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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,216 | OWR-17135-007 | Generalized Baues Problem for Hypersimplicial Subdivisions | For the cyclic polytope $C_{n,d}$ and a hypersimplicial parameter $k$, does the poset of hypersimplicial subdivisions have the homotopy type of $S^{n-d-2}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 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-17135-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The generalized Baues question is solved for convex polygons and for k equals 1, but the full cyclic-polytope hypersimplicial problem remains open. | [
{
"url": "https://doi.org/10.1007/s00029-021-00722-6",
"label": "Olarte and Santos, hypersimplicial subdivisions"
},
{
"url": "https://doi.org/10.1006/eujc.1999.0321",
"label": "Rambau and Santos, generalized Baues problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For the cyclic polytope $C_{n,d}$ and a hypersimplicial parameter $k$, does the poset of hypersimplicial subdivisions have the homotopy type of $S^{n-d-2}$? | For cyclic polytopes C_{n,d} and hypersimplicial parameter k, does the poset of hypersimplicial subdivisions have the homotopy type of S^{n-d-2}? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,217 | OWR-17135-008 | Lifting Hypersimplicial Subdivisions to Zonotopal Tilings | For which triples $(n,d,k)$ does every hypersimplicial subdivision of the cyclic polytope $C_{n,d}$ extend to a zonotopal tiling of the cyclic zonotope $Z(C_{n,d})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 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-17135-008",
"literature-status:partially-solved",
"owr-year:2019"
] | Non-liftability is proved for every odd cyclic-polytope dimension, while the requested classification of parameters and the remaining even-dimensional cases is not complete. | [
{
"url": "https://doi.org/10.1007/s00029-021-00722-6",
"label": "Olarte and Santos, hypersimplicial subdivisions"
},
{
"url": "https://arxiv.org/abs/1906.05764",
"label": "Olarte and Santos, primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For which triples $(n,d,k)$ does every hypersimplicial subdivision of the cyclic polytope $C_{n,d}$ extend to a zonotopal tiling of the cyclic zonotope $Z(C_{n,d})$? | For which parameters (n,d,k) does every hypersimplicial subdivision of C_{n,d} extend to a zonotopal tiling of the cyclic zonotope Z(C_{n,d})? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,218 | OWR-17135-009 | Regular Ball Decompositions of Totally Nonnegative Fibers | Are the natural cell decompositions of every fiber of the maps to totally nonnegative spaces regular CW complexes homeomorphic to closed balls? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-009",
"literature-status:open",
"owr-year:2019"
] | The fibers have cell stratifications with contractible interior dual block posets, but the stronger assertion that the decompositions are regular CW complexes homeomorphic to closed balls remains a conjecture. | [
{
"url": "https://arxiv.org/abs/1903.01420",
"label": "Davis, Hersh, and Miller, fibers of maps"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, fiber conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Are the natural cell decompositions of every fiber of the maps to totally nonnegative spaces regular CW complexes homeomorphic to closed balls? | For every fiber of the maps to totally nonnegative spaces, are the stated cell decompositions regular CW complexes homeomorphic to closed balls? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,219 | OWR-17135-010 | Matroid Structure and Hyperpaths in Collapsible Hypertrees | Do collapsible $d$-dimensional hypertrees admit a useful matroidal structure, and is there a satisfactory higher-dimensional analogue of a path for them? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-010",
"literature-status:open",
"owr-year:2019"
] | Sum complexes supply infinite collapsible and non-collapsible families, but the broader matroid-like behavior of collapsible hypertrees and a satisfactory d-hyperpath theory remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, hypertrees"
},
{
"url": "https://doi.org/10.1007/s00454-021-00360-x",
"label": "Dahari and Linial, hyperpaths"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Do collapsible $d$-dimensional hypertrees admit a useful matroidal structure, and is there a satisfactory higher-dimensional analogue of a path for them? | Do collapsible d-trees exhibit useful matroid-like behavior, and is there a satisfactory notion of a d-hyperpath? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,220 | OWR-17135-011 | Cocircuit Graph Diameter Conjecture for Oriented Matroids | If $M$ is an oriented matroid of rank $r$ on $n$ elements, must the diameter of its cocircuit graph satisfy $$\operatorname{diam}(G^*(M))\leq n-r+2$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-011",
"literature-status:open",
"owr-year:2019"
] | The n minus r plus 2 cocircuit-diameter conjecture remains open; low rank, low corank, and small ground-set cases are proved, together with quadratic general bounds. | [
{
"url": "https://doi.org/10.37236/9653",
"label": "Adler, De Loera, Klee, and Zhang, cocircuit diameters"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, oriented matroids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | If $M$ is an oriented matroid of rank $r$ on $n$ elements, must the diameter of its cocircuit graph satisfy $$\operatorname{diam}(G^*(M))\leq n-r+2$$? | If M is an oriented matroid of rank r on n elements, must \operatorname{diam}(G^*(M))\le n-r+2? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,221 | OWR-17135-013 | Clasp Formula for Local Intersection Numbers | Let $V=\mathbb C^n$, let $\lambda$ be dominant, and let $\mu$ be a weight of $\Lambda^kV$ such that $\lambda+\mu$ is dominant. If $\kappa_{\lambda,\mu}$ is the resulting one-dimensional local intersection form, is $$\kappa_{\lambda,\mu}=\prod_\alpha\frac{\langle\lambda+\rho,\alpha\rangle}{\langle\lambda+\rho+\mu,\alpha... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-013",
"literature-status:open",
"owr-year:2019"
] | The cited quadratic bound and counterexamples to stronger variants do not settle the main n minus r plus 2 conjecture, which remains open. | [
{
"url": "https://doi.org/10.37236/9653",
"label": "Adler, De Loera, Klee, and Zhang, cocircuit diameters"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, oriented matroids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $V=\mathbb C^n$, let $\lambda$ be dominant, and let $\mu$ be a weight of $\Lambda^kV$ such that $\lambda+\mu$ is dominant. If $\kappa_{\lambda,\mu}$ is the resulting one-dimensional local intersection form, is $$\kappa_{\lambda,\mu}=\prod_\alpha\frac{\langle\lambda+\rho,\alpha\rangle}{\langle\lambda+\rho+\mu,\alpha... | For V=\mathbb C^n, dominant \lambda, and a weight \mu of \Lambda^kV with \lambda+\mu dominant, does the local-intersection number satisfy \kappa_{\lambda,\mu}=\prod_{\alpha}\frac{\langle\lambda+\rho,\alpha\rangle}{\langle\lambda+\rho+\mu,\alpha\rangle}, where the product is over positive roots for which the denominator... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,222 | OWR-17135-015 | Combinatorial Explanation of the Clasp Conjecture | Give a combinatorial explanation of the product formula for the one-dimensional local intersection forms in the clasp conjecture for tensor products $L_\lambda\otimes\Lambda^k\mathbb C^n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-015",
"literature-status:open",
"owr-year:2019"
] | Elias's primary paper proves the product formula only for n\leq4 and states it as a conjecture for general n; later work gives evidence but no general combinatorial proof. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Give a combinatorial explanation of the product formula for the one-dimensional local intersection forms in the clasp conjecture for tensor products $L_\lambda\otimes\Lambda^k\mathbb C^n$. | Can one give a combinatorial explanation of the Clasp Conjecture formula for these local intersection forms? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,223 | OWR-17135-016 | Qualitative Differences Among Polytope and Sphere Face Vectors | For $d\geq4$, identify qualitative differences between the $f$-vectors of simplicial and general $d$-polytopes, and between the flag $f$-vectors of $d$-polytopes and regular CW $(d-1)$-spheres. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-016",
"literature-status:open",
"owr-year:2019"
] | The g-theorem completely describes simplicial f-vectors, but qualitative separation from general and flag f-vector sets remains unresolved; the 4-polytope f-vector set is still not characterized. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1711.01864",
"label": "Sjoeberg and Ziegler"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For $d\geq4$, identify qualitative differences between the $f$-vectors of simplicial and general $d$-polytopes, and between the flag $f$-vectors of $d$-polytopes and regular CW $(d-1)$-spheres. | For d\ge4, are there qualitative differences between the f-vectors of simplicial and general d-polytopes, and between flag f-vectors of d-polytopes and regular CW (d-1)-spheres? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,224 | OWR-17135-017 | Convex Geometry of General Polytope Face Vectors | For $d\geq4$, is $$\operatorname{Conv}(f(\mathcal P^d))=\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$$? Is this cone finitely generated, are its rays dense, and which polytopes determine its boundary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-017",
"literature-status:open",
"owr-year:2019"
] | The report leaves the convex-hull, finite-generation, density, and boundary questions open for general d\geq4; later work gives additive structure but not these equalities. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1515/advgeom-2018-0025",
"label": "Ziegler on f-vectors"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For $d\geq4$, is $$\operatorname{Conv}(f(\mathcal P^d))=\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$$? Is this cone finitely generated, are its rays dense, and which polytopes determine its boundary? | For d\ge4, is \operatorname{Conv}(f(\mathcal P^d))=\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d)); is this cone finitely generated; are the corresponding rays dense; and which polytopes lie on its boundaries? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,225 | OWR-17135-018 | Limit Rays and Fatness of Polytope Face Vector Cones | For $d>4$, is every ray of $\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$ a limit ray? In dimension $4$, is the fatness ratio $$(f_1+f_4)/(f_0+f_3)$$ bounded above by an absolute constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-018",
"literature-status:open",
"owr-year:2019"
] | Known d=4 ray-limit and fatness bounds do not settle the requested cone description or finite-generation question, and the corresponding higher-dimensional questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/math/0407042",
"label": "Projected products and fatness"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For $d>4$, is every ray of $\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$ a limit ray? In dimension $4$, is the fatness ratio $$(f_1+f_4)/(f_0+f_3)$$ bounded above by an absolute constant? | For d>4, are all rays in \operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d)) limit rays, and in dimension 4 is the fatness parameter (f_1+f_4)/(f_0+f_3) bounded above by a constant? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,226 | OWR-17135-019 | Computational Recognition of Polytope Face Vectors and Cones | For fixed $d$, can membership in $f(\mathcal P^d)$ be decided in time polynomial in the binary encoding length of the input vector? Is it decidable whether a hyperplane through $f(\sigma^d)$ supports $\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$ or contains an interior ray? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-019",
"literature-status:open",
"owr-year:2019"
] | Membership for simplicial polytopes is polynomial-time and general membership is decidable, but the requested polynomial bound for general polytopes and the cone-recognition decidability question remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For fixed $d$, can membership in $f(\mathcal P^d)$ be decided in time polynomial in the binary encoding length of the input vector? Is it decidable whether a hyperplane through $f(\sigma^d)$ supports $\operatorname{Cone}_{f(\sigma^d)}(f(\mathcal P^d))$ or contains an interior ray? | Can membership v\in f(\mathcal P^d) be decided in polynomial time in the binary encoding length of v, and is it decidable whether a hyperplane through f(\sigma^d) supports the associated cone or contains an interior ray? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,227 | OWR-17135-022 | Topology Algorithms and Curvature of Tropical Bisectors | Determine the topology of tropical bisectors of $k$ points in every dimension $d$, improve the expected $O(nd\log n)$ construction algorithm when possible, and define a useful tropical curvature for arbitrary polygonal space curves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-022",
"literature-status:open",
"owr-year:2019"
] | The cited work gives results for k=2 and k=3 and examples for k=4, but the all-k,d topology, algorithmic, and curvature questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s10208-021-09538-4",
"label": "Criado, Joswig, and Santos"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Determine the topology of tropical bisectors of $k$ points in every dimension $d$, improve the expected $O(nd\log n)$ construction algorithm when possible, and define a useful tropical curvature for arbitrary polygonal space curves. | What is the topological structure of tropical bisectors of k points in all dimensions d, can the expected O(nd\log n) algorithm be improved, and what is a suitable notion of tropical curvature for arbitrary polygonal space curves? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,228 | OWR-17135-023 | Equivariant Pancake Partitions of Spheres | Let $n>k\geq1$, let $p$ be an odd prime, and let $\mathbb Z/p$ act freely and orientation-preservingly on $S^n$. Suppose $c:\operatorname{CO}(S^n)\to S^n$ is a center map, $V$ is a real $k$-dimensional $\mathbb Z/p$-representation with $$e(V)\notin\operatorname{Index}_{\mathbb Z/p}(SO(n+1);\mathbb F_p),$$ and $f:S^n\to... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-023",
"literature-status:open",
"owr-year:2019"
] | The report presents the stronger p-adic Gromov--Borsuk--Ulam statement as a theorem being sought; no primary proof or disproof of that exact statement was found. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $n>k\geq1$, let $p$ be an odd prime, and let $\mathbb Z/p$ act freely and orientation-preservingly on $S^n$. Suppose $c:\operatorname{CO}(S^n)\to S^n$ is a center map, $V$ is a real $k$-dimensional $\mathbb Z/p$-representation with $$e(V)\notin\operatorname{Index}_{\mathbb Z/p}(SO(n+1);\mathbb F_p),$$ and $f:S^n\to... | For n>k\ge1 and odd prime p, with a free orientation-preserving \mathbb Z/p-action on S^n, a center map c:CO(S^n)\to S^n, a real \mathbb Z/p-representation V of dimension k satisfying e(V)\notin\operatorname{Index}_{\mathbb Z/p}(SO(n+1);\mathbb F_p), and an equivariant f:S^n\to V, does every \varepsilon>0 admit, for al... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,229 | OWR-17135-024 | Decidability of Piecewise Linear Complex Embeddings | For fixed positive integers $k\leq d$ and a finite $k$-dimensional simplicial complex $K$, decide whether $K$ admits a piecewise-linear embedding into $\mathbb R^d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 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-17135-024",
"literature-status:partially-solved",
"owr-year:2019"
] | The problem is polynomial-time decidable in the metastable range and undecidable for many pairs outside it, but current work still leaves intermediate dimension ranges unresolved. | [
{
"url": "https://doi.org/10.1137/1.9781611975994.47",
"label": "Filakovsky, Wagner, and Zhechev"
},
{
"url": "https://academic.oup.com/imrn/article/2024/17/12433/7728827",
"label": "Current embeddability classification"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For fixed positive integers $k\leq d$ and a finite $k$-dimensional simplicial complex $K$, decide whether $K$ admits a piecewise-linear embedding into $\mathbb R^d$. | Given fixed positive integers k\le d and a finite k-dimensional simplicial complex K, is there a piecewise-linear embedding of K into \mathbb R^d? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,230 | OWR-17135-027 | Cubical Facet Counts and Nonintersecting Spatial Triangles | Let $C(d,n)$ be the maximum number of facets of a cubical $d$-polytope with $n$ vertices. Is $C(d,n)=o(n^2)$ for every fixed $d$? Separately, let $t(n)$ be the maximum number of triangles with vertices in an $n$-point subset of $\mathbb R^3$ such that two triangles meet only in a common vertex or are disjoint. Determin... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-027",
"literature-status:open",
"owr-year:2019"
] | Only broad upper and lower bounds are known for C(d,n) and t(n); the requested asymptotics, including t(n)=o(n^2), remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/math/9908005",
