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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,616 | OWR-4990375-007 | Paramodular Correspondence for Abelian Surfaces and Fourfolds | For $N\in\mathbb N$, let $A_N$ be the isogeny classes of abelian surfaces over $\mathbb Q$ of conductor $N$ with $\operatorname{End}_{\mathbb Q}(A)=\mathbb Z$, let $B_N$ be the isogeny classes of quaternionic-multiplication abelian fourfolds over $\mathbb Q$ of conductor $N^2$, and let $P_N$ be the cuspidal nonlift Sie... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-4990375-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990375-007",
"literature-status:open",
"owr-year:2021"
] | The stated abelian-surface and quaternionic-multiplication fourfold parametrization is the Brumer--Kramer paramodular conjecture and is still not established for all levels and forms. | [
{
"url": "https://arxiv.org/abs/1004.4699",
"label": "Brumer--Kramer, paramodular conjecture"
},
{
"url": "https://arxiv.org/abs/2502.20645",
"label": "Boxer--Calegari--Gee--Pilloni, modularity theorems"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | For $N\in\mathbb N$, let $A_N$ be the isogeny classes of abelian surfaces over $\mathbb Q$ of conductor $N$ with $\operatorname{End}_{\mathbb Q}(A)=\mathbb Z$, let $B_N$ be the isogeny classes of quaternionic-multiplication abelian fourfolds over $\mathbb Q$ of conductor $N^2$, and let $P_N$ be the cuspidal nonlift Sie... | For N\in\mathbb N, let A_N be the isogeny classes of abelian surfaces over \mathbb Q of conductor N with End_\mathbb Q(A)=\mathbb Z, let B_N be the isogeny classes of quaternionic-multiplication abelian fourfolds over \mathbb Q of conductor N^2, and let P_N be suitable cuspidal nonlift Siegel paramodular newforms of le... | 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 | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,617 | OWR-4990375-008 | Paramodular Correspondence for Abelian Surfaces and Fourfolds | For N\in\mathbb N, let A_N be the isogeny classes of abelian surfaces over \mathbb Q of conductor N with End_\mathbb Q(A)=\mathbb Z, let B_N be the isogeny classes of quaternionic-multiplication abelian fourfolds over \mathbb Q of conductor N^2, and let P_N be suitable cuspidal nonlift Siegel paramodular newforms of le... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the detailed paramodular correspondence retained in OWR-4990375-007. No ) | [
"OWR-4990375-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990375-008",
"literature-status:open",
"owr-year:2021"
] | This fragment introduces the quaternionic-multiplication and suitable-paramodular-form cases of the full paramodular conjecture; later modularity results remain conditional or restricted and do not prove the global bijection. | [
{
"url": "https://arxiv.org/abs/1004.4699",
"label": "Brumer--Kramer, paramodular conjecture"
},
{
"url": "https://arxiv.org/abs/2502.20645",
"label": "Boxer--Calegari--Gee--Pilloni, modularity theorems"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | null | For N\in\mathbb N, let A_N be the isogeny classes of abelian surfaces over \mathbb Q of conductor N with End_\mathbb Q(A)=\mathbb Z, let B_N be the isogeny classes of quaternionic-multiplication abelian fourfolds over \mathbb Q of conductor N^2, and let P_N be suitable cuspidal nonlift Siegel paramodular newforms of le... | unrecoverable | The official report confirms that this is a duplicate extraction of the detailed paramodular correspondence retained in OWR-4990375-007. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,618 | OWR-4990375-010 | Kodaira Dimension of Odd Minimal Strata | For $g\geq12$, do the odd components of the minimal strata $\mathbb P\Omega\mathcal M_g(2g-2)^{\mathrm{odd}}$ have maximal Kodaira dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,021 | 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-4990375-011"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990375-010",
"literature-status:partially-solved",
"owr-year:2021"
] | The odd-spin minimal strata are proved to be of general type for genus greater than 12, but the report's threshold including genus 12 is not fully settled by that result. | [
{
"url": "https://arxiv.org/abs/2204.11943",
"label": "Chen--Costantini--Moller, Kodaira dimension"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | For $g\geq12$, do the odd components of the minimal strata $\mathbb P\Omega\mathcal M_g(2g-2)^{\mathrm{odd}}$ have maximal Kodaira dimension? | For g\geq 12, do the odd components of the minimal strata \mathbb P\Omega\mathcal M_g(2g-2)^{\mathrm{odd}} have maximal Kodaira dimension? | 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 | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,619 | OWR-4990375-011 | Kodaira Dimension of Odd Minimal Strata | For g\geq 12, do the odd components of the minimal strata \mathbb P\Omega\mathcal M_g(2g-2)^{\mathrm{odd}} have maximal Kodaira dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the Kodaira-dimension conjecture retained in OWR-4990375-010. No separat) | [
