id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,516 | OWR-12868-001 | Nonzerodivisors and Stabilization of Cohomology Annihilators | Let $\Lambda$ be a noetherian algebra finite over its center, let $\operatorname{ca}(\Lambda)$ be its cohomology-annihilator ideal, and let $\operatorname{ca}_s(\Lambda)$ denote its degree-$s$ approximation. Does $\operatorname{ca}(\Lambda)$ contain a nonzerodivisor? What is the least $s$ such that $\operatorname{ca}(\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | partially_solved | null | 2,014 | 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-12868-001",
"literature-status:partially-solved",
"owr-year:2014"
] | For broad classes of commutative noetherian and excellent rings, cohomology annihilators and strong generators are related to the singular locus and explicit bounds are proved; the general non-zerodivisor question and least exponent remain unsettled. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://www.math.nagoya-u.ac.jp/~takahashi/ua22.pdf",
"label": "Iyengar--Takahashi, annihilation and generation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | Let $\Lambda$ be a noetherian algebra finite over its center, let $\operatorname{ca}(\Lambda)$ be its cohomology-annihilator ideal, and let $\operatorname{ca}_s(\Lambda)$ denote its degree-$s$ approximation. Does $\operatorname{ca}(\Lambda)$ contain a nonzerodivisor? What is the least $s$ such that $\operatorname{ca}(\... | For a noetherian algebra Lambda finite over its center, let ca(Lambda) be the cohomology-annihilator ideal and let ca_s(Lambda) stabilize it. Does ca(Lambda) contain non-zerodivisors, and what is the least integer s such that ca(Lambda)=ca_s(Lambda)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,517 | OWR-12868-002 | Divisor Class Groups of Cluster Algebras | What is the divisor class group $\operatorname{Cl}(\mathcal A(\mathbf x,Q))$ of the cluster algebra associated with a quiver $Q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | partially_solved | null | 2,014 | 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-12868-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The divisor class group is explicitly computable for acyclic seeds and for every cluster algebra that is a Krull domain it is finitely generated and free abelian, but a uniform answer for all cluster algebras in the stated generality is not established. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://arxiv.org/abs/1712.06512",
"label": "Factoriality and class groups of cluster algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | What is the divisor class group $\operatorname{Cl}(\mathcal A(\mathbf x,Q))$ of the cluster algebra associated with a quiver $Q$? | What is the divisor class group Cl(A(x,Q)) of the cluster algebra associated with a quiver Q? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,518 | OWR-12868-003 | Torsion-Freeness of Cluster Algebra Class Groups | Is the divisor class group $\operatorname{Cl}(\mathcal A(\mathbf x,B))$ of every cluster algebra torsion-free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | solved | null | 2,014 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1016/j.aim.2019.106858",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved**. P. Lampe (OWR 8/2014, p. 486) conjectures that the divisor class group of a cluster algebra is always torsion-free. Garcia Elsener–Lampe–Smertnig, [Adv. Math. 358 (2019)](https://doi.org/10.1016/j.aim.2019.106858), Thm A: a cluster algebra with invertible frozen... | [
"owr",
"oberwolfach-reports",
"OWR-12868-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The torsion-free conjecture is proved for acyclic cluster algebras and, more generally, for cluster algebras that are Krull domains; the unrestricted formulation in the record is not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://arxiv.org/abs/1712.06512",
"label": "Garcia Elsener--Lampe--Smertnig"
},
{
"url": "https://arxiv.org/abs/2601.07520",
"label": "Class groups of upper cluster algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | Is the divisor class group $\operatorname{Cl}(\mathcal A(\mathbf x,B))$ of every cluster algebra torsion-free? | Conjecture: the divisor class group Cl(A(x,B)) of every cluster algebra is torsion-free. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,519 | OWR-12868-004 | Cluster Algebras of Open Richardson Varieties | For $v\leq w$ in the Bruhat order, is the cluster algebra $R_{v,w}$ equal to the coordinate ring $\mathbb C[\mathcal R_{v,w}]$ of the open Richardson variety $\mathcal R_{v,w}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | partially_solved | null | 2,014 | 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-12868-004",
"literature-status:partially-solved",
"owr-year:2014"
] | The conjectural equality between the categorical cluster algebra and the coordinate ring is proved in type A, while upper-cluster-algebra results and special cases are known more generally; the full stated generality remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://arxiv.org/abs/2210.13302",
"label": "Leclerc conjecture in type A"
},
{
"url": "https://arxiv.org/abs/2207.10184",
"label": "Open Richardson upper cluster algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | For $v\leq w$ in the Bruhat order, is the cluster algebra $R_{v,w}$ equal to the coordinate ring $\mathbb C[\mathcal R_{v,w}]$ of the open Richardson variety $\mathcal R_{v,w}$? | For v<=w in the Bruhat order, does the cluster algebra R_{v,w} equal the coordinate ring C[R_{v,w}] of the open Richardson variety R_{v,w}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,520 | OWR-12868-005 | Mixed Hodge Polynomials of Character Varieties | For a $k$-tuple of partitions $\mu$, let $\mathcal M_\mu$ be the corresponding generic $\operatorname{GL}_n(\mathbb C)$ character variety. Define $\mathbb H_\mu(z,w)$ by
$$
(z^2-1)(1-w^2)\operatorname{Log}\!\left(\sum_\lambda \mathcal H_\lambda(z,w)\prod_{i=1}^k\widetilde H_\lambda(x_i;z^2,w^2)\right)
=\sum_\mu\mathbb ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | partially_solved | null | 2,014 | 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-12868-005",
"literature-status:partially-solved",
"owr-year:2014"
] | The conjectural Hodge-polynomial formula has proved E-polynomial and integrality specializations, with further cases of the mixed-Hodge formula established, but the full mixed-Hodge statement for all M sub mu remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://arxiv.org/abs/0810.2076",
"label": "Hausel--Letellier--Rodriguez-Villegas"
},
{
"url": "https://www.mellit.org/publication/mellit-2018-integrality/",
"label": "Mellit, integrali... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | For a $k$-tuple of partitions $\mu$, let $\mathcal M_\mu$ be the corresponding generic $\operatorname{GL}_n(\mathbb C)$ character variety. Define $\mathbb H_\mu(z,w)$ by
$$
(z^2-1)(1-w^2)\operatorname{Log}\!\left(\sum_\lambda \mathcal H_\lambda(z,w)\prod_{i=1}^k\widetilde H_\lambda(x_i;z^2,w^2)\right)
=\sum_\mu\mathbb ... | Conjecture: the functions H_mu(z,w) defined by the generating-function expansion are polynomials in z and w that encode the mixed Hodge numbers of M_mu. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,521 | OWR-12868-006 | Periodic Simple Modules and Periodic Algebras | Let $A$ be a finite-dimensional algebra. If every simple module in $\operatorname{mod}A$ is periodic, must $A$ be a periodic algebra? Classify periodic algebras up to Morita and derived equivalence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | open | null | 2,014 | 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-12868-006",
"literature-status:open",
"owr-year:2014"
] | The implication from periodic simple modules to a periodic algebra and the requested classification of periodic algebras remain open in general, despite proofs for important families such as group blocks and finite representation type. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2009.09.012",
"label": "Periodic resolutions and self-injective algebras"
},
{
"url": "https://arxiv.org/abs/2012.11927",
"label": "Periodic trivial exten... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | Let $A$ be a finite-dimensional algebra. If every simple module in $\operatorname{mod}A$ is periodic, must $A$ be a periodic algebra? Classify periodic algebras up to Morita and derived equivalence. | Does periodicity of every simple module in mod A imply that A is a periodic algebra, and can all periodic algebras be classified up to Morita equivalence and derived equivalence? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,522 | OWR-12868-007 | Periodicity of Stable Auslander Algebras | Is the stable Auslander algebra of every hypersurface singularity of finite Cohen-Macaulay type periodic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | open | null | 2,014 | 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-12868-007",
"literature-status:open",
"owr-year:2014"
] | Periodicity is proved for several finite-type and Dynkin families, including the simple plane-curve cases cited in the report, but no general proof is known for stable Auslander algebras of all hypersurface singularities of finite Cohen--Macaulay type. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2009.09.012",
"label": "Periodic resolutions and stable Auslander algebras"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid%3Add7d9fb8-3a52-4b00-937e-ae7b89abc... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | Is the stable Auslander algebra of every hypersurface singularity of finite Cohen-Macaulay type periodic? | Is the stable Auslander algebra of every hypersurface singularity of finite Cohen-Macaulay type periodic? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,523 | OWR-12868-008 | Finite Generation for Gorenstein Algebras | For which finite-dimensional Gorenstein algebras does condition $\mathrm{Fg}$ hold; that is, when is the Hochschild cohomology ring noetherian and the Yoneda algebra of the direct sum of the simple modules finitely generated over it? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529](https://doi.org/10.4171/owr/2014/08)
## Literature revi... | 3 | partially_solved | null | 2,014 | 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-12868-008",
"literature-status:partially-solved",
"owr-year:2014"
] | The finite-generation condition implies Gorensteinness, and the converse is proved for finite-dimensional monomial algebras with further special classes characterized, but which Gorenstein algebras satisfy Fg in general remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/08",
"label": "Oberwolfach Report 08/2014"
},
{
"url": "https://arxiv.org/abs/1909.00487",
"label": "Finite generation for Gorenstein monomial algebras"
},
{
"url": "https://arxiv.org/abs/2301.05476",
"label": "Combinatorial characterisation... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/08 | null | null | null | For which finite-dimensional Gorenstein algebras does condition $\mathrm{Fg}$ hold; that is, when is the Hochschild cohomology ring noetherian and the Yoneda algebra of the direct sum of the simple modules finitely generated over it? | For which Gorenstein finite-dimensional algebras does condition Fg hold, namely that the Hochschild cohomology ring is noetherian and the Yoneda algebra of the sum of the simple modules is finitely generated over it? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/08, pp. 453--529 |
30,002,524 | OWR-12869-001 | Projective Fundamental Groups Among Kähler Groups | Does there exist a Kähler group that is not the fundamental group of any smooth complex projective variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-001",
"literature-status:open",
"owr-year:2014"
] | The inclusion of smooth projective fundamental groups among Kähler groups is established, but whether it is strict remains open in current literature. | [
{
"url": "https://link.springer.com/article/10.1007/s10231-024-01501-8",
"label": "Claudon and Höring, 2024"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Does there exist a Kähler group that is not the fundamental group of any smooth complex projective variety? | Is the inclusion of fundamental groups of smooth complex projective varieties into the class of Kahler groups strict? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,525 | OWR-12869-002 | Fundamental Groups of Singular Irreducible Projective Varieties | Which groups occur as fundamental groups of complex projective varieties when the varieties are required to be irreducible and their singularities are suitably controlled? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-002",
"literature-status:open",
"owr-year:2014"
] | Projective realizations of finitely presented groups with singularities are known, but the requested simultaneous control of singularities and irreducibility is not resolved. | [
{
"url": "https://doi.org/10.1007/s00222-013-0453-4",
"label": "Kapovich, 2013"
},
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Which groups occur as fundamental groups of complex projective varieties when the varieties are required to be irreducible and their singularities are suitably controlled? | Which groups occur as fundamental groups of complex projective varieties when the varieties are required to be irreducible and their singularities are suitably controlled? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,526 | OWR-12869-003 | Eliminating Whitney Umbrellas in Projective Group Realization | Can Whitney umbrellas be eliminated: does every finitely presented group occur as the fundamental group of an irreducible two-dimensional projective variety with only normal-crossing singularities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-003",
"literature-status:open",
"owr-year:2014"
] | Kapovich's irreducible projective realization still uses Whitney umbrellas in the stated theorem, and removing them is not established by the cited construction. | [
{
"url": "https://doi.org/10.1007/s00222-013-0453-4",
"label": "Kapovich, 2013"
},
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Can Whitney umbrellas be eliminated: does every finitely presented group occur as the fundamental group of an irreducible two-dimensional projective variety with only normal-crossing singularities? | Can Whitney umbrellas be eliminated: does every finitely presented group occur as the fundamental group of an irreducible two-dimensional projective variety with only normal-crossing singularities? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,527 | OWR-12869-004 | Generic Simplicity of Hyperbolic Dirichlet Tilings | Let $\Gamma<\operatorname{PO}(3,1)$ be discrete and torsion-free. For a generic base point $x\in\mathbb H^3$, is its Dirichlet tiling $D_x$ simple, with exactly three facets meeting along every edge and exactly four facets meeting at every vertex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-004",
"literature-status:open",
"owr-year:2014"
] | The generic simplicity conjecture for Dirichlet tilings in hyperbolic three-space has only partial results under extra hypotheses, so the unrestricted claim remains open. | [
{
"url": "https://doi.org/10.1007/s00222-013-0453-4",
"label": "Kapovich, 2013"
},
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Let $\Gamma<\operatorname{PO}(3,1)$ be discrete and torsion-free. For a generic base point $x\in\mathbb H^3$, is its Dirichlet tiling $D_x$ simple, with exactly three facets meeting along every edge and exactly four facets meeting at every vertex? | If Gamma is a discrete torsion-free subgroup of PO(3,1), is the Dirichlet tiling D_x of H^3 simple for a generic base point x in H^3, with every edge shared by exactly three facets and every vertex by exactly four facets? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,528 | OWR-12869-005 | Embedding Finitely Presented Groups into Kähler Groups | Does every finitely presented group occur as a subgroup of some Kähler group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-005",
"literature-status:open",
"owr-year:2014"
] | The conjecture that every finitely presented group embeds in a Kähler group remains an unresolved strengthening of known singular-projective realization results. | [
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
},
{
"url": "https://comptes-rendus.academie-sciences.fr/mathematique/item/10.5802/crmath.811.pdf",
"label": "Liu, 2026"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Does every finitely presented group occur as a subgroup of some Kähler group? | Does every finitely presented group occur as a subgroup of some Kahler group? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,529 | OWR-12869-006 | Virtual Second Cohomology of Infinite Kähler Groups | Does every infinite Kähler group have a finite-index subgroup whose second cohomology with real coefficients is nonzero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 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-12869-006",
"literature-status:open",
"owr-year:2014"
