id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,416 | OWR-17472-006 | Character Fields of Odd-Degree Representations | Which fields occur as $\mathbb Q(\chi)$ for odd-degree irreducible characters $\chi\in\operatorname{Irr}_{2'}(G)$ of finite groups $G$? Equivalently, determine
$$
F_2=\{\mathbb Q(\chi)/\mathbb Q\mid G\text{ finite},\ \chi\in\operatorname{Irr}_{2'}(G)\}
$$
. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | solved | null | 2,020 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (the fields are determined)**; the dataset currently labels it partially solved. G. Navarro, OWR 9/2020, p. 526: which fields ℚ(χ) occur for odd-degree irreducible characters χ of finite groups (the set F₂)? The same abstract states the answer on p. 527, proved in ... | [
"owr",
"oberwolfach-reports",
"OWR-17472-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The fields of values of p-prime-degree characters are classified for p equal to 2, while the analogous odd-prime classification remains conjectural and only partial results are known. | [
{
"url": "https://arxiv.org/abs/2601.15987",
"label": "Hung, Navarro, and Tiep, fields of values"
},
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/fields-of-values-of-characters-of-degree-not-divisible-by-p/0FE327DAE6088EC9B43A0CFAFC8E8D52",
"label": "Fields o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Which fields occur as $\mathbb Q(\chi)$ for odd-degree irreducible characters $\chi\in\operatorname{Irr}_{2'}(G)$ of finite groups $G$? Equivalently, determine
$$
F_2=\{\mathbb Q(\chi)/\mathbb Q\mid G\text{ finite},\ \chi\in\operatorname{Irr}_{2'}(G)\}
$$
. | Which fields occur as \mathbb Q(\chi) for odd-degree irreducible characters \chi\in\operatorname{Irr}_{2\prime}(G) of finite groups G; equivalently, what is the set F_2=\{\mathbb Q(\chi)/\mathbb Q\mid \chi\in\operatorname{Irr}_{2\prime}(G),\ G finite\}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,417 | OWR-17472-007 | Canonical Subsets in McKay Bijections | Which subset of $\operatorname{Irr}_{p^{\prime}}(G)$, if it exists, corresponds under a McKay bijection to $\operatorname{Irr}(N_G(P)/P)$, and what is the analogous answer for groups of Lie type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-007",
"literature-status:open",
"owr-year:2020"
] | Canonical McKay correspondences and the relevant subsets are known in several solvable and Lie-type cases, but the requested general description for groups of Lie type remains incomplete. | [
{
"url": "https://link.springer.com/article/10.1007/s00209-026-04040-5",
"label": "iMcKay--Navarro correspondence work"
},
{
"url": "https://doi.org/10.1112/blms.12584",
"label": "Giannelli, Law, Long, and Vallejo, Sylow branching"
},
{
"url": "https://doi.org/10.4171/owr/2020/9",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Which subset of $\operatorname{Irr}_{p^{\prime}}(G)$, if it exists, corresponds under a McKay bijection to $\operatorname{Irr}(N_G(P)/P)$, and what is the analogous answer for groups of Lie type? | Which subset of \operatorname{Irr}_{p\prime}(G), if it exists, corresponds under a McKay bijection to \operatorname{Irr}(N_G(P)/P), and what is the analogous answer for groups of Lie type? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,418 | OWR-17472-008 | Combinatorics of Sylow Branching Coefficients | Find a combinatorial description of the Sylow branching-coefficient map $Z^{\mathbf1_{P_n}}:\mathcal P(n)\to\mathbb N_0$, $\lambda\mapsto Z^{\mathbf1_{P_n}}_\lambda$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | partially_solved | null | 2,020 | 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-17472-008",
"literature-status:partially-solved",
"owr-year:2020"
] | The induced constituents and several special Sylow-branching families have explicit descriptions, but no general combinatorial formula for the full multiplicity map is known. | [
{
"url": "https://arxiv.org/abs/1712.02642",
"label": "Bessenrodt, Giannelli, and Wildon, branching multiplicities"
},
{
"url": "https://doi.org/10.1112/blms.12584",
"label": "Giannelli, Law, Long, and Vallejo, Sylow branching"
},
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Find a combinatorial description of the Sylow branching-coefficient map $Z^{\mathbf1_{P_n}}:\mathcal P(n)\to\mathbb N_0$, $\lambda\mapsto Z^{\mathbf1_{P_n}}_\lambda$. | Find a combinatorial description of the Sylow branching-coefficient map Z^{\mathbf 1_{P_n}}:\mathcal P(n)\to\mathbb N_0,\;\lambda\mapsto Z^{\mathbf 1_{P_n}}_{\lambda}. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,419 | OWR-17472-013 | Combinatorial Interpretation of Stable Kronecker Coefficients | Find a combinatorial interpretation of the stable (reduced) Kronecker coefficients, analogous to the Littlewood–Richardson rule. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-013",
"literature-status:open",
"owr-year:2020"
] | The general combinatorial-interpretation problem remains open: recent work proves that ordinary and reduced Kronecker coefficients encode equivalent problems, while only special families have combinatorial models. | [
{
"url": "https://doi.org/10.1017/fmp.2024.23",
"label": "Ikenmeyer and Panova, All Kronecker coefficients are reduced Kronecker coefficients"
},
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Find a combinatorial interpretation of the stable (reduced) Kronecker coefficients, analogous to the Littlewood–Richardson rule. | Find a combinatorial interpretation of the stable (reduced) Kronecker coefficients, analogous to the Littlewood--Richardson rule. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,420 | OWR-17472-014 | Chamber Structures of Schur-Positive Multiplicity Functions | Characterize the multiplicity functions $m_F$ arising from Schur-positive symmetric functions, including their piecewise-quasipolynomial chamber structures and the behavior of $m_F(\omega_0+k\omega)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-014",
"literature-status:open",
"owr-year:2020"
] | This is an underspecified research question about multiplicity functions, with no definite theorem or conjecture to verify and no general resolution identified. | [
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Characterize the multiplicity functions $m_F$ arising from Schur-positive symmetric functions, including their piecewise-quasipolynomial chamber structures and the behavior of $m_F(\omega_0+k\omega)$. | Characterize the multiplicity functions m_F arising from Schur-positive symmetric functions, including their piecewise-quasipolynomial chamber structures and the behavior of m_F(\omega_0+k\omega). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,421 | OWR-17472-016 | Maximality of Normalizers of Quasisimple Subgroups | In the Aschbacher–Scott setting, when is the normalizer $M=N_G(S)$ of a quasisimple subgroup $S<G$ acting irreducibly on $V$ a maximal subgroup of the classical group $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-016",
"literature-status:open",
"owr-year:2020"
] | The extract asks generally for a converse concerning maximal subgroups without specifying a precise theorem; no uniquely identifiable resolved claim can be assessed. | [
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | In the Aschbacher–Scott setting, when is the normalizer $M=N_G(S)$ of a quasisimple subgroup $S<G$ acting irreducibly on $V$ a maximal subgroup of the classical group $G$? | In the Aschbacher--Scott setting, when is the normalizer M=N_G(S) of a quasisimple subgroup S\lt G acting irreducibly on V actually a maximal subgroup of the classical group G? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,422 | OWR-17472-018 | Multiplicity Obstructions in Geometric Complexity Theory | For the polynomial orbit closures relevant to geometric complexity theory, can one find a partition $\lambda$ and degree $d$ such that
$$
\operatorname{mult}_\lambda\mathbb C[\overline{Gp}]_d>\operatorname{mult}_\lambda\mathbb C[\overline{Gq}]_d,
$$
thereby obtaining a multiplicity obstruction separating the orbit clos... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-018",
"literature-status:open",
"owr-year:2020"
] | The Mulmuley--Sohoni border-determinantal-complexity conjecture remains a major open separation problem; known work rules out important obstruction methods but does not prove superpolynomial border complexity. | [
{
"url": "https://doi.org/10.1137/S009753970038715X",
"label": "Mulmuley and Sohoni, Geometric Complexity Theory I"
},
{
"url": "https://doi.org/10.1016/j.difgeo.2017.07.001",
"label": "Ikenmeyer and Panova, Geometric complexity theory and matrix powering"
},
{
"url": "https://doi.org/10... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | For the polynomial orbit closures relevant to geometric complexity theory, can one find a partition $\lambda$ and degree $d$ such that
$$
\operatorname{mult}_\lambda\mathbb C[\overline{Gp}]_d>\operatorname{mult}_\lambda\mathbb C[\overline{Gq}]_d,
$$
thereby obtaining a multiplicity obstruction separating the orbit clos... | For the relevant polynomial orbit closures in geometric complexity theory, can one find a partition \lambda and degree d with mult_\lambda \mathbb C[\overline{Gp}]_d>mult_\lambda \mathbb C[\overline{Gq}]_d, thereby obtaining a multiplicity obstruction separating the orbit closures? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,423 | OWR-17472-019 | Arm-Length Refinements for Complementary Partitions | Find a representation-theoretic interpretation of the stronger arm-length-refined multiset identity for complementary partitions in a rectangle. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-019",
"literature-status:open",
"owr-year:2020"
] | The requested representation-theoretic interpretation is recorded as an open problem, and no subsequent general construction resolving this specific request was identified. | [
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Find a representation-theoretic interpretation of the stronger arm-length-refined multiset identity for complementary partitions in a rectangle. | Find a representation-theoretic interpretation of the stronger arm-length-refined multiset identity for complementary partitions in a rectangle. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,424 | OWR-17472-020 | Geometry behind a Plethystic Representation Isomorphism | Find a geometric or invariant-theoretic interpretation of the isomorphism $\nabla_{(3\ell-3,2^{\ell-1})}\operatorname{Sym}^{\ell}E\cong\nabla_{(\ell+1,1^{\ell-2})}\operatorname{Sym}^{3\ell-4}E$ for all $\ell\ge2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 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-17472-020",
"literature-status:open",
"owr-year:2020"
] | The requested geometric or invariant-theoretic interpretation is stated without a precise target theorem; it remains unresolved or unclear and is therefore classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | Find a geometric or invariant-theoretic interpretation of the isomorphism $\nabla_{(3\ell-3,2^{\ell-1})}\operatorname{Sym}^{\ell}E\cong\nabla_{(\ell+1,1^{\ell-2})}\operatorname{Sym}^{3\ell-4}E$ for all $\ell\ge2$. | Find a geometric or invariant-theoretic interpretation of the isomorphism \nabla_{(3\ell-3,2^{\ell-1})}\operatorname{Sym}^{\ell}E\cong\nabla_{(\ell+1,1^{\ell-2})}\operatorname{Sym}^{3\ell-4}E for all \ell\ge2. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
30,004,425 | OWR-17473-001 | Wall Crossing Between Adjacent Tropical Toric Degenerations | Given two adjacent maximal-dimensional prime cones in a tropicalization sharing a facet, how are the two associated toric degenerations related, including their wall-crossing maps and semigroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600](https://doi.org/10.4171/owr/2020/10)
## Literature review (checke... | 3 | open | null | 2,020 | 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-17473-001",
"literature-status:open",
"owr-year:2020"
] | The relation between the two toric degenerations across the facet is posed as a natural question, with no general answer identified in the primary literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2020/10",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/10 | null | null | null | Given two adjacent maximal-dimensional prime cones in a tropicalization sharing a facet, how are the two associated toric degenerations related, including their wall-crossing maps and semigroups? | Given two adjacent maximal-dimensional prime cones in a tropicalization sharing a facet, how are the two associated toric degenerations related, including their wall-crossing maps and semigroups? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600 |
30,004,426 | OWR-17473-002 | Mirror Symmetry for Maximally Degenerate Positive Calabi–Yau Pairs | Formulate and prove mirror symmetry for every maximally degenerate positive Calabi–Yau pair $(M,D)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600](https://doi.org/10.4171/owr/2020/10)
## Literature review (checke... | 3 | open | null | 2,020 | 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-17473-002",
"literature-status:open",
"owr-year:2020"
] | A mirror-symmetry conjecture valid for all stated maximally degenerate Calabi--Yau pairs is explicitly described as open, and no general proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/10",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/10 | null | null | null | Formulate and prove mirror symmetry for every maximally degenerate positive Calabi–Yau pair $(M,D)$. | Formulate and prove a mirror-symmetry conjecture that applies to all pairs (M,D) covered by the general construction of maximally degenerate positive Calabi--Yau pairs. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600 |
30,004,427 | OWR-17473-003 | Wrapped Fukaya Categories as Crepant Resolutions | For a maximally degenerate positive Calabi–Yau pair $(M,D)$ admitting a weak section, do the functors $\pi^*$ and $\pi_*$ make $\mathcal W(X)$ a categorical crepant resolution of $SH^0(X)$? In particular, is $\mathcal W(X)$ relatively Calabi–Yau over $SH^0(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600](https://doi.org/10.4171/owr/2020/10)
## Literature review (checke... | 3 | open | null | 2,020 | 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-17473-003",
"literature-status:open",
"owr-year:2020"
] | The categorical crepant-resolution conjecture is reduced in the report to proving a relative Calabi--Yau property; no general proof of that required property was identified. | [
{
"url": "https://doi.org/10.4171/owr/2020/10",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/10 | null | null | null | For a maximally degenerate positive Calabi–Yau pair $(M,D)$ admitting a weak section, do the functors $\pi^*$ and $\pi_*$ make $\mathcal W(X)$ a categorical crepant resolution of $SH^0(X)$? In particular, is $\mathcal W(X)$ relatively Calabi–Yau over $SH^0(X)$? | Conjecture: for a maximally degenerate positive Calabi--Yau pair (M,D) admitting a weak section, the functors \pi^* and \pi_* make W(X) a categorical crepant resolution of SH^0(X), in particular requiring W(X) to be relatively Calabi--Yau over SH^0(X). | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600 |
30,004,428 | OWR-17473-004 | Mutable Laurent Polynomials and Toric Smoothing Components | Let $F$ be a $3$-dimensional lattice polytope and let $U_F$ be the Gorenstein toric affine $3$-fold obtained from the cone over $F$ at height $1$. Are the smoothing components of the miniversal deformation of $U_F$ in one-to-one correspondence with the $0$-mutable Laurent polynomials having Newton polytope $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600](https://doi.org/10.4171/owr/2020/10)
## Literature review (checke... | 3 | open | null | 2,020 | 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-17473-004",
"literature-status:open",
"owr-year:2020"
] | The proposed generalization of Altmann's deformation construction for all relevant toric Gorenstein threefold singularities remains a conjectural expectation in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2020/10",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/10 | null | null | null | Let $F$ be a $3$-dimensional lattice polytope and let $U_F$ be the Gorenstein toric affine $3$-fold obtained from the cone over $F$ at height $1$. Are the smoothing components of the miniversal deformation of $U_F$ in one-to-one correspondence with the $0$-mutable Laurent polynomials having Newton polytope $F$? | Conjecture: if F is a 3-dimensional lattice polytope and U_F is the Gorenstein toric affine 3-fold from the cone over F at height 1, then the smoothing components of the miniversal deformation of U_F are in one-to-one correspondence with the 0-mutable Laurent polynomials having Newton polytope F. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Superpotentials in Algebra and Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/10, pp. 569--600 |
30,004,429 | OWR-17474-001 | Discontinuities of Two-Sided Specifications | Does the set of discontinuity points of the two-sided specification have measure zero, and does the analogous conclusion hold for long-range Ising models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-001",
"literature-status:open",