"OWR-4990375-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990375-011",
"literature-status:partially-solved",
"owr-year:2021"
] | The divisor and singularity program yields general type for the odd minimal strata in genus greater than 12, while the full conjectural range and remaining boundary cases are unresolved. | [
{
"url": "https://arxiv.org/abs/2204.11943",
"label": "Chen--Costantini--Moller, Kodaira dimension"
},
{
"url": "https://arxiv.org/abs/2410.18719",
"label": "Bud--Chen--Moller, even spin strata"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | null | For g\geq 12, do the odd components of the minimal strata \mathbb P\Omega\mathcal M_g(2g-2)^{\mathrm{odd}} have maximal Kodaira dimension? | unrecoverable | The official report confirms that this is a duplicate extraction of the Kodaira-dimension conjecture retained in OWR-4990375-010. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,620 | OWR-4990375-013 | Effective Surface Cone of Principally Polarized Abelian Threefolds | Is the cone $\operatorname{Eff}_2(\mathcal A_3)$ of effective surfaces on the toroidal compactification of the moduli space of principally polarized abelian threefolds equal to
$$
\mathbb R_{\geq0}S_A+\mathbb R_{\geq0}S_F+\mathbb R_{\geq0}S_D+\mathbb R_{\geq0}\sigma_{K3+1}+\mathbb R_{\geq0}\sigma_{C4}
$$
? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 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-4990375-013",
"literature-status:open",
"owr-year:2021"
] | The five displayed effective rays are known to be extremal, but the claimed equality for the effective cone of surfaces on the genus-three compactification remains a conjecture. | [
{
"url": "https://arxiv.org/abs/2007.02995",
"label": "Grushevsky--Hulek, effective surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | Is the cone $\operatorname{Eff}_2(\mathcal A_3)$ of effective surfaces on the toroidal compactification of the moduli space of principally polarized abelian threefolds equal to
$$
\mathbb R_{\geq0}S_A+\mathbb R_{\geq0}S_F+\mathbb R_{\geq0}S_D+\mathbb R_{\geq0}\sigma_{K3+1}+\mathbb R_{\geq0}\sigma_{C4}
$$
? | Is the codimension-two effective cone of the moduli space of principally polarized abelian threefolds equal to the cone generated by the five surfaces S_A, S_F, S_D, \sigma K3+1, and \sigma C4? | 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 | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,621 | OWR-4990375-014 | Codimension-Two Effective Cones of Principally Polarized Abelian Varieties | For $g\geq3$, is the cone $\operatorname{Eff}_2(\mathcal A_g)$ generated by the five surface classes $S_A$, $S_F$, $S_D$, $S_1$, and $S_2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359](https://doi.org/10.4171/owr/2021/6)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,021 | 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-4990375-014",
"literature-status:open",
"owr-year:2021"
] | The proposed generation of the effective cone of codimension-two cycles in all genera is stated as a conjecture; the available work proves extremality of several rays but not the asserted equality. | [
{
"url": "https://arxiv.org/abs/2007.02995",
"label": "Grushevsky--Hulek, effective surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2021/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/6 | null | null | null | For $g\geq3$, is the cone $\operatorname{Eff}_2(\mathcal A_g)$ generated by the five surface classes $S_A$, $S_F$, $S_D$, $S_1$, and $S_2$? | For the moduli space of principally polarized abelian varieties \mathcal A_g, is the codimension-two effective cone generated by the five surfaces S_A, S_F, S_D, S_1, and S_2? | 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 | Moduli spaces and Modular forms (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/6, pp. 301--359 |
30,004,622 | OWR-4990377-001 | Bicombing Convexity and Consistency in Metric Spaces | Does every metric space with a bicombing admit a convex bicombing, and does every metric space with a convex bicombing admit a consistent bicombing? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-001",
"literature-status:open",
"owr-year:2021"
] | The existence of a convex or consistent bicombing from an arbitrary bicombing is unresolved; a 2024 paper explicitly records the conical-to-consistent implication as an open question. | [
{
"url": "https://doi.org/10.1007/s00208-024-02905-w",
"label": "A non-compact convex hull"
},
{
"url": "https://arxiv.org/abs/2005.13941",
"label": "Basso, conical bicombings"
},