] | The Carlson--Toledo question about virtually nonzero second real cohomology of every infinite Kähler group has substantial partial results but no general proof or counterexample. | [
{
"url": "https://arxiv.org/abs/math/9903023",
"label": "Reznikov, 1999"
},
{
"url": "https://arxiv.org/abs/1004.3130",
"label": "Klingler, Koziarz, and Maubon, 2010"
},
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Does every infinite Kähler group have a finite-index subgroup whose second cohomology with real coefficients is nonzero? | Does every infinite Kahler group Gamma have a finite-index subgroup Gamma' with H^2(Gamma',R) nonzero? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,530 | OWR-12869-007 | Projective Realization of Torsion-Free Kähler Groups | Is every torsion-free Kähler group the fundamental group of a smooth projective variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553](https://doi.org/10.4171/owr/2014/09)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 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-12869-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The projectivity question for torsion-free Kähler groups remains open, while Campana--Claudon--Eyssidieux prove a substantial positive result for linear representations. | [
{
"url": "https://www.numdam.org/item/10.5802/jep.12.pdf",
"label": "Campana, Claudon, and Eyssidieux, 2014"
},
{
"url": "https://doi.org/10.4171/owr/2014/09",
"label": "Oberwolfach Report 9, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/09 | null | null | null | Is every torsion-free Kähler group the fundamental group of a smooth projective variety? | Is every torsion-free Kahler group the fundamental group of a smooth projective variety? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Kähler Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/09, pp. 531--553 |
30,002,531 | OWR-12870-001 | Bounded Negativity on Smooth Projective Surfaces | For every smooth projective complex surface $X$, does there exist a constant $b_X$ such that $C^2\geq-b_X$ for every reduced effective curve $C\subset X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 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-12870-001",
"literature-status:open",
"owr-year:2014"
] | The Bounded Negativity Conjecture is proved in important cases, but general boundedness of negative curves, including blowups of the projective plane, remains open. | [
{
"url": "https://doi.org/10.1515/advgeom-2023-0027",
"label": "Bauer et al., 2023"
},
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | For every smooth projective complex surface $X$, does there exist a constant $b_X$ such that $C^2\geq-b_X$ for every reduced effective curve $C\subset X$? | For every smooth projective complex surface X, does there exist a constant b_X such that C^2>=-b_X for every reduced effective curve C on X? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,532 | OWR-12870-002 | Higher-Dimensional Bounded Negativity for Algebraic Cycles | Which natural higher-dimensional generalizations of the Bounded Negativity Conjecture hold for cycles on smooth projective varieties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 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-12870-002",
"literature-status:open",
"owr-year:2014"
] | Higher-dimensional analogues of bounded negativity have no general established formulation or theorem resolving the research question. | [
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
},
{
"url": "https://doi.org/10.1515/advgeom-2023-0027",
"label": "Bauer et al., 2023"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | Which natural higher-dimensional generalizations of the Bounded Negativity Conjecture hold for cycles on smooth projective varieties? | Which natural higher-dimensional generalizations of the Bounded Negativity Conjecture hold for cycles on smooth projective varieties? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,533 | OWR-12870-003 | New Rational Lyapunov Exponents on Hilbert Modular Surfaces | Can one construct Kobayashi geodesics on Hilbert modular surfaces with rational Lyapunov exponents other than 1, 1/2, 1/3, 1/5, and 1/7? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12870-003",
"literature-status:open",
"owr-year:2014"
] | The known rational Lyapunov exponents for Kobayashi geodesics do not exhaust the possibilities, and constructing curves with further exponents remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
},
{
"url": "https://arxiv.org/abs/1111.2624",
"label": "Möller, 2012"
},
{
"url": "https://arxiv.org/abs/2512.09188",
"label": "Bogomolov et al., 2025"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | Can one construct Kobayashi geodesics on Hilbert modular surfaces with rational Lyapunov exponents other than 1, 1/2, 1/3, 1/5, and 1/7? | Can one construct Kobayashi geodesics on Hilbert modular surfaces with rational Lyapunov exponents other than 1, 1/2, 1/3, 1/5, and 1/7? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,534 | OWR-12870-007 | Finiteness of Negative Extremal Rays for KLT Pairs | Let $(X,\Delta)$ be a Kawamata log terminal pair with $\kappa(X,\Delta)\geq0$. Can the curves generating the $(K_X+\Delta)$-negative extremal rays in the cone theorem always be chosen from a finite collection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | partially_solved | null | 2,014 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; answered in the source)**. J. Lesieutre (OWR 10/2014, pp. 569–570) states KMM Problem 4-2-5: for a klt pair (X, Δ) with κ(X, Δ) ≥ 0, can the curves of the cone theorem be taken from a finite set? He reports there that the answer is no: Uehara pointed out a Cal... | [
"owr",
"oberwolfach-reports",
"OWR-12870-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The underlying extremal-ray conjecture has positive special cases in dimension three but fails for general klt pairs; the relevant smooth threefold case remains a restricted problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
},
{
"url": "https://doi.org/10.1007/s00222-013-0453-4",
"label": "Kapovich, 2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | Let $(X,\Delta)$ be a Kawamata log terminal pair with $\kappa(X,\Delta)\geq0$. Can the curves generating the $(K_X+\Delta)$-negative extremal rays in the cone theorem always be chosen from a finite collection? | Conjecture: If (X, Δ) is a klt pair with κ(X, Δ) ≥ 0, then the curves generating the (K_X + Δ)-negative extremal rays in the cone theorem can be chosen to be finite in number. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,535 | OWR-12870-008 | Finiteness of Minimal Models of Terminal Threefolds | For every terminal projective threefold $Y$, are there only finitely many minimal models reachable by the $K_Y$-minimal model program? In particular, are there only finitely many when the program is run with scaling by an ample divisor $H$ on $Y$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 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-12870-008",
"literature-status:open",
"owr-year:2014"
] | Finiteness of minimal-model outcomes for terminal projective threefolds, including the ample-scaling version stated here, is not settled in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3399/OWR_2014_10.pdf?isAllowed=y\\&sequence=1",
"label": "Oberwolfach Report 10 PDF"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | For every terminal projective threefold $Y$, are there only finitely many minimal models reachable by the $K_Y$-minimal model program? In particular, are there only finitely many when the program is run with scaling by an ample divisor $H$ on $Y$? | Conjecture: For every terminal projective threefold Y, only finitely many minimal models can be reached by the K_Y-MMP; in particular, only finitely many can occur when the MMP is run with scaling by an ample divisor H on Y. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,536 | OWR-12870-009 | Fujita's Global Generation and Very-Ampleness Conjecture | Let $L$ be an ample line bundle on a complex manifold $X$. Is $K_X\otimes L^m$ globally generated for $m\geq\dim X+1$ and very ample for $m\geq\dim X+2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 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-12870-009",
"literature-status:open",
"owr-year:2014"
] | Fujita's sharp global-generation and very-ampleness bounds remain open in general characteristic-zero dimension, despite many dimensional and weaker-bound results. | [
{
"url": "https://doi.org/10.1007/s10114-026-6229-8",
"label": "Siu, 2026"
},
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | Let $L$ be an ample line bundle on a complex manifold $X$. Is $K_X\otimes L^m$ globally generated for $m\geq\dim X+1$ and very ample for $m\geq\dim X+2$? | Fujita conjecture: If L is an ample line bundle on a complex manifold X, then K_X ⊗ L^m is globally generated for m ≥ dim(X)+1 and very ample for m ≥ dim(X)+2. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,537 | OWR-12870-012 | Probability Convergence of Metrics on Linear Series | Let $V_n\subset H^0(X,nL)$ be a multiplicative linear series, let $\varphi$ and $\psi$ be metrics on $L$, and choose a basis $(e_i)$ that is orthonormal for $\varphi_n$ and orthogonal for $\psi_n$. If $\lambda_i=\psi_n(e_i,e_i)$ and $Z_n$ is uniformly distributed on the values $\log(\lambda_i)/n$, does $Z_n$ converge i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593](https://doi.org/10.4171/owr/2014/10)
## Literature review (checked ... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (yes, for ample type; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes, for ample type; answered in the source)**. C. Maclean (joint with H. Chen; OWR 10/2014, pp. 587–588) poses this question; the Theorem on p. 588 answers it: Z_n converges when V_• is of Lazarsfeld–Mustață ample type. | [
"owr",
"oberwolfach-reports",
"OWR-12870-012",
"literature-status:open",
"owr-year:2014"
] | Chen--Maclean prove convergence in law for the logarithmic spectral measures, which is weaker and different from convergence in probability in the extracted formulation; no general probability result was found. | [
{
"url": "https://arxiv.org/abs/1304.5842",
"label": "Chen and Maclean, 2013"
},
{
"url": "https://doi.org/10.4171/owr/2014/10",
"label": "Oberwolfach Report 10, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/10 | null | null | null | Let $V_n\subset H^0(X,nL)$ be a multiplicative linear series, let $\varphi$ and $\psi$ be metrics on $L$, and choose a basis $(e_i)$ that is orthonormal for $\varphi_n$ and orthogonal for $\psi_n$. If $\lambda_i=\psi_n(e_i,e_i)$ and $Z_n$ is uniformly distributed on the values $\log(\lambda_i)/n$, does $Z_n$ converge i... | Given a multiplicative linear series V_n ⊂ H⁰(nL), metrics φ and ψ, and a φ_n-orthonormal, ψ_n-orthogonal basis with λ_i = ψ_n(e_i,e_i), let Z_n be uniformly distributed among log(λ_i)/n; does Z_n converge in probability? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Negative Curves on Algebraic Surfaces (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/10, pp. 555--593 |
30,002,538 | OWR-12871-001 | CAT(0) Actions of Artin Groups | Does every Artin group act properly and cocompactly by isometries on a CAT(0) space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634](https://doi.org/10.4171/owr/2014/11)
## Literat... | 3 | open | null | 2,014 | 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-12871-001",
"literature-status:open",
"owr-year:2014"
] | Artin groups are known to be CAT(0) in broad subclasses, but the all-Artin-groups CAT(0) conjecture remains an important open problem. | [
{
"url": "https://ems.press/content/serial-article-files/48578",
"label": "Kato and Oguni, 2024"
},
{
"url": "https://doi.org/10.5802/aif.3524",
"label": "Haettel, 2022"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/11 | null | null | null | Does every Artin group act properly and cocompactly by isometries on a CAT(0) space? | Charney's conjecture: Every Artin group acts properly and cocompactly by isometries on a CAT(0) space. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634 |
30,002,539 | OWR-12871-002 | Hopf Graphical Calculus for Deligne-Type Operations | What is the analogue, for the Hopf case, of the graphical calculus for operations in Deligne's conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634](https://doi.org/10.4171/owr/2014/11)
## Literat... | 3 | open | null | 2,014 | 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-12871-002",
"literature-status:open",
"owr-year:2014"
] | Feynman categories provide Hopf-algebra constructions, but no general analogue of the cited Deligne-type graphical calculus for the Hopf case has been established. | [
{
"url": "https://arxiv.org/abs/1312.1269",
"label": "Kaufmann and Ward, 2014"
},
{
"url": "https://doi.org/10.4171/owr/2014/11",
"label": "Oberwolfach Report 11, 2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/11 | null | null | null | What is the analogue, for the Hopf case, of the graphical calculus for operations in Deligne's conjecture? | What is the analogue, for the Hopf case, of the graphical calculus for operations in Deligne's conjecture? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634 |
30,002,540 | OWR-12871-003 | Tannakian Structures in Feynman Categories | Can fiber functors and their associated Tannakian categories be seen directly in the Feynman-category picture, what is the role of Hopf cyclic cohomology, and is there a categorification connecting this story to Hopf algebroids? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634](https://doi.org/10.4171/owr/2014/11)
## Literat... | 3 | open | null | 2,014 | 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-12871-003",
"literature-status:open",
"owr-year:2014"
] | Tannakian, Hopf-cyclic, and Hopf-algebroid frameworks exist separately, but no general direct Feynman-category construction answering all three questions is known. | [
{
"url": "https://arxiv.org/abs/1312.1269",
"label": "Kaufmann and Ward, 2014"
},
{
"url": "https://arxiv.org/abs/1803.09194",
"label": "Kowalzig and Krähmer, 2018"
},
{
"url": "https://arxiv.org/abs/0907.1578",
"label": "Böhm, 2010"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/11 | null | null | null | Can fiber functors and their associated Tannakian categories be seen directly in the Feynman-category picture, what is the role of Hopf cyclic cohomology, and is there a categorification connecting this story to Hopf algebroids? | Can fiber functors and their associated Tannakian categories be seen directly in the Feynman-category picture, what is the role of Hopf cyclic cohomology, and is there a categorification connecting this story to Hopf algebroids? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Batalin-Vilkovisky Algebras, Operads, and Hopf Algebroids (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/11, pp. 595--634 |
30,002,541 | OWR-12872-006 | Scaling Limits of Nonsubcritical Block Stable Random Graphs | Determine the distance scaling and scaling limits of random graphs drawn from block-stable classes that are not subcritical, with random planar graphs as the principal case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12872-006",
"literature-status:open",
"owr-year:2014"
] | Brownian-map scaling limits are known for important subclasses such as cubic planar graphs, but the extracted general planar or block-stable non-subcritical problem remains unresolved. | [
{
"url": "https://onlinelibrary.wiley.com/doi/10.1112/jlms.70018",
"label": "Stufler (2024)"
},
{
"url": "https://projecteuclid.org/journals/electronic-journal-of-probability/volume-28/issue-none/Random-cubic-planar-graphs-converge-to-the-Brownian-sphere/10.1214/23-EJP912.pdf",
"label": "Cubic p... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Determine the distance scaling and scaling limits of random graphs drawn from block-stable classes that are not subcritical, with random planar graphs as the principal case. | Determine the behavior of distances and scaling limits for random graphs from block-stable classes that are not subcritical, especially for random planar graphs. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,542 | OWR-12872-010 | Enumeration of Pairwise-Compatible Triple Families | Call triples $\{i,j,k\}$ and $\{a,b,c\}$ compatible when there exist integers $x_1<\cdots<x_n$ such that both $x_i,x_j,x_k$ and $x_a,x_b,x_c$ are arithmetic progressions. Let $\mathcal M_n$ be the pairwise-compatible families of triples in $[n]$. Is $|\mathcal M_n|=2^{\binom{n-1}{2}}$? Is the number of maximum-size fam... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | solved | null | 2,014 | 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": "resolution",
"evidence": "published"
} | Statement proved later in the same workshop report (marked unrecoverable/not an open problem in owr_statement_audit.json) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12872-010",
"literature-status:open",
"owr-year:2014"
] | Liu and Stanley prove both of Elkies’ conjectures. The source abstract states this on p. 697. In the even case n=2m, the final factor is $2^m-1$, not $2m-1$; this yields 28 and 960 for n=6 and n=8 respectively.