"label": "Neighborly cubical polytopes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $C(d,n)$ be the maximum number of facets of a cubical $d$-polytope with $n$ vertices. Is $C(d,n)=o(n^2)$ for every fixed $d$? Separately, let $t(n)$ be the maximum number of triangles with vertices in an $n$-point subset of $\mathbb R^3$ such that two triangles meet only in a common vertex or are disjoint. Determin... | Let C(d,n) be the maximum number of facets of a cubical d-polytope with n vertices, and let t(n) be the maximum number of triangles in R^3 with vertices in an n-point set such that any two triangles intersect only in a common vertex or not at all. Determine the growth of C(d,n) and t(n); in particular, is C(d,n)=o(n^2)... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,231 | OWR-17135-028 | Shellability and Homology of Totally Mixed Face Posets | Let $P_1,P_2\subset\mathbb R^n$. A face $F=F_1+F_2$ of $P_1+P_2$ is totally mixed if $F_i\subset P_i$, $\dim F_i>0$, and $\dim F=\dim F_1+\dim F_2$. Is the poset of totally mixed faces shellable, and does its geometric realization have the rational homology of a wedge of $(n-2)$-spheres? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-028",
"literature-status:open",
"owr-year:2019"
] | Results on mixed-face counts do not establish shellability or the claimed rational wedge-of-spheres homology for this totally mixed-face poset. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1607.00347",
"label": "Mixed subdivisions and faces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $P_1,P_2\subset\mathbb R^n$. A face $F=F_1+F_2$ of $P_1+P_2$ is totally mixed if $F_i\subset P_i$, $\dim F_i>0$, and $\dim F=\dim F_1+\dim F_2$. Is the poset of totally mixed faces shellable, and does its geometric realization have the rational homology of a wedge of $(n-2)$-spheres? | For polytopes P_1,P_2\subset\mathbb{R}^n, call a face F=F_1+F_2 of P_1+P_2 totally mixed if F_i\subset P_i, dim(F_i)>0, and dim(F)=dim(F_1)+dim(F_2). Is the poset of totally mixed faces shellable, and does its geometric realization have the rational homology of a wedge of (n-2)-spheres? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,232 | OWR-17135-030 | Symmetric Function Bases for Bipartite Determinant Inequalities | Let $G$ be bipartite with parts $X=[n]$ and $Y$, and set $X_S=|\{y\in Y:N(y)=S\}|$ for every nonempty $S\subseteq[n]$. Define the $n\times n$ matrix $M$ by $$M_{ii}=\sum_{S:i\in S}X_S,\qquad M_{ij}=\sum_{S:i\in S,\,j\notin S}\frac{X_S}{|S|}\quad(i\neq j)$$. Since $\det M$ and $\det(\operatorname{diag}M)$ are invariant ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial_progress",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-030",
"literature-status:open",
"owr-year:2019"
] | The source’s diagonal formula is a typo: $M_{ii}=\sum_{S\ni i}X_S=\deg(i)$. With that correction the determinant inequality corresponds to Ehrenborg’s spanning-tree conjecture, for which Ho gives an unrefereed proof with a claimed Lean formalisation. The present record asks for a natural symmetric-function basis, which... | [
{
"url": "https://arxiv.org/abs/2603.17997",
"label": "Ho, proof of Ehrenborg’s conjecture — unrefereed preprint"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472"... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $G$ be bipartite with parts $X=[n]$ and $Y$, and set $X_S=|\{y\in Y:N(y)=S\}|$ for every nonempty $S\subseteq[n]$. Define the $n\times n$ matrix $M$ by $$M_{ii}=\sum_{S:i\in S}X_S,\qquad M_{ij}=\sum_{S:i\in S,\,j\notin S}\frac{X_S}{|S|}\quad(i\neq j)$$. Since $\det M$ and $\det(\operatorname{diag}M)$ are invariant ... | For a bipartite graph G with X=[n], Y, and X_S=#{y\in Y:N(y)=S} for nonempty S\subset[n], define M by M_{ii}=\sum_{S:i\in S}|S| and M_{ij}=\sum_{S:i\in S, j\notin S}X_S/|S|. Since det(M) and det(diag(M)) are S_n-invariant polynomials in the X_S, is there a natural basis in symmetric-function theory for representing the... | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,233 | OWR-17135-031 | Nonnegative Square Decompositions of Bipartite Determinant Differences | Let $G$ be bipartite with parts $X=[n]$ and $Y$, set $X_S=|\{y\in Y:N(y)=S\}|$ for nonempty $S\subseteq[n]$, and define $M$ by $$M_{ii}=\sum_{S:i\in S}X_S,\qquad M_{ij}=\sum_{S:i\in S,\,j\notin S}\frac{X_S}{|S|}\quad(i\neq j)$$. Is there an identity $$\det(\operatorname{diag}M)-\det M=\sum_\mu c_\mu x^\mu+\sum_{\mu,\nu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17135-032"
] | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-031",
"literature-status:open",
"owr-year:2019"
] | The source’s diagonal formula is a typo: $M_{ii}=\sum_{S\ni i}X_S=\deg(i)$. With that correction the determinant inequality corresponds to Ehrenborg’s spanning-tree conjecture, for which Ho gives an unrefereed proof with a claimed Lean formalisation. The displayed refinement is false literally: for n=3 the difference i... | [
{
"url": "https://arxiv.org/abs/2603.17997",
"label": "Ho — related spanning-tree inequality"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472"
},
{
"url":... | 2026-09-28T00:00:00 | Ho — related spanning-tree inequality: https://arxiv.org/abs/2603.17997
Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472: https://doi.org/10.4171/owr/2019/39 | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $G$ be bipartite with parts $X=[n]$ and $Y$, set $X_S=|\{y\in Y:N(y)=S\}|$ for nonempty $S\subseteq[n]$, and define $M$ by $$M_{ii}=\sum_{S:i\in S}X_S,\qquad M_{ij}=\sum_{S:i\in S,\,j\notin S}\frac{X_S}{|S|}\quad(i\neq j)$$. Is there an identity $$\det(\operatorname{diag}M)-\det M=\sum_\mu c_\mu x^\mu+\sum_{\mu,\nu... | With M as defined for the bipartite-graph conjecture, experiments suggest det(diag(M))-det(M)=\sum_\mu c_\mu x^\mu+\sum_{\mu,\nu}c_{\mu\nu}(x^\mu-x^\nu)^2 with all c_\mu,c_{\mu\nu}\ge0. Is there a natural symmetric-function basis for these invariant polynomials, and is this more precise nonnegativity statement true? | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,234 | OWR-17135-032 | Nonnegative Square Decompositions of Bipartite Determinant Differences | For the matrix M associated with a bipartite graph by M_{ii}=\sum_{S:i\in S}|S| and M_{ij}=\sum_{S:i\in S, j\notin S}X_S/|S|, is the conjectural representation det(diag(M))-det(M)=\sum_\mu c_\mu x^\mu+\sum_{\mu,\nu}c_{\mu\nu}(x^\mu-x^\nu)^2 with c_\mu,c_{\mu\nu}\ge0 valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | Duplicate/merged OWR extraction (The official report contains one nonnegative square-decomposition question; this extraction duplicates the source-verified formulation retai) | [
"OWR-17135-031"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-032",
"literature-status:open",
"owr-year:2019"
] | Duplicate extraction; the canonical question is OWR-17135-031. The source’s diagonal formula is a typo: $M_{ii}=\sum_{S\ni i}X_S=\deg(i)$. With that correction the determinant inequality corresponds to Ehrenborg’s spanning-tree conjecture, for which Ho gives an unrefereed proof with a claimed Lean formalisation. The di... | [
{
"url": "https://arxiv.org/abs/2603.17997",
"label": "Ho — related spanning-tree inequality"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472"
},
{
"url":... | 2026-09-28T00:00:00 | Ho — related spanning-tree inequality: https://arxiv.org/abs/2603.17997
Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472: https://doi.org/10.4171/owr/2019/39 | https://doi.org/10.4171/owr/2019/39 | null | null | null | null | For the matrix M associated with a bipartite graph by M_{ii}=\sum_{S:i\in S}|S| and M_{ij}=\sum_{S:i\in S, j\notin S}X_S/|S|, is the conjectural representation det(diag(M))-det(M)=\sum_\mu c_\mu x^\mu+\sum_{\mu,\nu}c_{\mu\nu}(x^\mu-x^\nu)^2 with c_\mu,c_{\mu\nu}\ge0 valid? | unrecoverable | The official report contains one nonnegative square-decomposition question; this extraction duplicates the source-verified formulation retained as OWR-17135-031. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,235 | OWR-17135-033 | Triangle Equation Hyperplane Arrangements | Let $\mathcal H$ be the arrangement in $\mathbb R^{\binom n2}$ consisting, for every unordered triple $\{i,j,k\}\subseteq[n]$, of the hyperplane $$H_{i,j,k}=\{x:x_{i,j}+x_{j,k}=x_{i,k}\}$$. Determine the intersection lattice, characteristic polynomial, regions, and other combinatorial invariants of $\mathcal H$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-033",
"literature-status:open",
"owr-year:2019"
] | Classical Linial arrangements are well studied, but the distinct triangle-equation arrangement in the extracted record has no identified complete treatment; its requested properties remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1006/jcta.2000.3106",
"label": "Linial arrangement literature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $\mathcal H$ be the arrangement in $\mathbb R^{\binom n2}$ consisting, for every unordered triple $\{i,j,k\}\subseteq[n]$, of the hyperplane $$H_{i,j,k}=\{x:x_{i,j}+x_{j,k}=x_{i,k}\}$$. Determine the intersection lattice, characteristic polynomial, regions, and other combinatorial invariants of $\mathcal H$. | Let H be the arrangement in R^{\binom n2} whose hyperplanes, indexed by unordered triples {i,j,k}\subset[n], are H_{i,j,k}: x_{i,j}+x_{j,k}=x_{i,k}. What is known about this hyperplane arrangement? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,236 | OWR-17135-034 | Spanning Rank of Lattice Polytopes | For a $d$-dimensional lattice polytope $P$ with $\operatorname{aff}(P\cap\mathbb Z^d)=\mathbb Z^d$, let $\operatorname{SR}(P)$ be the least cardinality of a subset $B\subseteq P\cap\mathbb Z^d$ satisfying $\operatorname{aff}(B)=\mathbb Z^d$, and let $\operatorname{SR}(d)=\max_P\operatorname{SR}(P)$. Determine $\operato... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-034",
"literature-status:open",
"owr-year:2019"
] | Dimension-only boundedness of SR(P) is known and SR(1), SR(2), and SR(3) are known, but SR(4) and the asymptotic order of SR(d) remain open. | [
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1911.03511",
"label": "Averkov, Hofscheier, and Nill"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For a $d$-dimensional lattice polytope $P$ with $\operatorname{aff}(P\cap\mathbb Z^d)=\mathbb Z^d$, let $\operatorname{SR}(P)$ be the least cardinality of a subset $B\subseteq P\cap\mathbb Z^d$ satisfying $\operatorname{aff}(B)=\mathbb Z^d$, and let $\operatorname{SR}(d)=\max_P\operatorname{SR}(P)$. Determine $\operato... | For a d-dimensional lattice polytope P with aff(P\cap\mathbb{Z}^d)=\mathbb{Z}^d, let SR(P) be the minimum cardinality of B\subset P\cap\mathbb{Z}^d with aff(B)=\mathbb{Z}^d, and let SR(d)=\max_P SR(P). Given SR(1)=2, SR(2)=3, and SR(3)=5, what is SR(4), and what is the asymptotic order of SR(d)? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,237 | OWR-17135-035 | Equivariant Log-Concavity of Orlik–Solomon Algebras | Let $M$ be a matroid, let $W$ be a finite symmetry group of $M$, and regard its Orlik–Solomon algebra $OS^*(M)$ as a graded $W$-representation. For every $i$, does $OS^i(M)\otimes OS^i(M)$ contain $OS^{i-1}(M)\otimes OS^{i+1}(M)$ as a subrepresentation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17135-035",
"literature-status:open",
"owr-year:2019"
] | The general equivariant Orlik--Solomon log-concavity inclusion remains a conjecture; published work gives only low-degree computer-assisted cases for the braid arrangement. | [
{
"url": "https://doi.org/10.1093/imrn/rnab316",
"label": "Matherne, Miyata, Proudfoot, and Ramos"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Let $M$ be a matroid, let $W$ be a finite symmetry group of $M$, and regard its Orlik–Solomon algebra $OS^*(M)$ as a graded $W$-representation. For every $i$, does $OS^i(M)\otimes OS^i(M)$ contain $OS^{i-1}(M)\otimes OS^{i+1}(M)$ as a subrepresentation? | Let M be a matroid, W a finite group of symmetries of M, and OS^*(M) its Orlik--Solomon algebra as a graded W-representation. Is it true for every i that OS^i(M)\otimes OS^i(M) contains OS^{i-1}(M)\otimes OS^{i+1}(M) as a subrepresentation? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,238 | OWR-17135-036 | Extending Combinatorial Spheres on the Same Vertex Set | If $S$ is a combinatorial $d$-sphere on $n\geq d+3$ vertices, does there exist a combinatorial $(d+1)$-sphere $S'$ on the same vertex set such that $S$ is a subcomplex of $S'$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 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 | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **Combinatorial Spheres inside Spheres on the Same Vertex Set: Partial Results on a Question of Santos** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23065633) | [
"owr",
"oberwolfach-reports",
"OWR-17135-036",
"literature-status:partially-solved",
"owr-year:2019"
] | The same-vertex-set extension is proved for flag, stacked, and join spheres, but the general combinatorial-sphere question remains unresolved. | [
{
"url": "https://arxiv.org/abs/2006.04470",
"label": "Datta"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | If $S$ is a combinatorial $d$-sphere on $n\geq d+3$ vertices, does there exist a combinatorial $(d+1)$-sphere $S'$ on the same vertex set such that $S$ is a subcomplex of $S'$? | If S is a combinatorial d-sphere with n\ge d+3 vertices, does there always exist a combinatorial (d+1)-sphere S' on the same vertex set such that S is a subcomplex of S'? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,239 | OWR-17136-001 | Optimal Regularity of $p$-Harmonic Functions | Determine the optimal regularity of $p$-harmonic functions in dimensions $d\geq3$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Innovative Approaches to the Numerical Approximation of PDEs (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/40, pp. 2473--2540](https://doi.org/10.4171/owr/2019/40)
## Literature review... | 3 | open | null | 2,019 | 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-17136-001",
"literature-status:open",
"owr-year:2019"
] | The planar C^{p'} regularity conjecture is proved, while the sharp regularity of p-harmonic functions in dimensions d\geq3 remains an open problem. | [
{
"url": "https://academic.oup.com/imrn/article/2018/20/6481/3770476",
"label": "Higher-dimensional p-harmonic regularity"
},
{
"url": "https://doi.org/10.4171/owr/2019/40",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/40 | null | null | null | Determine the optimal regularity of $p$-harmonic functions in dimensions $d\geq3$. | Determine the optimal regularity of p-harmonic functions in dimensions d\ge3. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Innovative Approaches to the Numerical Approximation of PDEs (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/40, pp. 2473--2540 |
30,004,240 | OWR-17137-001 | Long-Time Landau–Pekar Dynamics of Strongly Coupled Polarons | For a strongly coupled polaron as $\alpha\to\infty$, can approximation of the quantum dynamics by the Landau–Pekar ansatz be proved on time scales longer than $\lvert t\rvert\lesssim\alpha^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603](https://doi.org/10.4171/owr/2019/41)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,019 | 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-17137-001",
"literature-status:open",
"owr-year:2019"
] | The published dynamics result reaches time scale O(alpha^2), but a rigorous approximation on larger time scales remains an open problem. | [
{
"url": "https://doi.org/10.2140/paa.2021.3.653",
"label": "Strongly coupled polaron dynamics"
},
{
"url": "https://doi.org/10.4171/owr/2019/41",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/41 | null | null | null | For a strongly coupled polaron as $\alpha\to\infty$, can approximation of the quantum dynamics by the Landau–Pekar ansatz be proved on time scales longer than $\lvert t\rvert\lesssim\alpha^2$? | For the strongly coupled polaron as the coupling constant \alpha\to\infty, can the known approximation of its quantum dynamics by the Landau--Pekar/Pekar ansatz be proved on time scales larger than the currently established scale |t|\lesssim\alpha^2? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603 |
30,004,241 | OWR-17137-002 | Logarithmic Entanglement Enhancement from Partial Delocalization | For entanglement entropy in disordered free-fermion systems, how much delocalization of the one-particle eigenvalues and eigenfunctions is needed to produce a logarithmic enhancement of the area law, even when the spectrum is not absolutely continuous? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603](https://doi.org/10.4171/owr/2019/41)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,019 | 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-17137-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The random-dimer model gives a logarithmically enhanced area law at critical energies with weak disorder, but the general amount of delocalisation needed remains unresolved. | [
{
"url": "https://doi.org/10.1007/s00220-019-03523-3",
"label": "Muller, Pastur, and Schulte"
},
{
"url": "https://doi.org/10.4171/owr/2019/41",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/41 | null | null | null | For entanglement entropy in disordered free-fermion systems, how much delocalization of the one-particle eigenvalues and eigenfunctions is needed to produce a logarithmic enhancement of the area law, even when the spectrum is not absolutely continuous? | For entanglement entropy in disordered free-fermion systems, how much delocalization of the one-particle eigenvalues and eigenfunctions is needed to produce a logarithmic enhancement of the area law, even when the spectrum is not absolutely continuous? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603 |
30,004,242 | OWR-17137-004 | Loop Operators and Microscopic Nonabelian Anyons | Can loop operators and the corresponding anyon description be constructed for microscopic models with nonabelian anyons, extending the known abelian construction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603](https://doi.org/10.4171/owr/2019/41)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,019 | 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-17137-004",
"literature-status:open",
"owr-year:2019"
] | The cited construction is for Abelian anyons; the report explicitly leaves the non-Abelian extension open, and no complete general construction was located by the cutoff. | [
{
