariate C¹ Splines on Generic Bipyramid Cells** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23057868) | [
"owr",
"oberwolfach-reports",
"OWR-13678-010",
"literature-status:open",
"owr-year:2015"
] | For trivariate C1 splines on bipyramid cells, the remaining cases where upper and lower dimension bounds differ are still conjectural; later lower-bound work does not prove the stated equality in all cases. | [
{
"url": "https://doi.org/10.4171/owr/2015/21",
"label": "Oberwolfach Report 21"
},
{
"url": "https://doi.org/10.1016/j.cagd.2015.12.001",
"label": "Colvin--DiMatteo--Sorokina"
},
{
"url": "https://doi.org/10.1137/20M1341118",
"label": "DiPasquale--Villamizar"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/21 | null | null | null | In the remaining cases where the upper and lower dimension bounds differ, does the dimension equal the upper bound? | In the remaining cases where the upper and lower dimension bounds differ, does the dimension equal the upper bound? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Multivariate Splines and Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/21, pp. 1139--1200 |
30,002,870 | OWR-13679-002 | Symmetric Landau–Ginzburg Mirrors of Homogeneous Spaces | For a homogeneous space $X$ and its Landau–Ginzburg mirror, can the relationship be made more symmetric? Can the mirror be expressed in coordinates naturally related to the cohomology of $X$? Does the map from cohomology to twisted de Rham cohomology extend to an isomorphism of bundles with connection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mirror Symmetry, Hodge Theory and Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/22, pp. 1201--1254](https://doi.org/10.4171/owr/2015/22)
## Literature review (ch... | 3 | partially_solved | null | 2,015 | 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-13679-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The mirror-symmetry and A/B-model connection is proved for selected homogeneous examples such as Grassmannians and quadrics, but the record's general conjectural bundle-with-connection statement remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/22",
"label": "Oberwolfach Report 22"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/22 | null | null | null | For a homogeneous space $X$ and its Landau–Ginzburg mirror, can the relationship be made more symmetric? Can the mirror be expressed in coordinates naturally related to the cohomology of $X$? Does the map from cohomology to twisted de Rham cohomology extend to an isomorphism of bundles with connection? | For a homogeneous space X and its Landau--Ginzburg mirror, can the relationship be made more symmetric, can the mirror be expressed in coordinates naturally related to the cohomology of X, and does the map from cohomology to twisted de Rham cohomology extend to an isomorphism of bundles with connection? | 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 | Mirror Symmetry, Hodge Theory and Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/22, pp. 1201--1254 |
30,002,871 | OWR-13679-003 | Hodge and Order Filtrations on GKZ Modules | For the GKZ modules $M_A^0$ and $M_A^{-c}$, the Hodge filtration equals the order filtration up to the shifts $F^H_\bullet M_A^0=F^{\mathrm{ord}}_{\bullet+d}M_A^0$ and $F^H_\bullet M_A^{-c}=F^{\mathrm{ord}}_{\bullet-n-c_0}M_A^{-c}$, where $c_0$ is the first component of $c\in NA\subset\mathbb Z^{d+1}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mirror Symmetry, Hodge Theory and Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/22, pp. 1201--1254](https://doi.org/10.4171/owr/2015/22)
## Literature review (ch... | 3 | partially_solved | null | 2,015 | 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-13679-003",
"literature-status:partially-solved",
"owr-year:2015"
] | The GKZ weight-filtration conjecture is established in normal and several low-dimensional or simplicial settings, with explicit image and filtration results, but the full saturated-semigroup assertion in the record is not proved generally. | [
{
"url": "https://doi.org/10.4171/owr/2015/22",
"label": "Oberwolfach Report 22"
},
{
"url": "https://arxiv.org/abs/1809.04247",
"label": "Reichelt--Walther, Weight Filtrations on GKZ-Systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/22 | null | null | null | For the GKZ modules $M_A^0$ and $M_A^{-c}$, the Hodge filtration equals the order filtration up to the shifts $F^H_\bullet M_A^0=F^{\mathrm{ord}}_{\bullet+d}M_A^0$ and $F^H_\bullet M_A^{-c}=F^{\mathrm{ord}}_{\bullet-n-c_0}M_A^{-c}$, where $c_0$ is the first component of $c\in NA\subset\mathbb Z^{d+1}$. | For the GKZ modules M_A^0 and M_A^{-c}, the Hodge filtration equals the order filtration up to the shifts F^H_\bullet M_A^0=F^{ord}_{\bullet+d}M_A^0 and F^H_\bullet M_A^{-c}=F^{ord}_{\bullet-n-c_0}M_A^{-c}, where c_0 is the first component of c\in NA\subset\mathbb Z^{d+1}. | 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 | Mirror Symmetry, Hodge Theory and Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/22, pp. 1201--1254 |
30,002,872 | OWR-13680-001 | Family Floer and Kontsevich–Soibelman Wall Crossing | How can wall-crossing formulas from family Floer homology be related to the Kontsevich–Soibelman wall-crossing formulas, and thereby to refined tropical counts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316](https://doi.org/10.4171/owr/2015/23)
## Literature review (checked ... | 3 | open | null | 2,015 | 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-13680-001",
"literature-status:open",
"owr-year:2015"
] | The report asks for a general relation between refined tropical counts and the relevant Fukaya or mirror-symmetry counts; known results cover special one-disc or restricted cases, not the general comparison. | [
{
"url": "https://doi.org/10.4171/owr/2015/23",
"label": "Oberwolfach Report 23"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/23 | null | null | null | How can wall-crossing formulas from family Floer homology be related to the Kontsevich–Soibelman wall-crossing formulas, and thereby to refined tropical counts? | How can wall-crossing formulas from family Floer homology be related to the Kontsevich--Soibelman wall-crossing formulas, and thereby to refined tropical counts? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316 |
30,002,873 | OWR-13680-004 | Fiber Genus of Rational Maps from Newton Hypersurfaces | Let $\Delta\subset\mathbb Z^n$ be a Newton polyhedron and $H$ a generic hypersurface with Newton polyhedron $\Delta$. For a dominant rational map $f:H\dashrightarrow\mathbb P^{n-2}$, determine the genus of the generic fiber $f^{-1}(x)$ for $x\in\mathbb P^{n-2}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316](https://doi.org/10.4171/owr/2015/23)
## Literature review (checked ... | 3 | open | null | 2,015 | 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-13680-004",
"literature-status:open",
"owr-year:2015"
] | The genus of the fibers of the indicated rational map is a natural unresolved question in the record; degree-of-irrationality results constrain related maps and fibers but do not give the requested general genus formula. | [
{
"url": "https://doi.org/10.4171/owr/2015/23",
"label": "Oberwolfach Report 23"
},
{
"url": "https://arxiv.org/abs/1803.02957",
"label": "Stapleton--Ullery, Degree of Irrationality of Hypersurfaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/23 | null | null | null | Let $\Delta\subset\mathbb Z^n$ be a Newton polyhedron and $H$ a generic hypersurface with Newton polyhedron $\Delta$. For a dominant rational map $f:H\dashrightarrow\mathbb P^{n-2}$, determine the genus of the generic fiber $f^{-1}(x)$ for $x\in\mathbb P^{n-2}$. | Let \Delta\subset\mathbb Z^n be a Newton polyhedron and H a generic hypersurface with Newton polyhedron \Delta. For a dominant rational map f:H\dashrightarrow\mathbb P^{n-2}, determine the genus of the generic fiber f^{-1}(x) for x\in\mathbb P^{n-2}. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316 |
30,002,874 | OWR-13680-005 | Maximal Real Betti Numbers of Tridegree Surfaces | For a nonsingular real algebraic surface $X\subset(\mathbb{CP}^1)^3$ of a prescribed multidegree, what is the maximal possible first Betti number $b_1(\mathbb RX)$ of its real part? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316](https://doi.org/10.4171/owr/2015/23)
## Literature review (checked ... | 3 | open | null | 2,015 | 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-13680-005",
"literature-status:open",
"owr-year:2015"
] | For real surfaces in the triple projective line, constructions give counterexamples and asymptotically near-maximal first Betti numbers, but the exact maximum for each prescribed multidegree remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/23",
"label": "Oberwolfach Report 23"
},
{
"url": "https://arxiv.org/abs/1511.02261",