**What remains.** Both enumeration formulas are proved. | [
{
"url": "https://doi.org/10.1007/s11139-014-9623-2",
"label": "F. Liu and R. Stanley, A distributive lattice connected with arithmetic progressions of length three (2015)"
},
{
"url": "https://doi.org/10.4171/owr/2014/12",
"label": "Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.... | 2026-09-28T00:00:00 | F. Liu and R. Stanley, A distributive lattice connected with arithmetic progressions of length three (2015): https://doi.org/10.1007/s11139-014-9623-2
Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720: https://doi.org/10.4171/owr/2014/12 | https://doi.org/10.4171/owr/2014/12 | null | null | null | Call triples $\{i,j,k\}$ and $\{a,b,c\}$ compatible when there exist integers $x_1<\cdots<x_n$ such that both $x_i,x_j,x_k$ and $x_a,x_b,x_c$ are arithmetic progressions. Let $\mathcal M_n$ be the pairwise-compatible families of triples in $[n]$. Is $|\mathcal M_n|=2^{\binom{n-1}{2}}$? Is the number of maximum-size fam... | For compatible 3-subsets of [n] defined by simultaneous arithmetic progressions, let M_n be the family of pairwise-compatible subfamilies; conjecturally #M_n = 2^(binom(n−1,2)), and the number of maximum-size elements is 2^(m(m−1)) for n = 2m+1 and 2^((m−1)(m−2))(2m−1) for n = 2m. | 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 | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,543 | OWR-12872-013 | Connectivity Under Weakened Bridge Addability | Which connectivity bounds and related asymptotic properties of bridge-addable graph classes remain valid when bridge-addability is replaced by a weaker closure condition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,014 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12872-013",
"literature-status:open",
"owr-year:2014"
] | Weaker notions such as relatively bridge-addable classes have substantial partial results, but there is no general replacement theorem or classification answering the extracted broad question. | [
{
"url": "https://doi.org/10.1017/S0963548317000128",
"label": "McDiarmid--Weller (2017)"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid%3A667a139e-6d2c-4f67-8487-04c3a0136226",
"label": "Weller thesis"
},
{
"url": "https://arxiv.org/abs/1504.06344",
"label": "Bridge-addable connecti... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Which connectivity bounds and related asymptotic properties of bridge-addable graph classes remain valid when bridge-addability is replaced by a weaker closure condition? | What connectivity and related asymptotic properties persist for graph classes when bridge-addability is replaced by a weaker condition? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,544 | OWR-12872-014 | Enumeration of Graphs with Prescribed Degree Sequences | Determine, exactly or asymptotically, the number of simple labelled graphs with a prescribed nonnegative degree sequence $\mathbf d=(d_1,\ldots,d_n)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,014 | 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-12872-014",
"literature-status:partially-solved",
"owr-year:2014"
] | There is no single general closed formula for all graphical degree sequences, but strong asymptotic enumeration formulas now cover broad sparse, dense, and heavy-tailed regimes. | [
{
"url": "https://doi.org/10.1016/j.aim.2015.09.002",
"label": "Gao--Wormald (2016)"
},
{
"url": "https://doi.org/10.4171/JEMS/1355",
"label": "Liebenau--Wormald (2024)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Determine, exactly or asymptotically, the number of simple labelled graphs with a prescribed nonnegative degree sequence $\mathbf d=(d_1,\ldots,d_n)$. | How many simple graphs are there with a prescribed nonnegative degree sequence d? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,545 | OWR-12872-015 | Combinatorial Proof of the Two-Thirds Leaf Limit | Let $T_n$ range over rooted plane trees whose child labels decrease, and choose uniformly both a tree and one of its vertices. Give a direct combinatorial proof, avoiding generating functions and induction, that the probability $p_n$ that the chosen vertex is a leaf satisfies $p_n\to 2/3$ as $n\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | solved | null | 2,014 | 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 | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved**. M. Bóna (OWR 12/2014, p. 707) asks for a proof without generating functions or induction that a random vertex of a random decreasing plane tree on [n] is a leaf with probability p_n → 2/3. | [
"owr",
"oberwolfach-reports",
"OWR-12872-015",
"literature-status:open",
"owr-year:2014"
] | The leaf proportion and its limit are established, but the extracted request is specifically for a simple combinatorial proof without generating functions or induction, and that proof challenge remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46502?nt=1",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1002/rsa.21138",
"label": "Bóna--Pittel (2023)"
},
{
"url": "https://arxiv.org/abs/2108.04989",
"label": "Bóna--Pittel preprint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Let $T_n$ range over rooted plane trees whose child labels decrease, and choose uniformly both a tree and one of its vertices. Give a direct combinatorial proof, avoiding generating functions and induction, that the probability $p_n$ that the chosen vertex is a leaf satisfies $p_n\to 2/3$ as $n\to\infty$. | Find a simple combinatorial proof, without generating functions or induction, that for rooted plane trees T_n with decreasing child labels, the probability p_n that a uniformly random vertex of a uniformly random tree is a leaf converges to 2/3 as n tends to infinity. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,546 | OWR-12872-017 | Combinatorial Interpretation of an $A_{2n}^{(2)}$ Rogers–Ramanujan Identity | For positive integers $m,n$, set $\kappa=2m+2n+1$. Find a combinatorial interpretation of the Hall–Littlewood identity
$$\sum_{\lambda_1\leq m}q^{|\lambda|}P_{2\lambda}(1,q,q^2,\ldots;q^{2n-1})
=\frac{(q^\kappa;q^\kappa)_\infty^n}{(q;q)_\infty^n}
\prod_{i=1}^n\theta(q^{i+m};q^\kappa)
\prod_{1\leq i<j\leq n}\theta(q^{j... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,014 | 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-12872-017",
"literature-status:partially-solved",
"owr-year:2014"
] | Combinatorial interpretations and proofs now exist for classical and low-rank A2 Rogers--Ramanujan families, but the full A_{2n}^{(2)} family and the other identities in the extracted statement still lack a complete interpretation. | [
{
"url": "https://doi.org/10.1090/btran/147",
"label": "Warnaar (2023)"
},
{
"url": "https://arxiv.org/abs/2011.12828",
"label": "Cylindric A2 identities"
},
{
"url": "https://doi.org/10.1090/proc/13373",
"label": "Corteel (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | For positive integers $m,n$, set $\kappa=2m+2n+1$. Find a combinatorial interpretation of the Hall–Littlewood identity
$$\sum_{\lambda_1\leq m}q^{|\lambda|}P_{2\lambda}(1,q,q^2,\ldots;q^{2n-1})
=\frac{(q^\kappa;q^\kappa)_\infty^n}{(q;q)_\infty^n}
\prod_{i=1}^n\theta(q^{i+m};q^\kappa)
\prod_{1\leq i<j\leq n}\theta(q^{j... | Find combinatorial interpretations for the displayed A₂n^(2) analogues of the Rogers-Ramanujan identities and for the other identities in the same family. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,547 | OWR-12872-018 | Growth Rate of Quadrant Loops | Let $Q_n(a)$ count length-$2n$ square-lattice loops confined to the nonnegative quadrant, weighted by $a$ for each northwest or east–south corner, and let $Q(a,u)=\sum_{n\geq 0}Q_n(a)u^n$. For every $a\geq -1$, is the exponential growth rate of $Q_n(a)$ equal to that of the corresponding unconfined loops? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,014 | 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-12872-018",
"literature-status:open",
"owr-year:2014"
] | The radius formula is proved for unconfined and half-plane loops, but the extracted conjecture concerns quarter-plane loops and the corresponding general case remains open. | [
{
"url": "https://arxiv.org/abs/1312.4487",
"label": "Albert--Bousquet-Mélou"
},
{
"url": "https://dmtcs.episciences.org/2425/pdf",
"label": "FPSAC paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Let $Q_n(a)$ count length-$2n$ square-lattice loops confined to the nonnegative quadrant, weighted by $a$ for each northwest or east–south corner, and let $Q(a,u)=\sum_{n\geq 0}Q_n(a)u^n$. For every $a\geq -1$, is the exponential growth rate of $Q_n(a)$ equal to that of the corresponding unconfined loops? | For quadrant loops counted by Q_n(a), conjecture that the exponential growth rate, equivalently the radius of Q(a,u) = Σ_n Q_n(a)u^n, is the same as for unconfined loops for every a ≥ −1. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,548 | OWR-12872-019 | Algebraicity and D-Finiteness of Group-Algebra Series | Let $G$ be a group, let $u\in\mathbb ZG$, define $f_u(n)=[1]u^n$ to be the coefficient of the identity in $u^n$, and set $F_u(x)=\sum_{n\geq 1}f_u(n)x^n$. Is $F_u(x)$ D-finite for every $u$ when $G=\operatorname{GL}(d,\mathbb Z)$? More generally, for which groups $G$ is $F_u(x)$ algebraic for every $u\in\mathbb ZG$, an... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720](https://doi.org/10.4171/owr/2014/12)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,014 | 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-12872-019",
"literature-status:open",
"owr-year:2014"
] | The general D-finiteness question for identity-coefficient series from group algebras of GL(d,Z) remains unresolved; undecidability of vanishing does not settle D-finiteness. | [
{
"url": "https://ems.press/content/serial-article-files/46502?nt=1",
"label": "Stanley Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/12 | null | null | null | Let $G$ be a group, let $u\in\mathbb ZG$, define $f_u(n)=[1]u^n$ to be the coefficient of the identity in $u^n$, and set $F_u(x)=\sum_{n\geq 1}f_u(n)x^n$. Is $F_u(x)$ D-finite for every $u$ when $G=\operatorname{GL}(d,\mathbb Z)$? More generally, for which groups $G$ is $F_u(x)$ algebraic for every $u\in\mathbb ZG$, an... | For a group G and u in its integral group algebra, is F_u(x) D-finite for every u when G = GL(d,ℤ), and more generally for which groups is F_u(x) algebraic or D-finite for all u? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Enumerative Combinatorics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/12, pp. 635--720 |
30,002,549 | OWR-12873-001 | Universal Almost-Sure Prediction for Stationary Gaussian Processes | Let $\{Y_n\}_{n\in\mathbb Z}$ be a stationary, ergodic, mean-zero Gaussian process. Does there exist a sequence of predictors $g_n$ such that
$$\mathbb E(Y_n\mid Y_1,\ldots,Y_{n-1})-g_n(Y_1,\ldots,Y_{n-1})\longrightarrow0$$
almost surely as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779](https://doi.org/10.4171/owr/2014/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-12873-001",
"literature-status:open",
"owr-year:2014"
] | Known predictors achieve almost-sure Cesaro consistency and stronger results under extra assumptions, but a universally strongly pointwise consistent predictor for all stationary ergodic Gaussian processes remains open. | [
{
"url": "https://doi.org/10.1007/978-1-4939-0569-0_12",
"label": "Györfi--Sancetta (2014)"
},
{
"url": "https://arxiv.org/abs/0712.2592",
"label": "Stationary ergodic forecasting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/13 | null | null | null | Let $\{Y_n\}_{n\in\mathbb Z}$ be a stationary, ergodic, mean-zero Gaussian process. Does there exist a sequence of predictors $g_n$ such that
$$\mathbb E(Y_n\mid Y_1,\ldots,Y_{n-1})-g_n(Y_1,\ldots,Y_{n-1})\longrightarrow0$$
almost surely as $n\to\infty$? | For every stationary and ergodic Gaussian process, does there exist a prediction rule g such that E(Y_n | Y₁,…,Y_{n−1}) − g_n(Y₁,…,Y_{n−1}) converges to 0 almost surely? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779 |
30,002,550 | OWR-12873-002 | Minimax Rates for Sparse Varying-Coefficient Models | Determine the minimax-optimal rates of convergence for estimation in sparse, high-dimensional varying-coefficient models. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779](https://doi.org/10.4171/owr/2014/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 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-12873-002",
"literature-status:partially-solved",
"owr-year:2014"
] | Klopp and Pensky established minimax lower bounds and adaptive estimators attaining them up to constants in homogeneous cases or a logarithmic factor otherwise, so the general exact minimax-rate question is not fully settled. | [
{
"url": "https://doi.org/10.1214/15-AOS1309",
"label": "Klopp--Pensky (2015)"
},
{
"url": "https://arxiv.org/abs/1312.4087",
"label": "Klopp--Pensky preprint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/13 | null | null | null | Determine the minimax-optimal rates of convergence for estimation in sparse, high-dimensional varying-coefficient models. | Determine the minimax-optimal rates of convergence for estimation in sparse, high-dimensional varying-coefficient models. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779 |
30,002,551 | OWR-12873-003 | Exact Minimax Asymptotics in Anisotropic Nonparametric Estimation | In the Gaussian white-noise model, determine the exact asymptotics, rather than only the rate order, of the minimax $L^p$-risk over anisotropic Nikol'skii classes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779](https://doi.org/10.4171/owr/2014/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-12873-003",
"literature-status:open",
"owr-year:2014"
] | The cited work provides rate bounds and adaptive procedures, but the exact asymptotic minimax risk requested in the extracted statement remains unproved for the general model. | [
{
"url": "https://doi.org/10.1214/15-AOS1309",
"label": "Klopp--Pensky (2015)"
},
{
"url": "https://arxiv.org/abs/1312.4087",
"label": "Klopp--Pensky preprint"
},
{
"url": "https://doi.org/10.4171/owr/2014/13",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/13 | null | null | null | In the Gaussian white-noise model, determine the exact asymptotics, rather than only the rate order, of the minimax $L^p$-risk over anisotropic Nikol'skii classes. | Determine the exact asymptotics of the minimax risk in the anisotropic nonparametric estimation setting described in the report. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779 |
30,002,552 | OWR-12873-005 | Simultaneous Adaptive Estimation Across Norms and Derivatives | For estimation over Hölder balls with unknown smoothness $\beta$ and radius $Q$, can one adapt simultaneously over all $L^p$ losses? Can one simultaneously attain sharp $L^2$ and $L^\infty$ rates for a function and its derivatives? Can adaptation be achieved without coefficientwise wavelet bounds, and can one character... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779](https://doi.org/10.4171/owr/2014/13)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-12873-005",
"literature-status:open",
"owr-year:2014"
] | Later work resolves particular simultaneous-adaptation settings, but the extracted list asks for a general all-norm, derivative, coefficient-class, and construction theory; no complete solution to all four questions was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/13",
"label": "Original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1312.4087",
"label": "Related adaptive estimator"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/13 | null | null | null | For estimation over Hölder balls with unknown smoothness $\beta$ and radius $Q$, can one adapt simultaneously over all $L^p$ losses? Can one simultaneously attain sharp $L^2$ and $L^\infty$ rates for a function and its derivatives? Can adaptation be achieved without coefficientwise wavelet bounds, and can one character... | For adaptive estimation with unknown smoothness β and radius Q, can one adapt simultaneously over all L^p norms; simultaneously attain clean L² and L∞ rates for a function and its derivatives; generalize the method without coefficientwise wavelet bounds; and characterize when simultaneous adaptation is possible and how... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Adaptive Statistical Inference (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/13, pp. 721--779 |
30,002,553 | OWR-12874-003 | Unconditional Uniqueness for Critical Equivariant Wave Maps | Let $M^n$ and $N^\ell$ be rotationally symmetric manifolds with metrics $dr^2+h(r)^2d\omega^2$ and $d\phi^2+g(\phi)^2d\chi^2$, where $n\geq 3$, $k\geq 1$, and $\ell=k(k+n-2)$. For an admissible $M$, consider the equivariant wave-map equation
$$\phi_{tt}-\phi_{rr}-(n-1)\frac{h'(r)}{h(r)}\phi_r+\frac{\ell}{h(r)^2}g(\phi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/14, pp. 781--868](https://doi.org/10.4171/owr/2014/14)
## Literature review (checked ... | 3 | open | null | 2,014 | 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-12874-003",
"literature-status:open",
"owr-year:2014"
] | The conjectured unconditional uniqueness at critical regularity is not established for the stated rotationally symmetric setting; D'Ancona--Zhang prove uniqueness only after increasing regularity, so the extracted conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/14",
"label": "Oberwolfach Report 2014/14"
},
{
"url": "https://doi.org/10.1093/imrn/rnv152",
"label": "D'Ancona--Zhang, IMRN"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/14 | null | null | null | Let $M^n$ and $N^\ell$ be rotationally symmetric manifolds with metrics $dr^2+h(r)^2d\omega^2$ and $d\phi^2+g(\phi)^2d\chi^2$, where $n\geq 3$, $k\geq 1$, and $\ell=k(k+n-2)$. For an admissible $M$, consider the equivariant wave-map equation
$$\phi_{tt}-\phi_{rr}-(n-1)\frac{h'(r)}{h(r)}\phi_r+\frac{\ell}{h(r)^2}g(\phi... | For the equivariant wave-map Cauchy problem on the admissible rotationally symmetric manifolds in the report, does unconditional uniqueness hold in the critical space H^(n/2) × H^(n/2−1), without the additional restrictions used in the theorem? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/14, pp. 781--868 |
30,002,554 | OWR-12875-002 | Congruence Deficiency of Veech Groups in $\mathcal H(4)$ | How far are the Veech groups of square-tiled surfaces in $\mathcal H(4)$, especially those in the Prym locus, from being congruence groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941](https://doi.org/10.4171/owr/2014/15)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,014 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12875-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The question is partially resolved: Weitze--Schmithusen proves precise deficiency results for origamis in H(2) and for the Prym locus in H(4), but no classification for all origamis is supplied. | [
{
"url": "https://doi.org/10.4171/owr/2014/15",
"label": "Oberwolfach Report 2014/15"
},
{
"url": "https://doi.org/10.1093/imrn/rnt268",