"url": "https://doi.org/10.4171/owr/2019/41",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1103/PhysRevB.101.085138",
"label": "Abelian anyon index paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/41 | null | null | null | Can loop operators and the corresponding anyon description be constructed for microscopic models with nonabelian anyons, extending the known abelian construction? | Can the construction of loop operators and the associated anyon description for microscopic models with Abelian anyons be extended to the non-Abelian case? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603 |
30,004,243 | OWR-17137-006 | Sharp Free Energy of the Two-Dimensional Heisenberg Ferromagnet | For the two-dimensional quantum Heisenberg ferromagnet, the free energy obeys
$$f^{2d}(\beta,S)\leq-\frac\pi{24}S^{-1}\beta^{-2}\left(1-O\bigl((\beta S)^{-\kappa}\bigr)\right)$$
for every $\kappa<1/3$. Can one prove a matching lower bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603](https://doi.org/10.4171/owr/2019/41)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,019 | 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-17137-006",
"literature-status:open",
"owr-year:2019"
] | The report identifies a missing matching lower bound for the two-dimensional free energy; no later primary source establishing that exact bound was located, so the problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/41",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/41 | null | null | null | For the two-dimensional quantum Heisenberg ferromagnet, the free energy obeys
$$f^{2d}(\beta,S)\leq-\frac\pi{24}S^{-1}\beta^{-2}\left(1-O\bigl((\beta S)^{-\kappa}\bigr)\right)$$
for every $\kappa<1/3$. Can one prove a matching lower bound? | For the two-dimensional quantum Heisenberg ferromagnet, the free energy satisfies the upper bound f^{2d}(\beta,S)\le-\frac{\pi}{24}S^{-1}\beta^{-2}(1-O((\beta S)^{-\kappa})) for any \kappa<1/3. Can one prove a matching lower bound? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Many-Body Quantum Systems (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/41, pp. 2541--2603 |
30,004,244 | OWR-17138-001 | Boltzmann Limits for Long-Range Lorentz Gases | For Lorentz gases and related particle systems with long-range interaction potentials, determine when the kinetic limit is governed by the Boltzmann equation, when it is governed by a different equation such as the Landau equation, and when no Markovian kinetic description is valid. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669](https://doi.org/10.4171/owr/2019/42)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-17138-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Long-range Lorentz-gas models have rigorous generalized-Holtsmark and Boltzmann or Landau limits, but the report's general validity question for long-range potentials remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/42",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1707.04193",
"label": "Long-range Lorentz-gas paper"
},
{
"url": "https://doi.org/10.1142/S0129055X18500071",
"label": "Published version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/42 | null | null | null | For Lorentz gases and related particle systems with long-range interaction potentials, determine when the kinetic limit is governed by the Boltzmann equation, when it is governed by a different equation such as the Landau equation, and when no Markovian kinetic description is valid. | For a Lorentz gas or related particle system with long-range interaction potentials, is the limiting kinetic equation the Boltzmann equation, or does the Boltzmann description fail? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669 |
30,004,245 | OWR-17138-003 | Airy Limits for Last Paths in Aztec Diamonds | For the lattice paths obtained from the height function of the two-periodic Aztec diamond, prove that an extremal path exists whose suitably centered and scaled limit is the Airy process, and determine the parameter regimes in which this limit holds. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669](https://doi.org/10.4171/owr/2019/42)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-17138-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Later work proves Airy-process convergence for a last path in a thin rough--smooth regime, but the original all-parameter expectation is not fully established. | [
{
"url": "https://doi.org/10.4171/owr/2019/42",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2302.04663",
"label": "Airy process at a thin rough region"
},
{
"url": "https://arxiv.org/abs/2602.24063",
"label": "Airy line ensemble at the boundary"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/42 | null | null | null | For the lattice paths obtained from the height function of the two-periodic Aztec diamond, prove that an extremal path exists whose suitably centered and scaled limit is the Airy process, and determine the parameter regimes in which this limit holds. | For the lattice paths constructed from the height function of the two-periodic Aztec diamond, can one prove that there is a last path whose suitably scaled limit is the Airy process? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669 |
30,004,246 | OWR-17138-004 | KdV Evolution from General Ergodic Random Fields | For the Korteweg–de Vries equation on $\mathbb R$, is the evolution almost surely well posed when the initial condition is a general ergodic random field, beyond the known white-noise case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669](https://doi.org/10.4171/owr/2019/42)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17138-004",
"literature-status:partially-solved",
"owr-year:2019"
] | KdV is well-posed in H^{-1} and white-noise dynamics are invariant, but almost-sure well-posedness for a general ergodic random field on R remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/42",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1802.04851",
"label": "KdV well-posedness paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/42 | null | null | null | For the Korteweg–de Vries equation on $\mathbb R$, is the evolution almost surely well posed when the initial condition is a general ergodic random field, beyond the known white-noise case? | For the KdV equation on R, is a solution started from a general ergodic random field almost surely well posed, beyond the known white-noise initial-data case? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669 |
30,004,247 | OWR-17138-005 | Kinetic Relaxation and Bootstrap Percolation Infection Times | For a kinetically constrained model with initial law $\mu$, determine whether the relaxation time $T_{\mathrm{rel}}$ and mean infection time $\mathbb E_\mu\tau_0$ have the same asymptotic scale as the typical bootstrap-percolation infection time $\tau_{\mathrm{BP}}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669](https://doi.org/10.4171/owr/2019/42)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-17138-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Random-constraint KCM work establishes direct comparisons and refined critical scaling bounds with bootstrap-percolation infection times, but the full proposed equivalence for arbitrary laws \mu is not proved. | [
{
"url": "https://doi.org/10.4171/owr/2019/42",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1812.00774",
"label": "Random-constraint KCM paper"
},
{
"url": "https://doi.org/10.1007/s00220-023-04874-8",
"label": "Refined universality paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/42 | null | null | null | For a kinetically constrained model with initial law $\mu$, determine whether the relaxation time $T_{\mathrm{rel}}$ and mean infection time $\mathbb E_\mu\tau_0$ have the same asymptotic scale as the typical bootstrap-percolation infection time $\tau_{\mathrm{BP}}$. | For kinetically constrained models with initial infection law \mu, is the scaling of the relaxation time T_{rel} and the mean infection time E(\tau_0) connected to the typical value of the bootstrap-percolation infection time \tau_{BP} under \mu? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669 |
30,004,248 | OWR-17138-006 | Low-Temperature Sampling by Randomly Initialized Glauber Dynamics | Can Glauber dynamics started from an efficiently samplable random initial state yield polynomial-time counting and sampling algorithms for the hard-core or Potts model at low temperature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669](https://doi.org/10.4171/owr/2019/42)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-17138-006",
"literature-status:partially-solved",
"owr-year:2019"
] | Polynomial or near-polynomial low-temperature Glauber algorithms are known for restricted or random initializations, while the general fast-algorithm question in the report remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/42",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1002/rsa.20968",
"label": "Fast algorithms at low temperatures"
},
{
"url": "https://arxiv.org/abs/2106.11296",
"label": "Random-initialization dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/42 | null | null | null | Can Glauber dynamics started from an efficiently samplable random initial state yield polynomial-time counting and sampling algorithms for the hard-core or Potts model at low temperature? | Can Glauber dynamics, started from a suitably chosen random initial state, be used to obtain fast counting and sampling algorithms for hard-core or Potts models at low temperatures? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/42, pp. 2605--2669 |
30,004,249 | OWR-17139-001 | Combinatorial Deformations of Toric Fano Varieties | Let $P$ be a reflexive polytope and let $X_P$ be the toric Fano variety associated with its face fan. Characterize the combinatorial data on $P$ that produce deformations or smoothings of $X_P$, and determine the general fibers of the resulting families. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726](https://doi.org/10.4171/owr/2019/43)
## Literature review (checked 2026-08-22)
**Status:** partially s... | 3 | partially_solved | null | 2,019 | 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-17139-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Combinatorial criteria now produce smoothings for broad classes such as Gorenstein toric Fano threefolds, but a general deformation theory and general-fibre classification for toric varieties remain incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2019/43",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2412.06500",
"label": "Smoothing Gorenstein toric Fano threefolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/43 | null | null | null | Let $P$ be a reflexive polytope and let $X_P$ be the toric Fano variety associated with its face fan. Characterize the combinatorial data on $P$ that produce deformations or smoothings of $X_P$, and determine the general fibers of the resulting families. | Let P be a reflexive polytope and X_P the toric Fano variety associated with its face fan. What combinatorial data on P produce deformations or smoothings of X_P, and what can be said about the general fibre X_t of a deformation constructed from such data? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726 |
30,004,250 | OWR-17139-002 | Deformations of Non-Gorenstein Toric Fano Varieties | Develop a combinatorial and deformation-theoretic description of $\mathbb Q$-Gorenstein deformations of toric Fano varieties with non-Gorenstein singularities. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726](https://doi.org/10.4171/owr/2019/43)
## Literature review (checked 2026-08-22)
**Status:** partially s... | 3 | partially_solved | null | 2,019 | 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-17139-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Q-Gorenstein deformation theory and classifications exist in restricted singularity classes, but no general solution for non-Gorenstein toric Fano varieties was located. | [
{
"url": "https://doi.org/10.4171/owr/2019/43",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1090/tran/8636",
"label": "Toric deformation spaces"
},
{
"url": "https://arxiv.org/abs/alg-geom/9403003",
"label": "Toric Q-Gorenstein singularities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/43 | null | null | null | Develop a combinatorial and deformation-theoretic description of $\mathbb Q$-Gorenstein deformations of toric Fano varieties with non-Gorenstein singularities. | What can be said about Q-Gorenstein deformations of toric Fano varieties whose singularities are not Gorenstein? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726 |
30,004,251 | OWR-17139-004 | Blue Sheaf Cohomology for Toric and Tropical Geometry | For distinguished generators in toric sheaf cohomology, determine when they form a basis, what structure they induce on the Cox ring, and how they can be used for explicit computations. Extend blue sheaf cohomology to toroidal, logarithmic, and tropical schemes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726](https://doi.org/10.4171/owr/2019/43)
## Literature review (checked 2026-08-22)
**Status:** partially s... | 3 | partially_solved | null | 2,019 | 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-17139-004",
"literature-status:partially-solved",
"owr-year:2019"
] | Cech blue sheaf cohomology is defined for important blueprint classes and refines toric cohomology, but the extracted questions about generators, applications, and tropical extension remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/43",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2017.04.029",
"label": "Cech cohomology over F1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/43 | null | null | null | For distinguished generators in toric sheaf cohomology, determine when they form a basis, what structure they induce on the Cox ring, and how they can be used for explicit computations. Extend blue sheaf cohomology to toroidal, logarithmic, and tropical schemes. | For the distinguished generators in toric sheaf cohomology, what do they mean, when do they form a basis, what additional structure do they induce on the Cox ring, and can they be used for explicit cohomology computations? Is blue sheaf cohomology useful for toroidal or logarithmic schemes, and how can it be extended t... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Toric Geometry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/43, pp. 2671--2726 |
30,004,252 | OWR-17140-003 | Localization of Types in Bruhat–Tits Buildings | Let $G$ be a connected reductive $p$-adic group, let $\mathcal B(G)$ be its Bruhat–Tits building, and let $x\in\mathcal B(G)$. For the finite-length representation $\tau(y,g)$ arising in the Mackey decomposition of a type, is there a bounded convex neighborhood $\Gamma$ of $x$, containing $\mathcal B(G)^H$, such that e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | open | null | 2,019 | 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-17140-003",
"literature-status:open",
"owr-year:2019"
] | The report states this as Conjecture 2 and notes that the general anisotropic-torus case is poorly understood; later results cover special unicity cases but do not establish the full conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2019/44",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1801.06721",
"label": "Unicity of types for toral supercuspidals"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Let $G$ be a connected reductive $p$-adic group, let $\mathcal B(G)$ be its Bruhat–Tits building, and let $x\in\mathcal B(G)$. For the finite-length representation $\tau(y,g)$ arising in the Mackey decomposition of a type, is there a bounded convex neighborhood $\Gamma$ of $x$, containing $\mathcal B(G)^H$, such that e... | Let G be a connected reductive p-adic group, B(G) its Bruhat--Tits building, x\in B(G), and \tau(y,g) the finite-length representation arising in the Mackey decomposition for a type. Is it true that there is a bounded convex neighbourhood \Gamma of x containing B(G)^H such that, for every z\in B(G)\setminus\Gamma, the ... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,253 | OWR-17140-004 | Unified Constructions of Supercuspidal Representations | Construct a common framework for supercuspidal representations of reductive $p$-adic groups that simultaneously generalizes the Bushnell–Kutzko and Yu constructions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | open | null | 2,019 | 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-17140-004",
"literature-status:open",
"owr-year:2019"
] | The statement is malformed and omits the objects and hypotheses needed to identify the claimed construction; related Yu-type constructions have been generalized in restricted settings, but this extracted claim remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/44",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.4007/annals.2021.193.1.4",
"label": "Types for tame p-adic groups"
},
{
"url": "https://arxiv.org/abs/2605.03638",
"label": "Characteristic-free Yu construction"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Construct a common framework for supercuspidal representations of reductive $p$-adic groups that simultaneously generalizes the Bushnell–Kutzko and Yu constructions. | Does there exist a construction generalizing both the Bushnell--Kutzko and Yu constructions of supercuspidal representations? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,254 | OWR-17140-008 | Derived Equivalence for Spherical Hamiltonian Duality | Let $\mathfrak o=k[[t]]$, where $k$ is finite or $k=\mathbb C$. Is the derived category of $G(\mathfrak o)$-equivariant constructible sheaves on $X(F)$ equivalent to the differential graded category of $\check G$-equivariant coherent sheaves on $$\check M\simeq\check V_X\times_{\check G_X}\check G$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | partially_solved | null | 2,019 | 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-17140-008",