"label": "Renaudineau, Real Algebraic Surfaces with Many Handles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/23 | null | null | null | For a nonsingular real algebraic surface $X\subset(\mathbb{CP}^1)^3$ of a prescribed multidegree, what is the maximal possible first Betti number $b_1(\mathbb RX)$ of its real part? | For a nonsingular real algebraic surface X\subset(\mathbb{CP}^1)^3 of a prescribed multidegree, what is the maximal possible first Betti number b_1(\mathbb RX) of its real part? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Tropical Aspects in Geometry, Topology and Physics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/23, pp. 1255--1316 |
30,002,875 | OWR-13681-004 | Donkin’s Good Filtration Conjecture | Let $k$ be algebraically closed of characteristic $p>0$, let $G$ be simple and simply connected, and let $\mathrm{St}_r=L((p^r-1)\rho)$ be the $r$th Steinberg module. Donkin's conjecture asserts that a finite-dimensional rational $G$-module $M$ has a good $(p,r)$-filtration if and only if $\mathrm{St}_r\otimes M$ has a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | open | null | 2,015 | 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-13681-004",
"literature-status:open",
"owr-year:2015"
] | The general composition-factor multiplicity problem for induced modules in modular reductive-group representation theory remains unresolved. | [
{
"url": "https://arxiv.org/abs/1610.06261",
"label": "Williamson, Algebraic representations and constructible sheaves"
},
{
"url": "https://doi.org/10.4171/owr/2015/24",
"label": "Oberwolfach Report 2015/24"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | Let $k$ be algebraically closed of characteristic $p>0$, let $G$ be simple and simply connected, and let $\mathrm{St}_r=L((p^r-1)\rho)$ be the $r$th Steinberg module. Donkin's conjecture asserts that a finite-dimensional rational $G$-module $M$ has a good $(p,r)$-filtration if and only if $\mathrm{St}_r\otimes M$ has a... | Let k be algebraically closed of characteristic p>0, let G be simple and simply connected, and let St_r=L((p^r-1)\rho) be the rth Steinberg module. Donkin's conjecture asserts that a finite-dimensional rational G-module M has a good (p,r)-filtration if and only if St_r\otimes M has a good filtration. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,876 | OWR-13681-006 | Steinberg Tensor Products with Good Filtrations | Let $G$ be a simple algebraic group over an algebraically closed field of characteristic $p > 0$, let $X^+$ be the set of dominant weights, let $L(\lambda)$ be the simple rational $G$-module of highest weight $\lambda \in X^+$, and let $\mathrm{St}_r = L((p^r - 1)\rho)$ be the $r$-th Steinberg representation. For which... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | open | null | 2,015 | 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-13681-006",
"literature-status:open",
"owr-year:2015"
] | The Steinberg-tensor good-filtration question is settled only in broad special ranges and cases; the general classification of lambda remains open. | [
{
"url": "https://arxiv.org/abs/1804.00613",
"label": "On tensoring with the Steinberg representation"
},
{
"url": "https://arxiv.org/abs/1901.06687",
"label": "Counterexamples to the Tilting and (p,r)-Filtration Conjectures"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | Let $G$ be a simple algebraic group over an algebraically closed field of characteristic $p > 0$, let $X^+$ be the set of dominant weights, let $L(\lambda)$ be the simple rational $G$-module of highest weight $\lambda \in X^+$, and let $\mathrm{St}_r = L((p^r - 1)\rho)$ be the $r$-th Steinberg representation. For which... | For which dominant weights \lambda\in X^+ does St_r\otimes L(\lambda) have a good filtration as a rational G-module? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,877 | OWR-13681-010 | Degree Spectra and Index of Brauer-Equivalent Azumaya Algebras | Given an Azumaya algebra $A$ on a connected ringed space $X$, what are the possible degrees of Azumaya algebras $A'$ that are Brauer-equivalent to $A$, and how can their greatest common divisor, the index $\operatorname{ind}([A])$, be characterized? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | open | null | 2,015 | 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-13681-010",
"literature-status:open",
"owr-year:2015"
] | Period-index methods determine important bounds and examples, but the general question asking for all possible degrees remains unresolved; the conjectural universal bound is now known to fail. | [
{
"url": "https://arxiv.org/abs/2608.03684",
"label": "Perry, Period-index bounds for Brauer classes"
},
{
"url": "https://arxiv.org/abs/2003.10539",
"label": "Antieau--Williams, The period-index problem for twisted topological K-theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | Given an Azumaya algebra $A$ on a connected ringed space $X$, what are the possible degrees of Azumaya algebras $A'$ that are Brauer-equivalent to $A$, and how can their greatest common divisor, the index $\operatorname{ind}([A])$, be characterized? | Given an Azumaya algebra A on a connected ringed space X, what are the possible degrees of Azumaya algebras A' Brauer-equivalent to A, and how can their greatest common divisor, the index ind([A]), be characterized? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,878 | OWR-13681-012 | Topological Period–Index Conjecture | For a $2d$-dimensional finite CW complex $X$ and $\alpha\in \operatorname{Br}(X)$, the topological period–index conjecture predicts $\operatorname{ind}_{\mathrm{topo}}(\alpha)\mid \operatorname{per}_{\mathrm{topo}}(\alpha)^{d-1}$, except possibly when $\operatorname{per}(\alpha)\equiv2\pmod 4$ and $d=3$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | solved | null | 2,015 | 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/10.1112/topo.12119",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (false as formulated)**. B. Williams (joint with B. Antieau; OWR 24/2015, p. 1359) conjectures that ind(α) | per(α)^{d−1} for Brauer classes α on finite 2d-dimensional CW complexes, unless per(α) ≡ 2 (mod 4) and d = 3. X. Gu, [J. Topol. 12 (2019)](https://doi.org/1... | [
"owr",
"oberwolfach-reports",
"OWR-13681-012",
"literature-status:partially-solved",
"owr-year:2015"
] | The low-dimensional cases and the sharp period-two dimension-three exception are established, and general prime-dependent bounds are known, but the exact all-dimensions straw-man formulation remains unresolved. | [
{
"url": "https://doi.org/10.1112/jtopol/jtt042",
"label": "Antieau--Williams, The period-index problem for twisted topological K-theory"
},
{
"url": "https://arxiv.org/abs/2003.10539",
"label": "Antieau--Williams, The topological period-index conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | For a $2d$-dimensional finite CW complex $X$ and $\alpha\in \operatorname{Br}(X)$, the topological period–index conjecture predicts $\operatorname{ind}_{\mathrm{topo}}(\alpha)\mid \operatorname{per}_{\mathrm{topo}}(\alpha)^{d-1}$, except possibly when $\operatorname{per}(\alpha)\equiv2\pmod 4$ and $d=3$. | For a 2d-dimensional finite CW complex X and \alpha\in Br(X), the topological period--index conjecture predicts ind_{topo}(\alpha)\mid per_{topo}(\alpha)^{d-1}, except possibly when per(\alpha)\equiv2\pmod 4 and d=3. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,879 | OWR-13681-013 | Hochschild-Cohomology Lie Structure of a Stratified Algebra | Let $K$ have characteristic $2$, let $B=\begin{pmatrix}K(\mathbb Z_2\times\mathbb Z_2)&K\mathbb Z_2\\0&K\end{pmatrix}$ with stratifying idempotent $e=\begin{pmatrix}0&0\\0&1\end{pmatrix}$. Determine the precise Lie algebra structure of $\operatorname{HH}^*(B)$, and decide whether the long exact sequence from $0\to BeB\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | solved | null | 2,015 | 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": "https://doi.org/10.1016/j.aim.2016.05.022",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved**. R. Hermann (OWR 24/2015, p. 1363, Question 5) asks, in characteristic 2, for the Lie structure of HH\*(B), B = [[K(Z2×Z2), KZ2],[0,K]] (Xu's category algebra, by Hermann, [Adv. Math. 299 (2016)](https://doi.org/10.1016/j.aim.2016.05.022), Lemma 9.7; now called t... | [
"owr",
"oberwolfach-reports",
"OWR-13681-013",
"literature-status:open",
"owr-year:2015"
] | The cited exact sequence does not by itself supply the requested Lie algebra computation for the displayed triangular algebra; no complete computation of that example was found. | [
{
"url": "https://arxiv.org/abs/2006.13871",
"label": "Briggs--Rubio y Degrassi, Stable invariance of restricted Lie structure"
},
{
"url": "https://doi.org/10.4171/owr/2015/24",