"label": "Weitze--Schmithusen, IMRN"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/15 | null | null | null | How far are the Veech groups of square-tiled surfaces in $\mathcal H(4)$, especially those in the Prym locus, from being congruence groups? | How far are the Veech groups of square-tiled surfaces in H(4), especially the Prym locus, from being congruence groups? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941 |
30,002,555 | OWR-12875-003 | Veech Groups with Prescribed End Spaces | Let $X$ be a closed subspace of the Cantor set and let $G\leq\operatorname{GL}^+(2,\mathbb R)$ be a countable subgroup without contracting elements. Can $G$ be realized as the Veech group of a tame infinite-genus translation surface $S$ without planar ends and with $\operatorname{Ends}(S)\cong X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941](https://doi.org/10.4171/owr/2014/15)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,014 | 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-12875-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The realization theorem is known for the one-ended Loch Ness monster and the blooming Cantor tree, but realization with an arbitrary prescribed closed end space remains open; the extracted general question is partially solved. | [
{
"url": "https://doi.org/10.4171/owr/2014/15",
"label": "Oberwolfach Report 2014/15"
},
{
"url": "https://doi.org/10.5802/aif.2625",
"label": "Przytycki--Schmithusen--Valdez, Annales de l'Institut Fourier"
},
{
"url": "https://arxiv.org/abs/1603.00503",
"label": "Ramirez Maluendas--... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/15 | null | null | null | Let $X$ be a closed subspace of the Cantor set and let $G\leq\operatorname{GL}^+(2,\mathbb R)$ be a countable subgroup without contracting elements. Can $G$ be realized as the Veech group of a tame infinite-genus translation surface $S$ without planar ends and with $\operatorname{Ends}(S)\cong X$? | Given a closed subspace X of the Cantor set and a countable subgroup G of GL⁺(2,ℝ) without contracting elements, can G be realized as the Veech group of a tame infinite-genus translation surface without planar ends and with Ends(S) homeomorphic to X? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941 |
30,002,556 | OWR-12875-004 | Finite-Area Infinite-Genus Surfaces with Lattice Veech Groups | Does there exist an infinite-genus, finite-area translation surface $S$ whose Veech group is a lattice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941](https://doi.org/10.4171/owr/2014/15)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,014 | 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-12875-004",
"literature-status:open",
"owr-year:2014"
] | The existence of a finite-area infinite-genus translation surface with lattice Veech group, in particular on Jacob's ladder, remains unresolved; recent finite-area constructions do not produce a lattice in the stated topology. | [
{
"url": "https://doi.org/10.4171/owr/2014/15",
"label": "Oberwolfach Report 2014/15"
},
{
"url": "https://arxiv.org/abs/2504.00956",
"label": "Veech groups of covers of Chamanara surface"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/15 | null | null | null | Does there exist an infinite-genus, finite-area translation surface $S$ whose Veech group is a lattice? | Does there exist an infinite-genus, finite-area translation surface S whose Veech group is a lattice? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941 |
30,002,557 | OWR-12875-007 | Looijenga's Dolbeault Dimension Conjecture | For the moduli space $\mathcal M_g$ of Riemann surfaces of genus $g\geq2$, is its Dolbeault cohomological dimension equal to $g-2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941](https://doi.org/10.4171/owr/2014/15)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,014 | 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-12875-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The equality \operatorname{cohdim}_{\mathrm{Dol}}(\mathcal M_g)=g-2 is known in low genus and general upper and lower bounds are available, but the conjectured equality for arbitrary genus is not proved. | [
{
"url": "https://doi.org/10.4171/owr/2014/15",
"label": "Oberwolfach Report 2014/15"
},
{
"url": "https://doi.org/10.1142/S0129167X16400085",
"label": "Mondello, International Journal of Mathematics"
},
{
"url": "https://arxiv.org/abs/1610.03768",
"label": "Fullarton--Putman, arXiv"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/15 | null | null | null | For the moduli space $\mathcal M_g$ of Riemann surfaces of genus $g\geq2$, is its Dolbeault cohomological dimension equal to $g-2$? | Looijenga's conjecture: For the moduli space M_g of Riemann surfaces of genus g ≥ 2, the Dolbeault cohomological dimension satisfies cohdim_Dol(M_g) = g−2. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Flat Surfaces and Dynamics on Moduli Space (2014), Oberwolfach Reports, DOI 10.4171/owr/2014/15, pp. 869--941 |
30,002,558 | OWR-12975-002 | Decidability and Finiteness of Rational Joint Spectral Radii | For rational matrices $A_1,\ldots,A_m$, is there an algorithm that halts in finite time and decides whether their joint spectral radius is strictly less than $1$? If the matrices have rational entries, is the joint spectral radius always attained by the spectral radius of a finite product, i.e., does equality hold for ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-002",
"literature-status:open",
"owr-year:2014"
] | For rational matrices, the strict decision problem \rho<1 remains unresolved, while the known undecidability result is for \rho\leq1; real-matrix counterexamples to finiteness do not establish a rational-entry counterexample, so the extracted rational questions remain open. | [
{
"url": "https://doi.org/10.1016/S0167-6911(00)00049-9",
"label": "Blondel--Tsitsiklis, Systems and Control Letters"
},
{
"url": "https://arxiv.org/abs/math/0702489",
"label": "On the finiteness property for rational matrices"
},
{
"url": "https://doi.org/10.4171/owr/2014/17",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | For rational matrices $A_1,\ldots,A_m$, is there an algorithm that halts in finite time and decides whether their joint spectral radius is strictly less than $1$? If the matrices have rational entries, is the joint spectral radius always attained by the spectral radius of a finite product, i.e., does equality hold for ... | For rational matrices A_1,\ldots,A_m, is there an algorithm that halts in finite time and decides whether their joint spectral radius is strictly less than one? If the matrices have rational entries, is the joint spectral radius always attained by the spectral radius of a finite product, i.e. does equality hold for som... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,559 | OWR-12975-003 | Spectrahedrality of Hyperbolicity Cones | Is every hyperbolicity cone of a real homogeneous hyperbolic polynomial spectrahedral? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-003",
"literature-status:open",
"owr-year:2014"
] | The record is a truncated introduction to hyperbolicity cones and the generalized Lax conjecture; it does not state a complete proposition, and the general spectrahedrality problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
},
{
"url": "https://doi.org/10.1016/j.indag.2025.06.008",
"label": "Current survey on hyperbolicity cones"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Is every hyperbolicity cone of a real homogeneous hyperbolic polynomial spectrahedral? | Generalized Lax conjecture: Is every hyperbolicity cone of a real homogeneous hyperbolic polynomial a spectrahedral cone? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,560 | OWR-12975-005 | Interior Maximizers of Mixed Characteristic Polynomials | In the mixed-characteristic-polynomial optimization problem, maximize the largest zero subject to $u_i$ lying in the hyperbolicity cone, $\operatorname{tr}(u_i)\leq\varepsilon$, and $\sum_i u_i=e$. Is the maximum attained when every $u_i$ is either in the interior of the cone or zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-005",
"literature-status:open",
"owr-year:2014"
] | The record truncates immediately before the stated conjecture and does not identify a mathematical claim; under the triage rule its unresolved content is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | In the mixed-characteristic-polynomial optimization problem, maximize the largest zero subject to $u_i$ lying in the hyperbolicity cone, $\operatorname{tr}(u_i)\leq\varepsilon$, and $\sum_i u_i=e$. Is the maximum attained when every $u_i$ is either in the interior of the cone or zero? | Conjecture: In the mixed-characteristic-polynomial optimization problem maximizing the largest zero subject to u_i in the hyperbolicity cone, tr(u_i)\leq\epsilon, and the sum of the u_i equal to e, the maximum is achieved when every u_i is either in the interior of the cone or identically zero. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,561 | OWR-12975-006 | Moment Vanishing and Polynomial Abel Equations | Let $\Omega\subset\mathbb R^n$ be a bounded domain and let $P$ and $q$ be polynomials. Determine necessary and sufficient conditions for all moments
$$m_k=\int_\Omega P(x)^kq(x)\,dx,\qquad k=0,1,\ldots,$$
to vanish. In particular, when $P'=p$, determine the corresponding closed-solution conditions for the polynomial Ab... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-006",
"literature-status:open",
"owr-year:2014"
] | The extracted passage is an incomplete setup for a moment-vanishing problem and contains no verifiable final assertion; the unresolved or unclear content is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Let $\Omega\subset\mathbb R^n$ be a bounded domain and let $P$ and $q$ be polynomials. Determine necessary and sufficient conditions for all moments
$$m_k=\int_\Omega P(x)^kq(x)\,dx,\qquad k=0,1,\ldots,$$
to vanish. In particular, when $P'=p$, determine the corresponding closed-solution conditions for the polynomial Ab... | Moment-vanishing problem: For a bounded domain Omega in R^n and polynomials P and q, determine necessary and sufficient conditions for all moments m_k=\int_{\Omega}P(x)^k q(x) dx, k=0,1,\ldots, to vanish; in particular, analyze the corresponding closed-solution conditions for the polynomial Abel equation y'=p(x)y^2+q(x... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,562 | OWR-12975-007 | Zero Thresholds for Positive Semidefinite Ternary Forms | Let $\alpha(k)$ be the least integer such that every positive semidefinite ternary form $p$ of degree $2k$ with more than $\alpha(k)$ projective zeros can be written $p=h^2q$ with $h$ indefinite. Is $\alpha(k)\geq k^2+1$ for every $k\geq3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | solved | null | 2,014 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s40879-019-00324-9",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. B. Reznick (joint with G. Blekherman; OWR 17/2014, p. 1011) conjectures α(k) ≥ k² + 1 for k ≥ 3, α(k) being the least integer such that every psd ternary form of degree 2k with more than α(k) zeros is h²q with h indefinite; they proved all but five k. Brug... | [
"owr",
"oberwolfach-reports",
"OWR-12975-007",
"literature-status:open",
"owr-year:2014"
] | The source explicitly presents \alpha(k)\geq k^2+1 as a conjecture and reports only that all but five values were proved; no authoritative proof of the remaining cases was identified, so the conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Let $\alpha(k)$ be the least integer such that every positive semidefinite ternary form $p$ of degree $2k$ with more than $\alpha(k)$ projective zeros can be written $p=h^2q$ with $h$ indefinite. Is $\alpha(k)\geq k^2+1$ for every $k\geq3$? | Conjecture: Let alpha(k) be the least integer such that every positive semidefinite ternary form of degree 2k with more than alpha(k) projective zeros has an indefinite form h with p=h^2 q. Then alpha(k)\geq k^2+1 for every k\geq3. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,563 | OWR-12975-008 | Efficient Moment Relaxations for Polynomial Optimization | Can moment-relaxation methods solve polynomial optimization over closed basic semialgebraic sets efficiently, including computing the infimum and the points where it is attained? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-008",
"literature-status:open",
"owr-year:2014"
] | Moment--SOS hierarchies give convergent lower bounds and finite exactness under additional hypotheses, but no generally efficient method for arbitrary polynomial optimization is known; the broad efficiency question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
},
{
"url": "https://arxiv.org/abs/2012.08873",
"label": "Mai--Lasserre--Magron--Wang, arXiv"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Can moment-relaxation methods solve polynomial optimization over closed basic semialgebraic sets efficiently, including computing the infimum and the points where it is attained? | Can moment-relaxation methods solve polynomial optimization over closed basic semialgebraic sets efficiently, including computing the infimum and the points where it is attained? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,564 | OWR-12975-010 | Finite-Dimensional Detection of Positivity in Surface Groups | For the fundamental group of every closed surface, is positivity of a Hermitian element in all unitary representations equivalent to positivity in all finite-dimensional unitary representations, and hence to membership in the cone of sums of Hermitian squares? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-010",
"literature-status:open",
"owr-year:2014"
] | Lubotzky--Shalom settle the finite-dimensional versus all-unitary-representation implication for surface groups, but the sum-of-hermitian-squares equivalence itself remains unresolved; the related F2 times F2 Connes-embedding formulation is known negative. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
},
{
"url": "https://doi.org/10.1090/conm/347/06272",
"label": "Lubotzky--Shalom, Property FD"
},
{
"url": "https://arxiv.org/abs/2001.04383",
"label": "MIP star equals RE"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | For the fundamental group of every closed surface, is positivity of a Hermitian element in all unitary representations equivalent to positivity in all finite-dimensional unitary representations, and hence to membership in the cone of sums of Hermitian squares? | Conjecture: For the fundamental group of every closed surface, positivity of a hermitian element in all unitary representations is equivalent to positivity in all finite-dimensional unitary representations, and hence to membership in the cone of sums of hermitian squares. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,565 | OWR-12975-011 | Completely Positive Separation for the Integer Lattice | Can the finite-dimensional completely-positive-functional and separation argument used for free groups be extended to $\mathbb Z^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-011",
"literature-status:open",
"owr-year:2014"
] | Scheiderer proves the relevant sums-of-squares characterization for \mathbb Z^2, but the extracted methodological request is not a precise theorem and no definitive resolution of that request is identifiable; it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Can the finite-dimensional completely-positive-functional and separation argument used for free groups be extended to $\mathbb Z^2$? | Can the finite-dimensional completely-positive-functional and separation argument used for free groups be carried out to understand the case of the group Z^2 better? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,566 | OWR-12975-012 | Uniform Sum-of-Squares Multipliers on Real Projective Curves | Let $X$ be an irreducible nondegenerate real projective curve with dense real points, and fix an even degree $2s$. Find an explicit integer $k$, depending only on $s$ and invariants of $X$, such that every nonnegative degree-$2s$ form $p$ on $X$ has a sum-of-squares multiplier $q$ of degree $2k$ for which $pq$ is a sum... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | partially_solved | null | 2,014 | 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-12975-012",
"literature-status:partially-solved",
"owr-year:2014"
] | Sharp multiplier-degree bounds are known for nondegenerate totally-real projective curves, while the extracted question asks for a general variety-level bound; the general problem is only partially solved. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
},
{
"url": "https://doi.org/10.1016/j.matpur.2018.12.010",
"label": "Blekherman--Smith--Velasco, Journal de Mathematiques Pures et Appliquees"
},
{
"url": "https://arxiv.org/abs/1104.1772",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | Let $X$ be an irreducible nondegenerate real projective curve with dense real points, and fix an even degree $2s$. Find an explicit integer $k$, depending only on $s$ and invariants of $X$, such that every nonnegative degree-$2s$ form $p$ on $X$ has a sum-of-squares multiplier $q$ of degree $2k$ for which $pq$ is a sum... | Given an even degree 2s and an irreducible non-degenerate real projective curve X with dense real points, find an explicit integer k depending only on s and invariants of X such that every nonnegative form p of degree 2s on X has a sum-of-squares multiplier q of degree 2k with pq a sum of squares of degree 2s+2k on X. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,567 | OWR-12975-013 | Definite Determinantal Multiples of Hyperbolic Polynomials | If $h$ is hyperbolic with respect to $e$, does there exist a hyperbolic polynomial $q$ with $C_h(e)\subseteq C_q(e)$ such that $qh$ has a definite determinantal representation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045](https://doi.org/10.4171/owr/2014/17)
## ... | 3 | open | null | 2,014 | 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-12975-013",
"literature-status:open",
"owr-year:2014"
] | The generalized Lax conjecture remains unresolved in the authoritative literature; a January 2026 unrefereed preprint claims a proof, but that claim is not independently validated, so the status remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/17",
"label": "Oberwolfach Report 2014/17"
},
{
"url": "https://doi.org/10.1016/j.indag.2025.06.008",
"label": "Current literature on hyperbolicity cones"
},
{
"url": "https://arxiv.org/abs/2601.12267",
"label": "January 2026 proof claim"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/17 | null | null | null | If $h$ is hyperbolic with respect to $e$, does there exist a hyperbolic polynomial $q$ with $C_h(e)\subseteq C_q(e)$ such that $qh$ has a definite determinantal representation? | Conjecture: If h is hyperbolic with respect to e, then there is a hyperbolic polynomial q with C_h(e) contained in C_q(e) such that qh has a definite determinantal representation. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Real Algebraic Geometry With A View Toward Systems Control and Free Positivity (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/17, pp. 977--1045 |