"owr-year:2020"
] | The two-sided Schonmann-projection discontinuity-set measure-zero question is explicitly unanswered; the one-sided analogue is known, but the two-sided claim remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | Does the set of discontinuity points of the two-sided specification have measure zero, and does the analogous conclusion hold for long-range Ising models? | Does the set of discontinuity points of the two-sided specification have measure zero, and does the analogous conclusion hold for long-range Ising models? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,430 | OWR-17474-002 | Existence Criteria for $g$-Measures | What conditions on the size or shape of the state set $D$ ensure the existence of a $g$-measure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-002",
"literature-status:open",
"owr-year:2020"
] | The extract asks for general size and shape conditions on D ensuring existence of a g-measure; it is not a single resolved theorem and remains an open classification problem. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | What conditions on the size or shape of the state set $D$ ensure the existence of a $g$-measure? | What conditions on the size or shape of the state set D ensure the existence of a g-measure? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,431 | OWR-17474-003 | Equivalence of Gibbs Measures and $g$-Measures | For an equilibrium state $\mu$ of a potential $f$, is the existence of a positive continuous eigenfunction equivalent to $\mu$ being a $g$-measure? More generally, are Gibbs measures and $g$-measures equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | partially_solved | null | 2,020 | 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-17474-003",
"literature-status:partially-solved",
"owr-year:2020"
] | A positive continuous transfer-operator eigenfunction yields a g-measure, while the converse and the full Gibbs--g-measure equivalence require extra regularity and have counterexamples in general; the unrestricted equivalence is not solved. | [
{
"url": "https://doi.org/10.1112/S0024610704006076",
"label": "Walters, Regularity Conditions and Bernoulli Properties of Equilibrium States and g-Measures"
},
{
"url": "https://arxiv.org/abs/1106.4188",
"label": "Bissacot, Endo and Van Enter, Regular g-measures are not always Gibbsian"
},
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | For an equilibrium state $\mu$ of a potential $f$, is the existence of a positive continuous eigenfunction equivalent to $\mu$ being a $g$-measure? More generally, are Gibbs measures and $g$-measures equivalent? | For an equilibrium state \mu of a potential f, is existence of a positive continuous eigenfunction equivalent to \mu being a g-measure, and more generally are Gibbs measures and g-measures equivalent? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,432 | OWR-17474-006 | Triangle Condition in Long-Range Percolation | In one-dimensional long-range percolation, is the triangle condition not satisfied for $s>4/3$, and what happens at the critical value $s=4/3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-006",
"literature-status:open",
"owr-year:2020"
] | The triangle condition is proved for 1<s<4/3, but the extract's questions for s>4/3 and at s=4/3 remain unresolved in the checked primary literature. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
},
{
"url": "https://doi.org/10.1007/s10955-008-9580-5",
"label": "Heydenreich, van der Hofstad and Sakai, Mean-field behavior for long- and finite-range models"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | In one-dimensional long-range percolation, is the triangle condition not satisfied for $s>4/3$, and what happens at the critical value $s=4/3$? | In one-dimensional long-range percolation, is the triangle condition not satisfied for s>4/3, and what happens at the critical value s=4/3? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,433 | OWR-17474-007 | Ends of Critical Long-Range Percolation Clusters | In one-dimensional long-range percolation with edge probabilities asymptotic to $\beta|k|^{-s}$, are both of the following true at $s=2$: at criticality the infinite cluster has exactly two ends, and in the supercritical regime it has infinitely many ends? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-007",
"literature-status:open",
"owr-year:2020"
] | The two-ended critical-cluster and infinitely-many-ended supercritical-cluster assertions at s=2 are posed as open problems in the primary report, and no general resolution was identified. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | In one-dimensional long-range percolation with edge probabilities asymptotic to $\beta|k|^{-s}$, are both of the following true at $s=2$: at criticality the infinite cluster has exactly two ends, and in the supercritical regime it has infinitely many ends? | In one-dimensional long-range percolation with edge probabilities asymptotic to \beta |k|^{-s}, are both of the following true at s=2: at criticality the infinite cluster has exactly two ends, and in the supercritical regime the infinite cluster has infinitely many ends? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,434 | OWR-17474-008 | Uniform Coupling under Gibbs Uniqueness | For a specification on $\mathbb Z^d$ with a unique Gibbs state, is it true that for every $\varepsilon>0$ there is an $N$ such that, for all $n\geq N$, every pair of boundary conditions outside the $n$-box induces inside-box measures that can be coupled with expected number of disagreements at most $\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-008",
"literature-status:open",
"owr-year:2020"
] | The proposed implication from uniqueness of the Gibbs state to uniform boundary-condition coupling is explicitly posed as a question; the checked literature does not establish it in the stated generality or provide a demonstrably decisive counterexample. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | For a specification on $\mathbb Z^d$ with a unique Gibbs state, is it true that for every $\varepsilon>0$ there is an $N$ such that, for all $n\geq N$, every pair of boundary conditions outside the $n$-box induces inside-box measures that can be coupled with expected number of disagreements at most $\varepsilon$? | For a specification on \mathbb{Z}^d with a unique Gibbs state, is it true that for every \varepsilon>0 there is N such that, for all n\ge N, every pair of boundary conditions outside the n-box induces inside-box measures that can be coupled with expected number of disagreements at most \varepsilon? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,435 | OWR-17474-009 | Probabilistic Equality of Left and Right Tail Fields | For a stationary process with finite spin state space, prove using only probability theory, without entropy theory, that the left and right tail sigma-fields coincide modulo null sets. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 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-17474-009",
"literature-status:open",
"owr-year:2020"
] | The equality of left and right tails for finite-state stationary processes is known, but the extracted problem specifically asks for a proof using only probability theory; no such proof was identified, so the method-restricted problem remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | For a stationary process with finite spin state space, prove using only probability theory, without entropy theory, that the left and right tail sigma-fields coincide modulo null sets. | For a stationary process with finite spin state space, prove using only probability theory, without entropy theory, that the left and right tail sigma-fields coincide modulo null sets. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,436 | OWR-17474-010 | Cardinality of Spin-Glass Ground-State Sets | For every graph and every distribution of linear growth, does the set $G(J)$ of spin-glass ground states satisfy $|G(J)|\in\{2,\infty\}$? More generally, is there a connection between random walks and spin-glass ground states on graphs beyond trees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637](https://doi.org/10.4171/owr/2020/11)
## Literature review... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23041936",
"checked_at": "2026-09-29",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-29] I have released an unrefereed preprint, **A Negative Answer to Bäumler's Question on the Number of Spin-Glass Ground States** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23041936) | [
"owr",
"oberwolfach-reports",
"OWR-17474-010",
"literature-status:open",
"owr-year:2020"
] | The assertions about the number of spin-glass ground states on all graphs and a random-walk connection beyond trees are explicitly listed as open problems, with no general resolution found. | [
{
"url": "https://ems.press/content/serial-article-files/46847",
"label": "OWR-2020-11"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/11 | null | null | null | For every graph and every distribution of linear growth, does the set $G(J)$ of spin-glass ground states satisfy $|G(J)|\in\{2,\infty\}$? More generally, is there a connection between random walks and spin-glass ground states on graphs beyond trees? | For every graph and every distribution of linear growth, does the set G(J) of spin-glass ground states satisfy |G(J)|\in\{2,\infty\}? More generally, is there a connection between random walks and spin-glass ground states on graphs beyond trees? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: One-sided and Two-sided Stochastic Descriptions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/11, pp. 601--637 |
30,004,437 | OWR-17475-002 | The Real-Zero Polynomial Amalgamation Conjecture | Let $p\in\mathbb R[x,y]$ and $q\in\mathbb R[x,z]$ be real-zero polynomials of degree at most $d\in\mathbb N_0$ with $p(x,0)=q(x,0)$. Does there exist a real-zero polynomial $r\in\mathbb R[x,y,z]$ of degree at most $d$ such that $r(x,y,0)=p(x,y)$ and $r(x,0,z)=q(x,z)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712](https://doi.org/10.4171/owr/2020/1... | 3 | solved | null | 2,020 | 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": null,
"checked_at": "2026-10-11",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **solved (no)**. M. Schweighofer, Oberwolfach Report 12/2020, p. 653, real zero amalgamation conjecture: for tuples x, y, z of ℓ, m, n variables, real zero polynomials p ∈ ℝ[x,y] and q ∈ ℝ[x,z] of degree ≤ d with p(x,0) = q(x,0) have a real zero amalgam r ∈ ℝ[x,y,z] of degr... | [
"owr",
"oberwolfach-reports",
"OWR-17475-002",
"literature-status:open",
"owr-year:2020"
] | The extracted real-zero amalgamation conjecture is not settled. Sawall and Schweighofer found counterexamples to the obvious necessary conditions and proved only special positive cases; their remaining two-shared-variable conjecture does not resolve the general record. | [
{
"url": "https://doi.org/10.1016/j.indag.2023.08.002",
"label": "Sawall--Schweighofer (2024)"
},
{
"url": "https://doi.org/10.4171/owr/2020/12",
"label": "Oberwolfach Report 12/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/12 | null | null | null | Let $p\in\mathbb R[x,y]$ and $q\in\mathbb R[x,z]$ be real-zero polynomials of degree at most $d\in\mathbb N_0$ with $p(x,0)=q(x,0)$. Does there exist a real-zero polynomial $r\in\mathbb R[x,y,z]$ of degree at most $d$ such that $r(x,y,0)=p(x,y)$ and $r(x,0,z)=q(x,z)$? | Real zero amalgamation conjecture: if p\in\mathbb{R}[x,y] and q\in\mathbb{R}[x,z] are real-zero polynomials of degree at most d\in\mathbb{N}_0 with p(x,0)=q(x,0), does there exist a real-zero polynomial r\in\mathbb{R}[x,y,z] of degree at most d such that r(x,y,0)=p and r(x,0,z)=q? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712 |
30,004,438 | OWR-17475-003 | Real Rational Maps with Exclusively Real Periodic Points | For $d\geq2$, let $\mathcal R_d$ be the set of real morphisms $\phi:\mathbb P^1\to\mathbb P^1$ of degree $d$ whose periodic points are all real. The existence question has an affirmative answer via Chebyshev maps; does $\mathcal R_d$ have full dimension, equivalently nonempty interior, in the space of real degree-$d$ m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712](https://doi.org/10.4171/owr/2020/1... | 3 | partially_solved | null | 2,020 | 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 | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (yes; preprint)**; the dataset currently labels it partially solved. K. Kozhasov, OWR 12/2020, p. 669, Question 2: does the set R_d of real degree-d morphisms of ℙ¹ with only real periodic points have nonempty interior? K. Kozhasov, M. Kummer, preprint arXiv:2004.1... | [
"owr",
"oberwolfach-reports",
"OWR-17475-003",
"literature-status:partially-solved",
"owr-year:2020"
] | The existence part is solved affirmatively by the Chebyshev morphism, which has only real periodic points. The question whether the corresponding locus has nonempty interior or full dimension remains open; only lower-dimensional families are known. | [
{
"url": "https://arxiv.org/abs/2004.10003",
"label": "Kozhasov--Kummer (2020)"
},
{
"url": "https://doi.org/10.4171/owr/2020/12",
"label": "Oberwolfach Report 12/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/12 | null | null | null | For $d\geq2$, let $\mathcal R_d$ be the set of real morphisms $\phi:\mathbb P^1\to\mathbb P^1$ of degree $d$ whose periodic points are all real. The existence question has an affirmative answer via Chebyshev maps; does $\mathcal R_d$ have full dimension, equivalently nonempty interior, in the space of real degree-$d$ m... | For d\ge2, does there exist a real morphism \phi:\mathbb{P}^1\to\mathbb{P}^1 of degree d with only real periodic points, and does the set of such real morphisms have full dimension, equivalently nonempty interior, in the space of all real degree-d morphisms? | corrected_verified | The official report was checked. The solved existence clause is distinguished from the remaining full-dimension question. | null | null | null | null | null | Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712 |
30,004,439 | OWR-17475-005 | Primal and Dual Geometry of SONC Relaxations | For the SONC-cone linear-programming relaxation, what is the relation between the primal polyhedron obtained by fixing the non-auxiliary variables and the SONC cone, and what is the relation between the dual SONC cone and sparse moment cones? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712](https://doi.org/10.4171/owr/2020/1... | 3 | open | null | 2,020 | 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-17475-005",
"literature-status:open",
"owr-year:2020"
] | The relations between the primal SONC cone, sparse nonnegative polynomials, the dual SONC cone, and sparse moment cones remain explicitly identified as future work; no general equivalence or characterization has been proved. | [
{
"url": "https://www.math.uni-frankfurt.de/~theobald/publications/s-cone.pdf",
"label": "Dressler--Iliman--de Wolff--Theobald, S-cone framework"
},
{
"url": "https://doi.org/10.4171/owr/2020/12",
"label": "Oberwolfach Report 12/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/12 | null | null | null | For the SONC-cone linear-programming relaxation, what is the relation between the primal polyhedron obtained by fixing the non-auxiliary variables and the SONC cone, and what is the relation between the dual SONC cone and sparse moment cones? | For the SONC-cone linear-programming relaxation, what is the relation between the primal polyhedron obtained by fixing the non-auxiliary variables and the SONC cone, and what is the relation between the dual SONC cone and sparse moment cones? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712 |
30,004,440 | OWR-17475-006 | Moment Inequalities from Positive Semidefinite Localization Matrices | What inequalities among moments follow from positive semidefiniteness of moment matrices? More generally, for measures supported on a basic semialgebraic set, what additional inequalities follow from positive semidefiniteness of the associated localization matrices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712](https://doi.org/10.4171/owr/2020/1... | 3 | partially_solved | null | 2,020 | 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-17475-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17475-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The workshop work gives explicit limitations and examples of moment inequalities not obtainable from sums of squares, while the 2025 paper gives combinatorial descriptions in important semialgebraic cases. A general classification of all inequalities learnable from SOS positivity remains open. | [
{
"url": "https://doi.org/10.1112/jlms.70311",
"label": "Blekherman--Rincon--Sinn--Vinzant--Yu (2025)"
},
{
"url": "https://doi.org/10.4171/owr/2020/12",