"label": "Oberwolfach Report 2015/24"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | Let $K$ have characteristic $2$, let $B=\begin{pmatrix}K(\mathbb Z_2\times\mathbb Z_2)&K\mathbb Z_2\\0&K\end{pmatrix}$ with stratifying idempotent $e=\begin{pmatrix}0&0\\0&1\end{pmatrix}$. Determine the precise Lie algebra structure of $\operatorname{HH}^*(B)$, and decide whether the long exact sequence from $0\to BeB\... | Let K have characteristic 2, let B=\begin{pmatrix}K(\mathbb Z_2\times\mathbb Z_2)&K\mathbb Z_2\\0&K\end{pmatrix} with stratifying idempotent e=\begin{pmatrix}0&0\\0&1\end{pmatrix}. Determine the precise Lie algebra structure of HH^*(B), and decide whether the long exact sequence from 0\to BeB\to B\to B/BeB\to0 determin... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,880 | OWR-13681-014 | Bilax Monoidal Structures for Stable Morita Equivalences | For a stable equivalence of Morita type $(M,N,\varphi,\psi)$ between algebras $A$ and $B$, can the functor $M\otimes_B(-)\otimes_B N:\operatorname{Mod}(B^{\mathrm{ev}})\to\operatorname{Mod}(A^{\mathrm{ev}})$ be made bilax monoidal with split-surjective unit map $M\otimes_B N\twoheadrightarrow A\oplus P\to A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | partially_solved | null | 2,015 | 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-13681-014",
"literature-status:partially-solved",
"owr-year:2015"
] | Stable equivalences of Morita type preserve the restricted Lie algebra structure and the relevant B-infinity structure in self-injective settings, but the broader formulation remains unresolved. | [
{
"url": "https://arxiv.org/abs/2006.13871",
"label": "Briggs--Rubio y Degrassi, Stable invariance of restricted Lie structure"
},
{
"url": "https://doi.org/10.4171/owr/2015/24",
"label": "Oberwolfach Report 2015/24"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | For a stable equivalence of Morita type $(M,N,\varphi,\psi)$ between algebras $A$ and $B$, can the functor $M\otimes_B(-)\otimes_B N:\operatorname{Mod}(B^{\mathrm{ev}})\to\operatorname{Mod}(A^{\mathrm{ev}})$ be made bilax monoidal with split-surjective unit map $M\otimes_B N\twoheadrightarrow A\oplus P\to A$? | For a stable equivalence of Morita type between algebras A and B given by bimodules M,N, can the functor M\otimes_B(-)\otimes_B N be made into a bilax monoidal functor with split-surjective unit map M\otimes_B N\twoheadrightarrow A, so that the induced stable Hochschild-cohomology map preserves the Lie bracket in the r... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,881 | OWR-13681-015 | Restriction Criteria for Endotrivial Modules | Let $S$ be a Sylow $p$-subgroup of a finite group $G$ and define $\rho_1(Q)=N_G(Q)'$ and $\rho_i(Q)=\langle N_G(Q)\cap\rho_{i-1}(R):1\ne R\subseteq S\rangle$, with $\rho^\infty(S)=\bigcup_i\rho_i(S)$. The conjecture is that a one-dimensional $kN_G(S)$-module $L$ is the restriction, modulo projectives, of an endo-trivia... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384](https://doi.org/10.4171/owr/2015/24)
## Literature review (... | 3 | partially_solved | null | 2,015 | 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 | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (yes)**; the dataset currently labels it partially solved. J. Thévenaz (with J. F. Carlson), OWR 24/2015, p. 1366, Conjecture: a one-dimensional kN_G(S)-module L is, modulo projectives, the restriction of an endo-trivial kG-module if and only if ρ^∞(S) ⊆ ker L (pro... | [
"owr",
"oberwolfach-reports",
"OWR-13681-015",
"literature-status:partially-solved",
"owr-year:2015"
] | The endo-trivial restriction conjecture is proved for groups with abelian Sylow p-subgroups, with further special Sylow cases known, but no general proof is established. | [
{
"url": "https://arxiv.org/abs/1408.3982",
"label": "Carlson--Thévenaz, The torsion subgroup of endotrivial modules"
},
{
"url": "https://doi.org/10.4171/owr/2015/24",
"label": "Oberwolfach Report 2015/24"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/24 | null | null | null | Let $S$ be a Sylow $p$-subgroup of a finite group $G$ and define $\rho_1(Q)=N_G(Q)'$ and $\rho_i(Q)=\langle N_G(Q)\cap\rho_{i-1}(R):1\ne R\subseteq S\rangle$, with $\rho^\infty(S)=\bigcup_i\rho_i(S)$. The conjecture is that a one-dimensional $kN_G(S)$-module $L$ is the restriction, modulo projectives, of an endo-trivia... | Let S be a Sylow p-subgroup of a finite group G and define \rho_1(Q)=N_G(Q)' and \rho_i(Q)=\langle N_G(Q)\cap\rho_{i-1}(R):1\ne R\subseteq S\rangle, with \rho^\infty(S)=\bigcup_i\rho_i(S). The conjecture is that a one-dimensional kN_G(S)-module L is the restriction, modulo projectives, of an endo-trivial kG-module if a... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/24, pp. 1317--1384 |
30,002,882 | OWR-13682-002 | Categorical Diagonalization of Coxeter Full Twists | For any finite Coxeter group $W$, is the Rouquier complex $F_T$ of the full twist categorically diagonalizable, with spectrum indexed by the two-sided cells of $W$ and with the predicted eigenshifts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | partially_solved | null | 2,015 | 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-13682-002",
"literature-status:partially-solved",
"owr-year:2015"
] | Categorical diagonalization of the full twist is proved in type A and several small or dihedral cases, but the asserted theorem for every finite Coxeter group remains open. | [
{
"url": "https://arxiv.org/abs/1801.00191",
"label": "Elias--Hogancamp, On the full twist"
},
{
"url": "https://doi.org/10.1215/00127094-2024-0078",
"label": "Elias--Hogancamp, published full-twist work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | For any finite Coxeter group $W$, is the Rouquier complex $F_T$ of the full twist categorically diagonalizable, with spectrum indexed by the two-sided cells of $W$ and with the predicted eigenshifts? | For any finite Coxeter group W, the Rouquier complex F_T attached to the full twist should be categorically diagonalizable, with spectrum in bijection with the two-sided cells of W and with the known eigenshifts. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,883 | OWR-13682-004 | Cluster Monomials in Dual Canonical Bases | Do all cluster monomials in quantum cluster algebras belong to the dual canonical basis? In Grothendieck-ring cluster algebras of quantum affine representations, do all cluster monomials belong to the basis of simple modules? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | partially_solved | null | 2,015 | 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-13682-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Cluster-monomial and dual-canonical-basis assertions are proved in substantial monoidal-categorification classes, but the broad conjectural formulation is not settled in full generality. | [
{
"url": "https://doi.org/10.1090/jams/895",
"label": "Kang--Kashiwara--Kim--Oh, Monoidal categorification"
},
{
"url": "https://arxiv.org/abs/1106.4971",
"label": "Gross--Hacking--Keel--Kontsevich, Canonical bases"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | Do all cluster monomials in quantum cluster algebras belong to the dual canonical basis? In Grothendieck-ring cluster algebras of quantum affine representations, do all cluster monomials belong to the basis of simple modules? | In the relevant quantum cluster algebras, all cluster monomials should belong to the dual canonical basis; in the Grothendieck-ring cluster algebras of quantum affine representations, all cluster monomials should belong to the basis of simple modules. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,884 | OWR-13682-005 | Common Triangular Bases for Quantum Cluster Algebras | Does every injective-reachable quantum cluster algebra admit a unique common triangular basis parametrized by tropical points, as predicted by the Fock–Goncharov conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | partially_solved | null | 2,015 | 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-13682-005",
"literature-status:partially-solved",
"owr-year:2015"
] | Common triangular-basis and monoidal-categorification statements are established for important classes, including the cited quantum-group settings, but not for the full generality of the record. | [
{
"url": "https://doi.org/10.1090/jams/895",
"label": "Kang--Kashiwara--Kim--Oh, Monoidal categorification"
},
{
"url": "https://arxiv.org/abs/1106.4971",
"label": "Gross--Hacking--Keel--Kontsevich, Canonical bases"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | Does every injective-reachable quantum cluster algebra admit a unique common triangular basis parametrized by tropical points, as predicted by the Fock–Goncharov conjecture? | Every injective-reachable quantum cluster algebra should admit a unique common triangular basis parametrized by tropical points, as predicted by the Fock--Goncharov conjecture. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,885 | OWR-13682-006 | K-Theoretic Geometric Satake Equivalence | For a semisimple complex group $G$ with Langlands dual $G^\vee$, let $\mathrm{Gr}$ be its affine Grassmannian. Is the convolution category $K\mathrm{Conv}(\mathrm{Gr})$ equivalent to a full subcategory of $U_q(\mathfrak g)$-equivariant $\mathcal O_q(G)$-modules? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | partially_solved | null | 2,015 | 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-13682-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The K-theoretic geometric Satake equivalence conjecture is proved for SL_n, while the stated general reductive-group equivalence remains open. | [