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Does every metric space with a bicombing admit a convex bicombing, and does every metric space with a convex bicombing admit a consistent bicombing? | Does every metric space with a bicombing admit a convex bicombing, and does every metric space with a convex bicombing admit a consistent bicombing? | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,623 | OWR-4990377-002 | Canonical Bicombings and Group Actions on Injective Spaces | For an injective metric space $X$, consider its canonical embedding $X=E(X)\to\Delta(X)$ and retraction $\Delta(X)\to E(X)$. Is the induced bicombing convex or consistent? Can a compact metric space admit distinct consistent bicombings? Must a group acting geometrically on an injective space be Helly, CAT(0), or biauto... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-002",
"literature-status:open",
"owr-year:2021"
] | The compound list contains unresolved questions about Artin groups, injective hulls, Helly actions, and buildings; current work gives classes and partial cases rather than answers to the full list. | [
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
},
{
"url": "https://www.numdam.org/item/10.5802/aif.3524.pdf",
"label": "XXL type Artin groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | For an injective metric space $X$, consider its canonical embedding $X=E(X)\to\Delta(X)$ and retraction $\Delta(X)\to E(X)$. Is the induced bicombing convex or consistent? Can a compact metric space admit distinct consistent bicombings? Must a group acting geometrically on an injective space be Helly, CAT(0), or biauto... | For an injective metric space X with its canonical embedding X=E(X)\to\Delta(X) and retraction \Delta(X)\to E(X), can one obtain more information, in particular whether the induced bicombing is convex or consistent; can compact metric spaces have different consistent bicombings; and do groups acting geometrically on in... | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,624 | OWR-4990377-003 | Artin Groups in Helly and Injective Geometry | Which two-dimensional Artin groups of hyperbolic type are virtually Helly; which Artin groups act properly on CAT(0) cube complexes; are parabolic subgroups stable under intersection; is the complex of proper parabolic two-dimensional Artin subgroups NPC; is the three-generator all-label-3 Artin group Helly; are all tw... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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"
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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-4990377-003",
"literature-status:open",
"owr-year:2021"
] | The listed Artin-group questions remain a mixed research program; recent results settle selected subclasses, while the general cubulation, systolic, hierarchical-hyperbolicity, and injective-space questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
},
{
"url": "https://www.numdam.org/item/10.5802/aif.3524.pdf",
"label": "XXL type Artin groups"
},
{
"url": "https://doi.org/10.4171/GGD/648",
"label": "Haettel, triangle-free Artin groups"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Which two-dimensional Artin groups of hyperbolic type are virtually Helly; which Artin groups act properly on CAT(0) cube complexes; are parabolic subgroups stable under intersection; is the complex of proper parabolic two-dimensional Artin subgroups NPC; is the three-generator all-label-3 Artin group Helly; are all tw... | Which two-dimensional Artin groups of hyperbolic type are virtually Helly; which Artin groups act properly on CAT(0) cube complexes; are parabolic subgroups stable under intersection; is the complex of proper parabolic two-dimensional Artin subgroups NPC; is the three-generator all-label-3 Artin group Helly; are all tw... | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,625 | OWR-4990377-004 | Non-Helly Coarse-Helly Actions and Coarse-Median Artin Groups | Does there exist a group acting geometrically on a coarse Helly graph that is not Helly, and which Artin groups are coarse median? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-004",
"literature-status:open",
"owr-year:2021"
] | The existence of a group acting geometrically on a coarse-Helly graph without being Helly is not settled in general, and the classification of coarse-median Artin groups also remains incomplete. | [
{
"url": "https://arxiv.org/abs/2012.03246",
"label": "Osajda--Valiunas, coarse Helly groups"
},
{
"url": "https://msp.org/gt/2025/29-1/gt-v29-n1-p01-s.pdf",
"label": "Helly groups 2025"
},
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Does there exist a group acting geometrically on a coarse Helly graph that is not Helly, and which Artin groups are coarse median? | Does there exist a group acting geometrically on a coarse Helly graph that is not Helly, and which Artin groups are coarse median? | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,626 | OWR-4990377-005 | Fixed Points for Infinite-Dimensional Locally Elliptic Actions | When does a locally elliptic action on an infinite-dimensional CAT(0) cube complex have a global fixed point? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-005",