"literature-status:partially-solved",
"owr-year:2019"
] | The Hamiltonian-duality framework and several semiclassical and low-rank cases are established, but the stated derived equivalence for general spherical data remains conjectural. | [
{
"url": "https://ems.press/content/serial-article-files/46824",
"label": "OWR 2019 44"
},
{
"url": "https://link.springer.com/article/10.1007/s00039-025-00702-4",
"label": "Feng--Wang 2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Let $\mathfrak o=k[[t]]$, where $k$ is finite or $k=\mathbb C$. Is the derived category of $G(\mathfrak o)$-equivariant constructible sheaves on $X(F)$ equivalent to the differential graded category of $\check G$-equivariant coherent sheaves on $$\check M\simeq\check V_X\times_{\check G_X}\check G$$? | When o=k[[t]] with k a finite field or the complex numbers, is the derived category of G(o)-equivariant constructible sheaves on X(F) equivalent to the differential graded category of \check{G}-equivariant coherent sheaves on the Hamiltonian space \check{M}\simeq \check{V}_{X}\times_{\check{G}_{X}}\check{G}? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,255 | OWR-17140-009 | Geometric Langlands Duals of Quantized Theta Sheaves | Let $M$ be a quantization whose geometric theta series is a distinguished $D$-module on $\operatorname{Bun}_G$. Is its geometric-Langlands dual a sheaf on the moduli space of $\check G$-local systems arising from a coherent quantization of $\check M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | partially_solved | null | 2,019 | 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-17140-009",
"literature-status:partially-solved",
"owr-year:2019"
] | The global theta-sheaf statement is part of the Ben-Zvi--Sakellaridis--Venkatesh conjectural program; semiclassical and selected low-rank examples provide evidence, not a general proof. | [
{
"url": "https://ems.press/content/serial-article-files/46824",
"label": "OWR 2019 44"
},
{
"url": "https://link.springer.com/article/10.1007/s00039-025-00702-4",
"label": "Feng--Wang 2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Let $M$ be a quantization whose geometric theta series is a distinguished $D$-module on $\operatorname{Bun}_G$. Is its geometric-Langlands dual a sheaf on the moduli space of $\check G$-local systems arising from a coherent quantization of $\check M$? | For a quantization M with geometric theta series given by a distinguished D-module on \operatorname{Bun}_{G}, is its dual under geometric Langlands a sheaf on the space of \check{G}-local systems arising from a suitable coherent quantization of \check{M}? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,256 | OWR-17140-010 | Stratified Equivalence for Bernstein Components | For each inertial class $s$, does the ABPS bijection $\mu_s$ between the Bernstein component $\operatorname{Irr}(G)_s$ and its twisted spectral extended quotient arise from a stratified equivalence between $\mathcal O(T_s)\rtimes W_s$ and the Bernstein algebra $\mathcal H(G,s)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | partially_solved | null | 2,019 | 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-17140-010",
"literature-status:partially-solved",
"owr-year:2019"
] | The ABPS bijection and stratified-equivalence conjecture are proved in important families, including inner forms of general linear groups and some principal series, but not for arbitrary p-adic reductive groups. | [
{
"url": "https://ems.press/content/serial-article-files/46824",
"label": "OWR 2019 44"
},
{
"url": "https://celebratio.org/Baum_P/article/714/",
"label": "Baum--Aubert--Plymen--Solleveld"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | For each inertial class $s$, does the ABPS bijection $\mu_s$ between the Bernstein component $\operatorname{Irr}(G)_s$ and its twisted spectral extended quotient arise from a stratified equivalence between $\mathcal O(T_s)\rtimes W_s$ and the Bernstein algebra $\mathcal H(G,s)$? | For each inertial class s, does the ABPS bijection \mu_s between the Bernstein component \operatorname{Irr}(G)_s and the twisted spectral extended quotient arise from a stratified equivalence between \mathcal{O}(T_s)\rtimes W_s and the Bernstein algebra H(G,s)? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,257 | OWR-17140-011 | Group-Level Realization of the c-Operation | Construct a group-level realization of the $c$-operation for a reductive $p$-adic group $G$ that recovers its known realization on the Iwahori–Hecke algebra. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | open | null | 2,019 | 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-17140-011",
"literature-status:open",
"owr-year:2019"
] | The report presents the group-level realization of the c-operation as a natural question and offers Bernstein projectives as a proposed route; no general construction or theorem resolving the extracted question was found. | [
{
"url": "https://ems.press/content/serial-article-files/46824",
"label": "OWR 2019 44"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Construct a group-level realization of the $c$-operation for a reductive $p$-adic group $G$ that recovers its known realization on the Iwahori–Hecke algebra. | How can the c-operation be realized for the group G itself, rather than only for its Iwahori--Hecke algebra? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,258 | OWR-17140-012 | Depth-Controlled Relative Local Character Expansions | Let a reductive group $H$ over $F$ act on $V$, let $\mathcal N_V$ be its nilpotent cone, and let $V_{r+}$ be the Moy–Prasad neighborhood. For an $H$-distinguished representation $\pi$ of depth $r$, is the relative local character expansion valid on $V_{r+}$? Equivalently, does $$\operatorname{res}_{D(V)_{r+}}\widetilde... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819](https://doi.org/10.4171/owr/2019/44)
## Literature review (... | 3 | partially_solved | null | 2,019 | 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-17140-012",
"literature-status:partially-solved",
"owr-year:2019"
] | Relative local character expansion is known on some nilpotent neighborhoods and in favorable symmetric or Galois cases, but the asserted depth-controlled neighborhood statement is not proved in general. | [
{
"url": "https://ems.press/content/serial-article-files/46824",
"label": "OWR 2019 44"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/44 | null | null | null | Let a reductive group $H$ over $F$ act on $V$, let $\mathcal N_V$ be its nilpotent cone, and let $V_{r+}$ be the Moy–Prasad neighborhood. For an $H$-distinguished representation $\pi$ of depth $r$, is the relative local character expansion valid on $V_{r+}$? Equivalently, does $$\operatorname{res}_{D(V)_{r+}}\widetilde... | Let H be reductive over F acting on V with nilpotent cone N_V and Moy--Prasad neighborhoods V_{r+}. For an H-distinguished representation \pi of depth r, is the relative local character expansion valid on V_{r+}; equivalently, for every r\in\mathbb{R}, does \operatorname{res}_{D(V)_{r+}}\widetilde{J}(V)_{r+}=\operatorn... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | New Developments in Representation Theory of p-adic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/44, pp. 2739--2819 |
30,004,259 | OWR-17288-001 | Reduced $C^*$-Algebras of Free Orthogonal Quantum Groups | For distinct positive integers $M$ and $N$, are the reduced $C^*$-algebras $C_r^*(\mathrm{FO}_M)$ and $C_r^*(\mathrm{FO}_N)$ isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867](https://doi.org/10.4171/owr/2019/45)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-17288-001",
"literature-status:open",
"owr-year:2019"
] | K-theory computations for reduced free-group C-star algebras do not recover the rank parameter, and the report explicitly leaves the isomorphism question for distinct ranks open. | [
{
"url": "https://ems.press/content/serial-article-files/46823",
"label": "OWR 2019 45"
},
{
"url": "https://arxiv.org/abs/0911.2999",
"label": "Voigt"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/45 | null | null | null | For distinct positive integers $M$ and $N$, are the reduced $C^*$-algebras $C_r^*(\mathrm{FO}_M)$ and $C_r^*(\mathrm{FO}_N)$ isomorphic? | For distinct positive integers M and N, are the reduced C^*-algebras C_r^*(F O_M^+) and C_r^*(F O_N^+) isomorphic? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867 |
30,004,260 | OWR-17288-002 | Unification of Free Products in Algebraic Probability | Does there exist a reduction or unification of the free product of algebraic probability spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867](https://doi.org/10.4171/owr/2019/45)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-17288-002",
"literature-status:open",
"owr-year:2019"
] | The extracted question asks for a reduction operation for free products of algebraic probability spaces; reductions are known for Boolean, monotone, and related independences, while a free-product reduction remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46823",
"label": "OWR 2019 45"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/45 | null | null | null | Does there exist a reduction or unification of the free product of algebraic probability spaces? | Does there exist a reduction or unification of the free product of algebraic probability spaces? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867 |
30,004,261 | OWR-17288-003 | Free Decompositions of Compact Quantum Groups | When does a compact matrix quantum group $(G,u)$ admit a free decomposition of the sequence $(\operatorname{Fix}(u^{\otimes n}))_{n\geq1}$? Is this equivalent to $G$ having a free fusion semiring, and how can the notion be generalized to allow negative free cumulants? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867](https://doi.org/10.4171/owr/2019/45)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-17288-003",
"literature-status:open",
"owr-year:2019"
] | Free decompositions of compact matrix quantum groups and a satisfactory extension involving negative free cumulants remain open; existing fusion-semiring results do not settle the proposed equivalence or extension. | [
{
"url": "https://ems.press/content/serial-article-files/46823",
"label": "OWR 2019 45"
},
{
"url": "https://www.imo.universite-paris-saclay.fr/~amaury.freslon/Documents/Free_fusion.pdf",
"label": "Freslon, Free fusion"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/45 | null | null | null | When does a compact matrix quantum group $(G,u)$ admit a free decomposition of the sequence $(\operatorname{Fix}(u^{\otimes n}))_{n\geq1}$? Is this equivalent to $G$ having a free fusion semiring, and how can the notion be generalized to allow negative free cumulants? | When does a compact matrix quantum group (G,u) admit a free decomposition of the sequence (\operatorname{Fix}(u^{\otimes n}))_{n\geq1}; is this equivalent to G having a free fusion semiring, and how can free decomposition be generalized to allow possibly negative free cumulants? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867 |
30,004,262 | OWR-17288-004 | Finite-Dimensional Uniform Embeddings of Compact Metric Spaces | A loose embedding of a metric space $(X,d)$ in $\mathbb R^N$ is a continuous map that preserves equality and inequality of pairwise distances. If every finite subspace of a compact metric space $(X,d)$ is loosely embeddable in the same $\mathbb R^N$, is $X$ itself loosely embeddable there? Does every compact Riemannian... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867](https://doi.org/10.4171/owr/2019/45)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-17288-004",
"literature-status:open",
"owr-year:2019"
] | The report explicitly leaves open loose embeddability of the constructed metric space and whether every compact Riemannian manifold with geodesic distance has the required property; no general resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46823",
"label": "OWR 2019 45"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/45 | null | null | null | A loose embedding of a metric space $(X,d)$ in $\mathbb R^N$ is a continuous map that preserves equality and inequality of pairwise distances. If every finite subspace of a compact metric space $(X,d)$ is loosely embeddable in the same $\mathbb R^N$, is $X$ itself loosely embeddable there? Does every compact Riemannian... | If every finite subspace of a compact metric space (X,d) is loosely embeddable in the same Euclidean space \mathbb{R}^{N}, is (X,d) itself uniformly embeddable in \mathbb{R}^{N}; and does every compact Riemannian manifold with its geodesic distance satisfy this hypothesis? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Operator Algebraic Quantum Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/45, pp. 2821--2867 |
30,004,263 | OWR-17289-004 | Orbit Closures in Degenerate Flag Varieties | For closures of $G_a$-orbits in the degenerate flag variety $\operatorname{Fl}^a(V)$, parametrized by tuples of coordinate subsets, what is the closure relation, what are the minimal singularities, and how can the intersection cohomology complexes of the orbit closures be described? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | partially_solved | null | 2,019 | 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-17289-004",
"literature-status:partially-solved",
"owr-year:2019"
] | Recent work gives combinatorial descriptions and smooth-locus criteria for broad classes of flat linear degenerations, but a general classification of minimal singularities and intersection cohomology complexes on all orbit closures remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
},
{
"url": "https://alco.centre-mersenne.org/articles/10.5802/alco.477/",
"label": "Di Trani 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | For closures of $G_a$-orbits in the degenerate flag variety $\operatorname{Fl}^a(V)$, parametrized by tuples of coordinate subsets, what is the closure relation, what are the minimal singularities, and how can the intersection cohomology complexes of the orbit closures be described? | For the closures of G_a-orbits in the degenerate flag variety Fl^a(V), parametrized by tuples of coordinate subsets, what is the closure relation, what are the minimal singularities, and how can the intersection cohomology complexes of the orbit closures be described? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,264 | OWR-17289-005 | Hall Multiplication on Principal Quiver Grassmannians | For principal quiver Grassmannians and the invariant-function space $A=\bigoplus_{[P],[I],e}\mathbb{Q}^{\operatorname{Aut}_{Q}(P\oplus I)}[\operatorname{Gr}_{e}(P\oplus I)]$, can one define a Hall-algebra-type multiplication making $A$ graded associative and inducing an isomorphism $U_q(\mathfrak b^+)\otimes U_q(\mathf... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | open | null | 2,019 | 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-17289-005",
"literature-status:open",
"owr-year:2019"
] | The proposed Hall-algebra type multiplication on principal quiver Grassmannian invariant functions is posed as a problem, and no general construction with the stated properties was found. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | For principal quiver Grassmannians and the invariant-function space $A=\bigoplus_{[P],[I],e}\mathbb{Q}^{\operatorname{Aut}_{Q}(P\oplus I)}[\operatorname{Gr}_{e}(P\oplus I)]$, can one define a Hall-algebra-type multiplication making $A$ graded associative and inducing an isomorphism $U_q(\mathfrak b^+)\otimes U_q(\mathf... | For principal quiver Grassmannians and the invariant-function space A=\bigoplus_{[P],[I],e}\mathbb{Q}^{\operatorname{Aut}_{Q}(P\oplus I)}[\operatorname{Gr}_{e}(P\oplus I)], can one define a Hall-algebra-type multiplication making A graded associative and inducing an isomorphism U_q(\mathfrak b^+)\otimes U_q(\mathfrak b... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,265 | OWR-17289-006 | Canonical Bases from Quiver Grassmannian Orbit Closures | How is the canonical basis formed by the intersection-cohomology functions $f_{\mathcal O}$ on quiver-Grassmannian orbit closures related to variants of Lusztig's canonical basis in quantized enveloping algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | open | null | 2,019 | 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-17289-006",
"literature-status:open",
"owr-year:2019"
] | The relationship between the proposed basis and variants of Lusztig canonical bases is explicitly posed as an open problem, with no general identification located. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | How is the canonical basis formed by the intersection-cohomology functions $f_{\mathcal O}$ on quiver-Grassmannian orbit closures related to variants of Lusztig's canonical basis in quantized enveloping algebras? | How is the canonical basis formed by the intersection-cohomology functions f_O on quiver-Grassmannian orbit closures related to variants of Lusztig's canonical basis in quantized enveloping algebras? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,266 | OWR-17289-007 | Singular Loci of Maximal Flat Flag Degenerations | For an irreducible component $C(A)$ of the maximal flat linear degeneration $\operatorname{Fl}^{mf}(V)$ of the flag variety, what is its singular locus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | partially_solved | null | 2,019 | 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-17289-007",
"literature-status:partially-solved",
"owr-year:2019"
] | Recent work supplies criteria for smooth points in broad flat linear degenerations, giving partial information about singular loci, but the singular locus of every component in the extracted family is not determined. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
},
{
"url": "https://alco.centre-mersenne.org/articles/10.5802/alco.477/",