30,002,568 | OWR-12976-001 | Robust Spectral Tensor Methods for Latent-Variable Learning | Can spectral tensor-decomposition methods for learning latent Dirichlet allocation and related multi-view latent-variable models be made more robust to noisy data, statistical uncertainty, and incorrect modeling assumptions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Physics meets Sparse Recovery (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/18, pp. 1047--1073](https://doi.org/10.4171/owr/2014/18)
## Literature review (c... | 3 | open | null | 2,014 | 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-12976-001",
"literature-status:open",
"owr-year:2014"
] | The extracted statement is only the fragment One open question is whether these and contains no identifiable mathematical claim; the unresolved or unclear content is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2014/18",
"label": "Oberwolfach Report 2014/18"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/18 | null | null | null | Can spectral tensor-decomposition methods for learning latent Dirichlet allocation and related multi-view latent-variable models be made more robust to noisy data, statistical uncertainty, and incorrect modeling assumptions? | Can spectral tensor-decomposition methods for learning latent Dirichlet allocation and related multi-view latent-variable models be made more robust to noisy data, statistical uncertainty, and incorrect modeling assumptions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Physics meets Sparse Recovery (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/18, pp. 1047--1073 |
30,002,569 | OWR-12976-002 | Support Uncertainty for Finite Cyclic Short-Time Fourier Transforms | Let $G$ be a finite cyclic group. Does there exist a nonzero window $\varphi\in\mathbb C^G$ such that the attainable support-size pairs
$$\bigl(\lVert x\rVert_0,\lVert V_\varphi x\rVert_0\bigr)$$
are exactly
$$\bigl(\lVert x\rVert_0,\lvert G\rvert^2-\lvert G\rvert+\lVert\widehat x\rVert_0\bigr),\qquad x\in\mathbb C^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Physics meets Sparse Recovery (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/18, pp. 1047--1073](https://doi.org/10.4171/owr/2014/18)
## Literature review (c... | 3 | open | null | 2,014 | 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-12976-002",
"literature-status:open",
"owr-year:2014"
] | The cyclic-group support-pair equality for Gabor systems remains an open question; generic general-linear-position and prime-order results do not establish the full equality for every cyclic group. | [
{
"url": "https://doi.org/10.4171/owr/2014/18",
"label": "Oberwolfach Report 2014/18"
},
{
"url": "https://doi.org/10.4230/DagSemProc.08492.4",
"label": "Krahmer--Pfander--Rashkov, Dagstuhl Proceedings"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/18 | null | null | null | Let $G$ be a finite cyclic group. Does there exist a nonzero window $\varphi\in\mathbb C^G$ such that the attainable support-size pairs
$$\bigl(\lVert x\rVert_0,\lVert V_\varphi x\rVert_0\bigr)$$
are exactly
$$\bigl(\lVert x\rVert_0,\lvert G\rvert^2-\lvert G\rvert+\lVert\widehat x\rVert_0\bigr),\qquad x\in\mathbb C^... | For a finite cyclic group G, does there exist a nonzero phi in C^G such that the attainable pairs of support sizes (||x||_0,||V_phi x||_0) equal exactly the pairs (||x||_0, |G|^2-|G|+||Fourier(x)||_0) for x in C^G? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Mathematical Physics meets Sparse Recovery (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/18, pp. 1047--1073 |
30,002,570 | OWR-12977-001 | Minimal Mechanistic Models of Cancer-Cell Invasion | Which subcellular processes are essential for cancer-cell invasive behavior, and what level of mechanistic detail is needed for a model that is realistic yet sufficiently simple? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-001",
"literature-status:open",
"owr-year:2014"
] | Multiscale models now include cytoskeletal, extracellular-matrix, confinement, and phenotype mechanisms, but no validated consensus identifies the essential subcellular processes or the minimal adequate level of detail. | [
{
"url": "https://doi.org/10.4171/owr/2014/19",
"label": "Oberwolfach report"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC10293590/",
"label": "Multiscale invasion model"
},
{
"url": "https://doi.org/10.1371/journal.pcbi.1004571",
"label": "Molecular-pathway invasion model"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | Which subcellular processes are essential for cancer-cell invasive behavior, and what level of mechanistic detail is needed for a model that is realistic yet sufficiently simple? | Which subcellular processes are essential for cancer-cell invasive behavior, and what level of mechanistic detail is needed for a model that is realistic yet sufficiently simple? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,571 | OWR-12977-002 | Mathematical Principles for Modelling Living Systems | Do the common structures of complex living systems provide a paradigm for deriving life-science models, and can applications reveal hallmarks of a mathematical theory of living systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-002",
"literature-status:open",
"owr-year:2014"
] | Mathematical biology has produced many useful frameworks and proposed hallmarks, but a generally accepted paradigm or unified mathematical theory of living systems has not been established. | [
{
"url": "https://doi.org/10.4171/owr/2014/19",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.plrev.2010.12.004",
"label": "Theory of living systems review"
},
{
"url": "https://arxiv.org/abs/2206.09516",
"label": "Open problems in mathematical biology"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | Do the common structures of complex living systems provide a paradigm for deriving life-science models, and can applications reveal hallmarks of a mathematical theory of living systems? | Do the common structures of complex living systems provide a paradigm for deriving life-science models, and can applications reveal hallmarks of a mathematical theory of living systems? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,572 | OWR-12977-003 | Multiscale Problems in Cancer-Cell Migration | Open cancer-migration problems include physical cell passage through obstacles; mechanics and modeling of collective motion; optimization of DTI and Q-ball methods; benchmarks for movement models; the moving-boundary problem for acid-mediated invasion; comparison of amoeboid, mesenchymal, and collective strategies and ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | open | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-003",
"literature-status:open",
"owr-year:2014"
] | Individual subquestions have partial results, including boundedness and global-existence theorems for restricted chemotaxis--haptotaxis systems and inverse identification methods, but the listed benchmark, imaging, invasion-speed, and general-bound questions remain unresolved as a package. | [
{
"url": "https://doi.org/10.4171/owr/2014/19",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1371/journal.pcbi.1008411",
"label": "Migration-model comparison review"
},
{
"url": "https://arxiv.org/abs/1711.10044",
"label": "Chemotaxis--haptotaxis global existence"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | Open cancer-migration problems include physical cell passage through obstacles; mechanics and modeling of collective motion; optimization of DTI and Q-ball methods; benchmarks for movement models; the moving-boundary problem for acid-mediated invasion; comparison of amoeboid, mesenchymal, and collective strategies and ... | Open cancer-migration problems include physical cell passage through obstacles; mechanics and modeling of collective motion; optimization of DTI and Q-ball methods; benchmarks for movement models; the moving-boundary problem for acid-mediated invasion; comparison of amoeboid, mesenchymal, and collective strategies and ... | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,573 | OWR-12977-004 | Leaderless Collective Cell Motion and Macroscopic Limits | Can collective cell movement develop without a leader, and what macroscopic limits result from microscopic or mesoscopic models of such movement? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | partially_solved | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-004",
"literature-status:partially-solved",
"owr-year:2014"
] | Leaderless collective motion is rigorously and computationally realized in self-organized particle models, and hydrodynamic limits are known for important alignment systems, but no universal macroscopic limit covers all collective-cell mechanisms. | [
{
"url": "https://doi.org/10.1016/S0167-2789(03)00102-7",
"label": "Leaderless collective motion"
},
{
"url": "https://doi.org/10.1137/15M1035665",
"label": "Hydrodynamic limit"
},
{
"url": "https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.32/",
"label": "Macroscopic c... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | Can collective cell movement develop without a leader, and what macroscopic limits result from microscopic or mesoscopic models of such movement? | Can collective cell movement develop without a leader, and what macroscopic limits result from microscopic or mesoscopic models of such movement? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,574 | OWR-12977-005 | Dynamic Constraints on Cancer-Cell Passage Through Tissue | How is cancer-cell movement restricted by obstacles, extracellular matrix, and fibers? Can a static squeezing criterion be replaced by a dynamic, time-dependent pore-passage condition such as $F-hv=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | partially_solved | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-005",
"literature-status:partially-solved",
"owr-year:2014"
] | Time-dependent computational and experimental models now relate pore size, pressure, membrane rheology, nuclear stiffness, and transit time, but a general dynamic squeezing criterion in terms of traction and stiffness has not been derived or validated. | [
{
"url": "https://doi.org/10.4171/owr/2014/19",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1177/0954406217730850",
"label": "Micropore immersed-boundary model"
},
{
"url": "https://doi.org/10.1007/s10237-023-01705-6",
"label": "Constricted-channel cancer-cell model... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | How is cancer-cell movement restricted by obstacles, extracellular matrix, and fibers? Can a static squeezing criterion be replaced by a dynamic, time-dependent pore-passage condition such as $F-hv=0$? | How is cancer-cell movement restricted by obstacles, extracellular matrix, and fibers, and can the static squeezing criterion be replaced by a dynamic time-dependent condition such as F-hv=0 for passage through a pore? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,575 | OWR-12977-006 | Transitions and Transport Among Cancer-Cell Migration Strategies | For amoeboid, mesenchymal, and collective cancer-cell movement, which strategy is advantageous for invasion; what triggers transitions between strategies; what dynamics occurs when all are present; and what are their transport properties such as invasion speeds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109](https://doi.org/10.4171/owr/2014/19)
## Literature review... | 3 | partially_solved | null | 2,014 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12977-006",
"literature-status:partially-solved",
"owr-year:2014"
] | Experiments and switching models identify environmental triggers for amoeboid--mesenchymal transitions, and hybrid models compare collective and solitary invasion and speeds, but the optimal strategy and fully coupled three-mode dynamics remain context-dependent and unresolved. | [
{
"url": "https://doi.org/10.1038/s41598-017-09300-3",
"label": "Migration-plasticity model"
},
{
"url": "https://doi.org/10.1021/acs.nanolett.9b01597",
"label": "Confinement transition model"
},
{
"url": "https://doi.org/10.1007/s11538-024-01286-0",
"label": "Hybrid multiscale invas... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/19 | null | null | null | For amoeboid, mesenchymal, and collective cancer-cell movement, which strategy is advantageous for invasion; what triggers transitions between strategies; what dynamics occurs when all are present; and what are their transport properties such as invasion speeds? | For amoeboid, mesenchymal, and collective cancer-cell movement, which strategy is advantageous for invasion; what triggers transitions between strategies; what dynamics occurs when all are present; and what are their transport properties such as invasion speeds? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109 |
30,002,576 | OWR-12978-001 | Structure and Finiteness of General Nichols Algebras | For a braided vector space $V$, describe the structure of its Nichols algebra $\mathcal B(V)$. Characterize when $\mathcal B(V)$ is finite-dimensional, noetherian, or of finite Gelfand–Kirillov dimension. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137](https://doi.org/10.4171/owr/2014/20)
## Literature review (checked 2... | 3 | open | null | 2,014 | 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-12978-001",
"literature-status:open",
"owr-year:2014"
] | Nichols algebras of diagonal type and several finite-Gelfand--Kirillov-dimensional families are classified, but the general structure of B(V) and simultaneous finite-dimensional, noetherian, and finite-growth criteria for arbitrary braided V remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/20",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1606.02521",
"label": "Finite-GK Nichols algebras"
},
{
"url": "https://arxiv.org/abs/2504.12206",
"label": "Finite-GK pre-Nichols algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/20 | null | null | null | For a braided vector space $V$, describe the structure of its Nichols algebra $\mathcal B(V)$. Characterize when $\mathcal B(V)$ is finite-dimensional, noetherian, or of finite Gelfand–Kirillov dimension. | For a braided vector space V, what is the general structure of its Nichols algebra B(V), and when is B(V) finite dimensional, noetherian, or of finite Gelfand-Kirillov dimension? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137 |
30,002,577 | OWR-12978-003 | Structure and Classification Problems for Noetherian Hopf Algebras | Let $H$ be a noetherian Hopf algebra. Are the quotients $H/P$ by minimal prime ideals Morita equivalent, and if not, which properties do they share, including polynomial-identity status and Gelfand–Kirillov dimension? Is every noetherian Hopf algebra strongly noetherian? For extensions of enveloping algebras by finite-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137](https://doi.org/10.4171/owr/2014/20)
## Literature review (checked 2... | 3 | open | null | 2,014 | 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-12978-003",
"literature-status:open",
"owr-year:2014"
] | Results classify important diagonal and low-growth cases, but the combined questions on minimal-prime quotients, strong noetherianity, non-diagonal extensions, diagram folding, and all liftings still have unresolved general cases. | [
{
"url": "https://doi.org/10.4171/owr/2014/20",
"label": "Oberwolfach open-questions report"
},
{
"url": "https://arxiv.org/abs/2504.12206",
"label": "Finite-GK pre-Nichols algebras"
},
{
"url": "https://arxiv.org/abs/2507.23730",
"label": "Pointed Hopf algebras and finiteness"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/20 | null | null | null | Let $H$ be a noetherian Hopf algebra. Are the quotients $H/P$ by minimal prime ideals Morita equivalent, and if not, which properties do they share, including polynomial-identity status and Gelfand–Kirillov dimension? Is every noetherian Hopf algebra strongly noetherian? For extensions of enveloping algebras by finite-... | For a noetherian Hopf algebra H, are the quotients H/P by minimal prime ideals Morita equivalent, and if not what properties do they share, including PI status and Gelfand-Kirillov dimension? Are all noetherian Hopf algebras strongly noetherian? For Hopf-algebra extensions of enveloping algebras by finite-dimensional p... | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137 |
30,002,578 | OWR-12978-004 | Diagram Folding and Structural Equivalence of Hopf Algebras | What does diagram folding of Nichols algebras represent under the associated representation-theoretic correspondence? If $H'$ is the maximal pointed Hopf subalgebra of a Hopf algebra $H$, does there exist a Hopf ideal $I$ such that $H=H'\oplus I$, and which algebraic and homological relations connect $H$ and $H'$? If t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137](https://doi.org/10.4171/owr/2014/20)
## Literature review (checked 2... | 3 | open | null | 2,014 | 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-12978-004",
"literature-status:open",
"owr-year:2014"
] | Diagram folding and indicator values have substantial invariant-theoretic theory, but the requested interpretation, splitting and homological relations for maximal pointed subalgebras, and the converse from indicator sets to gauge equivalence are not established in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/20",
"label": "Oberwolfach open-questions report"
},
{
"url": "https://arxiv.org/abs/1212.1435",
"label": "Total Frobenius--Schur indicators"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/20 | null | null | null | What does diagram folding of Nichols algebras represent under the associated representation-theoretic correspondence? If $H'$ is the maximal pointed Hopf subalgebra of a Hopf algebra $H$, does there exist a Hopf ideal $I$ such that $H=H'\oplus I$, and which algebraic and homological relations connect $H$ and $H'$? If t... | What is the interpretation of diagram folding for Nichols algebras under the corresponding representation-theoretic correspondence? For a Hopf algebra H and its maximal pointed Hopf subalgebra H', does there exist a Hopf ideal I with H=H' direct-sum I, and what algebraic and homological relations connect H and H'? Fina... | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137 |
30,002,579 | OWR-12978-005 | Quotient Rings and Homological Properties of Hopf-Module Algebras | For Hopf-module algebras, does every $H$-semiprime right-noetherian algebra have an artinian classical right quotient ring? Can an $H$-simple semiprime noetherian algebra finite over its center have infinite global dimension, or fail to be Gorenstein? If a cosemisimple Hopf algebra acts inner faithfully on a polynomial... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137](https://doi.org/10.4171/owr/2014/20)
## Literature review (checked 2... | 3 | open | null | 2,014 | 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-12978-005",
"literature-status:open",
"owr-year:2014"