"label": "Oberwolfach Report 12/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/12 | null | null | null | What inequalities among moments follow from positive semidefiniteness of moment matrices? More generally, for measures supported on a basic semialgebraic set, what additional inequalities follow from positive semidefiniteness of the associated localization matrices? | What moment inequalities can be deduced from sums of squares, equivalently from positive semidefiniteness of moment and localization matrices? | corrected_verified | The official report was checked. The general moment-matrix question and its localization-matrix extension are retained in the canonical record. | null | null | null | null | null | Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712 |
30,004,441 | OWR-17475-007 | Duplicate Moment-Matrix Question | What moment inequalities can be deduced from positive semidefiniteness of moment matrices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712](https://doi.org/10.4171/owr/2020/1... | 3 | partially_solved | null | 2,020 | 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 (This record repeats the first question represented canonically, together with its localization-matrix extension, by OWR-17475-006. No separa) | [
"OWR-17475-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17475-007",
"literature-status:partially-solved",
"owr-year:2020"
] | Known tropical and moment-cone results answer substantial special cases and exhibit permanent SOS limitations, but the broad question of which inequalities follow from positive semidefinite moment matrices is not fully characterized. | [
{
"url": "https://doi.org/10.1112/jlms.70311",
"label": "Blekherman--Rincon--Sinn--Vinzant--Yu (2025)"
},
{
"url": "https://doi.org/10.4171/owr/2020/12",
"label": "Oberwolfach Report 12/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/12 | null | null | null | null | What moment inequalities can be deduced from positive semidefiniteness of moment matrices? | unrecoverable | This record repeats the first question represented canonically, together with its localization-matrix extension, by OWR-17475-006. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/12, pp. 639--712 |
30,004,442 | OWR-17476-002 | Monolithic versus Staggered Magnetomechanical Relaxation | For coupled magnetomechanical systems, should relaxation be formulated monolithically or as a staggered sequence of partial relaxations, and under what conditions are the two procedures equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/13, pp. 713--783](https://doi.org/10.41... | 3 | open | null | 2,020 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17476-002",
"literature-status:open",
"owr-year:2020"
] | Existence theory now covers several coupled rate-dependent and rate-independent models, but there is no general result deciding whether coupled relaxation should be monolithic or staggered, nor a universal equivalence theorem for the two procedures. | [
{
"url": "https://doi.org/10.1137/15M1051567",
"label": "Rossi--Thomas (2017)"
},
{
"url": "https://doi.org/10.1007/s10231-022-01280-0",
"label": "Crismale--Lazzaroni--Rossi (2023)"
},
{
"url": "https://doi.org/10.4171/owr/2020/13",
"label": "Oberwolfach Report 13/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/13 | null | null | null | For coupled magnetomechanical systems, should relaxation be formulated monolithically or as a staggered sequence of partial relaxations, and under what conditions are the two procedures equivalent? | For coupled magnetomechanical relaxation, how should the relevant relaxation concepts be combined, and should relaxation be performed monolithically or in staggered fashion through sequential partial relaxations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/13, pp. 713--783 |
30,004,443 | OWR-17476-003 | Numerical Schemes for Coupled Fracture and Dissipation | For rate-independent fracture and damage models coupled with rate-dependent processes, are there efficient feasible numerical schemes that reliably approximate the intended solution class, and what mathematical and mechanical framework should describe the coupling? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/13, pp. 713--783](https://doi.org/10.41... | 3 | open | null | 2,020 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17476-003",
"literature-status:open",
"owr-year:2020"
] | There are existence and time-discretization results for important coupled systems, but the extracted request for efficient reliable schemes and a general mathematical and mechanical framework for rate-dependent/rate-independent coupling remains unanswered. | [
{
"url": "https://doi.org/10.1137/15M1051567",
"label": "Rossi--Thomas (2017)"
},
{
"url": "https://doi.org/10.4171/owr/2020/13",
"label": "Oberwolfach Report 13/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/13 | null | null | null | For rate-independent fracture and damage models coupled with rate-dependent processes, are there efficient feasible numerical schemes that reliably approximate the intended solution class, and what mathematical and mechanical framework should describe the coupling? | For rate-independent fracture and damage models coupled with rate-dependent processes, are there efficient feasible numerical schemes that reliably approximate the intended solution class, and what mathematical and mechanical framework should describe the coupling? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/13, pp. 713--783 |
30,004,444 | OWR-1703861-002 | Singular Cardinal Arithmetic Without Weak Square | For a singular cardinal $\kappa$, is $\operatorname{cof}(\operatorname{pp}(\kappa))>\kappa$? Also, can there be a singular strong-limit $\kappa$ such that weak square at $\kappa$ fails and $2^\kappa>\kappa^+$, or such that the tree property holds at $\kappa^+$ while $2^\kappa>\kappa^+$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-002",
"literature-status:open",
"owr-year:2020"
] | The displayed Shelah question about cof(pp(kappa)) is answered negatively by extender-based forcing, but the record truncates immediately after introducing a separate Woodin question. Because the full extracted problem is incomplete, its unresolved status is open. | [
{
"url": "https://doi.org/10.1142/S0219061320500130",
"label": "Gitik, Extender-based forcings (2020)"
},
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | For a singular cardinal $\kappa$, is $\operatorname{cof}(\operatorname{pp}(\kappa))>\kappa$? Also, can there be a singular strong-limit $\kappa$ such that weak square at $\kappa$ fails and $2^\kappa>\kappa^+$, or such that the tree property holds at $\kappa^+$ while $2^\kappa>\kappa^+$? | For a singular cardinal \kappa, is \operatorname{cof}(\operatorname{pp}(\kappa))>\kappa? Also, can there be a singular strong-limit \kappa such that weak square at \kappa fails and 2^\kappa>\kappa^+, or such that the tree property holds at \kappa^+ while 2^\kappa>\kappa^+? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,445 | OWR-1703861-003 | Indecomposable Ultrafilters Beyond Measurable Cardinals | Can there be an indecomposable ultrafilter on a cardinal that is neither measurable nor the limit of countably many measurable cardinals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-003",
"literature-status:partially-solved",
"owr-year:2020"
] | Sheard showed consistency of an indecomposable ultrafilter on an inaccessible non-weakly-compact cardinal, while canonical inner models give the opposite behavior; above a strongly compact cardinal, Goldberg proved the measurable-or-countable-limit classification. The unrestricted question is therefore independent or r... | [
{
"url": "https://doi.org/10.2307/2273664",
"label": "Sheard (1983)"
},
{
"url": "https://arxiv.org/abs/2007.04812",
"label": "Goldberg (2020)"
},
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | Can there be an indecomposable ultrafilter on a cardinal that is neither measurable nor the limit of countably many measurable cardinals? | Can there be an indecomposable ultrafilter on a cardinal that is neither measurable nor the limit of countably many measurable cardinals? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,446 | OWR-1703861-004 | Embedding Classification of Piecewise-Linear Interval Groups | For finitely generated subgroups of Thompson's group $F$ and of $\mathrm{PL}_o(I)$ ordered by homomorphic embedding, is there a substantial classifiable initial segment and where does the quasiorder become intractable? Which finitely generated subgroups are comparable with every finitely generated subgroup, and does $F... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,020 | 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-1703861-004",
"literature-status:open",
"owr-year:2020"
] | The record lists several open classification and embedding questions for finitely generated subgroups of PL-positive-I and explicitly says that the general F-obstruction converse is unknown. Later work supplies strong sufficient obstructions but not the requested classification. | [
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
},
{
"url": "https://doi.org/10.4171/GGD/708",
"label": "Hyde--Moore (2023)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | For finitely generated subgroups of Thompson's group $F$ and of $\mathrm{PL}_o(I)$ ordered by homomorphic embedding, is there a substantial classifiable initial segment and where does the quasiorder become intractable? Which finitely generated subgroups are comparable with every finitely generated subgroup, and does $F... | For finitely generated subgroups of Thompson's group F and of PLo_I ordered by homomorphic embedding, is there a substantial classifiable initial segment and where does the quasiorder become intractable? Which finitely generated subgroups are comparable with every finitely generated subgroup, and does F have this prope... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,447 | OWR-1703861-005 | Stationary Reflection and Large Power at Aleph Omega | Can the consistency result asserting that a strong-limit singular cardinal $\kappa$ of countable cofinality has simultaneous finite stationary-set reflection at $\kappa^+$ together with $2^\kappa=\kappa^{++}$ be obtained with $\kappa=\aleph_\omega$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-005",
"literature-status:open",
"owr-year:2020"
] | The specific Sigma-Prikry consistency result in the record was stated as open for kappa equal to aleph-omega; later literature discusses related ultrafilter and singular-cardinal constructions but does not establish this exact simultaneous consistency result. | [
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
},
{
"url": "https://link.springer.com/article/10.1007/s00153-025-00983-4",
"label": "Bilinsky--Gitik (2025)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | Can the consistency result asserting that a strong-limit singular cardinal $\kappa$ of countable cofinality has simultaneous finite stationary-set reflection at $\kappa^+$ together with $2^\kappa=\kappa^{++}$ be obtained with $\kappa=\aleph_\omega$? | Can the consistency result asserting that a strong-limit singular cardinal \kappa of countable cofinality has simultaneous finite stationary-set reflection at \kappa^+ together with 2^\kappa=\kappa^{++} be obtained with \kappa=\aleph_\omega? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,448 | OWR-1703861-006 | Choice Principles for Discontinuous Polish Group Homomorphisms | How much choice is needed to construct a discontinuous homomorphism between Polish groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-006",
"literature-status:partially-solved",
"owr-year:2020"
] | Rosendal proved strong continuity results for homomorphisms of Polish groups and derived lower bounds on the choice needed for discontinuous homomorphisms, but the exact minimal choice principle is not determined by the reported results. | [
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | How much choice is needed to construct a discontinuous homomorphism between Polish groups? | How much choice is needed to construct a discontinuous homomorphism between Polish groups? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,449 | OWR-1703861-007 | Weak Compactness in HOD from Iterated Embeddings | Suppose $(V,j)\models\mathrm{ZF}$ and $j:V\to V$ is elementary. Form the iterates $M_0=(V,j)$ and $M_\alpha=(N_\alpha,j_\alpha)$ by setting $M_{\alpha+1}=(N_\alpha,j_\alpha(j_\alpha))$ and taking direct limits at limit ordinals. If $\lambda=\sup_{n<\omega}\sup(\operatorname{crit}(j^n))$, is $\lambda$ weakly compact in ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-007",
"literature-status:open",
"owr-year:2020"
] | For the rank-into-rank iteration limit described in the record, the question whether lambda is weakly compact in HOD remains a stated open problem; known forcing results about other large cardinals in HOD do not decide this specific case. | [
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | Suppose $(V,j)\models\mathrm{ZF}$ and $j:V\to V$ is elementary. Form the iterates $M_0=(V,j)$ and $M_\alpha=(N_\alpha,j_\alpha)$ by setting $M_{\alpha+1}=(N_\alpha,j_\alpha(j_\alpha))$ and taking direct limits at limit ordinals. If $\lambda=\sup_{n<\omega}\sup(\operatorname{crit}(j^n))$, is $\lambda$ weakly compact in ... | In the setting of the report's iterated elementary-embedding construction, is the cardinal \lambda weakly compact in HOD? | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,450 | OWR-1703861-008 | Large Cardinal Foundations of MAX Universal Baireness | Is $\operatorname{MAX}(\mathrm{UB})$ a direct consequence of suitable large-cardinal axioms, where $\operatorname{MAX}(\mathrm{UB})$ asserts class many Woodin cardinals together with the stated universal-Baireness and generic-elementarity conditions for universally Baire sets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-008",
"literature-status:open",
"owr-year:2020"
] | MAX(UB) is known in generic extensions obtained by collapsing a supercompact and is preserved by further set forcing, but whether suitable large-cardinal axioms alone imply MAX(UB) remains open. | [
{
"url": "https://arxiv.org/abs/2101.07573",
"label": "Viale (2021)"
},
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | Is $\operatorname{MAX}(\mathrm{UB})$ a direct consequence of suitable large-cardinal axioms, where $\operatorname{MAX}(\mathrm{UB})$ asserts class many Woodin cardinals together with the stated universal-Baireness and generic-elementarity conditions for universally Baire sets? | Is MAX(UB) a direct consequence of suitable large-cardinal axioms, where MAX(UB) asserts class many Woodin cardinals together with the stated universal-Baireness and generic-elementarity conditions for universally Baire sets? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,451 | OWR-1703861-009 | Set-Theoretic Rigidity of Corona-Algebra Automorphisms | For every separable nonunital $C^*$-algebra $A$, does CH imply that $Q(A)$ has $2^{\aleph_1}$ automorphisms that are not topologically trivial, while PFA implies that all automorphisms of $Q(A)$ are topologically trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855](https://doi.org/10.4171/owr/2020/14)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,020 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703861-009",
"literature-status:partially-solved",
"owr-year:2020"
] | The PFA-side rigidity conjecture is proved for broad classes, including algebras with the metric approximation property and suitable approximate identities, and OCA plus MA gives topological triviality. The full all-separable-algebras conjecture, especially the uniform CH cardinality assertion, is not settled. | [
{
"url": "https://doi.org/10.1090/S0002-9947-2014-06146-1",
"label": "Coskey--Farah (2014)"
},
{
"url": "https://arxiv.org/abs/1806.09676",
"label": "McKenney--Vignati (2021)"
},
{
"url": "https://doi.org/10.4171/owr/2020/14",
"label": "Oberwolfach Report 14/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/14 | null | null | null | For every separable nonunital $C^*$-algebra $A$, does CH imply that $Q(A)$ has $2^{\aleph_1}$ automorphisms that are not topologically trivial, while PFA implies that all automorphisms of $Q(A)$ are topologically trivial? | For every separable nonunital C^*-algebra A, does CH imply that Q(A) has 2^{\aleph_1} automorphisms that are not topologically trivial, while PFA implies that all automorphisms of Q(A) are topologically trivial? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Set Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/14, pp. 797--855 |
30,004,452 | OWR-1703863-001 | Exotic Group $C^*$-Algebras for Nonamenable Locally Compact Groups | Does every nonamenable locally compact group admit an exotic group $C^*$-algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-001",
"literature-status:open",
"owr-year:2020"
] | The extracted claim remains unresolved in the locally compact setting. Existing work develops many exotic completions and explicitly leaves even the discrete every-nonamenable-group problem open, so the broader locally compact assertion is not solved. | [
{
"url": "https://doi.org/10.5802/aif.3441",
"label": "De Laat--Siebenand (2021)"
},
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | Does every nonamenable locally compact group admit an exotic group $C^*$-algebra? | Does every non-amenable locally compact group admit an exotic group C^*-algebra? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,453 | OWR-1703863-002 | Euler Characteristic and Coherence of Random Few-Relator Groups | In the few-relators random-group model $G(n,m,\ell)$, is a random group of Euler characteristic $\chi$ coherent when $\chi\leq0$ and incoherent when $\chi>0$, in each case with probability tending to $1$ as $\ell\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,020 | 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-1703863-002",