"label": "Di Trani 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | For an irreducible component $C(A)$ of the maximal flat linear degeneration $\operatorname{Fl}^{mf}(V)$ of the flag variety, what is its singular locus? | For an irreducible component C(A) of the maximal flat linear degeneration Fl^{mf}(V) of the flag variety, what is its singular locus? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,267 | OWR-17289-008 | Orbit Structure of Maximal Flat Flag Degenerations | For the natural action of $\operatorname{Aut}_Q(M)$ on $\operatorname{Fl}^{mf}(V)$, are there finitely many orbits, how can they be parametrized, and what is their closure relation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | open | null | 2,019 | 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-17289-008",
"literature-status:open",
"owr-year:2019"
] | The closure relation for the proposed stratification is explicitly requested in the report, and no general closure theorem resolving it was found. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | For the natural action of $\operatorname{Aut}_Q(M)$ on $\operatorname{Fl}^{mf}(V)$, are there finitely many orbits, how can they be parametrized, and what is their closure relation? | For the natural action of \operatorname{Aut}_{Q}(M) on Fl^{mf}(V), are there finitely many orbits, how can they be parametrized, and what is the closure relation among them? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,268 | OWR-17289-009 | Rank Stratifications and KLR Actions on Flag Degenerations | For the flat family $F_U\to U$ of linear degenerations, study the stratification by the rank conditions defining $S(A)$. Describe $H_*^{\mathrm{BM}}(F_U\times_U F_U)$ as a quotient of a quiver Hecke, or KLR, algebra, together with its standard representations indexed by Motzkin paths. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | open | null | 2,019 | 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-17289-009",
"literature-status:open",
"owr-year:2019"
] | Finiteness of Aut_Q(M)-orbits together with their parametrization and closure relation is posed as a problem; no general answer was located. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | For the flat family $F_U\to U$ of linear degenerations, study the stratification by the rank conditions defining $S(A)$. Describe $H_*^{\mathrm{BM}}(F_U\times_U F_U)$ as a quotient of a quiver Hecke, or KLR, algebra, together with its standard representations indexed by Motzkin paths. | For the flat family F_U\to U of linear degenerations, study the stratification by the rank conditions defining S(A); furthermore, describe H_*^{BM}(F_U\times_U F_U) as a quotient of a quiver Hecke/KLR algebra and its standard representations indexed by Motzkin paths. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,269 | OWR-17289-010 | Dyck-Path Inequalities for Newton–Okounkov Polytopes | Let $\Lambda_i=(\lambda_i^i,\ldots,\lambda_i^n)$ and put $\lambda_j^i=\lambda_j^j$ for $j>i$. Is the Newton–Okounkov polytope $\Delta_{v_0}(X_{w_0},L(\Lambda_1,\ldots,\Lambda_{n-1}))$ defined by $u_{lm}\geq0$ and
$$
\sum_{(l,m)\in D}u_{lm}\leq\sum_{s=1}^j(\lambda_k^s-\lambda_{i+j}^s)
$$
for every indicated Dyck path $D... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | partially_solved | null | 2,019 | 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-17289-010",
"literature-status:partially-solved",
"owr-year:2019"
] | Newton--Okounkov polytopes of Bott--Samelson varieties are related to Minkowski sums of FFLV polytopes and substantial constructions are known, but the extracted explicit all-Dyck-path inequality description is not established in full generality. | [
{
"url": "https://arxiv.org/abs/1801.00334",
"label": "Kiritchenko"
},
{
"url": "https://academic.oup.com/imrn/article/2023/4/3305/6454976",
"label": "Kiritchenko, IMRN 2023"
},
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | Let $\Lambda_i=(\lambda_i^i,\ldots,\lambda_i^n)$ and put $\lambda_j^i=\lambda_j^j$ for $j>i$. Is the Newton–Okounkov polytope $\Delta_{v_0}(X_{w_0},L(\Lambda_1,\ldots,\Lambda_{n-1}))$ defined by $u_{lm}\geq0$ and
$$
\sum_{(l,m)\in D}u_{lm}\leq\sum_{s=1}^j(\lambda_k^s-\lambda_{i+j}^s)
$$
for every indicated Dyck path $D... | Conjecture: if \Lambda_i=(\lambda_i^i,\ldots,\lambda_i^n) and \lambda_j^i=\lambda_j^j for j>i, then the Newton--Okounkov polytope \Delta_{v_0}(X_{w_0},L(\Lambda_1,\ldots,\Lambda_{n-1})) is defined by u_{lm}\geq0 and \sum_{(l,m)\in D}u_{lm}\leq\sum_{s=1}^{j}(\lambda_k^s-\lambda_{i+j}^s) for every Dyck path from \lambda_... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,270 | OWR-17289-013 | Hasse-Graph Descriptions of Valuation Semigroups | Is the weighted-Hasse-graph description of the valuation semigroup $\Gamma_C$ valid whenever, for every cover relation $p\gtrdot q$ of weight $b$, there is an $\eta\in K(\widehat Y_p)$ satisfying
$$
\eta^b=\frac{f_p}{f_q}
$$
in $K(\widehat Y_p)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909](https://doi.org/10.4171/owr/2019/46)
## Literature rev... | 3 | open | null | 2,019 | 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-17289-013",
"literature-status:open",
"owr-year:2019"
] | The semigroup conjecture for weighted Hasse graphs is explicitly stated in the report, and no later proof or counterexample resolving the stated general condition was found. | [
{
"url": "https://ems.press/content/serial-article-files/46825",
"label": "OWR 2019 46"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/46 | null | null | null | Is the weighted-Hasse-graph description of the valuation semigroup $\Gamma_C$ valid whenever, for every cover relation $p\gtrdot q$ of weight $b$, there is an $\eta\in K(\widehat Y_p)$ satisfying
$$
\eta^b=\frac{f_p}{f_q}
$$
in $K(\widehat Y_p)$? | Conjecture: the description of the semigroup \Gamma_C using only weighted-Hasse-graph data is valid whenever, for every edge p\cover q of weight b, there exists a rational function \eta\in K(\widehat{Y}_p) with \eta^b=f_{pq} in K(\widehat{Y}_p). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Degeneration Techniques in Representation Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/46, pp. 2869--2909 |
30,004,271 | OWR-17290-001 | Essential Self-Adjointness on Almost-Riemannian Regular Regions | Let $R$ be the regular region of an almost-Riemannian manifold. Is the Laplace–Beltrami operator $\Delta_g$, initially defined on $C_c^\infty(R)$, essentially self-adjoint on $L^2(R,\mu_g)$? In particular, is this true for every real-analytic two-dimensional almost-Riemannian structure without tangency points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | partially_solved | null | 2,019 | 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-17290-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Essential self-adjointness is proved under important regularity and non-characteristic hypotheses, but the broad real-analytic no-tangency conjecture in the extracted record remains unresolved for general almost-Riemannian structures. | [
{
"url": "https://doi.org/10.1007/s11118-018-09760-w",
"label": "Franceschi--Prandi--Rizzi"
},
{
"url": "https://ems.press/content/serial-article-files/46828",
"label": "OWR 2019 47"
},
{
"url": "https://ems.press/content/serial-article-files/33671?nt=1",
"label": "Quantum confinemen... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | Let $R$ be the regular region of an almost-Riemannian manifold. Is the Laplace–Beltrami operator $\Delta_g$, initially defined on $C_c^\infty(R)$, essentially self-adjoint on $L^2(R,\mu_g)$? In particular, is this true for every real-analytic two-dimensional almost-Riemannian structure without tangency points? | Is the Laplace--Beltrami operator \Delta_g on the regular region R, with domain C_c^\infty(R), essentially self-adjoint on L^2(R,\mu_g); in particular, is this true for every real-analytic almost-Riemannian structure on a 2-dimensional manifold with no tangency points? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,272 | OWR-17290-002 | Self-Adjointness for Degenerate No-Tangency Metrics | For the vector fields
$$X_1=\partial_x,\qquad X_2=x(x^{2\ell}+z^2)\partial_z$$
on $\mathbb R^2$, is the Laplace–Beltrami operator on the regular region essentially self-adjoint for every $\ell\geq1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | partially_solved | null | 2,019 | 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 | [Discussion #4 unrefereed claim, 2026-09-29] I have released an unrefereed preprint, **Essential Self-Adjointness of the Laplace–Beltrami Operator for a Family of Non-Regular Almost-Riemannian Structures** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23041946) | [
"owr",
"oberwolfach-reports",
"OWR-17290-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The explicit family is proved in the special case \ell=1, while the report states that the analogous essential-self-adjointness result for all positive \ell was expected but not proved. | [
{
"url": "https://ems.press/content/serial-article-files/46828",
"label": "OWR 2019 47"
},
{
"url": "https://doi.org/10.1007/s11118-018-09760-w",
"label": "Franceschi--Prandi--Rizzi"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | For the vector fields
$$X_1=\partial_x,\qquad X_2=x(x^{2\ell}+z^2)\partial_z$$
on $\mathbb R^2$, is the Laplace–Beltrami operator on the regular region essentially self-adjoint for every $\ell\geq1$? | For X_1=\partial_x and X_2=x(x^{2\ell}+z^2)\partial_z on \mathbb{R}^2, is the Laplace--Beltrami operator on the regular region essentially self-adjoint for every \ell\geq1; more generally, does the preceding real-analytic no-tangency conjecture hold? | corrected_verified | The general no-tangency question duplicated OWR-17290-001 and was removed; the distinct degenerate model was retained. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,273 | OWR-17290-003 | Self-Adjointness Across Almost-Riemannian Tangency Points | When an almost-Riemannian singular set has tangency points, is the Laplace–Beltrami operator on the regular region essentially self-adjoint? In particular, does this hold on $\mathbb R^2$ for
$$X_1=\partial_x,\qquad X_2=(z-x^2)\partial_z,$$
whose singular set is $z=x^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | open | null | 2,019 | 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-17290-003",
"literature-status:open",
"owr-year:2019"
] | The tangency-point parabola model is identified as the hardest unresolved case; results on operator closure and domains do not establish essential self-adjointness for this model. | [
{
"url": "https://ems.press/content/serial-article-files/46828",
"label": "OWR 2019 47"
},
{
"url": "https://doi.org/10.1007/s00025-022-01832-z",
"label": "Beschastnyi"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | When an almost-Riemannian singular set has tangency points, is the Laplace–Beltrami operator on the regular region essentially self-adjoint? In particular, does this hold on $\mathbb R^2$ for
$$X_1=\partial_x,\qquad X_2=(z-x^2)\partial_z,$$
whose singular set is $z=x^2$? | When the singular set has tangency points, is the Laplace--Beltrami operator on the regular region essentially self-adjoint; in particular, does this hold for X_1=\partial_x, X_2=(z-x^2)\partial_z on \mathbb{R}^2, whose singular set is z=x^2? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,274 | OWR-17290-004 | Dimensional Thresholds for Pointed Sub-Laplacian Self-Adjointness | For the pointed sub-Laplacian on a 3-dimensional equiregular sub-Riemannian structure modeled locally on the Heisenberg group, determine whether the topological dimension 3, the horizontal dimension 2, or the homogeneous dimension 4 governs essential self-adjointness. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | partially_solved | null | 2,019 | 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-17290-004",
"literature-status:partially-solved",
"owr-year:2019"
] | The three-dimensional genuine sub-Riemannian case, including the Heisenberg example, is now essentially self-adjoint after deleting a point; this gives substantial dimension-specific progress, but no general criterion identifies the relevant dimension for all pointed sub-Laplacians. | [
{
"url": "https://doi.org/10.1016/j.anihpc.2020.10.007",
"label": "Adami--Boscain--Franceschi--Prandi, Point interactions for 3D sub-Laplacians"
},
{
"url": "https://doi.org/10.4171/owr/2019/47",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | For the pointed sub-Laplacian on a 3-dimensional equiregular sub-Riemannian structure modeled locally on the Heisenberg group, determine whether the topological dimension 3, the horizontal dimension 2, or the homogeneous dimension 4 governs essential self-adjointness. | For the pointed sub-Laplacian on a 3-dimensional equiregular sub-Riemannian structure modeled locally on the Heisenberg group, determine whether the topological dimension 3, the horizontal dimension 2, or the homogeneous dimension 4 governs essential self-adjointness. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,275 | OWR-17290-005 | Self-Adjointness and Extensions of Infinite Metric-Graph Laplacians | For a metric graph with infinitely many edges and Kirchhoff Laplacian $H$, find geometric or combinatorial criteria guaranteeing self-adjointness. When self-adjointness fails, determine the deficiency indices and self-adjoint extensions of $H$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | open | null | 2,019 | 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-17290-005",
"literature-status:open",
"owr-year:2019"
] | Completeness, bounded degree, intrinsic metrics, and graph-end methods give important sufficient criteria and describe extensions, but the general self-adjointness criterion for arbitrary infinite metric graphs remains open. | [
{
"url": "https://arxiv.org/abs/1911.04735",
"label": "Nicolussi--Kostenko--Mugnolo, self-adjoint and Markovian extensions of infinite quantum graphs"
},
{
"url": "https://doi.org/10.4171/owr/2019/47",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | For a metric graph with infinitely many edges and Kirchhoff Laplacian $H$, find geometric or combinatorial criteria guaranteeing self-adjointness. When self-adjointness fails, determine the deficiency indices and self-adjoint extensions of $H$. | For a metric graph with infinitely many edges and Kirchhoff Laplacian H, find geometric or combinatorial criteria guaranteeing self-adjointness, and determine the deficiency indices and self-adjoint extensions when self-adjointness fails. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,276 | OWR-17290-006 | Spectrum of Boundary Problems with Noncompact Multiplier Weights | Let $P$ be an $n$-term self-similar function of zero spectral order such that its generalized derivative $P'$ is a noncompact Sobolev multiplier. For the singular Sturm–Liouville problem
$$-y''=\lambda P'y,\qquad y(0)=y(1)=0,$$
does the spectrum consist of $n-1$ possibly overlapping intervals of continuous spectrum, ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | open | null | 2,019 | 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-17290-006",
"literature-status:open",
"owr-year:2019"
] | Later work determines continuous spectrum and eigenvalue behavior for important noncompact-multiplier string models, but the complete spectral description requested for the general problem in the record has not been established. | [
{
"url": "https://www.mathnet.ru/php/archive.phtml?issue=4&jrnid=aa&option_lang=eng&volume=33&wshow=issue&year=2021",
"label": "Sharov--Sheipak, string equation with a noncompact multiplier"
},
{
"url": "https://doi.org/10.4171/owr/2019/47",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | Let $P$ be an $n$-term self-similar function of zero spectral order such that its generalized derivative $P'$ is a noncompact Sobolev multiplier. For the singular Sturm–Liouville problem
$$-y''=\lambda P'y,\qquad y(0)=y(1)=0,$$
does the spectrum consist of $n-1$ possibly overlapping intervals of continuous spectrum, ... | Determine the complete spectrum of the stated boundary-value problem when its weight is a non-compact multiplier, including its spectral type and eigenvalue behavior. | corrected_verified | The official report was checked. The dangling boundary-value reference was replaced by the singular Sturm–Liouville equation, boundary conditions, self-similar weight hypothesis, and precise spectral conjecture. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,277 | OWR-17290-007 | Essential Spectrum of Sign-Indefinite Transmission Laplacians | Let $L=-\nabla\cdot(h\nabla)$ on a bounded domain $\Omega$, where $h=1$ on $\Omega_+$ and $h=-\mu$ on $\Omega_-$, with interface $\Sigma$. When $\mu=1$, can the essential spectrum of $L$ contain more than one point or a nonempty interval? If it is a singleton, how do eigenvalues accumulate? Can boundary-triple methods ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950](https://doi.org/10.4171/owr/2019/47)
## Literature review (chec... | 3 | open | null | 2,019 | 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-17290-007",
"literature-status:open",
"owr-year:2019"
] | The smooth-interface theory settles special cases such as compact resolvent for strictly convex interfaces and essential spectrum at zero for flat parts, while the requested larger essential spectra, accumulation rates, other relative positions, and nonsmooth interfaces remain unresolved in general. | [
{
"url": "https://doi.org/10.1007/s11854-019-0057-z",
"label": "Cacciapuoti--Pankrashkin--Posilicano, self-adjoint indefinite Laplacians"
},
{
"url": "https://doi.org/10.4171/owr/2019/47",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/47 | null | null | null | Let $L=-\nabla\cdot(h\nabla)$ on a bounded domain $\Omega$, where $h=1$ on $\Omega_+$ and $h=-\mu$ on $\Omega_-$, with interface $\Sigma$. When $\mu=1$, can the essential spectrum of $L$ contain more than one point or a nonempty interval? If it is a singleton, how do eigenvalues accumulate? Can boundary-triple methods ... | For the sign-indefinite transmission Laplacian L on a bounded domain with contrast \mu=1 and interface \Sigma, determine whether its essential spectrum can contain more than one point or a nonempty interval; estimate eigenvalue accumulation when it is a singleton; and develop boundary-triple methods without \Omega_{-}\... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Self-adjoint Extensions in New Settings (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/47, pp. 2911--2950 |