"literature-status:open",
"owr-year:2021"
] | The regularizability implication for finitely generated Cremona subgroups and the fixed-point question for locally elliptic actions are not resolved over general fields or infinite-dimensional complexes. | [
{
"url": "https://doi.org/10.5802/jep.271",
"label": "Lonjou--Przytycki--Urech, Cremona subgroups"
},
{
"url": "https://arxiv.org/abs/2110.14605",
"label": "Genevois--Lonjou--Urech, finite-field regularisation"
},
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach r... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | When does a locally elliptic action on an infinite-dimensional CAT(0) cube complex have a global fixed point? | If a finitely generated subgroup G of the Cremona group has every element regularizable, must G itself be regularizable, and when do locally elliptic actions on infinite-dimensional CAT(0) cube complexes have global fixed points? | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,627 | OWR-4990377-006 | Fixed Points, Expanding Combings, and Lattices in Metric Geometry | Does every locally elliptic action of a finitely generated group on a finite-dimensional CAT(0) space, in particular on a Euclidean building of arbitrary dimension, have a global fixed point; does the analogous statement hold for finite-dimensional Helly complexes; do central extensions of hyperbolic groups admit coher... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-006",
"literature-status:open",
"owr-year:2021"
] | The compound questions remain open in their stated generality; low-dimensional fixed-point theorems and examples of proper actions do not settle arbitrary-dimensional buildings, combings, or lattice-generation questions. | [
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.4171/GGD/648",
"label": "Haettel, triangle-free Artin groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Does every locally elliptic action of a finitely generated group on a finite-dimensional CAT(0) space, in particular on a Euclidean building of arbitrary dimension, have a global fixed point; does the analogous statement hold for finite-dimensional Helly complexes; do central extensions of hyperbolic groups admit coher... | Does every locally elliptic action of a finitely generated group on a finite-dimensional CAT(0) space, in particular on a Euclidean building of arbitrary dimension, have a global fixed point; does the analogous statement hold for finite-dimensional Helly complexes; do central extensions of hyperbolic groups admit coher... | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,628 | OWR-4990377-009 | Fixed Subgroups of Right-Angled Artin Group Automorphisms | Given a right-angled Artin group $A_\Gamma$ and an automorphism $\phi\in\operatorname{Aut}(A_\Gamma)$, what can be said about the fixed subgroup $\operatorname{Fix}(\phi)\leq A_\Gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-009",
"literature-status:open",
"owr-year:2021"
] | Fixed subgroups are understood for important subclasses, but unrestricted automorphisms of general Artin or right-angled Artin groups remain unresolved; recent work explicitly poses the unrestricted large-type case as open. | [
{
"url": "https://arxiv.org/abs/2407.11839",
"label": "Jones--Vaskou, fixed subgroups in Artin groups"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.07.006",
"label": "Lei--Zhang, fixed subgroups"
},
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Given a right-angled Artin group $A_\Gamma$ and an automorphism $\phi\in\operatorname{Aut}(A_\Gamma)$, what can be said about the fixed subgroup $\operatorname{Fix}(\phi)\leq A_\Gamma$? | Given a right-angled Artin group A_\Gamma and an automorphism \phi\in\operatorname{Aut}(A_\Gamma), what can be said about the fixed subgroup Fix(\phi)\leq A_\Gamma? | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,629 | OWR-4990377-011 | Simultaneous Regularization of Cremona Subgroups | Let $G$ be a finitely generated subgroup of the plane Cremona group such that every element of $G$ is regularizable. Must $G$ itself be regularizable, equivalently conjugate to a subgroup of the automorphism group of a surface? Equivalently, must its locally elliptic action on the blow-up complex be globally elliptic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417](https://doi.org/10.4171/owr/2021/8)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 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-4990377-011",
"literature-status:open",
"owr-year:2021"
] | The regularizability implication is proved over finite fields, but published recent work states that the general-field question remains unknown. | [
{