"literature-status:partially-solved",
"owr-year:2020"
] | The conjectured coherence behavior is proved with high probability for negative Euler characteristic and in several positive-probability cases at zero Euler characteristic; incoherence is proved asymptotically for two-generator positive Euler characteristic. The full all-parameters conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2003.06354",
"label": "Kielak--Kropholler--Wilkes (2020)"
},
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | In the few-relators random-group model $G(n,m,\ell)$, is a random group of Euler characteristic $\chi$ coherent when $\chi\leq0$ and incoherent when $\chi>0$, in each case with probability tending to $1$ as $\ell\to\infty$? | Conjecture: in the few-relators random-group model G(n,m,\ell), a random group with Euler characteristic \chi is coherent when \chi\le0 and incoherent when \chi>0, both with asymptotic probability 1 as \ell\to\infty. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,454 | OWR-1703863-003 | Coxeter Quotients of Automorphism Groups of Coxeter Groups | For every infinite Coxeter group $W_\Gamma$, does $\operatorname{Aut}(W_\Gamma)$ virtually map onto an infinite Coxeter group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-003",
"literature-status:open",
"owr-year:2020"
] | The extracted record contains several conjectures about the subgroup quasiorder of PL-positive-I, including whether F is a bottleneck and whether F-obstructions are complete. Later work proves strong obstruction theorems but leaves the converse and classification questions open. | [
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
},
{
"url": "https://doi.org/10.4171/GGD/708",
"label": "Hyde--Moore (2023)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | For every infinite Coxeter group $W_\Gamma$, does $\operatorname{Aut}(W_\Gamma)$ virtually map onto an infinite Coxeter group? | Conjecture: for every infinite Coxeter group W_\Gamma, the automorphism group \operatorname{Aut}(W_\Gamma) virtually maps onto an infinite Coxeter group. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,455 | OWR-1703863-004 | Virtual Simplicity of Exotic Affine-Building Lattices | Is every $\widetilde A_2$-lattice whose associated building is not Bruhat–Tits virtually simple? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,020 | 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-1703863-004",
"literature-status:partially-solved",
"owr-year:2020"
] | Normal-subgroup theorems now show that cocompact lattices on tilde-A2 buildings have finite-index nontrivial normal subgroups, reducing the virtual-simplicity conjecture to residual-finiteness issues. The conjecture that every non-Bruhat--Tits lattice is virtually simple is not yet proved in full. | [
{
"url": "https://arxiv.org/abs/2310.13472",
"label": "Bader--Furman--Lecureux (2025)"
},
{
"url": "https://arxiv.org/abs/2605.06163",
"label": "Lecureux--Witzel (2026)"
},
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | Is every $\widetilde A_2$-lattice whose associated building is not Bruhat–Tits virtually simple? | Conjecture: every \widetilde{A}_2-lattice whose associated building is not Bruhat--Tits is virtually simple. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,456 | OWR-1703863-005 | $L^2$ Euler Characteristics and HNN Splittings | Let $G=F_n\rtimes_\alpha\mathbb Z$ be free-by-cyclic and let $\phi:G\to\mathbb Z$ be a character. Is
$$-\chi^{(2)}(\ker\phi)=\min\{-\chi(A):G=A*_{B}\text{ is an HNN splitting inducing }\phi,\ A,B\text{ finitely generated}\}$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-005",
"literature-status:open",
"owr-year:2020"
] | The associated polytope and the L2-Euler characteristic are computable, and the proposed equality with minimal HNN-splitting complexity is known for one-relator groups. The free-by-cyclic conjecture in the extracted record remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | Let $G=F_n\rtimes_\alpha\mathbb Z$ be free-by-cyclic and let $\phi:G\to\mathbb Z$ be a character. Is
$$-\chi^{(2)}(\ker\phi)=\min\{-\chi(A):G=A*_{B}\text{ is an HNN splitting inducing }\phi,\ A,B\text{ finitely generated}\}$$? | Conjecture: for a free-by-cyclic group G=F_n\rtimes_{\alpha}\mathbb Z and a character \phi:G\to\mathbb Z, -\chi^{(2)}(\ker\phi) equals the minimum of -\chi(A) over HNN splittings G=A*_B with A,B finitely generated and inducing \phi. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,457 | OWR-1703863-006 | Quasi-Isometric Rigidity of Acylindrical Hyperbolicity | Is acylindrical hyperbolicity invariant under quasi-isometry among finitely generated groups? More broadly, are finitely generated acylindrically hyperbolic groups quasi-isometrically rigid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-006",
"literature-status:open",
"owr-year:2020"
] | The record gives a special quasi-isometry result preserving acylindrical hyperbolicity, but the general quasi-isometry-invariance question for finitely generated acylindrically hyperbolic groups remains explicitly open, with only substantial partial criteria known. | [
{
"url": "https://doi.org/10.4153/S0008439523000012",
"label": "Hughes--Martinez-Pedroza (2023)"
},
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "Oberwolfach Report 16/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | Is acylindrical hyperbolicity invariant under quasi-isometry among finitely generated groups? More broadly, are finitely generated acylindrically hyperbolic groups quasi-isometrically rigid? | Is acylindrical hyperbolicity a quasi-isometry invariant for finitely generated groups; more broadly, is this class of groups quasi-isometrically rigid? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,458 | OWR-1703863-007 | Residual Finiteness and Minimal Presentations of Hyperbolic Groups | Is every hyperbolic group residually finite? Separately, what is the smallest total relator length in a presentation of an infinite hyperbolic group with Kazhdan property (T)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-007",
"literature-status:open",
"owr-year:2020"
] | The general residual-finiteness question remains open; the cited constructions give short hyperbolic Kazhdan groups but do not prove a minimum presentation length. | [
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/jlms.12668",
"label": "Caprace--Conder--Kaluba--Witzel"
},
{
"url": "https://arxiv.org/abs/1708.09772",
"label": "sixteen-relator presentation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | Is every hyperbolic group residually finite? Separately, what is the smallest total relator length in a presentation of an infinite hyperbolic group with Kazhdan property (T)? | Questions: is every hyperbolic group residually finite, and what is the smallest total length of a presentation of an infinite hyperbolic group with Kazhdan property (T)? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,459 | OWR-1703863-008 | Minimal Fold of Kazhdan Hyperbolic Triangle Groups | What is the smallest $k$ for which there exists a generalized $k$-fold triangle group that is hyperbolic and has Kazhdan property (T)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918](https://doi.org/10.4171/owr/2020/16)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,020 | 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-1703863-008",
"literature-status:open",
"owr-year:2020"
] | The primary construction establishes only the bounds 3\leq k\leq5, so the smallest k is still unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/16",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/jlms.12668",
"label": "generalized triangle groups paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/16 | null | null | null | What is the smallest $k$ for which there exists a generalized $k$-fold triangle group that is hyperbolic and has Kazhdan property (T)? | What is the smallest k for which there exists a generalized k-fold triangle group that is hyperbolic and has Kazhdan property (T)? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/16, pp. 877--918 |
30,004,460 | OWR-1703864-001 | The Riemann Hypothesis | Do all nontrivial zeros of the Riemann zeta function $\zeta(s)$ have real part $1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | open | null | 2,020 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
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"slug": "number-theory",
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"created_at": "2026-07-31T15:26:25.670Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate of canonical problem MPP-002 | [
"MPP-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-001",
"literature-status:open",
"owr-year:2020"
] | The record is contextual prose rather than a precise theorem; the underlying Riemann hypothesis remains an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
},
{
"url": "https://www.claymath.org/riemann/",
"label": "Clay Riemann hypothesis statement"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | Do all nontrivial zeros of the Riemann zeta function $\zeta(s)$ have real part $1/2$? | Riemann Hypothesis: every nontrivial zero of the Riemann zeta function \zeta(s) has real part 1/2. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,461 | OWR-1703864-002 | Comparison of Analytic and Periodic Cyclic Homology | For which bornological algebras is analytic cyclic homology isomorphic to periodic cyclic homology? In particular, can the known comparison results for analytically quasi-free algebras be extended to a broader class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"slug": "algebra",
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"id": 15,
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-002",
"literature-status:open",
"owr-year:2020"
] | Analytic cyclic homology has been constructed with strong formal properties and is known to coincide with periodic cyclic homology in special settings, but no general comparison theorem settles the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/2109.01470",
"label": "Meyer--Mukherjee"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | For which bornological algebras is analytic cyclic homology isomorphic to periodic cyclic homology? In particular, can the known comparison results for analytically quasi-free algebras be extended to a broader class? | For the analytic cyclic homology theory described in the report, under what conditions is it isomorphic to periodic cyclic homology? | corrected_verified | The official report was checked. The comparison question is stated without the dangling reference to a theory “described in the report,” and its known analytically quasi-free regime is included. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,462 | OWR-1703864-003 | Classification of Liquid Condensed Modules | How can liquid condensed $R$-modules be characterized? Equivalently, determine the liquidifications of the compact projective generators $R[\beta S]$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-003",
"literature-status:open",
"owr-year:2020"
] | The extracted sentence is an underspecified question about identifying a class called liquid; it gives no determinate mathematical statement whose resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | How can liquid condensed $R$-modules be characterized? Equivalently, determine the liquidifications of the compact projective generators $R[\beta S]$. | How can one characterize the liquid condensed R-modules, equivalently by identifying the liquidifications of the compact projective generators R[\beta S]? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,463 | OWR-1703864-004 | The Novikov Higher-Signature Conjecture | Novikov conjecture: the higher signatures of closed oriented smooth manifolds are invariant under orientation-preserving homotopy equivalences. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | open | null | 2,020 | 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"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-004",
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] | The Novikov conjecture is proved for many important group classes, but its general form for arbitrary groups remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1506.05408",
"label": "Rosenberg survey"
},
{
"url": "https://annals.math.princeton.edu/2003/158-1/p03",
"label": "Yu group-class theorem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | Novikov conjecture: the higher signatures of closed oriented smooth manifolds are invariant under orientation-preserving homotopy equivalences. | Novikov conjecture: the higher signatures of closed oriented smooth manifolds are invariant under orientation-preserving homotopy equivalences. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,464 | OWR-1703864-005 | Extension of Group Cyclic Cocycles to Smooth Subalgebras | Given a group $\Gamma$ and a suitable smooth dense subalgebra $A\subset C_r^*(\Gamma)$, when does a cyclic cocycle on $\mathbb C\Gamma$ extend continuously to a cyclic cocycle on $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
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"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-005",
"literature-status:partially-solved",
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] | The general-group question is still open, while the report records partial answers for degree-zero conjugacy-class traces under a sufficiently large spectral-gap hypothesis. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | Given a group $\Gamma$ and a suitable smooth dense subalgebra $A\subset C_r^*(\Gamma)$, when does a cyclic cocycle on $\mathbb C\Gamma$ extend continuously to a cyclic cocycle on $A$? | Given a group \Gamma and a suitable smooth dense subalgebra A\subset C_r^*(\Gamma), when does a cyclic cocycle on \mathbb C\Gamma extend to a cyclic cocycle on A? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,465 | OWR-1703864-006 | Convergence of Connes–Chern and Higher-Rho Pairings | Do pairings of Connes–Chern characters with higher rho invariants always converge? What further geometric hypotheses guarantee convergence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960](https://doi.org/10.4171/owr/2020/17)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
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"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703864-006",
"literature-status:partially-solved",
"owr-year:2020"
] | Convergence is established under smooth-subalgebra, cocycle-extension, and spectral-gap hypotheses, but convergence in the general geometric situation asked for is not known. | [
{
"url": "https://doi.org/10.4171/owr/2020/17",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1811.02086",
"label": "geometrically discrete groups theorem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/17 | null | null | null | Do pairings of Connes–Chern characters with higher rho invariants always converge? What further geometric hypotheses guarantee convergence? | For the Connes--Chern/higher-rho pairing appearing in the report, does the pairing always converge, and are there other geometric situations in which convergence holds? | corrected_verified | The official report was checked. The source-dependent phrase “appearing in the report” was removed while preserving both convergence questions. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/17, pp. 919--960 |
30,004,466 | OWR-1703865-001 | Maximum Excess Charge of Atoms | What is the maximal excess charge of atoms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/18, pp. 961--975](https://doi.org/10.4171/owr/2020/18)
## Literature review (checked 202... | 3 | open | null | 2,020 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "physics",
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"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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] | The maximal ionization problem remains open: rigorous bounds such as N_c(Z)<2Z+1 do not prove the conjectural Z+1 bound or even a Z+K bound with universal fixed K for the full many-electron atom. | [
{
"url": "https://doi.org/10.4171/owr/2020/18",
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{
"url": "https://www.math.kit.edu/iana1/~schulz/media/paper1_excess_charge.pdf",
"label": "Schulz--Hundertmark--Pattakos"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/18 | null | null | null | What is the maximal excess charge of atoms? | What is the maximal excess charge of atoms? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/18, pp. 961--975 |
30,004,467 | OWR-1703866-001 | Rational Cubic Fourfolds and K3 Categories | For a cubic fourfold $Y$, is $Y$ rational if and only if its Kuznetsov component $\operatorname{Ku}(Y)$ is equivalent to the derived category of a K3 surface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021](https://doi.org/10.4171/owr/2020/19)