] | Theorems settle several restricted Hopf-action situations, including module-finite-over-center cases, but the record combines broader quotient-ring, orbit, homological, Gorenstein, PI-degree, and braided-Hopf questions that remain unresolved in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/20",
"label": "Oberwolfach open-questions report"
},
{
"url": "https://dspace.kpfu.ru/xmlui/handle/net/139167",
"label": "Hopf algebra orbits"
},
{
"url": "https://doi.org/10.1017/S0017089516000185",
"label": "Hopf-module-algebra Gorensteinn... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/20 | null | null | null | For Hopf-module algebras, does every $H$-semiprime right-noetherian algebra have an artinian classical right quotient ring? Can an $H$-simple semiprime noetherian algebra finite over its center have infinite global dimension, or fail to be Gorenstein? If a cosemisimple Hopf algebra acts inner faithfully on a polynomial... | For Hopf-module algebras, does every H-semiprime right-noetherian algebra have an artinian classical right quotient ring; can suitable H-simple semiprime noetherian algebras finite over their centers have infinite global dimension; can suitable H-simple noetherian algebras finite over their centers fail to be Gorenstei... | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Infinite Dimensional Hopf Algebras (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/20, pp. 1111--1137 |
30,002,580 | OWR-12979-001 | Geometry and Spectral Theory of Generalized Radial-Part Algebras | Let $D\subset\mathbb C^n$ be a Cartan domain of rank $r$, let $G=\operatorname{Aut}(D)$, and form the continuous-parameter algebra $\mathcal R$ obtained from the $K$-radial parts of the $G$-invariant differential operators by allowing the dimension parameters to vary. Does $\mathcal R$ have a natural geometric realizat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,014 | 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-12979-001",
"literature-status:open",
"owr-year:2014"
] | Rank-one generalized radial operators have spectral and functional-calculus results, but the proposed general geometric realization, commutativity, normality, joint eigenfunctions, and canonical generators for the continuous-parameter family remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1002/mana.200610527",
"label": "One-parameter symmetric-domain calculus"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | Let $D\subset\mathbb C^n$ be a Cartan domain of rank $r$, let $G=\operatorname{Aut}(D)$, and form the continuous-parameter algebra $\mathcal R$ obtained from the $K$-radial parts of the $G$-invariant differential operators by allowing the dimension parameters to vary. Does $\mathcal R$ have a natural geometric realizat... | For the algebra R of generalized radial parts of invariant operators, does it have a natural geometric realization; is it commutative; are its members normal operators; do large families of joint eigenfunctions yield an analogue of the Harish-Chandra transform; and are its members canonical functions of a special gener... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,581 | OWR-12979-002 | Operator Models for Higher-Rank Cowen–Douglas Flag Classes | For $n>2$, develop a natural higher-rank Cowen–Douglas flag class extending
$$FB_2(\Omega)=\left\{\begin{pmatrix}T_0&S\\0&T_1\end{pmatrix}:T_i\in B_1(\Omega),\ T_0S=ST_1\right\},$$
and determine its unitary invariants and reproducing-kernel model. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,014 | 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-12979-002",
"literature-status:partially-solved",
"owr-year:2014"
] | Complete unitary invariants are known for the flag class in rank two, and a strongly flag subclass has later been classified by curvature data, but a general answer for all operators in FB_n(Omega) is not available. | [
{
"url": "https://doi.org/10.1016/j.crma.2014.04.001",
"label": "Flag-structure classification"
},
{
"url": "https://arxiv.org/abs/2311.15491",
"label": "Strong flag structure"
},
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | For $n>2$, develop a natural higher-rank Cowen–Douglas flag class extending
$$FB_2(\Omega)=\left\{\begin{pmatrix}T_0&S\\0&T_1\end{pmatrix}:T_i\in B_1(\Omega),\ T_0S=ST_1\right\},$$
and determine its unitary invariants and reproducing-kernel model. | What is the structure and operator-theoretic model of the class F B_n(Omega), generalizing the known characterization and reproducing-kernel model for F B_2(Omega)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,582 | OWR-12979-004 | Local Geometry and Algebraic Classification of Multiplier Varieties | For multiplier varieties, is there an intrinsic local definition of a variety, and are the classical irreducible components varieties in that sense? Are multiplier-biholomorphic irreducible varieties in a finite-dimensional ball associated with isomorphic multiplier algebras, and is multiplier biholomorphism an equival... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,014 | 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-12979-004",
"literature-status:open",
"owr-year:2014"
] | Isomorphism implies multiplier biholomorphism in broad finite-dimensional classes and homogeneous cases are understood, but the listed local-variety, converse-isomorphism, equivalence-relation, and character questions retain unresolved general cases. | [
{
"url": "https://arxiv.org/abs/1201.4072",
"label": "Operator algebras for analytic varieties"
},
{
"url": "https://arxiv.org/abs/1211.1116",
"label": "Complete-Pick isomorphism problem"
},
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | For multiplier varieties, is there an intrinsic local definition of a variety, and are the classical irreducible components varieties in that sense? Are multiplier-biholomorphic irreducible varieties in a finite-dimensional ball associated with isomorphic multiplier algebras, and is multiplier biholomorphism an equival... | For multiplier varieties, is there a local definition of a variety and are classical irreducible components varieties; are multiplier-biholomorphic irreducible varieties in the finite ball associated with isomorphic multiplier algebras; is multiplier biholomorphism an equivalence relation; and, for a proper embedding f... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,583 | OWR-12979-005 | Realization of Matricial Families by Tensor-Algebra Elements | Let $M$ be a $W^*$-algebra, let $E$ be a $W^*$-correspondence over $M$, and let $Z$ be an admissible sequence of weights defining the weighted tensor algebra $\mathcal T_+(E,Z)$. Every $F\in\mathcal T_+(E,Z)$ has a Berezin transform that forms a matricial family on the associated weighted intertwiner domains. Conversel... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,014 | 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-12979-005",
"literature-status:partially-solved",
"owr-year:2014"
] | The converse characterization of matricial Berezin transforms is proved in the unweighted case, while the weighted-correspondence version posed in the record is not settled by the cited theory. | [
{
"url": "https://arxiv.org/abs/1210.2964",
"label": "Tensorial function theory"
},
{
"url": "https://doi.org/10.1007/s00020-013-2062-4",
"label": "Published tensorial function theory"
},
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | Let $M$ be a $W^*$-algebra, let $E$ be a $W^*$-correspondence over $M$, and let $Z$ be an admissible sequence of weights defining the weighted tensor algebra $\mathcal T_+(E,Z)$. Every $F\in\mathcal T_+(E,Z)$ has a Berezin transform that forms a matricial family on the associated weighted intertwiner domains. Conversel... | Given that every F in the tensor algebra produces a matricial family of operator-valued functions \{\widehat F_{\sigma}\} on the domains D_{X,\sigma}, does every such matricial family arise from some F? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,584 | OWR-12979-006 | Schatten-Class Commutators for Homogeneous Polynomial Modules | Let $M$ be the submodule of the Drury–Arveson space $H_d^2$ generated by homogeneous polynomials $p_1,\ldots,p_m\in\mathbb C[z_1,\ldots,z_d]$, let $S_j$ be the compression of multiplication by $z_j$ to $M^\perp$, and let $Z(p)$ be the common zero set of the generators. Are all commutators $[S_j,S_k^*]$ in the Schatten ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,014 | 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-12979-006",
"literature-status:partially-solved",
"owr-year:2014"
] | The Arveson--Douglas essential-normality claim is proved for many special ideal and variety classes, with new one-dimensional and singularity results, but the full homogeneous-ideal conjecture remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.jfa.2015.03.014",
"label": "Essential normality and hyperrigidity"
},
{
"url": "https://doi.org/10.1016/j.aim.2024.109525",
"label": "One-dimensional geometric case"
},
{
"url": "https://arxiv.org/abs/2405.11929",
"label": "Strongly pseudoconvex qu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | Let $M$ be the submodule of the Drury–Arveson space $H_d^2$ generated by homogeneous polynomials $p_1,\ldots,p_m\in\mathbb C[z_1,\ldots,z_d]$, let $S_j$ be the compression of multiplication by $z_j$ to $M^\perp$, and let $Z(p)$ be the common zero set of the generators. Are all commutators $[S_j,S_k^*]$ in the Schatten ... | Let M be generated as a module by homogeneous polynomials p_1,\ldots,p_m\in\mathbb{C}[z_1,\ldots,z_d]. For the compressed coordinate operators S_j on M^\perp, are all commutators [S_j,S_k^*] in the Schatten class \mathcal S^q for every q>\dim Z(p)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,585 | OWR-12979-007 | Essential Normality for Homogeneous Varieties | For a homogeneous variety $V\subset\mathbb{C}^d$ and $M=\{f\in H_d^2:f(z)=0\text{ for all }z\in V\cap\mathbb B_d\}$, do the compressed coordinate commutators satisfy $[S_j,S_k^*]\in\mathcal S^q$ for every $q>\dim_{\mathbb C}V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,014 | 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-12979-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The geometric conjecture is established for several classes, including one-dimensional varieties and varieties with suitable regularity or isolated singularities, but remains open for general homogeneous varieties. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.109525",
"label": "One-dimensional geometric case"
},
{
"url": "https://arxiv.org/abs/1312.6777",
"label": "Smooth-away-from-origin case"
},
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | For a homogeneous variety $V\subset\mathbb{C}^d$ and $M=\{f\in H_d^2:f(z)=0\text{ for all }z\in V\cap\mathbb B_d\}$, do the compressed coordinate commutators satisfy $[S_j,S_k^*]\in\mathcal S^q$ for every $q>\dim_{\mathbb C}V$? | For a homogeneous variety V\subset\mathbb{C}^d and M=\{f\in H_d^2:f(z)=0 for all z\in V\cap\mathbb B_d\}, do the compressed coordinate commutators satisfy [S_j,S_k^*]\in\mathcal S^q for every q>\dim_{\mathbb C}V? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,586 | OWR-12979-008 | Choquet Boundaries and $C^*$-Envelopes of Commuting Tuples | For a commuting operator tuple $A=(A_1,\ldots,A_d)$, can one compute its noncommutative Choquet boundary and hence its $C^*$-envelope? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,014 | 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-12979-008",
"literature-status:open",
"owr-year:2014"
] | General theory identifies the C-star-envelope and boundary-representation framework and computes important special cases, but a general effective computation of the Choquet boundary for the relevant commuting tuples is still open. | [
{
"url": "https://doi.org/10.1016/j.jfa.2015.03.014",
"label": "Essential normality and hyperrigidity"
},
{
"url": "https://arxiv.org/abs/math/0701329",
"label": "Noncommutative Choquet boundary"
},
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | For a commuting operator tuple $A=(A_1,\ldots,A_d)$, can one compute its noncommutative Choquet boundary and hence its $C^*$-envelope? | For a commuting operator tuple A=(A_1,\ldots,A_d), can one compute its noncommutative Choquet boundary and hence its C^*-envelope? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,587 | OWR-12979-011 | Answered Drury–Arveson Kernel-Norm Question | For f\in H_n^2, does \sup_{|z|<1}\|f k_z\|<\infty imply that f is a multiplier of the Drury--Arveson space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219](https://doi.org/10.4171/owr/2014/21)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no, for n ≥ 2; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no, for n ≥ 2; answered in the source)**. J. Xia (joint with Q. Fang; OWR 21/2014, pp. 1199–1201) asks, for n ≥ 2, whether sup_{|z|<1} ‖f k_z‖ < ∞ makes f ∈ H²_n a Drury–Arveson multiplier, and Theorem 1.2 there gives an f with finite supremum that is not one (Fan... | [
"owr",
"oberwolfach-reports",
"OWR-12979-011",
"literature-status:partially-solved",
"owr-year:2014"
] | The full Carleson-measure characterization supplies a solution in principle, but the requested simpler direct criterion for the special derivative measures has not been obtained; natural kernel tests are insufficient. | [
{
"url": "https://doi.org/10.4171/owr/2014/21",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1310.4820",
"label": "Carleson-measure characterization"
},
{
"url": "https://doi.org/10.1512/IUMJ.2015.64.5506",
"label": "Multiplier counterexample"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/21 | null | null | null | null | For f\in H_n^2, does \sup_{|z|<1}\|f k_z\|<\infty imply that f is a multiplier of the Drury--Arveson space? | unrecoverable | The official report poses the implication and immediately answers it negatively by exhibiting a function that is not a multiplier although the displayed supremum is finite. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Hilbert Modules and Complex Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/21, pp. 1139--1219 |
30,002,588 | OWR-12980-009 | Multiplicity Formula for Elliptic Arthur Parameters | For every elliptic Arthur parameter $\phi$ of Ramanujan type, do we have $c_{\pi^{\psi_N}(\phi)}^{\psi_N}=|S_\phi|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/22, pp. 1221--1277](https://doi.org/10.4171/owr/2014/22)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,014 | 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-12980-009",
"literature-status:open",
"owr-year:2014"
] | The displayed Arthur-parameter multiplicity identity remains a conjecture in the generality stated; available results establish only local or restricted global cases, so the unresolved claim is classified as open. | [
{
"url": "https://doi.org/10.1016/j.jnt.2013.10.003",
"label": "Lapid--Mao, Whittaker--Fourier coefficients"
},
{
"url": "https://msp.org/ant/2017/11-3/ant-v11-n3-p07-s.pdf",
"label": "Lapid--Mao, metaplectic analogue"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/22 | null | null | null | For every elliptic Arthur parameter $\phi$ of Ramanujan type, do we have $c_{\pi^{\psi_N}(\phi)}^{\psi_N}=|S_\phi|$? | For every elliptic Arthur parameter \phi of Ramanujan type, do we have c_{\pi^{\psi_N}(\phi)}^{\psi_N}=|S_\phi|? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Modular Forms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/22, pp. 1221--1277 |
30,002,589 | OWR-12980-010 | Deligne's Conjecture for Critical Motive Values | For a motive $M$ over $\mathbb Q$ with coefficients in $E$, if $n\in\mathbb Z$ is critical, does Deligne's conjecture give $\frac{L(M,n)}{(2\pi i)^{d_{\pm}n}c_{\pm}(M)}\in E$, where the sign $\pm$ equals $(-1)^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/22, pp. 1221--1277](https://doi.org/10.4171/owr/2014/22)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,014 | 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-12980-010",
"literature-status:partially-solved",
"owr-year:2014"
] | The tensor-product Deligne algebraicity claim remains conjectural in general, but several critical regions and level, weight, or local cases are proved; the 2024 GSp(4) times GL(2) work records both full and partial cases. | [
{
"url": "https://academic.oup.com/qjmath/article/75/2/391/7645867",
"label": "Algebraicity of L-values for GSp(4) times GL(2)"
},
{
"url": "https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.016/",
"label": "Bhagwat--Voisin, periods for tensor-product motiv... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/22 | null | null | null | For a motive $M$ over $\mathbb Q$ with coefficients in $E$, if $n\in\mathbb Z$ is critical, does Deligne's conjecture give $\frac{L(M,n)}{(2\pi i)^{d_{\pm}n}c_{\pm}(M)}\in E$, where the sign $\pm$ equals $(-1)^n$? | For a motive M over \mathbb Q with coefficients in E, if n\in\mathbb Z is critical, does Deligne's conjecture give \frac{L(M,n)}{(2\pi i)^{d_{\pm}n}c_{\pm}(M)}\in E, where the sign \pm equals (-1)^n? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Modular Forms (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/22, pp. 1221--1277 |
30,002,590 | OWR-12983-001 | Homological Determinant of the Nakayama Automorphism | For every Artin–Schelter Gorenstein algebra $A$, is the homological determinant of its Nakayama automorphism equal to $1$; that is, does $\operatorname{hdet}(\mu_A)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/25, pp. 1365--1402](https://doi.org/10.4171/owr/2014/25)
## Literature ... | 3 | partially_solved | null | 2,014 | 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-12983-001",
"literature-status:partially-solved",
"owr-year:2014"
] | Reyes--Rogalski--Zhang prove hdet of the Nakayama automorphism equals one for noetherian connected AS Gorenstein algebras with D epsilon nonzero, including all noetherian AS-regular cases, while automatic nonvanishing and the unrestricted conjecture remain open. | [
{
"url": "https://doi.org/10.1090/tran/6640",
"label": "Reyes--Rogalski--Zhang, skew Calabi--Yau categories"
},
{
"url": "https://arxiv.org/abs/1408.0536",
"label": "Reyes--Rogalski--Zhang, arXiv version"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/25 | null | null | null | For every Artin–Schelter Gorenstein algebra $A$, is the homological determinant of its Nakayama automorphism equal to $1$; that is, does $\operatorname{hdet}(\mu_A)=1$? | For every Artin--Schelter Gorenstein algebra A, is the homological determinant of its Nakayama automorphism \operatorname{hdet}(\mu_A)=1? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/25, pp. 1365--1402 |
30,002,591 | OWR-12983-002 | Nonvanishing of Derived Categories for Gorenstein Algebras | Let $A$ be a connected graded Artin--Schelter Gorenstein algebra with Nakayama automorphism $\mu$, and for a graded algebra automorphism $\varepsilon$ of $A$ let $D_\varepsilon(A)$ be the triangulated category of $\varepsilon$-skew Calabi--Yau / twisted Cohen--Macaulay modules introduced by Reyes, Rogalski, and Zhang. ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/25, pp. 1365--1402](https://doi.org/10.4171/owr/2014/25)