30,004,278 | OWR-17292-001 | Conformal Field Theory Realizations of Subfactors | Does every finite-index subfactor admit a counterpart in conformal field theory, and can such a conformal net or vertex operator algebra be constructed directly from the subfactor data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,019 | 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-17292-001",
"literature-status:open",
"owr-year:2019"
] | Finite-index and small-index subfactor doubles have conformal-net realizations, but the general construction requested for every subfactor remains open; recent reports still describe Haagerup-type cases as lacking a known counterpart CFT. | [
{
"url": "https://ems.press/content/serial-article-files/46563?nt=1",
"label": "Jones, Does every subfactor arise in conformal field theory"
},
{
"url": "https://doi.org/10.4171/owr/2019/49",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1506.02606",
"labe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | Does every finite-index subfactor admit a counterpart in conformal field theory, and can such a conformal net or vertex operator algebra be constructed directly from the subfactor data? | Determine whether every subfactor has a corresponding conformal field theory, and construct or characterize such a CFT counterpart. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,279 | OWR-17292-002 | Equivalent Bicommutant Categories from Nonisomorphic Conformal Nets | Do there exist large families of pairwise nonisomorphic conformal nets whose associated bicommutant categories are equivalent as tensor categories? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,019 | 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-17292-002",
"literature-status:open",
"owr-year:2019"
] | Morita-equivalent unitary fusion categories are known to yield equivalent bicommutant categories, and finite-depth objects admit later classifications, but the stated existence of many non-isomorphic conformal nets with equivalent bicommutant tensor categories is not established by the cited literature. | [
{
"url": "https://arxiv.org/abs/2004.08271",
"label": "Henriques--Penneys, representations of fusion categories and commutants"
},
{
"url": "https://arxiv.org/abs/2307.13822",
"label": "Henriques--Penneys--Tener, finite-depth objects in bicommutant categories"
},
{
"url": "https://doi.or... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | Do there exist large families of pairwise nonisomorphic conformal nets whose associated bicommutant categories are equivalent as tensor categories? | There exist many pairwise non-isomorphic conformal nets whose associated bicommutant categories are equivalent as tensor categories. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,280 | OWR-17292-003 | Classification of Subnets of Conformal Nets | Given a conformal net $\mathcal A$, characterize all subnets $\mathcal B\subseteq\mathcal A$ by necessary and sufficient conditions that include information not determined by $\operatorname{Rep}(\mathcal A)$ alone. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,019 | 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-17292-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Quantum operations characterize every irreducible subnet as a fixed-point subnet and give a hypergroup Galois correspondence for discrete or finite-index inclusions, but a full characterization in the generality asked remains unavailable. | [
{
"url": "https://arxiv.org/abs/2204.14105",
"label": "Bischoff--Del Vecchio--Giorgetti, quantum operations on conformal nets"
},
{
"url": "https://doi.org/10.4171/owr/2019/49",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | Given a conformal net $\mathcal A$, characterize all subnets $\mathcal B\subseteq\mathcal A$ by necessary and sufficient conditions that include information not determined by $\operatorname{Rep}(\mathcal A)$ alone. | Given a conformal net A, characterize all subnets B\subseteq A, including sufficient as well as necessary conditions not determined by Rep(A) alone. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,281 | OWR-17292-005 | Small-Weight Quantum Operations on Lattice Conformal Nets | For a lattice conformal net or a strongly local vertex-operator-algebra net $\mathcal A$, find $\phi\in\operatorname{QuOp}(\mathcal A)$ satisfying $$\phi\circ\phi=w^{-1}\operatorname{id}+(1-w^{-1})\phi$$ for arbitrarily small real $w>1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,019 | 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-17292-005",
"literature-status:open",
"owr-year:2019"
] | The hypergroup and generalized-orbifold framework supplies examples and structural constraints, and numerical work gives evidence for Haagerup-related CFT behavior, but the requested quantum operation for the lattice or VOA examples, especially the Haagerup case, has not been constructed. | [
{
"url": "https://arxiv.org/abs/1608.00253",
"label": "Bischoff, generalized orbifold construction for conformal nets"
},
{
"url": "https://authors.library.caltech.edu/records/mgvpx-37124",
"label": "Osborne et al., numerical evidence for a Haagerup CFT"
},
{
"url": "https://doi.org/10.4... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | For a lattice conformal net or a strongly local vertex-operator-algebra net $\mathcal A$, find $\phi\in\operatorname{QuOp}(\mathcal A)$ satisfying $$\phi\circ\phi=w^{-1}\operatorname{id}+(1-w^{-1})\phi$$ for arbitrarily small real $w>1$. | For a lattice conformal net or a strongly local vertex-operator-algebra net A, find \phi\in\operatorname{QuOp}(A) such that \phi\circ\phi=w^{-1} \mathrm{id}+(1-w^{-1})\phi for arbitrarily small positive real w>1. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,282 | OWR-17292-006 | Hypergroup Correspondence for Discrete Conformal Subnets | For a strongly additive conformal net $\mathcal A$, establish a bijection between discrete subnets $\mathcal B\subseteq\mathcal A$ and compact hypergroups $K\subseteq\operatorname{QuOp}(\mathcal A)$, including intrinsic definitions that cover the infinite-index case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,019 | 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-17292-006",
"literature-status:partially-solved",
"owr-year:2019"
] | Compact-hypergroup invariants and Galois correspondences are proved for discrete or finite-index local subfactors, but the full infinite-index bijection and the required precise compact-type notions remain open. | [
{
"url": "https://arxiv.org/abs/2204.14105",
"label": "Bischoff--Del Vecchio--Giorgetti, quantum operations on conformal nets"
},
{
"url": "https://arxiv.org/abs/2007.12384",
"label": "Bischoff--Del Vecchio--Giorgetti, compact hypergroups from discrete subfactors"
},
{
"url": "https://do... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | For a strongly additive conformal net $\mathcal A$, establish a bijection between discrete subnets $\mathcal B\subseteq\mathcal A$ and compact hypergroups $K\subseteq\operatorname{QuOp}(\mathcal A)$, including intrinsic definitions that cover the infinite-index case. | For a strongly additive conformal net A, extend the subnet--quantum-operation correspondence to a bijection between discrete subnets B\subseteq A and compact hypergroups K\subseteq\operatorname{QuOp}(A), with precise definitions of both classes. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,283 | OWR-17292-007 | Universal Grading of Hyperfinite Factor Bimodules | Determine the universal grading group $U_R$ of the tensor category of dualizable $R$-$R$ bimodules, where $R$ is the hyperfinite $\mathrm{II}_1$ factor. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,019 | 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-17292-007",
"literature-status:open",
"owr-year:2019"
] | The universal grading group of bifinite bimodules over the hyperfinite factor is explicitly identified as an open question in the literature; positive real modular distortion gives a grading, but its universality is not proved. | [
{
"url": "https://dml.cz/bitstream/handle/10338.dmlcz/153425/HigherStructures_004-2020-2_2.pdf",
"label": "Penneys, unitary pivotal structures and modular distortion"
},
{
"url": "https://doi.org/10.4171/DM/1011",
"label": "Bischoff et al., distortion for multifactor bimodules"
},
{
"url... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | Determine the universal grading group $U_R$ of the tensor category of dualizable $R$-$R$ bimodules, where $R$ is the hyperfinite $\mathrm{II}_1$ factor. | Determine the universal grading group U_R of the category of dualizable R-R bimodules, where R is the hyperfinite II_1 factor. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,284 | OWR-17292-009 | Parametrization of Turaev–Viro Three-Manifold Invariants | For the fusion categories $\mathcal C_{N,1,0}$ with $N\in\mathbb N_{>0}$, find a uniform parametrization of the associated Turaev–Viro $3$-manifold invariants as $N$ varies. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,019 | 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-17292-009",
"literature-status:partially-solved",
"owr-year:2019"
] | The record reports that the exceptional quantum-subgroup fusion-rule question was answered, while the separate conjecture that the associated Turaev--Viro three-manifold invariant admits the proposed parametrization is not shown to be proved. | [
{
"url": "https://doi.org/10.4171/owr/2019/49",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/0040-9383(92)90015-A",
"label": "Turaev--Viro, state-sum invariants and quantum 6j-symbols"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | For the fusion categories $\mathcal C_{N,1,0}$ with $N\in\mathbb N_{>0}$, find a uniform parametrization of the associated Turaev–Viro $3$-manifold invariants as $N$ varies. | Conjecture: the three-manifold invariant associated with the Turaev--Viro TQFTs of the fusion categories C_{N,1,0}, for N\in\mathbb N_{>0}, admits a parameterization as N varies. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,285 | OWR-17292-011 | Canonical Equivalence of Complex and Lagrangian Quantizations | Given a compact symplectic manifold equipped both with a compatible-complex-structure quantization and with a Lagrangian-fibration quantization, construct a canonical isomorphism between the resulting quantum Hilbert spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140](https://doi.org/10.4171/owr/2019/49)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,019 | 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-17292-011",
"literature-status:partially-solved",
"owr-year:2019"
] | Spectral-convergence work proves convergence and comparisons of quantum Hilbert spaces for nonsingular Lagrangian and toric settings, with canonical identifications in special examples, but no canonical isomorphism is available for arbitrary pairs of quantizations. | [
{
"url": "https://arxiv.org/abs/1912.07994",
"label": "Hattori--Yamashita, spectral convergence in geometric quantization"
},
{
"url": "https://arxiv.org/abs/2002.12495",
"label": "Hattori--Yamashita, toric symplectic manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2019/49",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/49 | null | null | null | Given a compact symplectic manifold equipped both with a compatible-complex-structure quantization and with a Lagrangian-fibration quantization, construct a canonical isomorphism between the resulting quantum Hilbert spaces. | Given a compact symplectic manifold with a compatible-complex-structure quantization and a Lagrangian-fibration quantization, construct a canonical isomorphism between the two resulting quantum Hilbert spaces. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Subfactors and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/49, pp. 3053--3140 |
30,004,286 | OWR-17293-002 | Optimal Exponent for Counting Monogenic Number Fields | The exponent $1/2+1/n$ in the lower bound for the number of degree-$n$ monogenic number fields with Galois group $S_n$ and discriminant less than $X$ is optimal. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-002",
"literature-status:open",
"owr-year:2019"
] | Bhargava--Shankar--Wang prove the lower bound \gg X^{1/2+1/n} and explicitly conjecture that its exponent is optimal; later heuristic work supports the expected scale but does not prove the matching upper bound or asymptotic. | [
{
"url": "https://arxiv.org/abs/1611.09806",
"label": "Bhargava--Shankar--Wang, squarefree polynomial discriminants"
},
{
"url": "https://arxiv.org/abs/2006.09620",
"label": "Shankar, heuristics for S_n-number fields"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "origi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | The exponent $1/2+1/n$ in the lower bound for the number of degree-$n$ monogenic number fields with Galois group $S_n$ and discriminant less than $X$ is optimal. | The exponent 1/2+1/n in the lower bound for the number of degree-n monogenic number fields with Galois group S_n and discriminant less than X is optimal. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,287 | OWR-17293-003 | Brauer–Manin Obstruction for Rationally Connected Varieties | For every smooth, proper, geometrically integral, rationally connected variety, the Brauer–Manin obstruction is the only obstruction to the Hasse principle. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-003",
"literature-status:open",
"owr-year:2019"
] | The Colliot--Thélène conjecture remains a conjecture in the stated generality: current results prove the Brauer--Manin principle only for important special families and continue to use the general statement conditionally. | [
{
"url": "https://academic.oup.com/imrn/article/2021/6/4255/5292483",
"label": "Bright--Browning--Loughran, rational points and zero-cycles"
},
{
"url": "https://annals.math.princeton.edu/2023/197-3/p03",
"label": "Browning--Loughran--Sofos, Hasse principle for random Fano hypersurfaces"
},
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For every smooth, proper, geometrically integral, rationally connected variety, the Brauer–Manin obstruction is the only obstruction to the Hasse principle. | For every smooth, proper, geometrically integral, rationally connected variety, the Brauer--Manin obstruction is the only obstruction to the Hasse principle. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,288 | OWR-17293-004 | CFKRS Formula for Shifted Zeta Function Moments | The CFKRS conjecture predicts an asymptotic formula for smoothed averages of products of zeta-functions with small complex shifts: the main term is the sum of all equal-cardinality swap terms, with Dirichlet-series factor $B(C,D)=\sum_{n\geq 1}\tau_C(n)\tau_D(n)/n$, and an error $O(T^{1-\delta})$ as $T\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-004",
"literature-status:open",
"owr-year:2019"
] | The shifted product-of-quadratic-L-functions recipe remains conjectural in full generality; available proofs establish only restricted ranges or conditional special cases, so the extracted conjectural formula is not settled. | [
{
"url": "https://doi.org/10.1007/s00209-025-03848-x",
"label": "Conrey--Rodgers, quadratic twists of long Dirichlet polynomials"
},
{
"url": "https://arxiv.org/abs/2208.01783",
"label": "Conrey--Rodgers, preprint and stated range"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | The CFKRS conjecture predicts an asymptotic formula for smoothed averages of products of zeta-functions with small complex shifts: the main term is the sum of all equal-cardinality swap terms, with Dirichlet-series factor $B(C,D)=\sum_{n\geq 1}\tau_C(n)\tau_D(n)/n$, and an error $O(T^{1-\delta})$ as $T\to\infty$. | The CFKRS conjecture predicts an asymptotic formula for smoothed averages of products of zeta-functions with small complex shifts: the main term is the sum of all equal-cardinality swap terms, with Dirichlet-series factor B(C,D)=\sum_{n\ge1}\tau_C(n)\tau_D(n)/n, and an error O(T^{1-\delta}) as T\to\infty. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,289 | OWR-17293-005 | Long Dirichlet-Polynomial Recipe for Quadratic L-Functions | For fundamental discriminants $d$ and quadratic characters $\chi_d$, the long-polynomial recipe conjectures the stated smoothed average of $\sum_{n\leq X}\tau_A(n)\chi_d(n)/\sqrt n$ is given by the corresponding integral of the quadratic $L$-function swap terms, up to $O(D^{1-\delta})$ as $D\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Conrey--Rodgers prove the recipe in a conditional range where the polynomial length has exponent below 2, corresponding to the 0- and 1-swap terms; the longer range and full shifted-moment prediction in the record remain open. | [
{
"url": "https://doi.org/10.1007/s00209-025-03848-x",
"label": "Conrey--Rodgers, quadratic twists of long Dirichlet polynomials"
},
{
"url": "https://arxiv.org/abs/2208.01783",
"label": "Conrey--Rodgers, conditional theorem"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For fundamental discriminants $d$ and quadratic characters $\chi_d$, the long-polynomial recipe conjectures the stated smoothed average of $\sum_{n\leq X}\tau_A(n)\chi_d(n)/\sqrt n$ is given by the corresponding integral of the quadratic $L$-function swap terms, up to $O(D^{1-\delta})$ as $D\to\infty$. | For fundamental discriminants d and quadratic characters \chi_d, the long-polynomial recipe conjectures the stated smoothed average of \sum_{n\le X}\tau_A(n)\chi_d(n)/\sqrt n is given by the corresponding integral of the quadratic L-function swap terms, up to O(D^{1-\delta}) as D\to\infty. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,290 | OWR-17293-006 | Typical Size of the Erdős–Hooley Function | For a typical integer $n$, determine the asymptotic size of the Erdős–Hooley divisor-concentration function