{
"url": "https://arxiv.org/abs/1509.00112",
"label": "Kamnitzer--Webster--Weekes--Yacoby, Quantum K-theoretic geometric Satake"
},
{
"url": "https://doi.org/10.1112/S0010437X17007564",
"label": "Quantum K-theoretic geometric Satake, SL_n case"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | For a semisimple complex group $G$ with Langlands dual $G^\vee$, let $\mathrm{Gr}$ be its affine Grassmannian. Is the convolution category $K\mathrm{Conv}(\mathrm{Gr})$ equivalent to a full subcategory of $U_q(\mathfrak g)$-equivariant $\mathcal O_q(G)$-modules? | For a semisimple complex group G with Langlands dual G^\vee, the category KConv(Gr) should be equivalent to a full subcategory of U_q(\mathfrak g)-equivariant O_q(G)-modules. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,886 | OWR-13682-007 | Characteristic Varieties of Rigid-Analytic D-Modules | Develop a satisfactory theory of characteristic varieties for co-admissible D-modules on smooth rigid-analytic spaces, analogous to the characteristic-variety theory for algebraic D-modules. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | open | null | 2,015 | 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-13682-007",
"literature-status:open",
"owr-year:2015"
] | Dimension theory, weak holonomicity, and Kashiwara-type results are available, but a satisfactory general characteristic-variety theory for coadmissible D-modules remains unresolved. | [
{
"url": "https://arxiv.org/abs/1501.02215",
"label": "Ardakov--Wadsley, D-modules on rigid analytic spaces I"
},
{
"url": "https://arxiv.org/abs/1904.13280",
"label": "Ardakov--Bode--Wadsley, D-modules on rigid analytic spaces III"
},
{
"url": "https://publications.mfo.de/bitstream/hand... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | Develop a satisfactory theory of characteristic varieties for co-admissible D-modules on smooth rigid-analytic spaces, analogous to the characteristic-variety theory for algebraic D-modules. | Develop a satisfactory theory of characteristic varieties for co-admissible D-modules on smooth rigid-analytic spaces, analogous to the characteristic-variety theory for algebraic D-modules. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,887 | OWR-13682-009 | Minimal Rational Curves on Complete Symmetric Varieties | Develop a theory of minimal rational curves on complete symmetric varieties, namely toroidal compactifications of symmetric spaces $G/H$ with $G$ reductive, extending the theory for wonderful group compactifications. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | open | null | 2,015 | 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-13682-009",
"literature-status:open",
"owr-year:2015"
] | Complete and toroidal symmetric varieties have a substantial colored-fan and low-rank theory, but the requested general extension of the results to all symmetric spaces G/H remains open. | [
{
"url": "https://ems.press/content/serial-article-files/41168",
"label": "Ruzzi, Fano symmetric varieties with low rank"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3472/OWR_2015_25.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 2015/25"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | Develop a theory of minimal rational curves on complete symmetric varieties, namely toroidal compactifications of symmetric spaces $G/H$ with $G$ reductive, extending the theory for wonderful group compactifications. | Extend the results on minimal rational curves for wonderful group compactifications to complete symmetric varieties, namely toroidal compactifications of symmetric spaces G/H with G reductive. | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,888 | OWR-13682-010 | Forgetful Functors for Mixed Perverse Sheaves | Does there exist a forgetful functor $\operatorname{For}:DS^{\mathrm{mix}}(X,F)\to DS^b(X,F)$ that makes $\operatorname{Perv}^{\mathrm{mix}}_S(X,F)$ a graded version of $\operatorname{Perv}_S(X,F)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447](https://doi.org/10.4171/owr/2015/25)
## Literature review (che... | 3 | open | null | 2,015 | 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-13682-010",
"literature-status:open",
"owr-year:2015"
] | The Oberwolfach report explicitly says that the existence of this forgetful functor is unknown in general; later mixed-perverse results provide special cases but not the stated general construction. | [
{
"url": "https://doi.org/10.4171/owr/2015/25",
"label": "Oberwolfach report 25"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/25 | null | null | null | Does there exist a forgetful functor $\operatorname{For}:DS^{\mathrm{mix}}(X,F)\to DS^b(X,F)$ that makes $\operatorname{Perv}^{\mathrm{mix}}_S(X,F)$ a graded version of $\operatorname{Perv}_S(X,F)$? | Does there exist a forgetful functor For:DS^{mix}(X,F)\to DS^b(X,F) that makes Perv^{mix}_S(X,F) a graded version of Perv_S(X,F)? | 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 | Enveloping Algebras and Geometric Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/25, pp. 1385--1447 |
30,002,889 | OWR-13683-001 | Minimax Estimation of Queue Service-Time Distributions | What is the optimal achievable estimation accuracy, in minimax risk, for estimating the service-time distribution in the $M/G/\infty$ queue from queue-length observations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498](https://doi.org/10.4171/owr/2015/26)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,015 | 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-13683-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Rate-optimal nonparametric estimation has been established for several observation schemes and smoothness classes, including queue-length and arrival-departure data, but the broad question has no single universal accuracy statement without specifying the observation model and parameter class. | [
{
"url": "https://doi.org/10.1017/apr.2016.67",
"label": "Goldenshluger, Advances in Applied Probability"
},
{
"url": "https://doi.org/10.3150/17-BEJ936",
"label": "Goldenshluger, Bernoulli"
},
{
"url": "https://doi.org/10.1007/s11134-024-09921-2",
"label": "Adaptive minimax estimati... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/26 | null | null | null | What is the optimal achievable estimation accuracy, in minimax risk, for estimating the service-time distribution in the $M/G/\infty$ queue from queue-length observations? | What is the optimal achievable estimation accuracy, in minimax risk, for estimating the service-time distribution in the M/G/\infty queue from queue-length observations? | 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 | Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498 |
30,002,890 | OWR-13683-002 | Spectral Norms of Gaussian Matrices with Variance Profiles | Let $X$ be a symmetric Gaussian random matrix whose entries on and above the diagonal are independent and have prescribed variances $b_{ij}^2$. Determine or sharply bound its operator norm, especially the spectral edge, in terms of the variance profile. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498](https://doi.org/10.4171/owr/2015/26)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,015 | 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-13683-002",
"literature-status:partially-solved",
"owr-year:2015"
] | For the extracted structured Gaussian setting, sharp spectral-norm estimates are known; for random matrices in the broader sense, the question remains model-dependent and is not a single completely solved problem. | [
{
"url": "https://doi.org/10.1007/s00222-018-0817-x",
"label": "Latała--van Handel--Youssef, Inventiones Mathematicae"
},
{
"url": "https://doi.org/10.4171/owr/2015/26",
"label": "Oberwolfach report 26"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/26 | null | null | null | Let $X$ be a symmetric Gaussian random matrix whose entries on and above the diagonal are independent and have prescribed variances $b_{ij}^2$. Determine or sharply bound its operator norm, especially the spectral edge, in terms of the variance profile. | Let X be a symmetric Gaussian random matrix with independent entries and arbitrary prescribed variances b_{ij}^2. Determine or sharply bound its operator norm, especially the spectral edge, in terms of the variance pattern. | 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 | Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498 |
30,002,891 | OWR-13683-005 | Practical Confidence Regions for Matrix Estimation | Develop practical trace-norm confidence intervals and trace-norm certificates, characterize confidence intervals in other norms, and analyze alternative construction methods such as Bayesian and bootstrap procedures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498](https://doi.org/10.4171/owr/2015/26)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,015 | 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-13683-005",