## Literature ... | 3 | open | null | 2,014 | 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-12983-002",
"literature-status:open",
"owr-year:2014"
] | The authors prove D epsilon nonzero in broad classes, but leave automatic nonvanishing for all AS Gorenstein algebras as a conjecture; no later general proof was located. | [
{
"url": "https://doi.org/10.1090/tran/6640",
"label": "Reyes--Rogalski--Zhang, skew Calabi--Yau categories"
},
{
"url": "https://doi.org/10.4171/owr/2014/25",
"label": "Oberwolfach Report 25"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/25 | null | null | null | Let $A$ be a connected graded Artin--Schelter Gorenstein algebra with Nakayama automorphism $\mu$, and for a graded algebra automorphism $\varepsilon$ of $A$ let $D_\varepsilon(A)$ be the triangulated category of $\varepsilon$-skew Calabi--Yau / twisted Cohen--Macaulay modules introduced by Reyes, Rogalski, and Zhang. ... | For every Artin--Schelter Gorenstein algebra A, is the triangulated category D_\varepsilon(A) nonzero? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/25, pp. 1365--1402 |
30,002,592 | OWR-12984-002 | Deformation K-Theory of Pure Braid Groups | For a pure braid group $PB_n$, can the identification $K_{\mathrm{def}}(G)\cong H_*(\operatorname{Irr}(G))$ between deformation $K$-theory and the homology of the topological monoid of irreducible representations be extended to $G=PB_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-002",
"literature-status:open",
"owr-year:2014"
] | Bryden proves excision and a free-group formula for pure-braid deformation K-theory, but the extracted extension problem and the associated full Artin-braid representation-ring construction remain unresolved in the current literature search. | [
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Bryden, Algebraic Structures in Low-Dimensional Topology"
},
{
"url": "https://arxiv.org/abs/2105.07848",
"label": "Azzali et al., K-theory of pure braid groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | For a pure braid group $PB_n$, can the identification $K_{\mathrm{def}}(G)\cong H_*(\operatorname{Irr}(G))$ between deformation $K$-theory and the homology of the topological monoid of irreducible representations be extended to $G=PB_n$? | Can the deformation K-theory theorem identifying K_{\mathrm{def}}(G) with the homology of the irreducible-representation monoid be extended to pure braid groups, and can the corresponding Artin-braid-group deformation and complex topological K-theories be identified? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,593 | OWR-12984-003 | Deformation K-Theory of Artin Braid Groups | For an Artin braid group $B_n$, does deformation $K$-theory satisfy $K_{\mathrm{def}}(B_n)\cong H_*(\operatorname{Irr}(B_n))$? Is the deformation $K$-theory of $B_n$ isomorphic to its complex topological $K$-theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-003",
"literature-status:open",
"owr-year:2014"
] | The two Artin-braid questions remain open as stated: later work computes selected ordinary K-theory groups, but does not establish the requested general representation-ring construction or the deformation-K-theory isomorphism. | [
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Bryden, Algebraic Structures in Low-Dimensional Topology"
},
{
"url": "https://arxiv.org/abs/2105.07848",
"label": "Azzali et al., K-theory of pure braid groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | For an Artin braid group $B_n$, does deformation $K$-theory satisfy $K_{\mathrm{def}}(B_n)\cong H_*(\operatorname{Irr}(B_n))$? Is the deformation $K$-theory of $B_n$ isomorphic to its complex topological $K$-theory? | For Artin braid groups, can the deformation K-theory theorem be extended, and can deformation K-theory be proved isomorphic to complex topological K-theory in this case? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,594 | OWR-12984-004 | Étale Homotopy Realization of Khovanov Homology | Can the Khovanov homology of a link $K$ be represented by an appropriate étale homotopy type that is itself an invariant of $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-004",
"literature-status:open",
"owr-year:2014"
] | The report presents the etale-homotopy realization of Khovanov homology as a conjecture, and no authoritative proof or disproof of this link-invariant realization was located. | [
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Bryden--Kauffman, a topos-theoretic interpretation of Khovanov homology"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | Can the Khovanov homology of a link $K$ be represented by an appropriate étale homotopy type that is itself an invariant of $K$? | Can the Khovanov homology of a link K be represented by an appropriate etale homotopy type that is an invariant of K? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,595 | OWR-12984-005 | Classification of Cyclic Covers of Two-Bridge Knots | For every two-bridge knot $K$ and integer $n>1$, determine whether the cyclic branched cover $\Sigma_n(K)$ is a total L-space, whether $\pi_1(\Sigma_n(K))$ is left-orderable, and whether $\Sigma_n(K)$ is excellent. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-005",
"literature-status:open",
"owr-year:2014"
] | Results now settle important subclasses of cyclic branched covers of two-bridge knots, but a complete classification for all two-bridge knots and all covering degrees, as asked in the record, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Oberwolfach Report 26, cyclic branched covers"
},
{
"url": "https://doi.org/10.2140/agt.2015.15.399",
"label": "Hu, left-orderability and cyclic branched coverings"
},
{
"url": "https://doi.org/10.1112/blms.12950",
"label": "I... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | For every two-bridge knot $K$ and integer $n>1$, determine whether the cyclic branched cover $\Sigma_n(K)$ is a total L-space, whether $\pi_1(\Sigma_n(K))$ is left-orderable, and whether $\Sigma_n(K)$ is excellent. | Can the behavior of the cyclic branched covers \Sigma_n(K) be completely determined for all 2-bridge knots K and n>1, including when they are total L-spaces, have left-orderable fundamental groups, or are excellent? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,596 | OWR-12984-006 | Relations Among Algebraic PL and Fourier Knot Degrees | For a knot $K$, establish inequalities in both directions among its algebraic, piecewise-linear, and Fourier degrees. Determine the extrema of their three pairwise quotients and whether those quotients have limits along sequences of knots with crossing number tending to infinity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-006",
"literature-status:open",
"owr-year:2014"
] | The known inequalities give only one-sided bounds such as a-deg bounded by a constant times F-deg and a-deg bounded by twice PL-deg; the requested reverse inequalities, quotient extrema, and asymptotic limits remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Klaus, algebraic, PL and Fourier degrees of knots"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | For a knot $K$, establish inequalities in both directions among its algebraic, piecewise-linear, and Fourier degrees. Determine the extrema of their three pairwise quotients and whether those quotients have limits along sequences of knots with crossing number tending to infinity. | For knot K, can one prove inequalities in both directions among the algebraic, PL, and Fourier degrees and compute the minimum and maximum of their three pairwise quotients, as well as determine whether the quotients have limits along knots of increasing crossing number?} | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,597 | OWR-12984-009 | Bounding Immersed Curves by Stable Singular Disk Maps | Given a generically immersed closed curve $\gamma$ in an oriented surface $S_g$, does there exist a compact $3$-manifold $M$ with $\partial M=S_g$ and a proper map $D\to M$ from a disk, having only stable singularities, such that $\partial D=D\cap S_g=\gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-009",
"literature-status:open",
"owr-year:2014"
] | Parity gives obstructions and the free-knot case has substantial partial results, but no general existence criterion for a bounding 3-manifold and stable-singularity disk map for every immersed curve was found. | [
{
"url": "https://doi.org/10.1070/SM2012v203n02ABEH004219",
"label": "Manturov, Parity and cobordism of free knots"
},
{
"url": "https://doi.org/10.4171/owr/2014/26",
"label": "Oberwolfach Report 26, stable-singularity disk problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | Given a generically immersed closed curve $\gamma$ in an oriented surface $S_g$, does there exist a compact $3$-manifold $M$ with $\partial M=S_g$ and a proper map $D\to M$ from a disk, having only stable singularities, such that $\partial D=D\cap S_g=\gamma$? | Given a generically immersed curve \gamma in an oriented surface S_g, does there exist a 3-manifold M with \partial M=S_g and a proper map D\to M having only stable singularities such that \partial D=D\cap S_g=\gamma? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,598 | OWR-12984-011 | Weighted $q$-Boundaries for Presimplicial Modules | Given a presimplicial module with boundary $\partial_n=\sum_{i=0}^n(-1)^i d_i$, what useful homological structure can be extracted from the weighted operator $\partial_n^q=\sum_{i=0}^n q^i d_i$ on $C_n^q=C_n\otimes_k\mathbb Z[q]$, despite the fact that these operators do not generally form a chain complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458](https://doi.org/10.4171/owr/2014/26)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-12984-011",
"literature-status:open",
"owr-year:2014"
] | The report poses the q-version as an exploratory question and notes that the weighted map is not generically a chain differential; no authoritative source found that settles a useful general theory for this construction. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3416/OWR_2014_26.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 26/2014"
},
{
"url": "https://arxiv.org/abs/1406.6499",
"label": "Przytycki, Progress in distributive homology"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/26 | null | null | null | Given a presimplicial module with boundary $\partial_n=\sum_{i=0}^n(-1)^i d_i$, what useful homological structure can be extracted from the weighted operator $\partial_n^q=\sum_{i=0}^n q^i d_i$ on $C_n^q=C_n\otimes_k\mathbb Z[q]$, despite the fact that these operators do not generally form a chain complex? | Given a presimplicial module with \partial_n=\sum_{i=0}^n(-1)^i d_i, is it useful to form the q-version C_n^q=C_n\otimes_k\mathbb Z[q] with \partial_n^q=\sum_{i=0}^n q^i d_i, despite its generally failing to be a chain complex? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic Structures in Low-Dimensional Topology (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/26, pp. 1403--1458 |
30,002,599 | OWR-12985-001 | Combinatorial Positivity of Schubert CSM Coefficients | Is there a combinatorial proof that the coefficients $\gamma_{\alpha,\beta}$ in the Chern–Schwartz–MacPherson expansion of a Schubert cell are nonnegative? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513](https://doi.org/10.4171/owr/2014/27)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,014 | 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-12985-001",
"literature-status:open",
"owr-year:2014"
] | Nonnegativity itself is proved, including for generalized flag varieties, but the extracted question asks for a combinatorial proof and the cited primary literature supplies geometric and representation-theoretic proofs rather than a general combinatorial one. | [
{
"url": "https://arxiv.org/abs/1508.01535",
"label": "Aluffi--Mihalcea, CSM classes for Schubert cells"
},
{
"url": "https://arxiv.org/abs/1709.08697",
"label": "Aluffi--Mihalcea--Schuermann--Su, positivity theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/27 | null | null | null | Is there a combinatorial proof that the coefficients $\gamma_{\alpha,\beta}$ in the Chern–Schwartz–MacPherson expansion of a Schubert cell are nonnegative? | Is there a combinatorial proof that the coefficients \gamma_{\alpha,\beta} in the Chern--Schwartz--MacPherson expansion of a Schubert cell are nonnegative? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513 |
30,002,600 | OWR-12985-002 | CSM Positivity Beyond Grassmannian Schubert Cells | Are the analogous Chern–Schwartz–MacPherson coefficients nonnegative for Schubert cells in flag varieties other than Grassmannians? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513](https://doi.org/10.4171/owr/2014/27)
## Literature review (checked 2026-08-21)
**Sta... | 3 | solved | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1215/00127094-2022-0101",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. J. Huh (OWR 27/2014, p. 1502, Question (B)) asks whether the Chern–Schwartz–MacPherson classes of Schubert cells in flag varieties G/P other than Grassmannians have nonnegative coefficients in the Schubert basis, and expects yes. Aluffi–Mihalcea–Schürmann–... | [
"owr",
"oberwolfach-reports",
"OWR-12985-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The conjectured nonnegativity is proved for all Schubert cells in generalized flag manifolds, while the stronger equivariant positivity conjecture remains only partially established. | [
{
"url": "https://arxiv.org/abs/1709.08697",
"label": "Aluffi--Mihalcea--Schuermann--Su, positivity theorem"
},
{
"url": "https://arxiv.org/abs/1508.01535",
"label": "Aluffi--Mihalcea, flag-manifold conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/27 | null | null | null | Are the analogous Chern–Schwartz–MacPherson coefficients nonnegative for Schubert cells in flag varieties other than Grassmannians? | Are the analogous Chern--Schwartz--MacPherson coefficients nonnegative for Schubert cells in flag varieties other than Grassmannians? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513 |
30,002,601 | OWR-12985-003 | Finiteness of Common Zeros of Coprime Exponential Sums | Let $f$ and $g$ be one-variable exponential sums with no nonconstant common divisor. Is the common zero set $\{z:f(z)=g(z)=0\}$ finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513](https://doi.org/10.4171/owr/2014/27)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,014 | 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-12985-003",
"literature-status:open",
"owr-year:2014"
] | The one-variable coprime exponential-sum common-zero finiteness conjecture is still described in current primary surveys as far from proved; special cases follow from Mordell--Lang or Skolem--Mahler--Lech type results. | [
{
"url": "https://ems.press/content/serial-article-files/46517",
"label": "Oberwolfach Report 27/2014"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/blms.12719",
"label": "Heittokangas et al., exponential polynomials survey"
},
{
"url": "https://www.mathnet.ru... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/27 | null | null | null | Let $f$ and $g$ be one-variable exponential sums with no nonconstant common divisor. Is the common zero set $\{z:f(z)=g(z)=0\}$ finite? | For exponential sums f,g of one variable with no nontrivial common divisor, is the common zero set \{z:f(z)=g(z)=0\} finite; and, in the stated Mordell--Lang generalization, is (A\setminus A')\cap G finite under the finite-rank and anomalous-subvariety hypotheses? | corrected_verified | The official report states this exponential-sum conjecture separately from its later higher-dimensional Mordell–Lang generalization. The clean statement removes the duplicated second conjecture, which is represented by OWR-12985-004. | null | null | null | null | null | Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513 |
30,002,602 | OWR-12985-004 | Mordell–Lang Finiteness Outside Anomalous Loci | Let $A\subset(\mathbb C^*)^n$ have codimension greater than $k$, let $A'$ be a subvariety of its anomalous points, and let $L\subset\mathbb C^n$ have dimension $k$ with $\exp(L)\subset G$ and $G/\exp(L)$ of finite rank. Is $(A\setminus A')\cap G$ finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513](https://doi.org/10.4171/owr/2014/27)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,014 | 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-12985-004",
"literature-status:open",
"owr-year:2014"
] | The k=0 Mordell--Lang case is a theorem and anomalous loci are understood, but the stated exponential-subspace generalization, including the k=1 strengthening, is not established in full generality. | [
{
"url": "https://ems.press/content/serial-article-files/46517",
"label": "Oberwolfach Report 27/2014"
},
{
"url": "https://doi.org/10.1093/imrn/rnm057",
"label": "Bombieri--Masser--Zannier, anomalous subvarieties"
},
{
"url": "https://www.mathnet.ru/php/getFT.phtml?jrnid=rm&option_lang=... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/27 | null | null | null | Let $A\subset(\mathbb C^*)^n$ have codimension greater than $k$, let $A'$ be a subvariety of its anomalous points, and let $L\subset\mathbb C^n$ have dimension $k$ with $\exp(L)\subset G$ and $G/\exp(L)$ of finite rank. Is $(A\setminus A')\cap G$ finite? | Let A\subset(\mathbb C^*)^n have codimension greater than k, let A' be a subvariety of its anomalous points, and let L\subset\mathbb C^n have dimension k with \exp(L)\subset G and G/\exp(L) of finite rank. Is (A\setminus A')\cap G finite? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Okounkov Bodies and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/27, pp. 1459--1513 |
30,002,603 | OWR-12986-001 | Linear Segments in Optimal-Path Shape Functions | Consider lazy paths $S:\{0,\ldots,n\}\to\mathbb Z$ with $\lvert S(i+1)-S(i)\rvert\leq1$ in the product random potential $V(x,i)=F(x)b(i)$, where the fields $\{F(x)\}$ and $\{b(i)\}$ are independent and i.i.d., the potential has a compactly supported density positive on the interior of its support, and $\mathbb E[b(i)]=... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Stochastic Analysis: Around the KPZ Universality Class (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/28, pp. 1515--1568](https://doi.org/10.4171/owr/2014/28)
## Literature review (chec... | 3 | partially_solved | null | 2,014 | 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-12986-001",
"literature-status:partially-solved",
"owr-year:2014"
] | For the product-type random environment, later work proves a flat linear edge near the origin under an explicit power-law condition on the density at the support edge; this establishes the conjecture in a substantial regime but not under every assumption stated in the extracted record. | [
{
"url": "https://arxiv.org/abs/2310.08379",
"label": "Bakhtin--Khanin--Meszaros--Voltz, last passage percolation"
},
{
"url": "https://ems.press/content/serial-article-files/46518",