## Lite... | 3 | open | null | 2,020 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-1703866-001",
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] | The extracted record contains the Kuznetsov rationality conjecture for cubic fourfolds; known rational families and categorical criteria provide evidence and cases, but the stated if-and-only-if remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2020/19",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/0808.3351",
"label": "Kuznetsov cubic fourfolds"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/19 | null | null | null | For a cubic fourfold $Y$, is $Y$ rational if and only if its Kuznetsov component $\operatorname{Ku}(Y)$ is equivalent to the derived category of a K3 surface? | Conjecture: for a cubic fourfold Y, Y is rational if and only if its Kuznetsov component Ku(Y) is equivalent to the derived category of a K3 surface. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021 |
30,004,468 | OWR-1703866-003 | Semiorthogonal Decompositions in Algebraic Families | How do semiorthogonal decompositions of derived categories behave in algebraic families? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021](https://doi.org/10.4171/owr/2020/19)
## Lite... | 3 | open | null | 2,020 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-1703866-003",
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{
"url": "https://doi.org/10.4171/owr/2020/19",
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{
"url": "https://doi.org/10.1016/j.geomphys.2025.105600",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/19 | null | null | null | How do semiorthogonal decompositions of derived categories behave in algebraic families? | How do semiorthogonal decompositions of derived categories behave in algebraic families? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021 |
30,004,469 | OWR-1703866-005 | Equivariant Derived Categories of Symplectic Surfaces | If a finite group acts suitably on the derived category of a symplectic surface $S$, is the equivariant category equivalent, possibly with a Brauer twist, to the derived category of a symplectic surface $S'$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021](https://doi.org/10.4171/owr/2020/19)
## Lite... | 3 | partially_solved | null | 2,020 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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"url": "https://arxiv.org/abs/2006.13899",
"label": "Beckmann--Oberdieck"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/19 | null | null | null | If a finite group acts suitably on the derived category of a symplectic surface $S$, is the equivariant category equivalent, possibly with a Brauer twist, to the derived category of a symplectic surface $S'$? | If a finite group acts suitably on the derived category of a symplectic surface S, is the equivariant category equivalent, possibly with a Brauer twist, to the derived category of a symplectic surface S'? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021 |
30,004,470 | OWR-1703866-006 | Stable-Pairs and Gromov–Witten Series for K3 Times Elliptic Curves | For a K3 surface $S$ and an elliptic curve $E$, does the Igusa cusp-form identity $F_{PT}=F_{GW}+F$ hold, where $F_{PT}$ and $F_{GW}$ are the stable-pairs and Gromov–Witten generating series and $F$ is an explicit correction term? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021](https://doi.org/10.4171/owr/2020/19)
## Lite... | 3 | solved | null | 2,020 | 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/10.1017/fms.2024.48",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. D. Nesterov (OWR 19/2020, pp. 1000–1001, Conjecture 3.1): for S × E, S a K3 surface, in classes primitive in S, −1/χ₁₀ = F_PT = F_GW + F, where F_GW is the reduced genus-1 Gromov–Witten series of Hilbⁿ(S) for fixed E; the report calls the second equality o... | [
"owr",
"oberwolfach-reports",
"OWR-1703866-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The first equality of the stated Igusa cusp form conjecture is proved and quasimaps establish important wall-crossing and Hilbert-scheme cases, but the second equality remains open in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2020/19",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1706.10100",
"label": "Oberdieck--Pixton"
},
{
"url": "https://arxiv.org/abs/2111.11425",
"label": "quasimaps to K3 sheaf moduli"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/19 | null | null | null | For a K3 surface $S$ and an elliptic curve $E$, does the Igusa cusp-form identity $F_{PT}=F_{GW}+F$ hold, where $F_{PT}$ and $F_{GW}$ are the stable-pairs and Gromov–Witten generating series and $F$ is an explicit correction term? | For a K3 surface S and an elliptic curve E, does the Igusa cusp-form identity F_{PT}=F_{GW}+F hold, where F_{PT} and F_{GW} are the stable-pairs and Gromov--Witten generating series and F is an explicit correction term? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/19, pp. 977--1021 |
30,004,471 | OWR-1703867-001 | Characterization of Integral Models of Shimura Varieties | What is a good general characterization of integral models of Shimura varieties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 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-1703867-001",
"literature-status:open",
"owr-year:2020"
] | The record explicitly says that a good general characterization is still open; Fargues' related characterization of integral local-Shimura models does not settle the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | What is a good general characterization of integral models of Shimura varieties? | What is a good general characterization of integral models of Shimura varieties? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,472 | OWR-1703867-002 | Hard Lefschetz for Arbitrary $\ell$-Adic Sheaves | Does hard Lefschetz hold for every $\ell$-adic local system $\mathcal F$ on a polarized smooth projective $d$-fold $X$; namely, is $\eta^i\cup-:H^{d-i}(X,\mathcal F)\to H^{d+i}(X,\mathcal F)$ an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 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-1703867-002",
"literature-status:open",
"owr-year:2020"
] | Rank-one and arithmetic semisimple cases of hard Lefschetz are proved, but the conjectural statement for arbitrary semisimple perverse l-adic sheaves, and hence the broader all-sheaves question, remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00029-021-00681-y",
"label": "Esnault--Kerz"
},
{
"url": "https://arxiv.org/abs/1908.08291",
"label": "rank-one hard Lefschetz"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | Does hard Lefschetz hold for every $\ell$-adic local system $\mathcal F$ on a polarized smooth projective $d$-fold $X$; namely, is $\eta^i\cup-:H^{d-i}(X,\mathcal F)\to H^{d+i}(X,\mathcal F)$ an isomorphism? | Does the hard Lefschetz property hold for all \ell-adic sheaves; namely, is \cup^i\eta:H^{d-i}(X,\mathcal F)\to H^{d+i}(X,\mathcal F) an isomorphism for a polarized smooth projective d-fold X and every relevant \ell-adic local system \mathcal F? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,473 | OWR-1703867-003 | Whittaker-Normalized Functors for Reductive Groups | For every reductive triple $(G,B,T)$ with Whittaker datum $\psi$, does there exist a fully faithful $Z_G$-linear functor
$$
R_G^\psi:D^+(\operatorname{Rep}_{[T,1]}G)\longrightarrow D^+\operatorname{QCoh}([\mathcal X_{\check G}/\check G])
$$
that is compatible with parabolic induction for every $B\subset P\subset G$, ag... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | null | 2,020 | 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-1703867-003",
"literature-status:partially-solved",
"owr-year:2020"
] | The fully faithful Whittaker-normalized functor and its parabolic compatibilities remain conjectural in general, while principal-block and related cases have substantial proved results. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/S0010437X23007145",
"label": "Iwahori--Hecke derived category"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | For every reductive triple $(G,B,T)$ with Whittaker datum $\psi$, does there exist a fully faithful $Z_G$-linear functor
$$
R_G^\psi:D^+(\operatorname{Rep}_{[T,1]}G)\longrightarrow D^+\operatorname{QCoh}([\mathcal X_{\check G}/\check G])
$$
that is compatible with parabolic induction for every $B\subset P\subset G$, ag... | Conjecture: for every reductive triple (G,B,T) with Whittaker datum \psi, there is a fully faithful Z_G-linear functor R_G^\psi:D^+(\operatorname{Rep}_{[T,1]}G)\to D^+\operatorname{QCoh}([\mathcal X_{\check G}/\check G]), compatible with parabolic induction and the stated torus and compact-induction normalizations. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,474 | OWR-1703867-004 | Frobenius-Stable Loci and Dense Arithmetic Points | Let $X/\overline{\mathbb F}_p$ be smooth, connected, and of finite type; let $S_{\bar\rho}$ parametrize semisimple $\overline{\mathbb Q}_\ell$-local systems with residual representation $\bar\rho$; and let $A_{\bar\rho}$ be its arithmetic points. If a Zariski-closed subset $Z\subset S_{\bar\rho}$ is stable under a powe... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 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-1703867-004",
"literature-status:open",
"owr-year:2020"
] | This is only a fragment asserting that an unspecified conjecture has known cases; without the missing cases or the conjecture statement it is not independently triageable, so it remains open under the requested rule. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | Let $X/\overline{\mathbb F}_p$ be smooth, connected, and of finite type; let $S_{\bar\rho}$ parametrize semisimple $\overline{\mathbb Q}_\ell$-local systems with residual representation $\bar\rho$; and let $A_{\bar\rho}$ be its arithmetic points. If a Zariski-closed subset $Z\subset S_{\bar\rho}$ is stable under a powe... | Let X/\overline{\mathbb F}_p be smooth connected of finite type, let S_{\bar\rho} parametrize semisimple \overline{\mathbb Q}_\ell-local systems with residual representation \bar\rho, and let A_{\bar\rho} be its arithmetic points. If a Zariski-closed Z\subset S_{\bar\rho} is stable under some power of Frobenius, then A... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,475 | OWR-1703867-005 | $p$-Adic Regulators for Triple-Product $L$-Functions | In the indefinite triple-product setting, can one formulate and prove a Bloch–Kato-style $p$-adic regulator law governing the behavior of $L_p(f,g,h)$ near $(2,1,1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | null | 2,020 | 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-1703867-005",
"literature-status:partially-solved",
"owr-year:2020"
] | The restricted second-derivative formula is a proved theorem under explicit hypotheses, while the broader p-adic Bloch--Kato or Birch--Swinnerton-Dyer expectation in the record remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.24033/asens.2227",
"label": "Darmon--Rotger diagonal cycles I"
},
{
"url": "https://web.mat.upc.edu/victor.rotger/docs/DR2.pdf",
"label": "Darmon--Rotger diagonal cycles II"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | In the indefinite triple-product setting, can one formulate and prove a Bloch–Kato-style $p$-adic regulator law governing the behavior of $L_p(f,g,h)$ near $(2,1,1)$? | In the indefinite case, the behavior at (2,1,1) of the p-adic L-function L_p(f,g,h) is expected to be governed by a p-adic regulator via a Bloch--Kato conjecture generalizing Birch--Swinnerton-Dyer; in a restricted setting \left.\partial_k^2L_p(f,g,h)\right|_{(2,1,1)}=\log_p(P_\phi)\log_p(P_\psi). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,476 | OWR-1703867-006 | Canonical Triple-Product $p$-Adic $L$-Values and Rational Points | Is there a canonical multiple $L_p^{\mathrm{can}}(f,g,h)$ of $L_p(f,g,h)$ whose value at $(2,1,1)$ equals the formal-group logarithm of a rational point $P_\rho\in E(\overline{\mathbb Q})_\rho$, with $P_\rho$ nontrivial if and only if $L(E,\rho,s)$ has a simple zero at $s=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | null | 2,020 | 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-1703867-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The Conjecture 5 value and nontriviality criterion are not proved in general; Darmon--Rotger establish new analytic-rank-zero cases and conditional higher-rank Selmer consequences, giving partial progress. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
},
{
"url": "https://web.mat.upc.edu/victor.rotger/docs/DR2.pdf",
"label": "Darmon--Rotger diagonal cycles II"
},
{
"url": "https://arxiv.org/abs/2207.01314",
"label": "p-adic families of diagonal cycles"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | Is there a canonical multiple $L_p^{\mathrm{can}}(f,g,h)$ of $L_p(f,g,h)$ whose value at $(2,1,1)$ equals the formal-group logarithm of a rational point $P_\rho\in E(\overline{\mathbb Q})_\rho$, with $P_\rho$ nontrivial if and only if $L(E,\rho,s)$ has a simple zero at $s=1$? | Conjecture: there is a canonical multiple L_p^{\mathrm{can}}(f,g,h) of L_p(f,g,h) whose value at (2,1,1) equals the formal-group logarithm of a rational point P_\rho\in E(\overline{\mathbb Q})_\rho, and P_\rho is nontrivial if and only if L(E,\rho,1) has a simple zero at s=1. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,477 | OWR-1703867-008 | Galois Descent of Special Hodge Subvarieties | If a polarized variation of integral Hodge structure is defined over a number field $K$, is every associated special subvariety defined over a finite extension of $K$, with all of its finitely many $\operatorname{Gal}(\overline{\mathbb Q}/K)$-conjugates again special? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 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-1703871-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703867-008",
"literature-status:open",
"owr-year:2020"
] | The Galois-descent assertion for all special subvarieties of a ZVHS remains conjectural; Voisin and Saito--Schnell provide important sufficient criteria, not a proof of the full statement. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | If a polarized variation of integral Hodge structure is defined over a number field $K$, is every associated special subvariety defined over a finite extension of $K$, with all of its finitely many $\operatorname{Gal}(\overline{\mathbb Q}/K)$-conjugates again special? | Conjecture: if a polarized variation of integral Hodge structure is defined over a number field K, then every associated special subvariety is defined over a finite extension of K and all of its finitely many \operatorname{Gal}(\overline{\mathbb Q}/K)-conjugates remain special subvarieties. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,478 | OWR-1703867-009 | Effective Enumeration of Rational Points on Curves | Given equations for a smooth geometrically irreducible projective curve $C$ of genus at least $2$ over a number field $F$, is there an algorithm that produces the complete list of points in $C(F)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082](https://doi.org/10.4171/owr/2020/20)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 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-1703867-009",
"literature-status:open",
"owr-year:2020"
] | An effective algorithm producing all rational points on an arbitrary curve is still unknown; Dimitrov--Gao--Habegger prove strong uniform cardinality bounds depending on genus, field degree, and Jacobian rank, but this does not supply the missing complete-list algorithm. | [
{
"url": "https://doi.org/10.4171/owr/2020/20",
"label": "original OWR report"
},
{
"url": "https://annals.math.princeton.edu/2021/194-1/p04",
"label": "Dimitrov--Gao--Habegger"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/20 | null | null | null | Given equations for a smooth geometrically irreducible projective curve $C$ of genus at least $2$ over a number field $F$, is there an algorithm that produces the complete list of points in $C(F)$? | For a smooth projective curve C/F of genus at least 2 over a number field, does an algorithm produce a complete list of F-rational points C(F), and can \#C(F) be bounded above using suitable known invariants of C? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arithmetic Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/20, pp. 1023--1082 |
30,004,479 | OWR-1703868-001 | Graph Complex Invariants and Classical Embedding Invariants | For the natural finite-to-one map from components of high-dimensional embedding spaces to Maurer–Cartan elements of the associated hairy graph complex, is it related to classical embedding invariants such as the Boechat–Haefliger and Whitney–Skopenkov invariants and linking invariants? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/21, pp. 1083--1137](https://doi.org/10.4171/owr/2020/21)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,020 | 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-1703868-001",
"literature-status:open",
"owr-year:2020"
] | The record only conjectures a relationship between a rational homotopy invariant of embedding spaces and classical embedding invariants; later classifications of several embedding families do not establish this proposed general identification. | [