"literature-status:partially-solved",
"owr-year:2015"
] | Later work supplies practical and nonasymptotic confidence regions in several trace or related norms, but the extracted list also asks for general certificates, other norms, and bootstrap or Bayesian constructions, so the whole agenda remains incomplete. | [
{
"url": "https://quantum-journal.org/papers/q-2022-10-20-844/",
"label": "Projected Least-Squares Quantum Process Tomography"
},
{
"url": "https://doi.org/10.1103/PhysRevLett.117.010404",
"label": "Faist--Renner, Physical Review Letters"
},
{
"url": "https://doi.org/10.4171/owr/2015/26"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/26 | null | null | null | Develop practical trace-norm confidence intervals and trace-norm certificates, characterize confidence intervals in other norms, and analyze alternative construction methods such as Bayesian and bootstrap procedures. | Develop practical trace-norm confidence intervals and trace-norm certificates, characterize confidence intervals in other norms, and analyze alternative construction methods such as Bayesian and bootstrap procedures. | 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 | Probabilistic Techniques in Modern Statistics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/26, pp. 1449--1498 |
30,002,892 | OWR-13684-002 | Existence of Time-Dependent Bivariational Quantum Dynamics | For the time-dependent bivariational initial-value problem used to approximate quantum dynamics, does an approximate trajectory exist, and under what mathematical conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Molecular Dynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/27, pp. 1499--1569](https://doi.org/10.4171/owr/2015/27)
## Literature review (checked ... | 3 | open | null | 2,015 | 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-13684-002",
"literature-status:open",
"owr-year:2015"
] | The source report states that the mathematical foundation of the time-dependent bivariational principle was not worked out, including existence of approximate dynamics; no general existence theorem resolving this formulation was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/27",
"label": "Oberwolfach report 27"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/27 | null | null | null | For the time-dependent bivariational initial-value problem used to approximate quantum dynamics, does an approximate trajectory exist, and under what mathematical conditions? | For the time-dependent bivariational initial-value problem used to approximate quantum dynamics, does an approximate trajectory exist, and under what mathematical conditions? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematical Methods in Quantum Molecular Dynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/27, pp. 1499--1569 |
30,002,893 | OWR-13685-001 | Regularity of Polynomial Laws in Free Probability | What regularity properties does the distribution $\mu_Y$ of $Y=P(X_1,\ldots,X_n)$ have under various assumptions on self-adjoint $X_1,\ldots,X_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629](https://doi.org/10.4171/owr/2015/28)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,015 | 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-13685-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Non-atomicity and other regularity properties of polynomial laws are proved under strong free-entropy-dimension hypotheses, while the report conjecture that finite free entropy is preserved for general polynomials remains unresolved. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0022123616300830",
"label": "Charlesworth--Shlyakhtenko, regularity of free polynomials"
},
{
"url": "https://arxiv.org/abs/1408.0580",
"label": "Regularity of Polynomials in Free Variables"
},
{
"url": "https://doi.org/10.4171... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/28 | null | null | null | What regularity properties does the distribution $\mu_Y$ of $Y=P(X_1,\ldots,X_n)$ have under various assumptions on self-adjoint $X_1,\ldots,X_n$? | What regularity properties does the distribution \mu_Y of Y=P(X_1,\ldots,X_n) have under various assumptions on self-adjoint X_1,\ldots,X_n? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629 |
30,002,894 | OWR-13685-002 | Eigenvalue Counts for Low-Degree Random Regular Graphs | Can the eigenvalue-counting estimate for uniformly random regular graphs be improved when $d\lesssim(\log n)^4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629](https://doi.org/10.4171/owr/2015/28)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,015 | 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-13685-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The logarithmic-degree threshold was substantially improved in fixed-large-degree random regular graphs by the local Kesten--McKay law, but the full optimal threshold question in the original regime is not settled by that result. | [
{
"url": "https://doi.org/10.1007/s00220-019-03345-3",
"label": "Bauerschmidt--Huang--Yau, Communications in Mathematical Physics"
},
{
"url": "https://arxiv.org/abs/1503.08702",
"label": "Local semicircle law for random regular graphs"
},
{
"url": "https://doi.org/10.4171/owr/2015/28",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/28 | null | null | null | Can the eigenvalue-counting estimate for uniformly random regular graphs be improved when $d\lesssim(\log n)^4$? | Can the eigenvalue-counting estimate for uniformly random regular graphs be improved when d\lesssim(\log n)^4? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629 |
30,002,895 | OWR-13685-004 | Small Singular Values of Matrix-Valued Free Functions | Can the small singular values of general matrix-valued functions $F(X_1,\ldots,X_m)$ be controlled? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629](https://doi.org/10.4171/owr/2015/28)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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-13685-004",
"literature-status:open",
"owr-year:2015"
] | Free-probability linearization and realization methods solve limiting spectral distributions for broad polynomial and rational classes, but general control of the smallest singular values for arbitrary matrix-valued functions remains an unresolved problem. | [
{
"url": "https://doi.org/10.1016/j.jfa.2017.10.003",
"label": "Helton--Mai--Speicher, Journal of Functional Analysis"
},
{
"url": "https://arxiv.org/abs/1408.1732",
"label": "Asymptotic Spectra of Matrix-Valued Functions"
},
{
"url": "https://doi.org/10.4171/owr/2015/28",
"label": "... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/28 | null | null | null | Can the small singular values of general matrix-valued functions $F(X_1,\ldots,X_m)$ be controlled? | Can the small singular values of general matrix-valued functions F(X_1,\ldots,X_m) be controlled? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629 |
30,002,896 | OWR-13685-005 | Coupling Markov Shifts to Bernoulli Shifts | Is each Markov shift $\rho(x_n)$ representable as a coupling to a Bernoulli shift? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629](https://doi.org/10.4171/owr/2015/28)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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-13685-005",
"literature-status:open",
"owr-year:2015"
] | The report presents the coupling of the specified nonsingular Markov shifts to Bernoulli shifts as an open problem; later work gives substantial classification and orbit-equivalence results but does not settle this general coupling assertion. | [
{
"url": "https://doi.org/10.4171/owr/2015/28",
"label": "Oberwolfach report 28"
},
{
"url": "https://arxiv.org/abs/1706.09483",
"label": "All properly ergodic Markov chains over a free group are orbit equivalent"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/28 | null | null | null | Is each Markov shift $\rho(x_n)$ representable as a coupling to a Bernoulli shift? | Is each Markov shift \rho(x_n) representable as a coupling to a Bernoulli shift? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629 |
30,002,897 | OWR-13685-006 | Generation of Tail Algebras by Diagonal Subalgebras | In free probability theory, let $(A, \phi)$ be a $W^*$-probability space generated by a sequence of random variables $(x_n)_{n \geq 1}$ with tail algebra $T_\phi = \bigcap_{n \geq 1} W^*(x_k : k \geq n)$ and exchangeable/distributional symmetry algebra $D_\phi$. Is the tail von Neumann algebra $T_\phi$ generated as a v... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629](https://doi.org/10.4171/owr/2015/28)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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-13685-006",
"literature-status:open",
"owr-year:2015"
] | The later report still lists generation of the von Neumann tail algebra T by D as an open question; related de Finetti and amalgamated-freeness theorems do not prove this generation statement. | [