$$\Delta(n)=\max_i\#\{d\mid n:e^i\leq d\leq e^{i+1}\}.$$
In particular, is the exponent $\eta\approx0.353$ in the almost-all lower bound $\Delta(n)\gg(\log\log n)^{\eta+o(1)}$ optimal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17293-007",
"OWR-17293-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The general distribution question has substantial progress: the Erdős--Hooley function has sharp-looking lower bounds and extensive structural analysis, but no complete description of the divisors of a typical integer is known. | [
{
"url": "https://arxiv.org/abs/1908.00378",
"label": "Ford--Green--Koukoulopoulos, equal sums and divisor concentration"
},
{
"url": "https://doi.org/10.1112/plms.12572",
"label": "Koukoulopoulos--Tao, upper mean-value bound"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For a typical integer $n$, determine the asymptotic size of the Erdős–Hooley divisor-concentration function
$$\Delta(n)=\max_i\#\{d\mid n:e^i\leq d\leq e^{i+1}\}.$$
In particular, is the exponent $\eta\approx0.353$ in the almost-all lower bound $\Delta(n)\gg(\log\log n)^{\eta+o(1)}$ optimal? | Determine the concentration of the divisors of a typical integer n, specifically the typical size of the Erdős--Hooley function \Delta(n)=\max_i\#\{d\mid n:e^i\le d\le e^{i+1}\}. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,291 | OWR-17293-007 | Duplicate Erdős–Hooley Typical-Size Extraction | For almost all integers n, determine how large the Erdős--Hooley divisor-concentration function \Delta(n) is, including the optimal exponent in its polylogarithmic lower bound. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the typical-size question and optimal-exponent conjecture represented canonically ) | [
"OWR-17293-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-007",
"literature-status:partially-solved",
"owr-year:2019"
] | Ford--Green--Koukoulopoulos obtain the exponent \eta=0.35332277\ldots as an almost-all lower bound, while later work gives upper bounds of larger order; the expected exact size is therefore unresolved. | [
{
"url": "https://arxiv.org/abs/1908.00378",
"label": "Ford--Green--Koukoulopoulos, divisor concentration"
},
{
"url": "https://doi.org/10.1112/plms.12572",
"label": "Koukoulopoulos--Tao, upper mean-value bound"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OW... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | null | For almost all integers n, determine how large the Erdős--Hooley divisor-concentration function \Delta(n) is, including the optimal exponent in its polylogarithmic lower bound. | unrecoverable | The official report confirms that this extraction repeats the typical-size question and optimal-exponent conjecture represented canonically by OWR-17293-006. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,292 | OWR-17293-008 | Duplicate Erdős–Hooley Optimal-Exponent Extraction | The exponent \eta=\log 2/\log(2/\rho) in the lower bound for \Delta(n) is optimal, where \rho\approx0.281 is defined by the recurrence and equation given in the report. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the optimal-exponent part of the Erdős–Hooley question represented canonically by ) | [
"OWR-17293-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-008",
"literature-status:partially-solved",
"owr-year:2019"
] | The conjectured exponent is supported by the proved lower bound and by the random-set model, but the matching upper bound for almost all integers has not been proved. | [
{
"url": "https://arxiv.org/abs/1908.00378",
"label": "Ford--Green--Koukoulopoulos, equal sums and concentration"
},
{
"url": "https://doi.org/10.1112/plms.12572",
"label": "Koukoulopoulos--Tao, upper mean-value bound"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "orig... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | null | The exponent \eta=\log 2/\log(2/\rho) in the lower bound for \Delta(n) is optimal, where \rho\approx0.281 is defined by the recurrence and equation given in the report. | unrecoverable | The official report confirms that this extraction repeats the optimal-exponent part of the Erdős–Hooley question represented canonically by OWR-17293-006. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,293 | OWR-17293-009 | Maximum Additive Multiplicity in Logarithmic Random Sets | For a logarithmic random set $A\subseteq\mathbb{N}$, with each $i$ selected independently with probability $1/i$, determine $\max_x r_A(x)$, where $r_A(x)$ counts representations of $x$ as a sum of elements of $A$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 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-17293-009",
"literature-status:open",
"owr-year:2019"
] | The unrestricted random-set maximum \max_x r_A(x) is not determined; the main paper instead studies truncated variants and obtains partial lower bounds or variational characterizations. | [
{
"url": "https://arxiv.org/abs/1908.00378",
"label": "Ford--Green--Koukoulopoulos, equal sums in random sets"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For a logarithmic random set $A\subseteq\mathbb{N}$, with each $i$ selected independently with probability $1/i$, determine $\max_x r_A(x)$, where $r_A(x)$ counts representations of $x$ as a sum of elements of $A$. | For a logarithmic random set A\subseteq\mathbb N, with each i selected independently with probability 1/i, determine \max_x r_A(x), where r_A(x) counts representations of x as a sum of elements of A. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,294 | OWR-17293-011 | Gilbreath Conjecture for Iterated Prime Differences | Does current knowledge about the primes suffice to prove Gilbreath's conjecture that every row after the first in the iterated unsigned-difference table of consecutive primes begins with 1? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-011",
"literature-status:open",
"owr-year:2019"
] | This is Gilbreath's conjecture. Numerical verifications and recent analysis of a Cramér random model provide evidence and heuristics, but the prime sequence conjecture itself remains unproved. | [
{
"url": "https://arxiv.org/abs/2607.08712",
"label": "Chase--Hunter--Tao, Cramér model and deterministic analysis"
},
{
"url": "https://doi.org/10.1090/S0025-5718-1993-1182247-7",
"label": "Odlyzko, iterated absolute differences of primes"
},
{
"url": "https://doi.org/10.4171/owr/2019/5... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | Does current knowledge about the primes suffice to prove Gilbreath's conjecture that every row after the first in the iterated unsigned-difference table of consecutive primes begins with 1? | Does current knowledge about the primes suffice to prove Gilbreath's conjecture that every row after the first in the iterated unsigned-difference table of consecutive primes begins with 1? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,295 | OWR-17293-012 | Optimal Pólya–Vinogradov Constants Across Dirichlet Characters | For a prime $p$ and nonprincipal Dirichlet characters $\chi\pmod p$, determine the best constant $C$ such that $\min_{\chi}\max_{0\leq x\leq p}\left|\sum_{0<n\leq x}\chi(n)\right|<C\sqrt p$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-012",
"literature-status:open",
"owr-year:2019"
] | The extremal minimum over characters in the stated Pólya--Vinogradov normalization is not known exactly; distribution theorems for typical characters and general lower bounds do not determine the best constant. | [
{
"url": "https://doi.org/10.4171/JEMS/799",
"label": "Bober--Goldmakher--Granville--Koukoulopoulos, large character sums"
},
{
"url": "https://doi.org/10.1112/S002557931200109X",
"label": "Bober--Goldmakher, distribution of maximum character sums"
},
{
"url": "https://doi.org/10.4171/ow... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For a prime $p$ and nonprincipal Dirichlet characters $\chi\pmod p$, determine the best constant $C$ such that $\min_{\chi}\max_{0\leq x\leq p}\left|\sum_{0<n\leq x}\chi(n)\right|<C\sqrt p$. | For a prime p and nonprincipal Dirichlet characters \chi\pmod p, determine the best constant C such that \min_{\chi}\max_{0\le x\le p}\left|\sum_{0<n\le x}\chi(n)\right|<C\sqrt p. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,296 | OWR-17293-014 | Counting Integer Matrices with Prescribed Minor Scales | Let $f(n)$ be one of $\sqrt n,n,n^{3/2},n^2,n^3$, let $M=[f(m_{ij})]$, let $\Delta_k$ be the maximum absolute determinant of a $k\times k$ minor, and count the tuples $(m_{ij})$ with prescribed scales $\Delta_k\asymp D_k$; what upper bounds can be obtained for this counting function? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-014",
"literature-status:open",
"owr-year:2019"
] | The matrix-minor counting function in the record is posed as an open restriction-theoretic problem; existing determinant and restriction estimates do not provide the requested general upper bounds. | [
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | Let $f(n)$ be one of $\sqrt n,n,n^{3/2},n^2,n^3$, let $M=[f(m_{ij})]$, let $\Delta_k$ be the maximum absolute determinant of a $k\times k$ minor, and count the tuples $(m_{ij})$ with prescribed scales $\Delta_k\asymp D_k$; what upper bounds can be obtained for this counting function? | Let f(n) be one of \sqrt n,n,n^{3/2},n^2,n^3, let M=[f(m_{ij})], let \Delta_k be the maximum absolute determinant of a k\times k minor, and count the tuples (m_{ij}) with prescribed scales \Delta_k\asymp D_k; what upper bounds can be obtained for this counting function? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,297 | OWR-17293-015 | Bounded Weighted Integral Points on a Rank-One Elliptic Curve | For integer solutions $(x,y,z)$ with $|x|,|y|,|z|\leq B$ of $zy^2+yz^2=x^3-xz^2$, is the counting quantity $\sum r_0(z)$, where $r_0(z)=1$ if $z$ is a sum of two squares and $0$ otherwise, bounded as $B\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-015",
"literature-status:open",
"owr-year:2019"
] | The record gives an o(\sqrt{\log B}) estimate for the weighted integral-point count on a rank-one elliptic curve and asks whether it is bounded; no general boundedness theorem for this count is established. | [
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | For integer solutions $(x,y,z)$ with $|x|,|y|,|z|\leq B$ of $zy^2+yz^2=x^3-xz^2$, is the counting quantity $\sum r_0(z)$, where $r_0(z)=1$ if $z$ is a sum of two squares and $0$ otherwise, bounded as $B\to\infty$? | For integer solutions (x,y,z) with |x|,|y|,|z|\le B of zy^2+yz^2=x^3-xz^2, is the counting quantity \sum r_0(z), where r_0(z)=1 if z is a sum of two squares and 0 otherwise, bounded as B\to\infty? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,298 | OWR-17293-016 | Coefficient Normalization of Positive Definite Homogeneous Forms | If $\psi\in\mathbb{R}[t_1,\ldots,t_m]$ is homogeneous of degree $d$ and positive definite, with $\psi(t)=\sum n(j_1,\ldots,j_d)t_{j_1}\cdots t_{j_d}$, is every such form linearly equivalent to a form $\psi'$ satisfying $n(j_1,\ldots,j_d)\leq\bigl(n(j_1,\ldots,j_1)\cdots n(j_d,\ldots,j_d)\bigr)^{1/d}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem () | null | null | [Discussion #4 literature review, 2026-09-29] . The answer depends on the coefficient convention. | [
"owr",
"oberwolfach-reports",
"OWR-17293-016",
"literature-status:open",
"owr-year:2019"
] | The proposed coefficient normalization for arbitrary positive-definite homogeneous forms is still an unresolved general equivalence problem; standard reduction results do not imply the stated inequality in higher degree and dimension. | [
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | If $\psi\in\mathbb{R}[t_1,\ldots,t_m]$ is homogeneous of degree $d$ and positive definite, with $\psi(t)=\sum n(j_1,\ldots,j_d)t_{j_1}\cdots t_{j_d}$, is every such form linearly equivalent to a form $\psi'$ satisfying $n(j_1,\ldots,j_d)\leq\bigl(n(j_1,\ldots,j_1)\cdots n(j_d,\ldots,j_d)\bigr)^{1/d}$? | If \psi\in\mathbb R[t_1,\ldots,t_m] is homogeneous of degree d and positive definite, with \psi(t)=\sum n(j_1,\ldots,j_d)t_{j_1}\cdots t_{j_d}, is every such form linearly equivalent to a form \psi' satisfying n(j_1,\ldots,j_d)\le\bigl(n(j_1,\ldots,j_1)\cdots n(j_d,\ldots,j_d)\bigr)^{1/d}? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,299 | OWR-17293-017 | Absolutely Convergent Multiplicative Expansions of the von Mangoldt Function | Does there exist, for the von Mangoldt function $\Lambda(n)$, a representation $\Lambda(n)=F(n)\sum_{q=1}^{\infty}G(q,n)$ in which $F(n)$ is multiplicative, $G(q,n)$ is multiplicative in $q$ for each fixed $n$, and the sum is absolutely convergent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem () | null | null | [Discussion #4 literature review, 2026-09-29] . As printed, the answer is trivially yes: F = 1, G(1,n) = 1, G(2,n) = Λ(n) − 1 and G(q,n) = 0 for q ≥ 3. | [
"owr",
"oberwolfach-reports",
"OWR-17293-017",
"literature-status:open",
"owr-year:2019"
] | Hardy's Ramanujan expansion is not absolutely convergent, and later work on truncated or smoothed Ramanujan expansions does not supply the requested multiplicative F,G representation with absolute convergence. | [
{
"url": "https://doi.org/10.1007/s12188-024-00282-4",
"label": "On Ramanujan expansions and primes in arithmetic progressions"
},
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | Does there exist, for the von Mangoldt function $\Lambda(n)$, a representation $\Lambda(n)=F(n)\sum_{q=1}^{\infty}G(q,n)$ in which $F(n)$ is multiplicative, $G(q,n)$ is multiplicative in $q$ for each fixed $n$, and the sum is absolutely convergent? | Does there exist, for the von Mangoldt function \Lambda(n), a representation \Lambda(n)=F(n)\sum_{q=1}^{\infty}G(q,n) in which F(n) is multiplicative, G(q,n) is multiplicative in q for each fixed n, and the sum is absolutely convergent? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,300 | OWR-17293-018 | Equal Sum Counts for Increasing Ratio Sequences | Given real numbers $1<a_1<a_2<\cdots$ whose successive ratios $a_{n+1}/a_n$ are increasing, what can be said about the number of solutions of $a_{i_1}+\cdots+a_{i_k}=a_{j_1}+\cdots+a_{j_k}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205](https://doi.org/10.4171/owr/2019/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17293-018",
"literature-status:open",
"owr-year:2019"
] | Known lacunary and geometric-ratio methods do not cover increasing, nonconstant ratios in the equal-k-sums problem; no general estimate for the size of such a set is established. | [
{
"url": "https://doi.org/10.4171/owr/2019/50",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/50 | null | null | null | Given real numbers $1<a_1<a_2<\cdots$ whose successive ratios $a_{n+1}/a_n$ are increasing, what can be said about the number of solutions of $a_{i_1}+\cdots+a_{i_k}=a_{j_1}+\cdots+a_{j_k}$? | Given real numbers 1<a_1<a_2<\cdots whose successive ratios a_{n+1}/a_n are increasing, what can be said about the number of solutions of a_{i_1}+\cdots+a_{i_k}=a_{j_1}+\cdots+a_{j_k}? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Analytic Number Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/50, pp. 3141--3205 |
30,004,301 | OWR-17294-001 | Structure Algebras of Yang–Baxter Solutions | For a set-theoretic Yang–Baxter solution $(X,r)$ with structure algebra $kM(X,r)$ and associated injective $1$-cocycle $\pi$, when is $\pi$ injective, and what is the algebraic structure of $kM(X,r)$ in the injective and general cases? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-001",
"literature-status:partially-solved",
"owr-year:2019"
] | For finite solutions, the 1-cocycle is characterized as bijective exactly in the left-nondegenerate case, and recent work determines large parts of the associated structure algebras; the three requested classifications remain open in full generality. | [
{
"url": "https://arxiv.org/abs/1912.09710",
"label": "Cedó--Jespers--Verwimp, structure monoids"
},
{
"url": "https://arxiv.org/abs/2305.06023",
"label": "Colazzo--Jespers--Kubat--Van Antwerpen, structure algebras"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2026.04.044",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For a set-theoretic Yang–Baxter solution $(X,r)$ with structure algebra $kM(X,r)$ and associated injective $1$-cocycle $\pi$, when is $\pi$ injective, and what is the algebraic structure of $kM(X,r)$ in the injective and general cases? | For a set-theoretic Yang--Baxter solution (X,r) with structure algebra kM(X,r) and associated injective 1-cocycle \pi, determine precisely when \pi is injective, determine the algebraic structure of kM(X,r) when it is injective, and determine the algebraic structure of kM(X,r) for arbitrary solutions. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,302 | OWR-17294-002 | Involutivity and Cancellativity of Yang–Baxter Solutions | For a set-theoretic Yang–Baxter solution $(X,r)$ with structure algebra $kM(X,r)$, characterize in ring-theoretic or homological terms when $(X,r)$ is involutive and when the structure monoid $M$ is cancellative. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Recent finite left-nondegenerate results relate involutivity, cancellativity, primeness, domain properties, and homological dimensions, but the requested ring-theoretic and homological characterization for arbitrary solutions is not complete. | [
{
"url": "https://arxiv.org/abs/2305.06023",
"label": "Colazzo--Jespers--Kubat--Van Antwerpen, structure algebras"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2026.04.044",