{
"url": "https://ems.press/content/serial-article-files/46858",
"label": "OWR Topology report"
},
{
"url": "https://www.mathnet.ru/eng/mmj787",
"label": "Crowley--Skopenkov, Embeddings of non-simply-connected 4-manifolds in 7-space"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/21 | null | null | null | For the natural finite-to-one map from components of high-dimensional embedding spaces to Maurer–Cartan elements of the associated hairy graph complex, is it related to classical embedding invariants such as the Boechat–Haefliger and Whitney–Skopenkov invariants and linking invariants? | For the natural finite-to-one map from components of high-dimensional embedding spaces to Maurer--Cartan elements of the associated hairy graph complex, is it related to classical embedding invariants such as the Boechat--Haefliger and Whitney--Skopenkov invariants and linking invariants? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Topologie (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/21, pp. 1083--1137 |
30,004,480 | OWR-1703868-002 | Imprecise Kashiwara–Vergne Symmetry Relation | The symmetry group KV of the Kashiwara--Vergne solutions is conjecturally closely related to the prounipotent Grothendieck--Teichmuller group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/21, pp. 1083--1137](https://doi.org/10.4171/owr/2020/21)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,020 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report says only that the approach illuminates a close relationship conjectured elsewhere between the Kashiwara–Vergne symmetry) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703868-002",
"literature-status:open",
"owr-year:2020"
] | The Kashiwara--Vergne problem itself is solved and its symmetry group is related to Grothendieck--Teichmuller groups, but the extracted welded-foam claim is explicitly a conjectural close relationship without a proved equality or complete formulation. | [
{
"url": "https://arxiv.org/abs/2106.02373",
"label": "Dancso--Halacheva--Robertson, A topological characterisation of the KV groups"
},
{
"url": "https://arxiv.org/abs/2211.11370",
"label": "Dancso--Hogan--Robertson, A knot-theoretic approach to KV and GT groups"
},
{
"url": "https://em... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/21 | null | null | null | null | The symmetry group KV of the Kashiwara--Vergne solutions is conjecturally closely related to the prounipotent Grothendieck--Teichmuller group. | unrecoverable | The official report says only that the approach illuminates a close relationship conjectured elsewhere between the Kashiwara–Vergne symmetry group and the prounipotent Grothendieck–Teichmüller group; it does not formulate a precise mathematical claim to publish as a standalone problem. No separate clean statement is pr... | null | null | null | null | null | Topologie (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/21, pp. 1083--1137 |
30,004,481 | OWR-1703869-001 | Rigidity, Regularity, and Vectorial Nucleation in Nonlinear Inclusions | For geometrically nonlinear differential inclusions, is there a critical threshold separating rigid and flexible regimes, and can one bound the maximal regularity of irregular solutions? Can scalar nucleation models for shape-memory alloys be extended to vectorial models with compatibility conditions, related to convex... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-001",
"literature-status:open",
"owr-year:2020"
] | The passage lists broad unresolved questions about rigid-flexible thresholds, regularity of irregular solutions, vectorial nucleation, and stochastic descriptions; no general resolution of these claims was found. | [
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | For geometrically nonlinear differential inclusions, is there a critical threshold separating rigid and flexible regimes, and can one bound the maximal regularity of irregular solutions? Can scalar nucleation models for shape-memory alloys be extended to vectorial models with compatibility conditions, related to convex... | For geometrically nonlinear differential inclusions, is there a critical threshold separating rigid and flexible regimes, and can one bound the maximal regularity of irregular solutions? Can scalar nucleation models for shape-memory alloys be extended to vectorial models with compatibility conditions, related to convex... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,482 | OWR-1703869-002 | Three-Dimensional Nucleation Structures and Stochastic Microstructure Models | Can analogous nucleation structures be produced in three dimensions, and how do such structures scale with a prescribed disclination angle? Can stochastic partial differential equations describing the resulting microstructure be derived? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-002",
"literature-status:open",
"owr-year:2020"
] | The proposed three-dimensional microstructure, scaling, and stochastic-PDE program remains an open research direction; the source itself presents these as open problems and no general solution was located. | [
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | Can analogous nucleation structures be produced in three dimensions, and how do such structures scale with a prescribed disclination angle? Can stochastic partial differential equations describing the resulting microstructure be derived? | Can analogous nucleation structures be produced in three dimensions, and how do such structures scale with a prescribed disclination angle? Can stochastic partial differential equations describing the resulting microstructure be derived? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,483 | OWR-1703869-003 | Boundary Branch Singularities of Area-Minimizing Currents | Let $T$ be an area-minimizing two-dimensional current with analytic prescribed boundary curve $\Gamma\subset\mathbb R^{2+n}$. Is the set of branched singular points of $T$ at the boundary isolated, with $T$ having finite topology locally at each such point? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-003",
"literature-status:open",
"owr-year:2020"
] | For analytic boundary curves, the linear Dirichlet-energy model has discrete singular set results, but the asserted isolation and finite local topology for general area-minimizing currents remains presented as a conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
},
{
"url": "https://arxiv.org/abs/1906.09488",
"label": "De Lellis--De Philippis--Hirsch, Nonclassical minimizing surfaces with smooth boundary"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | Let $T$ be an area-minimizing two-dimensional current with analytic prescribed boundary curve $\Gamma\subset\mathbb R^{2+n}$. Is the set of branched singular points of $T$ at the boundary isolated, with $T$ having finite topology locally at each such point? | Let T be an area-minimizing two-dimensional current with analytic prescribed boundary curve \Gamma\subset\mathbb{R}^{2+n}. Is the set of branched singular points of T at the boundary isolated, with T having finite topology locally at each such point? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,484 | OWR-1703869-004 | Topology and Morse Theory of Allen-Cahn Moduli Spaces | For the moduli space $M_{2m}$ of $2m$-ended solutions of the planar Allen–Cahn equation $\Delta u+u-u^3=0$, is $M_{2m}$ connected, what is its dimension, and what is the Morse index of its solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-004",
"literature-status:open",
"owr-year:2020"
] | Although four-ended solutions are classified, the record asks for connectivity, dimension, and Morse-index classification of the general 2m-ended Allen--Cahn moduli space, which remains incomplete. | [
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
},
{
"url": "https://arxiv.org/abs/1109.5604",
"label": "Pacard--Kowalczyk--Liu, Classification of four-end solutions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | For the moduli space $M_{2m}$ of $2m$-ended solutions of the planar Allen–Cahn equation $\Delta u+u-u^3=0$, is $M_{2m}$ connected, what is its dimension, and what is the Morse index of its solutions? | For the moduli space M_{2m} of 2m-ended solutions of the planar Allen--Cahn equation \Delta u+u-u^3=0, is M_{2m} connected, what is its dimension, and what is the Morse index of its solutions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,485 | OWR-1703869-005 | Branching Complexity in the Branched Transportation Mailing Problem | For an optimizer of the mailing problem in branched transportation, does it have finite graph structure in every ball outside the supports of the initial and target measures, and is the number of branches at a branching point uniformly bounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-005",
"literature-status:open",
"owr-year:2020"
] | The question concerns uniform branching complexity in optimal traffic plans; the cited research context records it as open, and no general uniform bound was found. | [
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | For an optimizer of the mailing problem in branched transportation, does it have finite graph structure in every ball outside the supports of the initial and target measures, and is the number of branches at a branching point uniformly bounded? | For an optimizer of the mailing problem in branched transportation, does it have finite graph structure in every ball outside the supports of the initial and target measures, and is the number of branches at a branching point uniformly bounded? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,486 | OWR-1703869-006 | Energy-Angular Momentum Relations for Rotating Skyrmions | How do the minimal energies of skyrmion solutions depend on the magnitude of angular momentum, and can this dependence be used to estimate the rotation frequency $\omega$ and prove that the resulting Landau–Lifshitz solution is non-static? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196](https://doi.org/10.4171/owr/2020/22)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,020 | 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-1703869-006",
"literature-status:open",
"owr-year:2020"
] | Existence of localized rotating Landau--Lifshitz solutions is known, but the energy versus angular-momentum law and proof that the constructed motion is non-static remain explicitly open. | [
{
"url": "https://arxiv.org/abs/1902.04881",
"label": "Melcher--Sakellaris, Curvature stabilized skyrmions with angular momentum"
},
{
"url": "https://ems.press/content/serial-article-files/46860",
"label": "OWR Calculus of Variations report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/22 | null | null | null | How do the minimal energies of skyrmion solutions depend on the magnitude of angular momentum, and can this dependence be used to estimate the rotation frequency $\omega$ and prove that the resulting Landau–Lifshitz solution is non-static? | How do the minimal energies of skyrmion solutions depend on the magnitude of angular momentum, and can this dependence be used to estimate the rotation frequency \omega and prove that the resulting Landau--Lifshitz solution is non-static? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Calculus of Variations (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/22, pp. 1139--1196 |
30,004,487 | OWR-1703870-001 | Transfer Operations in Homology of Finite Categories | For the homology and cohomology of finite categories, how can restriction, corestriction or transfer, conjugation, and inflation be formulated, and what properties should a categorical transfer map satisfy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/23, pp. 1197--1261](https://doi.org/10.4171/owr/2020/23)
## Literature review (... | 3 | open | null | 2,020 | 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-1703870-001",
"literature-status:open",
"owr-year:2020"
] | The fragment asks for a general theory of cohomology operations and transfer maps for categories without specifying a precise conjecture; the extracted problem is therefore unresolved and unclear. | [
{
"url": "https://ems.press/content/serial-article-files/46862",
"label": "OWR Cohomology of Finite Groups report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/23 | null | null | null | For the homology and cohomology of finite categories, how can restriction, corestriction or transfer, conjugation, and inflation be formulated, and what properties should a categorical transfer map satisfy? | For the homology and cohomology of finite categories, how can restriction, corestriction or transfer, conjugation, and inflation be formulated, and what properties should a categorical transfer map satisfy? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/23, pp. 1197--1261 |
30,004,488 | OWR-1703870-003 | Biset-Functor Structure of Dade-Type Groups | For a finite group $G$ and an odd prime $p$, is $C_{ba+}(G,p)=\ker\Psi_G$? Does $D_\Omega(G)$ admit a well-defined biset-functor structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/23, pp. 1197--1261](https://doi.org/10.4171/owr/2020/23)
## Literature review (... | 3 | open | null | 2,020 | 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-1703870-003",
"literature-status:open",
"owr-year:2020"
] | The p=2 exact sequence is established, while the record explicitly leaves the odd-prime equality and the corresponding well-defined biset-functor structure of D\Omega open; no later general resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46862",
"label": "OWR Cohomology of Finite Groups report"
},
{
"url": "https://www.lamfa.u-picardie.fr/bouc/boya.pdf",
"label": "Bouc--Yalcin, Borel--Smith functions and the Dade group"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/23 | null | null | null | For a finite group $G$ and an odd prime $p$, is $C_{ba+}(G,p)=\ker\Psi_G$? Does $D_\Omega(G)$ admit a well-defined biset-functor structure? | For a finite group G and an odd prime p, does the equality C_{ba+}(G,p)=\ker\Psi_G hold, and does D_{\Omega}(G) admit a well-defined biset-functor structure? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Cohomology of Finite Groups: Interactions and Applications (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/23, pp. 1197--1261 |
30,004,489 | OWR-1703871-002 | Brauer Groups of Smooth Models of Symmetric Powers | Let $X_m=\operatorname{Sym}^m(X)$ and let $X'_m$ be a smooth model of $X_m$. Can $\operatorname{Br}(X'_m)$ be estimated in terms of $\operatorname{Br}(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | open | null | 2,020 | 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-1703871-002",
"literature-status:open",
"owr-year:2020"
] | The Brauer-group question for smooth models of symmetric powers is still posed as an open problem; existing work on specialness and rationality does not supply the requested general estimate or vanishing theorem. | [
{
"url": "https://www.numdam.org/item/JEP_2022__9__381_0.pdf",
"label": "Cadorel--Campana--Rousseau, Hyperbolicity and specialness of symmetric powers"
},
{
"url": "https://ems.press/content/serial-article-files/46857",
"label": "OWR Complex Analysis report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | Let $X_m=\operatorname{Sym}^m(X)$ and let $X'_m$ be a smooth model of $X_m$. Can $\operatorname{Br}(X'_m)$ be estimated in terms of $\operatorname{Br}(X)$? | For the varieties X_m associated to a variety X, can the Brauer group of a smooth model X'_m be estimated from the Brauer group of X? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,490 | OWR-1703871-003 | Galois Arithmetic of Special Subvarieties in Hodge Variations | Conjecture: every special subvariety associated with a Zariski variation of Hodge structure defined over a number field K is defined over a finite extension L of K, and its finitely many Gal(\mathbb{Q}/K)-conjugates are again special subvarieties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | open | null | 2,020 | 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 (Cross-report comparison confirms that this is a second extraction of the special-subvariety descent conjecture retained in OWR-1703867-008. ) | [
"OWR-1703867-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703871-003",
"literature-status:open",
"owr-year:2020"
] | The Galois-definition and conjugacy conjecture for special subvarieties of general ZVHS remains open in full generality; current work proves cases under monodromy hypotheses and reduces the general arithmetic issue to special points. | [
{
"url": "https://arxiv.org/abs/2010.03359",
"label": "Klingler--Otwinowska--Urbanik, On the fields of definition of Hodge loci"
},
{
"url": "https://ems.press/content/serial-article-files/46857",
"label": "OWR Complex Analysis report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | null | Conjecture: every special subvariety associated with a Zariski variation of Hodge structure defined over a number field K is defined over a finite extension L of K, and its finitely many Gal(\mathbb{Q}/K)-conjugates are again special subvarieties. | unrecoverable | Cross-report comparison confirms that this is a second extraction of the special-subvariety descent conjecture retained in OWR-1703867-008. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,491 | OWR-1703871-006 | Infinite Transverse Actions on Codimension-One Foliations | If $X$ is a projective manifold, $\mathcal F$ is a codimension-one foliation on $X$, and $f\in\operatorname{End}(X,\mathcal F)$ has infinite transverse action, is $\mathcal F$ virtually transversely additive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | open | null | 2,020 | 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-1703871-006",