"label": "Oberwolfach Report 28/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/28 | null | null | null | Consider lazy paths $S:\{0,\ldots,n\}\to\mathbb Z$ with $\lvert S(i+1)-S(i)\rvert\leq1$ in the product random potential $V(x,i)=F(x)b(i)$, where the fields $\{F(x)\}$ and $\{b(i)\}$ are independent and i.i.d., the potential has a compactly supported density positive on the interior of its support, and $\mathbb E[b(i)]=... | For the point-to-point optimal-path model described in the report, does the shape function have a nontrivial linear piece in a neighborhood of the origin? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Stochastic Analysis: Around the KPZ Universality Class (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/28, pp. 1515--1568 |
30,002,604 | OWR-12987-004 | Non-Kähler Analogues of Yau's Monge–Ampère Theorem | Are there non-Kähler analogues of Yau's solution of the complex Monge–Ampère equation and of the resulting resolution of the Calabi conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/29, pp. 1569--1623](https://doi.org/10.4171/owr/2014/29)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,014 | 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-12987-004",
"literature-status:partially-solved",
"owr-year:2014"
] | Non-Kahler analogues are available for Gauduchon metrics on all compact complex manifolds and for balanced or astheno-Kahler settings, but no single full analogue of all Kahler results is known. | [
{
"url": "https://arxiv.org/abs/1503.04491",
"label": "Szekelyhidi--Tosatti--Weinkove, prescribed volume form"
},
{
"url": "https://arxiv.org/abs/1310.6326",
"label": "Tosatti--Weinkove, Hermitian Monge--Ampere"
},
{
"url": "https://ems.press/content/serial-article-files/46519",
"lab... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/29 | null | null | null | Are there non-Kähler analogues of Yau's solution of the complex Monge–Ampère equation and of the resulting resolution of the Calabi conjecture? | Are there analogues for non-Kahler metrics of Yau's solution of the complex Monge--Ampere equation and its resulting Calabi-conjecture statement? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometrie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/29, pp. 1569--1623 |
30,002,605 | OWR-12988-001 | Peridynamics as a Multiscale Mechanics Model | Why is peridynamics a useful mathematical model for mechanics, particularly as a multiscale model that behaves nonlocally at small scales, locally at large scales, and transitions between these regimes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681](https://doi.org/10.4171/owr/2014/30)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,014 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The phrase is a rhetorical heading followed by an explanation of why peridynamics is useful) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12988-001",
"literature-status:open",
"owr-year:2014"
] | The report gives strong modeling motivations for peridynamics, including nonlocal-to-local behavior and crack handling, but why it should be preferred is application-dependent rather than a settled mathematical claim. | [
{
"url": "https://ems.press/content/serial-article-files/46520",
"label": "Oberwolfach Report 30/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/30 | null | null | null | null | Why is peridynamics a useful mathematical model for mechanics, particularly as a multiscale model that behaves nonlocally at small scales, locally at large scales, and transitions between these regimes? | unrecoverable | Checked against the official Oberwolfach report. The phrase is a rhetorical heading followed by an explanation of why peridynamics is useful; it does not state an unresolved mathematical problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681 |
30,002,606 | OWR-12988-002 | Adaptive Galerkin Discretization of Peridynamics | How can peridynamics (PD) be discretized as a computational multiscale mono-model by choosing h_j<\delta with discontinuous Galerkin elements near defects and h_j>\delta with continuous Galerkin elements away from defects, together with detection, refinement, and suitable quadrature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681](https://doi.org/10.4171/owr/2014/30)
## Literature review (checked 2026-08-21)
**Sta... | 3 | partially_solved | null | 2,014 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The source presents the listed finite-element choices as a proposed computational construct) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12988-002",
"literature-status:partially-solved",
"owr-year:2014"
] | A concrete mono-model recipe is given using horizon-relative mesh size, adaptive refinement, and continuous versus discontinuous finite elements, with one-dimensional analysis; higher-dimensional implementation and analysis remain incomplete. | [
{
"url": "https://ems.press/content/serial-article-files/46520",
"label": "Oberwolfach Report 30/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/30 | null | null | null | null | How can peridynamics (PD) be discretized as a computational multiscale mono-model by choosing h_j<\delta with discontinuous Galerkin elements near defects and h_j>\delta with continuous Galerkin elements away from defects, together with detection, refinement, and suitable quadrature? | unrecoverable | Checked against the official Oberwolfach report. The source presents the listed finite-element choices as a proposed computational construction and reports one-dimensional results, rather than posing the extraction as a standalone open problem. No separate clean statement is promoted; the original record remains public... | null | null | null | null | null | Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681 |
30,002,607 | OWR-12988-003 | Basis Design for Numerical Homogenization | Is there a general method for constructing accurate finite-dimensional basis functions for numerical homogenization of partial differential equations with arbitrary rough or multiscale coefficients? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681](https://doi.org/10.4171/owr/2014/30)
## Literature review (checked 2026-08-21)
**Sta... | 3 | partially_solved | null | 2,014 | 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-12988-003",
"literature-status:partially-solved",
"owr-year:2014"
] | Bayesian numerical homogenization supplies a general decision framework and derives optimal-recovery bases for broad integro-differential problems, but a universally optimal basis-design recipe for arbitrary multiscale operators is not established. | [
{
"url": "https://arxiv.org/abs/1406.6668",
"label": "Owhadi, Bayesian numerical homogenization"
},
{
"url": "https://ems.press/content/serial-article-files/46520",
"label": "Oberwolfach Report 30/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/30 | null | null | null | Is there a general method for constructing accurate finite-dimensional basis functions for numerical homogenization of partial differential equations with arbitrary rough or multiscale coefficients? | Can the identification of accurate basis elements for numerical homogenization with rough or multiscale PDE coefficients be facilitated, and is there a general recipe or decision framework for designing such basis elements? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Computational Multiscale Methods (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/30, pp. 1625--1681 |
30,002,608 | OWR-13101-001 | Green's Syzygy Conjecture for Arbitrary Curves | Does Green's conjecture on the higher syzygies of canonical ideals of curves hold for all curves, beyond the generic cases? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-13101-001",
"literature-status:open",
"owr-year:2014"
] | This is Green's canonical syzygy conjecture for arbitrary smooth curves: generic curves and several special classes are settled, but the full arbitrary-curve statement remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46521",
"label": "Oberwolfach Report 31/2014"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2026.108254",
"label": "Generic Green conjecture in positive characteristic"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Does Green's conjecture on the higher syzygies of canonical ideals of curves hold for all curves, beyond the generic cases? | Does Green's conjecture on the higher syzygies of canonical ideals of curves hold for all curves, beyond the generic cases? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,609 | OWR-13101-002 | Duplicate Summary: Canonical Bases for Log Calabi–Yau Varieties | Does the canonical-basis phenomenon for regular functions on the torus example admit the proposed vast generalization to affine log Calabi--Yau varieties with maximal boundary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The source sentence is an introductory summary of the detailed Gross–Hacking–Keel conjecture represented by OWR-13101-003, not a separate ma) | [
"OWR-13101-003"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13101-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The proposed vast generalization of the toric canonical-basis construction is proved for log Calabi--Yau surfaces and for cluster varieties in all dimensions, but not for every affine log Calabi--Yau with maximal boundary. | [
{
"url": "https://arxiv.org/abs/1411.1394",
"label": "Gross--Hacking--Keel--Kontsevich, canonical bases"
},
{
"url": "https://www.numdam.org/item/PMIHES_2015__122__65_0/",
"label": "Gross--Hacking--Keel, log Calabi--Yau surfaces"
},
{
"url": "https://ems.press/content/serial-article-file... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | null | Does the canonical-basis phenomenon for regular functions on the torus example admit the proposed vast generalization to affine log Calabi--Yau varieties with maximal boundary? | unrecoverable | The source sentence is an introductory summary of the detailed Gross–Hacking–Keel conjecture represented by OWR-13101-003, not a separate mathematical problem. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,610 | OWR-13101-003 | Tropical-Disc Mirror Algebras for Log Calabi–Yau Varieties | Let $U$ be an affine log Calabi–Yau variety with maximal boundary, and let
$$A=\bigoplus_{p\in U^t(\mathbb Z)}\mathbb C\vartheta_p.$$
Does $A$ have a natural finitely generated commutative associative algebra structure whose integer structure constants in
$$\vartheta_p\vartheta_q=\sum_r\alpha(p,q,r)\vartheta_r$$
count ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13101-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13101-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The GHK canonical-basis conjecture is proved for cluster varieties and in dimension two, with further theta-function constructions, but the stated general affine log Calabi--Yau claim remains open beyond these classes. | [
{
"url": "https://arxiv.org/abs/1411.1394",
"label": "Gross--Hacking--Keel--Kontsevich, canonical bases"
},
{
"url": "https://arxiv.org/abs/1601.07081",
"label": "Gross--Hacking--Siebert, theta functions"
},
{
"url": "https://ems.press/content/serial-article-files/46521",
"label": "O... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Let $U$ be an affine log Calabi–Yau variety with maximal boundary, and let
$$A=\bigoplus_{p\in U^t(\mathbb Z)}\mathbb C\vartheta_p.$$
Does $A$ have a natural finitely generated commutative associative algebra structure whose integer structure constants in
$$\vartheta_p\vartheta_q=\sum_r\alpha(p,q,r)\vartheta_r$$
count ... | For an affine log Calabi--Yau variety U with maximal boundary, does the vector space with basis indexed by U^t(\mathbb{Z}) carry a natural finitely generated commutative associative algebra structure whose integer structure constants count tropical discs, with U^\vee=\operatorname{Spec}(A) an affine log Calabi--Yau mir... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,611 | OWR-13101-004 | Ulrich Bundles on Smooth Projective Varieties | Does every smooth projective variety $X$ of dimension $n$ admit an Ulrich vector bundle? Equivalently, does its cone of cohomology tables coincide with that of $\mathbb P^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-13101-004",
"literature-status:open",
"owr-year:2014"
] | The question is the Eisenbud--Schreyer Ulrich-bundle conjecture that every smooth projective variety carries an Ulrich vector bundle; it remains a major open problem despite many special cases. | [
{
"url": "https://arxiv.org/abs/1610.02771",
"label": "Beauville, introduction to Ulrich bundles"
},
{
"url": "https://doi.org/10.1007/s00009-026-03109-z",
"label": "Current Ulrich-bundle status"
},
{
"url": "https://ems.press/content/serial-article-files/46521",
"label": "Oberwolfac... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Does every smooth projective variety $X$ of dimension $n$ admit an Ulrich vector bundle? Equivalently, does its cone of cohomology tables coincide with that of $\mathbb P^n$? | Does every n-dimensional smooth projective variety X admit an Ulrich vector bundle, equivalently does its cone of cohomology tables coincide with that of projective n-space? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,612 | OWR-13101-006 | Beauville–Voisin Conjecture for Hyperkähler Manifolds | Let $X$ be a projective hyperkähler manifold. Is every polynomial $z$ in first Chern classes of line bundles and in the Chern classes of $T_X$ that is numerically trivial also rationally equivalent to zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 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-13101-006",
"literature-status:partially-solved",
"owr-year:2014"
] | The Beauville--Voisin conjecture is proved for several deformation families and special Hilbert schemes, generalized Kummers, cubic-fourfold Fano varieties, and other cases, but remains open for arbitrary projective hyperkaehler manifolds. | [
{
"url": "https://doi.org/10.1016/j.indag.2024.10.004",
"label": "Beauville--Voisin--Franchetta conjecture and LLSS eightfolds"
},
{
"url": "https://arxiv.org/abs/math/0602400",
"label": "Voisin, hyperkaehler Chow rings"
},
{
"url": "https://arxiv.org/abs/1309.4977",
"label": "Fu, ge... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Let $X$ be a projective hyperkähler manifold. Is every polynomial $z$ in first Chern classes of line bundles and in the Chern classes of $T_X$ that is numerically trivial also rationally equivalent to zero? | For a projective hyperkähler manifold X, is every polynomial z in the first Chern classes of line bundles and the Chern classes of T_X that is numerically trivial rationally equivalent to zero? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,613 | OWR-13101-008 | Chow Decompositions of Hilbert Schemes of K3 Surfaces | For $X=S^{[m]}$ with $S$ a projective K3 surface, does the Chow decomposition $CH^i_{(j)}(X)$ satisfy $CH^i_{(j)}(X)=0$ for $j<0$, and does the cycle-class map $CH^i_{(0)}(X)\to H^{2i}(X)$ remain injective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 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-13101-008",
"literature-status:partially-solved",
"owr-year:2014"
] | The general Hilbert-scheme-of-K3 case remains unresolved, while later work proves weak or conditional forms and substantial bounded or motivic cases; the extracted 2014 claim is therefore still accurate in general. | [
{
"url": "https://arxiv.org/abs/1904.05262",
"label": "Maulik--Negut, Lehn's formula and Beauville--Voisin"
},
{
"url": "https://doi.org/10.1016/j.indag.2024.10.004",
"label": "Beauville--Voisin--Franchetta conjecture and LLSS eightfolds"
},
{
"url": "https://arxiv.org/abs/1404.0171",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | For $X=S^{[m]}$ with $S$ a projective K3 surface, does the Chow decomposition $CH^i_{(j)}(X)$ satisfy $CH^i_{(j)}(X)=0$ for $j<0$, and does the cycle-class map $CH^i_{(0)}(X)\to H^{2i}(X)$ remain injective? | For X=S^{[m]} with S a projective K3 surface, does the Chow decomposition CH^i_{(j)}(X) satisfy CH^i_{(j)}(X)=0 for j<0 and does the cycle-class map CH^i_{(0)}(X)\to H^{2i}(X) remain injective? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,614 | OWR-13101-009 | Rationally Connected Fibration of a Brill–Noether Moduli Space | Does the maximal rationally connected fibration of the moduli space $M_{15,16}$ of curves of genus 15 and degree 16 have a three-dimensional base? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,014 | 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-13101-009",
"literature-status:open",
"owr-year:2014"
] | Schreyer's published paper presents the three-dimensional-base statement only as evidence for a conjecture about the maximal rationally connected fibration of the Brill--Noether moduli space; no proof of that conjecture was found. | [
{
"url": "https://doi.org/10.14231/AG-2015-021",
"label": "Schreyer, matrix factorizations and genus 15"
},
{
"url": "https://arxiv.org/abs/1311.6962",
"label": "Schreyer, original preprint"
},
{
"url": "https://ems.press/content/serial-article-files/46521",
"label": "Oberwolfach Rep... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Does the maximal rationally connected fibration of the moduli space $M_{15,16}$ of curves of genus 15 and degree 16 have a three-dimensional base? | Does the maximal rationally connected fibration of the moduli space M_{15,16} of curves of genus 15 and degree 16 have a three-dimensional base? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
30,002,615 | OWR-13101-011 | Mixed-Spin Fields and All-Genus Quintic Invariants | Do moduli spaces of mixed-spin-$P$ fields provide an effective algorithm for computing all-genus FJRW invariants of the Fermat quintic with multiple insertions and all-genus Gromov–Witten invariants $N_g(d)$ of the quintic threefold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745](https://doi.org/10.4171/owr/2014/31)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,014 | 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-13101-011",
"literature-status:partially-solved",
"owr-year:2014"
] | The extracted record truncates Conjecture 0.16, whose identifiable claim is an all genus FJRW algorithm; later MSP work proves broad effective recurrences but explicitly leaves initial data unresolved. | [
{
"url": "https://doi.org/10.4310/jdg/1645207466",
"label": "Chang--Li--Li--Liu, effective theory of quintic invariants"
},
{
"url": "https://doi.org/10.4171/owr/2014/31",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/31 | null | null | null | Do moduli spaces of mixed-spin-$P$ fields provide an effective algorithm for computing all-genus FJRW invariants of the Fermat quintic with multiple insertions and all-genus Gromov–Witten invariants $N_g(d)$ of the quintic threefold? | Will the moduli of mixed-spin-P fields provide an effective algorithm for determining all genus FJRW invariants of the Fermat quintic polynomial with multiple insertions and all genus Gromov--Witten invariants N_g(d) of the quintic threefold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Classical Algebraic Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/31, pp. 1695--1745 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.