"label": "2026 structure-algebra results"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"label": "orig... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For a set-theoretic Yang–Baxter solution $(X,r)$ with structure algebra $kM(X,r)$, characterize in ring-theoretic or homological terms when $(X,r)$ is involutive and when the structure monoid $M$ is cancellative. | For a set-theoretic Yang--Baxter solution (X,r) with structure algebra kM(X,r), characterize in ring-theoretic or homological terms when (X,r) is involutive and when the structure monoid M is cancellative. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,303 | OWR-17294-003 | Semiprime Yang–Baxter Structure Algebras | When is the structure algebra $kM(X,r)$ semiprime, and how does its semiprimeness affect the Yang–Baxter solution $(X,r)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Semiprimeness is characterized in several finite bijective and idempotent families, and recent work gives structural consequences, but its effect on arbitrary YBE solutions is not classified. | [
{
"url": "https://arxiv.org/abs/2305.06023",
"label": "Colazzo--Jespers--Kubat--Van Antwerpen, structure algebras"
},
{
"url": "https://academic.oup.com/imrn/article/2024/7/5458/7240113",
"label": "Colazzo et al., finite idempotent solutions"
},
{
"url": "https://doi.org/10.1016/j.jalgeb... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | When is the structure algebra $kM(X,r)$ semiprime, and how does its semiprimeness affect the Yang–Baxter solution $(X,r)$? | When is the structure algebra kM(X,r) semiprime, and how does its semiprimeness affect the Yang--Baxter solution (X,r)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,304 | OWR-17294-004 | Prime Quotients of Yang–Baxter Structure Algebras | For a prime ideal $P$ of $kM(X,r)$, determine the structure of $kM(X,r)/P$, including when it is a domain, a maximal order, Koszul, Auslander-regular, Cohen–Macaulay, or otherwise homologically well behaved. When does the quotient come from a related Yang–Baxter solution, and how do its properties affect $(X,r)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-004",
"literature-status:partially-solved",
"owr-year:2019"
] | Prime spectra and substantial domain, Noetherian, GK-dimension, and homological results are now available for finite left-nondegenerate cases, but the full list of prime-image properties in the question remains unresolved. | [
{
"url": "https://arxiv.org/abs/2305.06023",
"label": "Colazzo--Jespers--Kubat--Van Antwerpen, structure algebras"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2026.04.044",
"label": "2026 structure-algebra results"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"label": "orig... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For a prime ideal $P$ of $kM(X,r)$, determine the structure of $kM(X,r)/P$, including when it is a domain, a maximal order, Koszul, Auslander-regular, Cohen–Macaulay, or otherwise homologically well behaved. When does the quotient come from a related Yang–Baxter solution, and how do its properties affect $(X,r)$? | For a prime ideal P of kM(X,r), determine the structure of kM/P, including when it is a domain, a maximal order, Koszul, Auslander-regular, Cohen--Macaulay, or otherwise homologically well behaved; determine when kM/P comes from a related Yang--Baxter solution and how these properties affect the original solution (X,r)... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,305 | OWR-17294-005 | Related Solutions from Prime Structure-Algebra Quotients | For prime quotients $kM(X,r)/P$ that arise from related Yang–Baxter solutions, how do the properties of those solutions, as $P$ varies, reflect the properties of $(X,r)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Semiprime structure algebras admit strong embedding and representation results in nondegenerate settings, while recent work treats further finite degenerate cases; the requested matrix representations and their effect on solutions are not general theorems. | [
{
"url": "https://arxiv.org/abs/1812.02026",
"label": "Colazzo--Jespers--Van Antwerpen--Verwimp, structure monoid and algebra"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2026.04.044",
"label": "2026 structure-algebra results"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For prime quotients $kM(X,r)/P$ that arise from related Yang–Baxter solutions, how do the properties of those solutions, as $P$ varies, reflect the properties of $(X,r)$? | For the prime quotients kM/P of the structure algebra of (X,r) that arise from related Yang--Baxter solutions, how do the properties of those solutions for varying P reflect the properties of (X,r)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,306 | OWR-17294-006 | Algebraic Invariants of Yang–Baxter Map Order | Is there an algebraic invariant that determines the order of the Yang–Baxter map $r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-006",
"literature-status:open",
"owr-year:2019"
] | Derived permutation groups, retractions, and related invariants provide partial information about YBE solutions, but no general algebraic invariant determining the order of r has been established. | [
{
"url": "https://arxiv.org/abs/1507.02602",
"label": "Gateva--Ivanova, derived symmetric and permutation groups"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Is there an algebraic invariant that determines the order of the Yang–Baxter map $r$? | Is there an algebraic invariant that determines the order of the Yang--Baxter map r? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,307 | OWR-17294-007 | Second-Cohomology Torsion of Finite Abelian Quandles | Compute the torsion subgroup of the second cohomology groups $H^2$ of finite abelian quandles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-007",
"literature-status:partially-solved",
"owr-year:2019"
] | Lebed--Mortier give an explicit structural description of the torsion for finite abelian quandles in terms of finite-group quotients and settle important subclasses, but a uniform explicit computation for all finite abelian quandles remains unavailable. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106474",
"label": "Lebed--Mortier, abelian quandles and structure groups"
},
{
"url": "https://arxiv.org/abs/1908.06745",
"label": "Lebed--Mortier, detailed preprint"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"label": "original O... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Compute the torsion subgroup of the second cohomology groups $H^2$ of finite abelian quandles. | Compute the torsion subgroup of the second cohomology groups H^2 of finite abelian quandles. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,308 | OWR-17294-008 | Abelian Derived Racks and Their Structure Groups | For a left nondegenerate Yang–Baxter solution $(X,r)$ and its derived rack, what property of $(X,r)$ corresponds to the derived rack having an abelian structure group, and what property corresponds to the rack itself being abelian? Does splitting of the associated central extension, with an additional condition, charac... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-008",
"literature-status:partially-solved",
"owr-year:2019"
] | Finite rack and quandle structure groups, permutation and derived racks, and abelian-quandle cases have substantial classifications, but no general correspondence or group-theoretic characterization answering all four questions is known. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106474",
"label": "Lebed--Mortier, abelian quandles and structure groups"
},
{
"url": "https://arxiv.org/abs/1912.09710",
"label": "Cedó--Jespers--Verwimp, derived structure monoids"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For a left nondegenerate Yang–Baxter solution $(X,r)$ and its derived rack, what property of $(X,r)$ corresponds to the derived rack having an abelian structure group, and what property corresponds to the rack itself being abelian? Does splitting of the associated central extension, with an additional condition, charac... | For a left non-degenerate Yang--Baxter solution (X,r) and its derived rack, what property of (X,r) corresponds to the derived rack having an abelian structure group, and what property corresponds to the derived rack itself being abelian? Does splitting of the associated central extension, with an additional condition, ... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,309 | OWR-17294-009 | Solvability and Realizability of Finite Skew Braces | Is the multiplicative group of a finite skew left brace with solvable additive group solvable? Is every finite nilpotent group of class two the multiplicative group of a two-sided skew brace of abelian type? Is there a non-IYB finite group all of whose Sylow subgroups are IYB groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial_progress",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17294-009",
"literature-status:open",
"owr-year:2019"
] | Di Matteo–Ferrara–Trombetti give a finite skew brace with solvable additive group and nonsolvable multiplicative group, disproving the first (Byott) question. This is a July 2026 unrefereed preprint. The record also contains Vendramin’s Problems 3 and 5; a counterexample to Problem 1 does not answer them.
**What remai... | [
{
"url": "https://arxiv.org/abs/2607.22795",
"label": "Di Matteo–Ferrara–Trombetti, counterexample to Byott’s conjecture — unrefereed preprint"
},
{
"url": "https://doi.org/10.4171/owr/2019/51",
"label": "Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Rep... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Is the multiplicative group of a finite skew left brace with solvable additive group solvable? Is every finite nilpotent group of class two the multiplicative group of a two-sided skew brace of abelian type? Is there a non-IYB finite group all of whose Sylow subgroups are IYB groups? | Is the multiplicative group of a finite skew left brace with solvable additive group solvable? Is every finite nilpotent group of class two the multiplicative group of a two-sided skew brace of abelian type? Is there a non-IYB finite group all of whose Sylow subgroups are IYB groups? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,310 | OWR-17294-010 | Prevalence of Multipermutation Yang–Baxter Solutions | Does the ratio of the number of multipermutation Yang–Baxter solutions of size $n$ to the total number of solutions of size $n$ tend to $1$ as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-010",
"literature-status:open",
"owr-year:2019"
] | Finite enumeration and structural results for multipermutation solutions do not establish the proposed asymptotic ratio, which remains an open counting problem. | [
{
"url": "https://link.springer.com/chapter/10.1007/978-3-031-90653-4_1",
"label": "Incremental SAT-based enumeration of Yang--Baxter solutions"
},
{
"url": "https://arxiv.org/abs/2509.11001",
"label": "Ferrara, Trombetti, and Tsang, Cardinalities and multipermutation level"
},
{
"url": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Does the ratio of the number of multipermutation Yang–Baxter solutions of size $n$ to the total number of solutions of size $n$ tend to $1$ as $n\to\infty$? | Does the ratio of the number of multipermutation Yang--Baxter solutions of size n to the total number of solutions of size n tend to 1 as n\to\infty? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,311 | OWR-17294-011 | Simple Braces as Asymmetric Products | Let $B$ be a nontrivial finite simple left brace whose multiplicative group is metabelian with abelian Sylow subgroups. Is $B$ the asymmetric product of two trivial left braces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-011",
"literature-status:open",
"owr-year:2019"
] | Asymmetric products construct important families of finite simple braces, but no classification proves that every brace in the stated metabelian and Sylow setting has this form. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2025.108025",
"label": "New simple solutions of the Yang--Baxter equation"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0001870821004072",
"label": "Constructing finite simple solutions"
},
{
"url": "https://ems.press/conten... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Let $B$ be a nontrivial finite simple left brace whose multiplicative group is metabelian with abelian Sylow subgroups. Is $B$ the asymmetric product of two trivial left braces? | Let B be a nontrivial finite simple left brace whose multiplicative group is metabelian with abelian Sylow subgroups. Is B the asymmetric product of two trivial left braces? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,312 | OWR-17294-012 | Kegel–Wielandt Theory for Skew Braces | For skew left braces, is the sum of a trivial skew left brace and a right-nilpotent skew left brace right-nilpotent? Can the Kegel–Wielandt theorem be adapted to skew left braces? Can Huppert's result that finite sums of finite cyclic groups are supersolvable be adapted to skew left braces, and what are the correspondi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | partially_solved | null | 2,019 | 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-17294-012",
"literature-status:partially-solved",
"owr-year:2019"
] | Factorization results cover strong trivial summands and give right-nilpotency bounds, while examples rule out a naive Kegel--Wielandt analogue; the full sum and adaptation questions remain open. | [
{
"url": "https://notablesdelaciencia.conicet.gov.ar/bitstream/handle/11336/136170/CONICET_Digital_Nro.11b9658a-b246-481f-ae3c-c31eaf455ce5_X.pdf?isAllowed=y\\&sequence=5",
"label": "Factorizations of skew braces"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869323006233",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | For skew left braces, is the sum of a trivial skew left brace and a right-nilpotent skew left brace right-nilpotent? Can the Kegel–Wielandt theorem be adapted to skew left braces? Can Huppert's result that finite sums of finite cyclic groups are supersolvable be adapted to skew left braces, and what are the correspondi... | For skew left braces, is the sum of a trivial skew left brace and a right-nilpotent skew left brace right-nilpotent? Can the Kegel--Wielandt theorem be adapted to skew left braces? Can Huppert's result that finite sums of finite cyclic groups are supersolvable be adapted to skew left braces, and what are the correspond... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,313 | OWR-17294-014 | Yang–Baxter Solutions from Generalized Left Semi-Braces | Which generalized left semi-braces $S$ have the property that
$$
r(a,b)=\bigl(a\circ(a^{-}+b),(a^{-}+b)^{-}\circ b\bigr)
$$
is a set-theoretic solution of the Yang–Baxter equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-014",
"literature-status:open",
"owr-year:2019"
] | Necessary and sufficient criteria are known for narrower left semi-brace settings, and sufficient constructions exist for generalized left semi-braces, but the requested full characterization is not known. | [
{
"url": "https://doi.org/10.1515/forum-2020-0082",
"label": "Set-theoretic solutions to Yang--Baxter and generalized semi-braces"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869317302284",
"label": "Semi-braces and the Yang--Baxter equation"
},
{
"url": "https://... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Which generalized left semi-braces $S$ have the property that
$$
r(a,b)=\bigl(a\circ(a^{-}+b),(a^{-}+b)^{-}\circ b\bigr)
$$
is a set-theoretic solution of the Yang–Baxter equation? | Which generalized left semi-braces S have the property that the map r(a,b)=\bigl(a\circ(a^{-}+b),(a^{-}+b)^{-}\circ b\bigr) is a set-theoretic solution of the Yang--Baxter equation? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,314 | OWR-17294-015 | Yang–Baxter Solutions from Skew Lattices | Can skew lattices be used to describe more set-theoretic solutions of the Yang–Baxter equation, and what kinds of solutions result? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-015",
"literature-status:open",
"owr-year:2019"
] | Skew-lattice constructions now characterize several families of set-theoretic Yang--Baxter solutions, but describing all further solutions obtainable from skew lattices remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2019.10.007",
"label": "Skew lattices and set-theoretic solutions of Yang--Baxter"
},
{
"url": "https://arxiv.org/abs/2109.04978",
"label": "Yang--Baxter semitrusses"
},
{
"url": "https://link.springer.com/article/10.1007/s00233-025-10606-2",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Can skew lattices be used to describe more set-theoretic solutions of the Yang–Baxter equation, and what kinds of solutions result? | Can skew lattices be used to describe more set-theoretic solutions of the Yang--Baxter equation, and what kinds of solutions result? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,315 | OWR-17294-016 | Yang–Baxter Solutions from Noncommutative Lattices | Do the Yang–Baxter solutions obtained from skew lattices remain solutions for other noncommutative lattices, and do noncommutative lattices yield new solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 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-17294-016",
"literature-status:open",
"owr-year:2019"
] | The skew-lattice case is established and broader brace-like structures yield additional solutions, but no general theorem covers arbitrary noncommutative lattices. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2019.10.007",
"label": "Skew lattices and set-theoretic solutions of Yang--Baxter"
},
{
"url": "https://link.springer.com/article/10.1007/s00233-025-10606-2",
"label": "Generalized digroups and di-skew braces"
},
{
"url": "https://arxiv.org/ab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Do the Yang–Baxter solutions obtained from skew lattices remain solutions for other noncommutative lattices, and do noncommutative lattices yield new solutions? | Do the Yang--Baxter solutions obtained from skew lattices remain solutions for other noncommutative lattices, and do noncommutative lattices yield new solutions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.