"literature-status:open",
"owr-year:2020"
] | The conjecture remains open in general: it is proved in several restricted settings, including low-dimensional orbit closures and Picard-rank-one endomorphisms, while the source explicitly presents the unrestricted statement as a conjecture. | [
{
"url": "https://doi.org/10.1515/crelle-2022-0023",
"label": "Lo Bianco--Pereira--Rousseau--Touzet, Rational endomorphisms of codimension one foliations"
},
{
"url": "https://ems.press/content/serial-article-files/46857",
"label": "OWR Complex Analysis report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | If $X$ is a projective manifold, $\mathcal F$ is a codimension-one foliation on $X$, and $f\in\operatorname{End}(X,\mathcal F)$ has infinite transverse action, is $\mathcal F$ virtually transversely additive? | Conjecture: if X is a projective manifold, F is a codimension-one foliation on X, and f\in\operatorname{End}(X,F) has infinite transverse action, then F is virtually transversely additive. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,492 | OWR-1703871-008 | Natural Completions of Period Maps | Given a smooth projective variety $B$ with reduced normal-crossing divisor $Z$, a period map $\Phi:B\setminus Z\to\Gamma\backslash D$, and image $\mathcal P=\Phi(B\setminus Z)$, what natural completions of $\Phi$ to a map from $B$ exist, and what properties do they have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | partially_solved | null | 2,020 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703871-008",
"literature-status:partially-solved",
"owr-year:2020"
] | A proper topological SBB-type completion with projective fibers and quasi-projective image strata has been constructed, but the general algebraic completion and its full properties remain incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2020/24",
"label": "Oberwolfach Report 24/2020"
},
{
"url": "https://arxiv.org/abs/2010.06720",
"label": "Global asymptotic structure of period mappings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | Given a smooth projective variety $B$ with reduced normal-crossing divisor $Z$, a period map $\Phi:B\setminus Z\to\Gamma\backslash D$, and image $\mathcal P=\Phi(B\setminus Z)$, what natural completions of $\Phi$ to a map from $B$ exist, and what properties do they have? | Given a smooth projective variety B with reduced normal-crossing divisor Z, a period map \Phi:B\setminus Z\to\Gamma\backslash D, and image \mathcal{P}=\Phi(B\setminus Z), what natural completions of \Phi to a map from B exist, and what properties do these completions have? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,493 | OWR-1703871-009 | Projectivity of the Stein-Factorized Period-Map Completion | For the Stein factorization $B\xrightarrow{\widehat{\Phi}}\widehat{\mathcal{P}}\to\mathcal{P}$ of the period map, where $\widehat{\mathcal{P}}$ is open in a compact complex analytic variety $\widehat{\mathcal{P}}^{T}$, is $\widehat{\mathcal{P}}^{T}$ a projective completion of $\widehat{\mathcal{P}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | partially_solved | null | 2,020 | 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-1703871-009",
"literature-status:partially-solved",
"owr-year:2020"
] | The proposed completion is known as a Hausdorff topological and finite normal analytic completion, with projective fibers, but its being projective algebraic is still posed as a conjecture in the primary literature. | [
{
"url": "https://arxiv.org/abs/2010.06720",
"label": "Global asymptotic structure of period mappings"
},
{
"url": "https://arxiv.org/abs/2506.10109",
"label": "Geometric and Hodge-theoretic completion of period mappings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | For the Stein factorization $B\xrightarrow{\widehat{\Phi}}\widehat{\mathcal{P}}\to\mathcal{P}$ of the period map, where $\widehat{\mathcal{P}}$ is open in a compact complex analytic variety $\widehat{\mathcal{P}}^{T}$, is $\widehat{\mathcal{P}}^{T}$ a projective completion of $\widehat{\mathcal{P}}$? | For the Stein factorization B\xrightarrow{\widehat{\Phi}}\widehat{\mathcal{P}}\to\mathcal{P} of the period map, where \widehat{\mathcal{P}} is open in a compact complex analytic variety \widehat{\mathcal{P}}^{T}, is \widehat{\mathcal{P}}^{T} a projective completion of \widehat{\mathcal{P}}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,494 | OWR-1703871-010 | Boundary-Corrected Ampleness of Extended Hodge Bundles | Let $B$ be smooth and projective, let $Z=\bigcup_iZ_i$ be a simple normal-crossing divisor, and let $\Lambda^e$ be the canonical extension of the Hodge line bundle for a period map whose logarithmic differential is injective. Do there exist integers $a_i\geq0$ and $m_0$ such that
$$
m\Lambda^e-\sum_i a_i[Z_i]
$$
is amp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | partially_solved | null | 2,020 | 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-1703871-010",
"literature-status:partially-solved",
"owr-year:2020"
] | The ampleness conjecture is proved when the boundary is irreducible and in dimension two under stronger hypotheses; the general normal-crossing-boundary assertion remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/24",
"label": "Oberwolfach Report 24/2020"
},
{
"url": "https://arxiv.org/abs/2102.06310",
"label": "Natural line bundles on completions of period mappings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | Let $B$ be smooth and projective, let $Z=\bigcup_iZ_i$ be a simple normal-crossing divisor, and let $\Lambda^e$ be the canonical extension of the Hodge line bundle for a period map whose logarithmic differential is injective. Do there exist integers $a_i\geq0$ and $m_0$ such that
$$
m\Lambda^e-\sum_i a_i[Z_i]
$$
is amp... | Under suitable local-Torelli-type assumptions, do there exist integers a_i\geq 0 and m_0 such that m\Lambda^e-\sum_i a_i[Z_i] is ample for every m\geq m_0? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,495 | OWR-1703871-011 | Positivity of Log Canonical Bundles under Local Torelli | Does generic local Torelli for the period map imply that $K_B+[Z]$ is nef and big, and does local Torelli imply that $K_B+[Z]$ is free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313](https://doi.org/10.4171/owr/2020/24)
## Literature review (checked ... | 3 | partially_solved | null | 2,020 | 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-1703871-011",
"literature-status:partially-solved",
"owr-year:2020"
] | Under the stronger local Torelli condition on the triple, the log canonical bundle is proved nef and big and a multiple is free; the stated generic-local-Torelli and local-Torelli conjectures are not established in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2020/24",
"label": "Oberwolfach Report 24/2020"
},
{
"url": "https://arxiv.org/abs/2102.06310",
"label": "Natural line bundles on completions of period mappings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/24 | null | null | null | Does generic local Torelli for the period map imply that $K_B+[Z]$ is nef and big, and does local Torelli imply that $K_B+[Z]$ is free? | Does generic local Torelli for the period map imply that K_B+[Z] is nef and big, and does local Torelli imply that K_B+[Z] is free? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Komplexe Analysis - Algebraicity and Transcendence (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/24, pp. 1263--1313 |
30,004,496 | OWR-1703872-002 | Large Values of Arithmetic Hyperbolic Three-Manifold Eigenfunctions | Let $f$ be a normalized Hecke–Laplace eigenfunction on a compact arithmetic hyperbolic $3$-manifold $M$, with
$$\int_M|f|^2\,d\mu=1.$$
Must $|f|$ attain values much larger than its root-mean-square size $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (yes, for infinitely many f; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, for infinitely many f; answered in the source)**. W. Sawin (OWR 26/2020, pp. 1330–1331) opens by asking whether Hecke–Maass forms f with ‖f‖₂ = 1 on his compact arithmetic 3-manifold M take values much larger than 1, and answers it: by Milićević, [GAFA 21 (20... | [
"owr",
"oberwolfach-reports",
"OWR-1703872-002",
"literature-status:open",
"owr-year:2020"
] | The qualitative large-values question for normalized Hecke-Laplace eigenfunctions is recorded as an open question, and the extracted wording supplies no quantitative threshold that has been proved. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Let $f$ be a normalized Hecke–Laplace eigenfunction on a compact arithmetic hyperbolic $3$-manifold $M$, with
$$\int_M|f|^2\,d\mu=1.$$
Must $|f|$ attain values much larger than its root-mean-square size $1$? | For a normalized Hecke--Laplace eigenfunction f on the compact arithmetic hyperbolic three-manifold M with \int_M|f|^2d\mu=1, does |f| take values much larger than its average value 1? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,497 | OWR-1703872-003 | Subconvex Pointwise Equidistribution of Hecke–Laplace Eigenfunctions | Does there exist $\delta>0$ such that, for $y\in D^\times(\mathbb A_\mathbb Q)$ and every Hecke–Laplace eigenfunction $f$ of eigenvalue $\lambda$,
$$f(y)=\int_{D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)}f(x)\,d\mu(x)+O(\lambda^{1/4-\delta})$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-003",
"literature-status:open",
"owr-year:2020"
] | The proposed power-saving asymptotic for point values and the period integral of all relevant eigenfunctions is posed as a question in the report; no unconditional result resolving this exact assertion was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Does there exist $\delta>0$ such that, for $y\in D^\times(\mathbb A_\mathbb Q)$ and every Hecke–Laplace eigenfunction $f$ of eigenvalue $\lambda$,
$$f(y)=\int_{D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)}f(x)\,d\mu(x)+O(\lambda^{1/4-\delta})$$? | Does there exist \delta>0 such that, for y\in D^{\times}(\mathbb{A}_{\mathbb{Q}}) and every Hecke--Laplace eigenfunction f of eigenvalue \lambda, \ f(y)=\int_{D^{\times}(\mathbb{Q})\backslash D^{\times}(\mathbb{A}_{\mathbb{Q}})}f(x)d\mu(x)+O(\lambda^{1/4-\delta})? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,498 | OWR-1703872-004 | Pointwise Asymptotics of Special Quaternionic Eigenfunctions | For $y\in D^\times(\mathbb A_\mathbb Q)$ and every special eigenfunction $f$, is
$$f(y)=(1+o(1))\int_{D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)}f(x)\,d\mu(x)$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-004",
"literature-status:open",
"owr-year:2020"
] | The special-eigenfunction asymptotic and the required period-integral estimates are presented as expectations and conditional reduction targets; the exact question remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | For $y\in D^\times(\mathbb A_\mathbb Q)$ and every special eigenfunction $f$, is
$$f(y)=(1+o(1))\int_{D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)}f(x)\,d\mu(x)$$? | For y\in D^{\times}(\mathbb{A}_{\mathbb{Q}}) and every special eigenfunction f, is f(y)=(1+o(1))\int_{D^{\times}(\mathbb{Q})\backslash D^{\times}(\mathbb{A}_{\mathbb{Q}})}f(x)d\mu(x)? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,499 | OWR-1703872-005 | Local Maxima of Special Eigenfunctions at Spherical Points | Assume there are no nonzero functions on
$$D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)/\bigl((K_\infty\cap D^\times(\mathbb A_\mathbb Q))Z(D^\times(\mathbb A_\mathbb Q))\bigr)$$
that transform according to the $3$-dimensional spherical representation of $\operatorname{SO}(3)$. For all but finitely man... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-005",
"literature-status:open",
"owr-year:2020"
] | The extracted text is a continuation fragment describing conditional methods for period integrals and a local-maximum question; it records no proof of the underlying general claim. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Assume there are no nonzero functions on
$$D^\times(\mathbb Q)\backslash D^\times(\mathbb A_\mathbb Q)/\bigl((K_\infty\cap D^\times(\mathbb A_\mathbb Q))Z(D^\times(\mathbb A_\mathbb Q))\bigr)$$
that transform according to the $3$-dimensional spherical representation of $\operatorname{SO}(3)$. For all but finitely man... | If there are no nonzero functions on D^{\times}(\mathbb{Q})\backslash D^{\times}(\mathbb{A}_{\mathbb{Q}})/(K_\infty\cap D^{\times}(\mathbb{A}_{\mathbb{Q}}))Z(D^{\times}(\mathbb{A}_{\mathbb{Q}})) transforming according to the 3-dimensional spherical representation of SO(3), then for all but finitely many special eigenfu... | corrected_verified | The official report was checked. The adelic quotient, spherical representation, exceptional finite set, and pointwise local-maximum question were restored from Question 3. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,500 | OWR-1703872-006 | Lower Bounds for Function-Field Quaternionic Periods | Fix a quaternion algebra $D$ over $\mathbb F_q(t)$. Let $F/\mathbb F_q(t)$ vary over quadratic extensions of genus $g$, let $K\subset D^\times(\mathbb A_F)$ be compact, and let $m$ be the index of $K\cap D^\times(\mathbb A_{\mathbb F_q(t)})$ in a maximal compact subgroup. For every normalized Hecke eigenfunction $f$ on... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-006",
"literature-status:open",
"owr-year:2020"
] | The function-field lower-bound question is only checked in the split standard-level case in the source passage, while the asserted universal bound for varying extensions and compact subgroups remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Fix a quaternion algebra $D$ over $\mathbb F_q(t)$. Let $F/\mathbb F_q(t)$ vary over quadratic extensions of genus $g$, let $K\subset D^\times(\mathbb A_F)$ be compact, and let $m$ be the index of $K\cap D^\times(\mathbb A_{\mathbb F_q(t)})$ in a maximal compact subgroup. For every normalized Hecke eigenfunction $f$ on... | In the function-field genus-aspect setting described in the report, does there exist a universal constant C such that the period integral \int_{D^{\times}(\mathbb F_q(t))\backslash D^{\times}(\mathbb A_{\mathbb F_q(t)})} f(x) d\mu(x)=\Omega(m^{-C}q^{g/2}) for every normalized Hecke eigenfunction f? | corrected_verified | The official report was checked. The quaternion algebra, varying quadratic extension, genus, compact subgroup, index, automorphic quotient, and parameter dependence were restored. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,501 | OWR-1703872-007 | Pointwise Function-Field Equidistribution from Period Integrals | Fix a quaternion algebra $D$ over $\mathbb F_q(t)$. Let $F/\mathbb F_q(t)$ vary over quadratic extensions of genus $g$, let $K\subset D^\times(\mathbb A_F)$ be compact, and let $m$ be the index of $K\cap D^\times(\mathbb A_{\mathbb F_q(t)})$ in a maximal compact subgroup. For a normalized Hecke eigenfunction $f$ on
$$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-007",
"literature-status:open",
"owr-year:2020"
] | The universal function-field asymptotic with a power saving is stated as Question 6; the report gives only a split-case calculation and suspicion that the formula is correct. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Fix a quaternion algebra $D$ over $\mathbb F_q(t)$. Let $F/\mathbb F_q(t)$ vary over quadratic extensions of genus $g$, let $K\subset D^\times(\mathbb A_F)$ be compact, and let $m$ be the index of $K\cap D^\times(\mathbb A_{\mathbb F_q(t)})$ in a maximal compact subgroup. For a normalized Hecke eigenfunction $f$ on
$$... | In the same function-field setting, do there exist universal constants C and \delta>0 such that, for every y\in D^{\times}(\mathbb A_{\mathbb F_q(t)}), f(y)=\int_{D^{\times}(\mathbb F_q(t))\backslash D^{\times}(\mathbb A_{\mathbb F_q(t)})}f(x) d\mu(x)+O(m^Cq^{(1-\delta)g/2}), with the implicit constant independent of F... | corrected_verified | The official report was checked. The common setup is supplied by the canonical neighboring record OWR-1703872-006, and the exact dependence of all constants is retained. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,502 | OWR-1703872-010 | Sharp Moments of Zeta and Character Averages | Are both estimates below sharp for every $0\leq q\leq1$?
$$\frac1T\int_T^{2T}\left(\int_{-1/2}^{1/2}|\zeta(1/2+it+ih)|^2\,dh\right)^qdt
\ll\left(\frac{\log T}{1+(1-q)\sqrt{\log\log T}}\right)^q,$$
and, for a prime $r$, $1\leq x\leq r$, and $L=\min\{x,r/x\}$,
$$\frac1{r-2}\sum_{\substack{\chi\ ({\rm mod}\ r)\\\chi\ne... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-010",
"literature-status:open",
"owr-year:2020"
] | The sharpness assertion is explicitly stated as a conjecture in the source, and no primary result establishing both sharp bounds was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Are both estimates below sharp for every $0\leq q\leq1$?