{
"url": "https://doi.org/10.4171/owr/2015/28",
"label": "Oberwolfach report 28"
},
{
"url": "https://arxiv.org/abs/1305.7293",
"label": "Quantum symmetric states on free product C-star algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/28 | null | null | null | In free probability theory, let $(A, \phi)$ be a $W^*$-probability space generated by a sequence of random variables $(x_n)_{n \geq 1}$ with tail algebra $T_\phi = \bigcap_{n \geq 1} W^*(x_k : k \geq n)$ and exchangeable/distributional symmetry algebra $D_\phi$. Is the tail von Neumann algebra $T_\phi$ generated as a v... | Is the tail algebra T_\phi generated as a von Neumann algebra by D_\phi? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Free Probability Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/28, pp. 1571--1629 |
30,002,898 | OWR-13686-003 | Rigidity of Continuous Orbit Equivalence | For which topologically free actions of countable groups on compact spaces does continuous orbit equivalence imply conjugacy? In particular, which hypotheses beyond the known duality-group-versus-solvable-group criterion rule out the counterexamples that occur for higher-rank free abelian groups and nonabelian free gro... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,015 | 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-13686-003",
"literature-status:partially-solved",
"owr-year:2015"
] | Continuous orbit equivalence rigidity has positive and negative results for important classes, and semigroup versions are now characterized by groupoid methods, but no general reversal of the one-sided implication is known. | [
{
"url": "https://arxiv.org/abs/1503.01704",
"label": "Li, Continuous orbit equivalence rigidity"
},
{
"url": "https://doi.org/10.1007/s10114-023-2608-6",
"label": "Qiang--Hou, Acta Mathematica Sinica"
},
{
"url": "https://doi.org/10.4171/owr/2015/29",
"label": "Oberwolfach report 29... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | For which topologically free actions of countable groups on compact spaces does continuous orbit equivalence imply conjugacy? In particular, which hypotheses beyond the known duality-group-versus-solvable-group criterion rule out the counterexamples that occur for higher-rank free abelian groups and nonabelian free gro... | Does continuous orbit equivalence imply conjugacy for the relevant topologically free actions? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,899 | OWR-13686-006 | Helton's Sum-of-Squares Theorem for Low-Dimensional Group Rings | Does Helton's sum-of-squares theorem hold for group rings of groups of cohomological dimension at most two? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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-13686-006",
"literature-status:open",
"owr-year:2015"
] | The Helton-type sums-of-squares conjecture for group rings of all groups of cohomological dimension at most two is stated as a conjecture in the source, with only selected cases such as Z squared and free groups known. | [
{
"url": "https://doi.org/10.4171/owr/2015/29",
"label": "Oberwolfach report 29"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | Does Helton's sum-of-squares theorem hold for group rings of groups of cohomological dimension at most two? | Does Helton's sum-of-squares theorem hold for group rings of groups of cohomological dimension at most two? | 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 | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,900 | OWR-13686-007 | Injectivity of the Baum–Connes Assembly Map | For every discrete group $\Gamma$ and $i\in\{0,1\}$, is the Baum–Connes assembly map $\mu:K_i^\Gamma(E\Gamma)\to K_i(C_r^*(\Gamma))$ injective, where $E\Gamma$ is the universal space for proper $\Gamma$-actions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,015 | 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-13686-007",
"literature-status:partially-solved",
"owr-year:2015"
] | The Witt-space higher-signature construction and its cobordism and stratified-homotopy invariance are proved, and the underlying strong Novikov conjecture is known for many group classes, but the general assembly-map injectivity claim remains open. | [
{
"url": "https://arxiv.org/abs/1308.4744",
"label": "Weinberger--Yu, finite part of operator K-theory"
},
{
"url": "https://doi.org/10.4171/owr/2015/29",
"label": "Oberwolfach report 29"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | For every discrete group $\Gamma$ and $i\in\{0,1\}$, is the Baum–Connes assembly map $\mu:K_i^\Gamma(E\Gamma)\to K_i(C_r^*(\Gamma))$ injective, where $E\Gamma$ is the universal space for proper $\Gamma$-actions? | Is the Baum--Connes assembly map \mu:K_i^\Gamma(E\Gamma)\to K_i(C_r^*(\Gamma)) injective in the stated generality? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,901 | OWR-13686-008 | Finite-Order Projections outside the Assembly-Map Image | For a nonidentity finite-order element $g\in G$ of order $d$, set $p_g=d^{-1}\sum_{k=1}^d g^k\in\mathbb QG$. If $g_1,\ldots,g_n$ have distinct finite orders, do $[p_{g_1}],\ldots,[p_{g_n}]$ generate a rank-$n$ subgroup of the finite part of $K_0(C^*(G))$, every nonzero element of which lies outside the assembly-map ima... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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-13686-008",
"literature-status:open",
"owr-year:2015"
] | The finite-part K-theory conjecture is proved for broad classes such as finitely embeddable groups, but the report and subsequent literature do not establish its general validity for arbitrary groups. | [
{
"url": "https://msp.org/gt/2015/19-5/gt-v19-n5-p08-p.pdf",
"label": "Weinberger--Yu, Geometry and Topology"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.11.030",
"label": "Higher rho invariants and the finite-part conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2015/29",
"l... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | For a nonidentity finite-order element $g\in G$ of order $d$, set $p_g=d^{-1}\sum_{k=1}^d g^k\in\mathbb QG$. If $g_1,\ldots,g_n$ have distinct finite orders, do $[p_{g_1}],\ldots,[p_{g_n}]$ generate a rank-$n$ subgroup of the finite part of $K_0(C^*(G))$, every nonzero element of which lies outside the assembly-map ima... | For nontrivial elements g_1,\ldots,g_n\in G of distinct finite orders, do [p_{g_1}],\ldots,[p_{g_n}] generate a rank-n subgroup of K_0^{\mathrm{fin}}(C^*(G)), with every nonzero element outside the assembly-map image? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,902 | OWR-13686-009 | Lower Bounds for Reduced Structure Groups | Let $M$ be a compact oriented manifold of dimension $4k-1$ with $k>1$ and fundamental group $G$. Is $\operatorname{rank}\widetilde{\mathcal S}(M)\geq N_{\mathrm{fin}}(G)$, where $\widetilde{\mathcal S}(M)$ is the structure group modulo classes induced by orientation-preserving self-homotopy equivalences and $N_{\mathrm... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,015 | 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... | [
"OWR-13686-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13686-009",
"literature-status:open",
"owr-year:2015"
] | The rank lower bound for reduced structure groups is proved under additional residual-finiteness and torsion hypotheses, but its general validity and the claim that the detected elements represent distinct manifolds remain conjectural. | [
{
"url": "https://msp.org/gt/2015/19-5/gt-v19-n5-p08-p.pdf",
"label": "Weinberger--Yu, Geometry and Topology"
},
{
"url": "https://doi.org/10.4171/owr/2015/29",
"label": "Oberwolfach report 29"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | Let $M$ be a compact oriented manifold of dimension $4k-1$ with $k>1$ and fundamental group $G$. Is $\operatorname{rank}\widetilde{\mathcal S}(M)\geq N_{\mathrm{fin}}(G)$, where $\widetilde{\mathcal S}(M)$ is the structure group modulo classes induced by orientation-preserving self-homotopy equivalences and $N_{\mathrm... | Are the elements of the structure group distinguished by this method actually represented by different manifolds? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,903 | OWR-13686-010 | Duplicate Reduced-Structure-Group Lower Bound | If M is compact oriented of dimension 4k-1 with k>1 and \pi_1(M)=G, is \operatorname{rank}\widetilde S(M)\ge N_{\mathrm{fin}}(G)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700](https://doi.org/10.4171/owr/2015/29)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,015 | 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/merged OWR extraction (This extraction repeats the reduced-structure-group rank conjecture represented canonically and with definitions by OWR-13686-009. No separa) | [
"OWR-13686-009"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13686-010",
"literature-status:partially-solved",
"owr-year:2015"
] | The conjectured lower bound is proved under the stated residually finite quotient with torsion-free kernel, while the general conjecture remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2015/29",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.2140/gt.2015.19.2767",