$$\frac1T\int_T^{2T}\left(\int_{-1/2}^{1/2}|\zeta(1/2+it+ih)|^2\,dh\right)^qdt
\ll\left(\frac{\log T}{1+(1-q)\sqrt{\log\log T}}\right)^q,$$
and, for a prime $r$, $1\leq x\leq r$, and $L=\min\{x,r/x\}$,
$$\frac1{r-2}\sum_{\substack{\chi\ ({\rm mod}\ r)\\\chi\ne... | Harper conjectures that both stated upper bounds for the q-th moments of the Riemann-zeta averages and Dirichlet-character averages are sharp, including their displayed logarithmic factors. | corrected_verified | The official report was checked. Both conjecturally sharp moment bounds and every parameter were restored in place of the dangling “stated upper bounds.” | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,503 | OWR-1703872-011 | Plancherel Volumes of Rankin–Selberg Metric Balls | For the local Rankin–Selberg pseudometric on irreducible supercuspidal representations of $\operatorname{GL}_n(F)$, what is the Plancherel measure of the ball $B_r(\pi)$ of radius $r$ centered at $\pi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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-1703872-011",
"literature-status:open",
"owr-year:2020"
] | The Plancherel-measure question for the stated ball in the supercuspidal representation space is left as a natural question, with no cited computation resolving it. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | For the local Rankin–Selberg pseudometric on irreducible supercuspidal representations of $\operatorname{GL}_n(F)$, what is the Plancherel measure of the ball $B_r(\pi)$ of radius $r$ centered at $\pi$? | For the local Rankin--Selberg pseudometric on irreducible supercuspidal representations of GL_n(F), what is the Plancherel measure of the ball B_r(\pi) of radius r centered at \pi? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,504 | OWR-1703872-012 | Short-Interval Möbius Orthogonality to Polynomial Phases | For every $k\geq1$ and every $H=H(X)\to\infty$ as $X\to\infty$, is it true that for almost all $x\in[X,2X]$, $\sup_{P\in\mathbb{R}[t], \deg P=k}\left|\sum_{x\leq n\leq x+H}\mu(n)e(P(n))\right|=o(H)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-012",
"literature-status:open",
"owr-year:2020"
] | The full short-interval polynomial-phase conjecture allows arbitrarily slowly growing intervals; primary work proves only power-scale ranges, and the logarithmic-scale barrier remains. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
},
{
"url": "https://arxiv.org/abs/2007.15644",
"label": "Higher uniformity of bounded multiplicative functions"
},
{
"url": "https://arxiv.org/abs/2411.05770",
"label": "Higher uniformity of arithm... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | For every $k\geq1$ and every $H=H(X)\to\infty$ as $X\to\infty$, is it true that for almost all $x\in[X,2X]$, $\sup_{P\in\mathbb{R}[t], \deg P=k}\left|\sum_{x\leq n\leq x+H}\mu(n)e(P(n))\right|=o(H)$? | For every k\geq1 and every H=H(X)\to\infty as X\to\infty, is it true that for almost all x\in[X,2X], \sup_{P\in\mathbb R[t], \deg P=k}\left|\sum_{x\leq n\leq x+H}\mu(n)e(P(n))\right|=o(H)? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,505 | OWR-1703872-013 | Short-Interval Möbius Orthogonality to Nilsequences | Let $G/\Gamma$ be a nilmanifold of degree $k\geq1$ and $H=H(X)\to\infty$. For every fixed Lipschitz map $F:G/\Gamma\to\mathbb{C}$, is it true that for almost all $x\in[X,2X]$, $\sup_{g\in\operatorname{Poly}(\mathbb{Z}\to G)}\left|\sum_{x\leq n\leq x+H}\mu(n)F(g(n)\Gamma)\right|=o(H)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-013",
"literature-status:open",
"owr-year:2020"
] | The full nilsequence uniformity conjecture for intervals of arbitrary diverging length remains open; the main theorem establishes a substantial power-scale range but not the stated endpoint. | [
{
"url": "https://doi.org/10.4171/owr/2020/26",
"label": "Oberwolfach Report 26/2020"
},
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"url": "https://arxiv.org/abs/2007.15644",
"label": "Higher uniformity of bounded multiplicative functions"
},
{
"url": "https://arxiv.org/abs/2411.05770",
"label": "Higher uniformity of arithm... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Let $G/\Gamma$ be a nilmanifold of degree $k\geq1$ and $H=H(X)\to\infty$. For every fixed Lipschitz map $F:G/\Gamma\to\mathbb{C}$, is it true that for almost all $x\in[X,2X]$, $\sup_{g\in\operatorname{Poly}(\mathbb{Z}\to G)}\left|\sum_{x\leq n\leq x+H}\mu(n)F(g(n)\Gamma)\right|=o(H)$? | Let G/\Gamma be a nilmanifold of degree k\geq1 and H=H(X)\to\infty. For every fixed Lipschitz map F:G/\Gamma\to\mathbb C, is it true that for almost all x\in[X,2X], \sup_{g\in\operatorname{Poly}(\mathbb Z\to G)}\left|\sum_{x\leq n\leq x+H}\mu(n)F(g(n)\Gamma)\right|=o(H)? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,506 | OWR-1703872-016 | Sphere-Packing Bounds and Fourier Eigenfunction Constructions | The linear-programming upper bound for sphere-packing density in $\mathbb R^n$ is conjectured to be $2^{-(\lambda+o(1))n}$ with $\lambda\approx0.6044$, and there is conjectured to exist a nonzero Schwartz function $f:\mathbb R^2\times\mathbb R^2\to\mathbb R$ with $f(0,0)=0$, $\widehat f=-f$, and $f(x,y)\geq0$ whenever ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,020 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-016",
"literature-status:open",
"owr-year:2020"
] | The asymptotic linear-programming exponent near 0.6044 is supported by numerical extrapolation, while the primary paper explicitly leaves the conjecture unproved and the classical 0.5990 exponent remains the best general bound. | [
{
"url": "https://doi.org/10.1007/JHEP12(2020)066",
"label": "High-dimensional sphere packing and the modular bootstrap"
},
{
"url": "https://cohn.mit.edu/modular-bootstrap/",
"label": "Henry Cohn modular-bootstrap status page"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | The linear-programming upper bound for sphere-packing density in $\mathbb R^n$ is conjectured to be $2^{-(\lambda+o(1))n}$ with $\lambda\approx0.6044$, and there is conjectured to exist a nonzero Schwartz function $f:\mathbb R^2\times\mathbb R^2\to\mathbb R$ with $f(0,0)=0$, $\widehat f=-f$, and $f(x,y)\geq0$ whenever ... | The linear-programming upper bound for sphere-packing density in \mathbb R^n is conjectured to be 2^{-(\lambda+o(1))n} with \lambda\approx0.6044, and there is conjectured to exist a nonzero Schwartz function f:\mathbb R^2\times\mathbb R^2\to\mathbb R with f(0,0)=0,\widehat f=-f, and f(x,y)\geq0 whenever |x|^2-|y|^2\in2... | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,507 | OWR-1703872-017 | Subconvexity for Symmetric-Square L-Functions | Let $u_j$ be a Hecke--Maass cusp form on $\mathrm{SL}_2(\mathbb{Z})$ with Laplace eigenvalue $1/4 + t_j^2$, and let $L(\operatorname{sym}^2 u_j, s)$ be its symmetric-square $L$-function. Prove a subconvexity bound in the spectral $t_j$-aspect at the central point $s = 1/2$, i.e., $L(\operatorname{sym}^2 u_j, 1/2) \ll t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,020 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-017",
"literature-status:partially-solved",
"owr-year:2020"
] | Subconvexity is proved in off-central or mixed ranges and strong moments are known, but subconvexity at the central point in the spectral parameter remains the outstanding problem identified in the record. | [
{
"url": "https://arxiv.org/abs/2009.08419",
"label": "Moments and hybrid subconvexity for symmetric-square L-functions"
},
{
"url": "https://arxiv.org/abs/2302.07236",
"label": "Subconvexity for symmetric-square L-functions off-centre"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | Let $u_j$ be a Hecke--Maass cusp form on $\mathrm{SL}_2(\mathbb{Z})$ with Laplace eigenvalue $1/4 + t_j^2$, and let $L(\operatorname{sym}^2 u_j, s)$ be its symmetric-square $L$-function. Prove a subconvexity bound in the spectral $t_j$-aspect at the central point $s = 1/2$, i.e., $L(\operatorname{sym}^2 u_j, 1/2) \ll t... | Prove a subconvexity bound in the t_j-aspect for the symmetric-square L-function L(\operatorname{sym}^2u_j,1/2). | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,508 | OWR-1703872-019 | Fourier Uniqueness from Vanishing on General Surfaces | For Fourier-uniqueness problems in which a test function and its Fourier transform vanish on prescribed spheres, do analogous uniqueness or integration-by-parts results hold when the vanishing sets are replaced by other surfaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383](https://doi.org/10.4171/owr/2020/26)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,020 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703872-019",
"literature-status:partially-solved",
"owr-year:2020"
] | Uniqueness is proved for concentric spherical shells and for several perturbations of those spheres, but the broad question about arbitrary other surfaces remains open. | [
{
"url": "https://arxiv.org/abs/2002.11627",
"label": "Fourier interpolation from spheres"
},
{
"url": "https://arxiv.org/abs/2103.12015",
"label": "Perturbed Fourier uniqueness and interpolation"
},
{
"url": "https://doi.org/10.1073/pnas.2023227118",
"label": "Fourier uniqueness in ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/26 | null | null | null | For Fourier-uniqueness problems in which a test function and its Fourier transform vanish on prescribed spheres, do analogous uniqueness or integration-by-parts results hold when the vanishing sets are replaced by other surfaces? | For Fourier-uniqueness problems in which a test function and its Fourier transform vanish on prescribed spheres, do analogous uniqueness or integration-by-parts results hold when the vanishing sets are replaced by other surfaces? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Automorphic Forms and Arithmetic (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/26, pp. 1317--1383 |
30,004,509 | OWR-1703875-001 | Nondissipative Dynamics from Antisymmetric Large Deviations | Does the dynamics generated by the time-antisymmetric large-deviation rate function $L_F^{\mathrm{asym}}$ provide a counterpart of gradient flow that describes purely nondissipative dynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467](https://doi.org/10.4171/owr/2020/29)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,020 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-1703875-001",
"literature-status:open",
"owr-year:2020"
] | The abstract Hamiltonian or non-dissipative interpretation remains a conjecture; later work proves it only in selected particle models and leaves the general framework formal. | [
{
"url": "https://publications.imp.fu-berlin.de/2564/1/2103.14384.pdf",
"label": "Patterson--Renger--Sharma, Variational Structures Beyond Gradient Flows"
},
{
"url": "https://ems.press/content/serial-article-files/46865",
"label": "Oberwolfach Reports 2020/29"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/29 | null | null | null | Does the dynamics generated by the time-antisymmetric large-deviation rate function $L_F^{\mathrm{asym}}$ provide a counterpart of gradient flow that describes purely nondissipative dynamics? | The dynamics generated by the time-antisymmetric large-deviation rate function L_F^{\mathrm{asym}} should be a counterpart of a gradient flow and should describe purely nondissipative dynamics. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467 |
30,004,510 | OWR-1703875-002 | Force-Flux Gradient Structures for Finite-State Markov Chains | Do analogous force–flux, large-deviation, and gradient-flow structures exist for finite-state Markov chains, including in the irreversible case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467](https://doi.org/10.4171/owr/2020/29)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,020 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 update, 2026-10-16] Source-scope clarification for OWR-1703875-002: finite Markov-chain structures | [
"owr",
"oberwolfach-reports",
"OWR-1703875-002",
"literature-status:partially-solved",
"owr-year:2020"
] | Markov-chain large-deviation and gradient-flow structures are established for independent jump processes and several particle systems, but no general Markov-chain theorem settles the question. | [
{
"url": "https://arxiv.org/abs/1312.7591",
"label": "Mielke--Renger--Peletier, Markov Chains and Diffusion"
},
{
"url": "https://link.springer.com/article/10.1007/s10955-024-03233-8",
"label": "Patterson--Renger--Sharma, Journal of Statistical Physics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/29 | null | null | null | Do analogous force–flux, large-deviation, and gradient-flow structures exist for finite-state Markov chains, including in the irreversible case? | Do analogous force--flux, large-deviation, and gradient-flow structures exist for finite-state Markov chains, including in the irreversible case? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467 |
30,004,511 | OWR-1703875-003 | Sharp Waiting-Time Estimates for Variational PDE Discretizations | Can the variational/Lagrangian approach for the porous-medium and thin-film equations be sharpened to give mesh-independent, quantitatively sharper estimates for the waiting-time phenomenon and to match the observed behavior of adapted discretization meshes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467](https://doi.org/10.4171/owr/2020/29)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,020 | 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-1703875-003",
"literature-status:open",
"owr-year:2020"
] | The phenomenon is rigorously analyzed for spatially discretized porous-medium and thin-film equations, but the record's broader numerical-fidelity claim is not a general theorem. | [
{
"url": "https://doi.org/10.1137/19M1300017",
"label": "Fischer--Matthes, SIAM Journal on Numerical Analysis"
},
{
"url": "https://arxiv.org/abs/1911.04185",
"label": "Fischer--Matthes, preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/29 | null | null | null | Can the variational/Lagrangian approach for the porous-medium and thin-film equations be sharpened to give mesh-independent, quantitatively sharper estimates for the waiting-time phenomenon and to match the observed behavior of adapted discretization meshes? | Can the variational/Lagrangian approach for the porous-medium and thin-film equations be sharpened to give mesh-independent, quantitatively sharper estimates for the waiting-time phenomenon and to match the observed behavior of adapted discretization meshes? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Variational Methods for Evolution (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/29, pp. 1391--1467 |
30,004,512 | OWR-1703876-005 | Helly–Radon–Tverberg Theory for Nonconvex Systems | For nonconvex set systems or their associated closure operators, what general Helly–Radon–Tverberg, fractional-Helly, weak-$\varepsilon$-net, and $(p,q)$-type theorems and quantitative bounds can be obtained? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,020 | 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-1703876-005",
"literature-status:partially-solved",
"owr-year:2020"
] | Betti-number and topological-complexity hypotheses yield Radon and Helly-type bounds for many nonconvex families, while the unrestricted question remains open. | [
{
"url": "https://doi.org/10.4230/LIPIcs.SoCG.2020.61",
"label": "Patakova, Bounding Radon Numbers via Betti Numbers"
},
{
"url": "https://arxiv.org/abs/1908.01677",
"label": "Patakova, preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | For nonconvex set systems or their associated closure operators, what general Helly–Radon–Tverberg, fractional-Helly, weak-$\varepsilon$-net, and $(p,q)$-type theorems and quantitative bounds can be obtained? | For nonconvex set systems or their associated closure operators, what general Helly--Radon--Tverberg, fractional-Helly, weak-\varepsilon-net, and (p,q)-type theorems and quantitative bounds can be obtained? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,513 | OWR-1703876-006 | Sharp Constrained-Drawing Bounds for Closure Operators | Let $\operatorname{cl}$ be a closure operator on $\mathbb R^2$ such that $\operatorname{cl}(S)$ has at most $b$ path-connected components for every finite $S\subset\mathbb R^2$. Are $kb+1$ points always sufficient to obtain a constrained drawing of the star $K_{1,k}$? What sharper bounds hold for constrained drawings o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23062843",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **A Proof of Paták's kb+1 Conjecture for Constrained Stars, with Improved Bounds for Complete Graphs** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23062843) | [
"owr",
"oberwolfach-reports",
"OWR-1703876-006",
"literature-status:open",
"owr-year:2020"
] | The available bound for a constrained star is quadratic in b, while the conjectured kb+1 bound is still posed as an open improvement. | [
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | Let $\operatorname{cl}$ be a closure operator on $\mathbb R^2$ such that $\operatorname{cl}(S)$ has at most $b$ path-connected components for every finite $S\subset\mathbb R^2$. Are $kb+1$ points always sufficient to obtain a constrained drawing of the star $K_{1,k}$? What sharper bounds hold for constrained drawings o... | For a closure operator on a space with at most b path-connected components in each closure, is the conjectured bound kb+1 sufficient to find a constrained drawing of the star K_{1,k}; can the bounds for constrained drawings of K_n be improved; and can the method handle nontrivial homology or homotopy in higher dimensio... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,514 | OWR-1703876-007 | Barycentric Hyperplanes Through Convex Body Centroids | If $K\subset\mathbb{R}^n$ is a convex body, does the barycenter of $K$ always lie on at least $n+1$ distinct barycentric hyperplanes, meaning hyperplanes through it for which it is the barycenter of the corresponding section $K\cap h$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 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-1703876-007",
"literature-status:open",
"owr-year:2020"
] | The proposed n+1 barycentric-cut statement was reopened after a proof error; only lower bounds such as four cuts in dimensions at least three are known. | [
{
"url": "https://doi.org/10.4230/LIPIcs.SoCG.2020.62",
"label": "Patakova--Tancer--Wagner, Barycentric Cuts"
},
{
"url": "https://arxiv.org/abs/2003.13536",
"label": "Patakova--Tancer--Wagner, preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | If $K\subset\mathbb{R}^n$ is a convex body, does the barycenter of $K$ always lie on at least $n+1$ distinct barycentric hyperplanes, meaning hyperplanes through it for which it is the barycenter of the corresponding section $K\cap h$? | If K\subset\mathbb R^n is a convex body, does the barycenter of K always lie on at least n+1 distinct barycentric hyperplanes, meaning hyperplanes through it for which it is the barycenter of the corresponding section K\cap h? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
30,004,515 | OWR-1703876-008 | Tverberg Depth Bounds from Tukey Depth | For a finite point set $S\subset\mathbb{R}^d$ and $q\in\mathbb{R}^d$, is the Tverberg depth conjecturally bounded below by $\operatorname{TvD}(S,q)\geq\frac{1}{d-1}\operatorname{TD}(S,q)$ for $d\geq 2$, with this bound being tight? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528](https://doi.org/10.4171/owr/2020/30)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,020 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 literature review, 2026-10-10] **replace "for d ≥ 2" by "for d ≥ 3"**. P. Schnider, Oberwolfach Report 30/2020, p. 1504: the bound TvD(S, q) ≥ TD(S, q)/(d−1) is conjectured for higher dimensions only; for the plane it states TvD(S, q) = min{TD(S, q), |S|/3}. For d = 2 the inequality would read TvD ≥ TD, ... | [
"owr",
"oberwolfach-reports",
"OWR-1703876-008",
"literature-status:open",
"owr-year:2020"
] | The general bound TvD greater than or equal to TD divided by d is known, but the stronger conjectured factor 1 divided by d-1 is not settled. | [
{
"url": "https://link.springer.com/article/10.1007/s00493-023-00045-4",
"label": "Schnider, Enclosing Depth and Other Depth Measures"
},
{
"url": "https://ems.press/content/serial-article-files/46867",
"label": "Oberwolfach Reports 2020/30"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/30 | null | null | null | For a finite point set $S\subset\mathbb{R}^d$ and $q\in\mathbb{R}^d$, is the Tverberg depth conjecturally bounded below by $\operatorname{TvD}(S,q)\geq\frac{1}{d-1}\operatorname{TD}(S,q)$ for $d\geq 2$, with this bound being tight? | For a finite point set S\subset\mathbb R^d and q\in\mathbb R^d, is the Tverberg depth conjecturally bounded below by \operatorname{TvD}(S,q)\geq\frac{1}{d-1}\operatorname{TD}(S,q) for d\geq2, with this bound being tight? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Discrete Geometry (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/30, pp. 1469--1528 |
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