"label": "Weinberger and Yu primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/29 | null | null | null | null | If M is compact oriented of dimension 4k-1 with k>1 and \pi_1(M)=G, is \operatorname{rank}\widetilde S(M)\ge N_{\mathrm{fin}}(G)? | unrecoverable | This extraction repeats the reduced-structure-group rank conjecture represented canonically and with definitions by OWR-13686-009. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Noncommutative Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/29, pp. 1631--1700 |
30,002,904 | OWR-13687-003 | Generic Infinite Index Subgroups of Integral Special Linear Groups | For $G=\mathrm{SL}_n(\mathbb{Z})$ and $B_X=\{g\in G:\lVert g\rVert\leq X\}$, does the probability that $\langle g_1,g_2\rangle$ has infinite index tend to 1 as $X\to\infty$ when $g_1,g_2$ are chosen uniformly from $B_X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | partially_solved | null | 2,015 | 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-13687-003",
"literature-status:partially-solved",
"owr-year:2015"
] | Generic thin free groups are proved in a symmetrized Euclidean-ball model, but the ordinary Euclidean-ball question recorded here is not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
},
{
"url": "https://academic.oup.com/imrn/article/2017/17/5385/3056825",
"label": "Fuchs and Rivin primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | For $G=\mathrm{SL}_n(\mathbb{Z})$ and $B_X=\{g\in G:\lVert g\rVert\leq X\}$, does the probability that $\langle g_1,g_2\rangle$ has infinite index tend to 1 as $X\to\infty$ when $g_1,g_2$ are chosen uniformly from $B_X$? | For G=\mathrm{SL}_n(\mathbb Z) and B_X=\{g\in G:\|g\|\le X\}, does the probability that \langle g_1,g_2\rangle has infinite index tend to 1 as X\to\infty when g_1,g_2 are chosen uniformly from B_X? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,905 | OWR-13687-004 | Minimal Dilatations of Pseudo-Anosov Maps | What are the exact values and qualitative properties of pseudo-Anosov maps realizing the minimal length $\ell_g$, or more generally with $\log\lambda(f)\asymp g^{-1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | open | null | 2,015 | 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-13687-004",
"literature-status:open",
"owr-year:2015"
] | Exact minimum pseudo-Anosov dilatations are known in low genus and bounded in further ranges, but no general formula or complete determination is established. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.5802/aif.2599",
"label": "Lanneau and Thiffeault primary paper"
},
{
"url": "https://arxiv.org/abs/1409.6983",
"label": "Agol Leininger and Margalit primary paper"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | What are the exact values and qualitative properties of pseudo-Anosov maps realizing the minimal length $\ell_g$, or more generally with $\log\lambda(f)\asymp g^{-1}$? | What are the exact values and qualitative properties of pseudo-Anosov maps realizing the minimal length \ell_g, or more generally with \log\lambda(f)\asymp g^{-1}? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,906 | OWR-13687-005 | Cohomological Purity for Finite Index Mapping Class Subgroups | For sufficiently natural finite-index subgroups $\Delta_g<\Gamma_g$, is $H^k(M_{\Delta_g})\to H^k(\Delta_g)$ onto for $g\gg 0$, equivalently is $H^k(\Delta_g)$ pure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | open | null | 2,015 | 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-13687-005",
"literature-status:open",
"owr-year:2015"
] | The extracted homological purity question is not accompanied by a later theorem that settles it, and the available record leaves it unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | For sufficiently natural finite-index subgroups $\Delta_g<\Gamma_g$, is $H^k(M_{\Delta_g})\to H^k(\Delta_g)$ onto for $g\gg 0$, equivalently is $H^k(\Delta_g)$ pure? | For sufficiently natural finite-index subgroups \Delta_g<\Gamma_g, is H^k(M_{\Delta_g})\to H^k(\Delta_g) onto for g\gg0, equivalently is H^k(\Delta_g) pure? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,907 | OWR-13687-006 | Invariant Prym Homology and Arithmetic Monodromy | Let $S_K\to S_{g,n}$ be the finite Galois cover defined by a mapping-class-invariant finite-index subgroup $K\subset\pi_1(S_{g,n})$, let $H_K=H_1(\overline{S}_K;\mathbb{Q})$, let $N_K$ be the group of lifted mapping classes, and let $\mathcal G_K$ be the Zariski closure of its monodromy representation $\rho$. For $g\ge... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | open | null | 2,015 | 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-13687-006",
"literature-status:open",
"owr-year:2015"
] | The extracted record asks unresolved questions about the higher Prym homology and arithmetic image; its abbreviated notation does not support a stronger classification. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | Let $S_K\to S_{g,n}$ be the finite Galois cover defined by a mapping-class-invariant finite-index subgroup $K\subset\pi_1(S_{g,n})$, let $H_K=H_1(\overline{S}_K;\mathbb{Q})$, let $N_K$ be the group of lifted mapping classes, and let $\mathcal G_K$ be the Zariski closure of its monodromy representation $\rho$. For $g\ge... | For g\ge3, is H_K^{G_K^\circ}=0, and is \rho(N_K) arithmetic in G_K? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,908 | OWR-13687-007 | Nontrivial Actions on Invariant Prym Homology | In the Prym-homology setting, let $\mathcal D_K$ be the connected normal subgroup generated by the one-parameter subgroups arising from lifted Dehn twists. Are there examples with $H_K^{\mathcal D_K}\neq0$ on which $\mathcal G_K^\circ/\mathcal D_K$ acts nontrivially? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | open | null | 2,015 | 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-13687-007",
"literature-status:open",
"owr-year:2015"
] | The extracted request for examples with nonzero homology and nontrivial action is unresolved in the cited record, with no verified complete answer located. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | In the Prym-homology setting, let $\mathcal D_K$ be the connected normal subgroup generated by the one-parameter subgroups arising from lifted Dehn twists. Are there examples with $H_K^{\mathcal D_K}\neq0$ on which $\mathcal G_K^\circ/\mathcal D_K$ acts nontrivially? | Do there exist examples with H_K^{D_K}\ne0 on which G_K^\circ/D_K acts nontrivially? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,909 | OWR-13687-008 | Virtual Surjectivity and Generalized Torelli Kernels | For a finite quotient $p:\pi_1(\Sigma_g)\twoheadrightarrow H$, is the induced Prym representation $\rho_{H,p}$ virtually surjective onto every component of the centralizer of $H$ in the relevant symplectic group? Are the kernels of these representations, viewed as generalized Torelli groups, finitely generated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | open | null | 2,015 | 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-13687-008",
"literature-status:open",
"owr-year:2015"
] | The general virtual-surjectivity question for the representations indexed by arbitrary subgroups and primes remains open, even though related Ivanov-type consequences have seen progress. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s40879-023-00637-w",
"label": "current survey of the Putman Wieland problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | For a finite quotient $p:\pi_1(\Sigma_g)\twoheadrightarrow H$, is the induced Prym representation $\rho_{H,p}$ virtually surjective onto every component of the centralizer of $H$ in the relevant symplectic group? Are the kernels of these representations, viewed as generalized Torelli groups, finitely generated? | Is \rho_{H,p} virtually surjective onto each component of the indicated centralizer for arbitrary H,p, and are the associated generalized Torelli kernels finitely generated? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,910 | OWR-13687-009 | Counting Hyperbolic Manifolds with Fixed Cusp Number | What is known about $\rho_n^c(V)$, the number of complete hyperbolic n-manifolds with exactly $c>0$ cusps and volume less than V? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | partially_solved | null | 2,015 | 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-13687-009",
"literature-status:partially-solved",
"owr-year:2015"
] | The four-dimensional fixed-cusp counting function is established to have growth of the form C to the power of V log V, but a complete general-dimensional description remains unavailable. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00039-013-0247-2",
"label": "Kolpakov and Martelli primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | What is known about $\rho_n^c(V)$, the number of complete hyperbolic n-manifolds with exactly $c>0$ cusps and volume less than V? | What is known about \rho_n^c(V), the number of complete hyperbolic n-manifolds with exactly c>0 cusps and volume less than V? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,911 | OWR-13687-010 | Generic Uniqueness for Skein-Algebra Representations | Let $A$ be a primitive $2N$-th root of unity with $N$ odd. Is there a Zariski-dense open subset of the $\mathrm{SL}_2(\mathbb{C})$ character variety of a surface on which an irreducible finite-dimensional representation of its Kauffman bracket skein algebra is uniquely determined by its classical shadow and compatible ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746](https://d... | 3 | solved | null | 2,015 | 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/10.1007/s00222-018-0833-x",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. H. Wong (joint with F. Bonahon; OWR 30/2015, p. 1742) conjectures that, for A a primitive 2N-th root of unity with N odd, irreducible finite-dimensional representations of the Kauffman bracket skein algebra are determined by their classical shadow and punc... | [
"owr",
"oberwolfach-reports",
"OWR-13687-010",
"literature-status:open",
"owr-year:2015"
] | The generic one-to-one correspondence conjecture for the quantum character data is still stated as a conjecture; the cited classification results do not prove it. | [
{
"url": "https://doi.org/10.4171/owr/2015/30",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/math/0407086",
"label": "Bonahon and Liu primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/30 | null | null | null | Let $A$ be a primitive $2N$-th root of unity with $N$ odd. Is there a Zariski-dense open subset of the $\mathrm{SL}_2(\mathbb{C})$ character variety of a surface on which an irreducible finite-dimensional representation of its Kauffman bracket skein algebra is uniquely determined by its classical shadow and compatible ... | Is the correspondence in Theorems 1 and 2 one-to-one on a Zariski-dense open subset of the \mathrm{SL}_2(\mathbb C) character variety? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | New Perspectives on the Interplay between Discrete Groups in Low-Dimensional Topology and Arithmetic Lattices (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/30, pp. 1701--1746 |
30,002,912 | OWR-13852-001 | Numerical Criterion for Deformed Hermitian–Yang–Mills Metrics | For a holomorphic line bundle $L$ over a compact Kähler manifold $X$, does the deformed Hermitian–Yang–Mills equation admit a solution if and only if every irreducible holomorphic subvariety $V\subset X$ satisfies $\operatorname{Arg}\left(\int_V e^{-i\omega}\operatorname{ch}(L)\right)>-\operatorname{Arg}\left(\int_X e^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807](https://doi.org/10.4171/owr/2015/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 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-13852-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13852-001",
"literature-status:partially-solved",
"owr-year:2015"
] | The dHYM existence criterion is verified on surfaces and under important additional hypotheses, but the full compact Kahler higher-dimensional conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2015/31",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4310/CJM.2020.V8.N2.A4",
"label": "Collins Jacob and Yau primary paper"
},
{
"url": "https://arxiv.org/abs/2201.01438",
"label": "Lin primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/31 | null | null | null | For a holomorphic line bundle $L$ over a compact Kähler manifold $X$, does the deformed Hermitian–Yang–Mills equation admit a solution if and only if every irreducible holomorphic subvariety $V\subset X$ satisfies $\operatorname{Arg}\left(\int_V e^{-i\omega}\operatorname{ch}(L)\right)>-\operatorname{Arg}\left(\int_X e^... | For a holomorphic line bundle L over a compact Kähler manifold X, does the deformed Hermitian--Yang--Mills equation admit a solution if and only if every irreducible holomorphic subvariety V\subset X satisfies \operatorname{Arg}\left(\int_V e^{-i\omega}\operatorname{ch}(L)\right)>-\operatorname{Arg}\left(\int_X e^{-i\o... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807 |
30,002,913 | OWR-13852-002 | Duplicate Deformed Hermitian–Yang–Mills Stability Criterion | For a holomorphic line bundle L over a compact Kähler manifold X, does the deformed Hermitian--Yang--Mills equation admit a solution if and only if every irreducible holomorphic subvariety V\subset X satisfies \operatorname{Arg}\left(\int_V e^{-i\omega}\operatorname{ch}(L)\right)>-\operatorname{Arg}\left(\int_X e^{-i\o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807](https://doi.org/10.4171/owr/2015/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 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 contains one numerical subvariety criterion for solvability of the deformed Hermitian–Yang–Mills equation, represented c) | [
"OWR-13852-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13852-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The dHYM conjecture is proved in the surface case and several supercritical or stability regimes, but its stated general higher-dimensional equivalence is open. | [
{
"url": "https://doi.org/10.4171/owr/2015/31",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4310/CJM.2020.V8.N2.A4",
"label": "Collins Jacob and Yau primary paper"
},
{
"url": "https://arxiv.org/abs/2201.01438",
"label": "Lin primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/31 | null | null | null | null | For a holomorphic line bundle L over a compact Kähler manifold X, does the deformed Hermitian--Yang--Mills equation admit a solution if and only if every irreducible holomorphic subvariety V\subset X satisfies \operatorname{Arg}\left(\int_V e^{-i\omega}\operatorname{ch}(L)\right)>-\operatorname{Arg}\left(\int_X e^{-i\o... | unrecoverable | The official report contains one numerical subvariety criterion for solvability of the deformed Hermitian–Yang–Mills equation, represented canonically by OWR-13852-001. This record repeats it verbatim. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807 |
30,002,914 | OWR-13852-004 | Smoothing and Deforming Metric Cones by Ricci Expanders | Which metric cones can be smoothed by gradient Ricci expanders, can conical gradient Ricci expanders be deformed implicitly, and are such deformations globally unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807](https://doi.org/10.4171/owr/2015/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 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-13852-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Implicit deformation and unique-continuation results are proved for important conical Ricci expander classes, while global uniqueness and unrestricted deformation remain open. | [
{
"url": "https://doi.org/10.4171/owr/2015/31",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1093/imrn/rnw110",
"label": "Deruelle primary paper"
},
{
"url": "https://arxiv.org/abs/1607.03546",
"label": "Conlon and Deruelle primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/31 | null | null | null | Which metric cones can be smoothed by gradient Ricci expanders, can conical gradient Ricci expanders be deformed implicitly, and are such deformations globally unique? | Which metric cones can be smoothed by gradient Ricci expanders, can conical gradient Ricci expanders be deformed implicitly, and are such deformations globally unique? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807 |
30,002,915 | OWR-13852-005 | Cross-Report Duplicate of the Normal Mod-Two Current Question | Is every normal mod-2 current equivalent to a normal integral current? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807](https://doi.org/10.4171/owr/2015/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 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 | Duplicate/merged OWR extraction (This report repeats exactly the normal mod-two current question already represented by the earlier OWR-13103-005 record from Oberwolfach Rep) | [
"OWR-13103-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13852-005",
"literature-status:open",
"owr-year:2015"
] | The mod-2 versus integral normal-current equivalence question remains an open geometric measure theory problem; later filling-volume work does not settle the stated equivalence. | [
{
"url": "https://doi.org/10.4171/owr/2015/31",
"label": "original Oberwolfach report"
},
{
"url": "https://aif.centre-mersenne.org/articles/10.5802/aif.3610/",
"label": "2024 primary paper on real and integral filling volumes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/31 | null | null | null | null | Is every normal mod-2 current equivalent to a normal integral current? | unrecoverable | This report repeats exactly the normal mod-two current question already represented by the earlier OWR-13103-005 record from Oberwolfach Report 2014/33. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807 |
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