"url": "https://doi.org/10.5802/jep.271",
"label": "Lonjou--Przytycki--Urech, Cremona subgroups"
},
{
"url": "https://arxiv.org/abs/2110.14605",
"label": "Genevois--Lonjou--Urech, finite-field regularisation"
},
{
"url": "https://doi.org/10.4171/owr/2021/8",
"label": "Oberwolfach r... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/8 | null | null | null | Let $G$ be a finitely generated subgroup of the plane Cremona group such that every element of $G$ is regularizable. Must $G$ itself be regularizable, equivalently conjugate to a subgroup of the automorphism group of a surface? Equivalently, must its locally elliptic action on the blow-up complex be globally elliptic? | Let G be a finitely generated subgroup of the Cremona group such that every element of G is regularizable. Must G be regularizable, meaning a subgroup of the automorphism group of a surface; equivalently, must its locally elliptic action on the blow-up complex be globally elliptic? | 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 | Nonpositively Curved Complexes (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/8, pp. 383--417 |
30,004,630 | OWR-4990378-001 | Quadratic Growth without Quadratic Control Regularization | For distributed optimal control of the $H^1$-critical defocusing wave equation on a bounded domain in $\mathbb R^3$, do the strong quadratic-growth property and the resulting stability estimates remain valid when $\beta_2=0$, so that the objective has no quadratic $L^2$ control penalty? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Challenges in Optimization with Complex PDE-Systems (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/9, pp. 419--506](https://doi.org/10.4171/owr/2021/9)
## Literature review (checked 202... | 3 | open | null | 2,021 | 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-4990378-001",
"literature-status:open",
"owr-year:2021"
] | The cited optimal-control analysis still requires a positive quadratic control regularization coefficient; the beta-2 equal to zero case remains explicitly open. | [
{
"url": "https://doi.org/10.4171/owr/2021/9",
"label": "Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/46884?nt=1",
"label": "Challenges in optimal control"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/9 | null | null | null | For distributed optimal control of the $H^1$-critical defocusing wave equation on a bounded domain in $\mathbb R^3$, do the strong quadratic-growth property and the resulting stability estimates remain valid when $\beta_2=0$, so that the objective has no quadratic $L^2$ control penalty? | In the quadratic-growth analysis for the stated PDE optimal-control problem, can the strong quadratic-growth and stability results be extended from the fully quadratic regularization case \beta_2>0 to the open case \beta_2=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 | Challenges in Optimization with Complex PDE-Systems (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/9, pp. 419--506 |
30,004,631 | OWR-4990379-001 | Smooth Optimal Transport Estimation beyond Dimensionality | Can strong smoothness assumptions on the probability distributions be used to overcome the curse of dimensionality in statistical estimation of optimal transport? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | partially_solved | null | 2,021 | 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-4990379-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Dimension-free statistical and computational rates are known for sufficiently smooth optimal transport estimation, but a general lifting of the curse of dimensionality and dimension-robust constants remain unresolved. | [
{
"url": "https://proceedings.mlr.press/v134/vacher21a.html",
"label": "Vacher et al., dimension-free smooth OT"
},
{
"url": "https://arxiv.org/abs/2505.04721",
"label": "Sparse regularized OT"
},
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | Can strong smoothness assumptions on the probability distributions be used to overcome the curse of dimensionality in statistical estimation of optimal transport? | Can strong smoothness assumptions on the probability distributions be used to overcome the curse of dimensionality in statistical estimation of optimal transport? | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,632 | OWR-4990379-002 | Global Optimality of Domain-Decomposition Transport Algorithms | For the limiting iterates of a domain-decomposition algorithm for optimal transport, what sufficient conditions on the cost function and transport data guarantee convergence to a globally optimal transport plan? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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-4990379-002",
"literature-status:open",
"owr-year:2021"
] | The asymptotic limit trajectory of the domain-decomposition algorithm can fail to be globally optimal in general, and the 2023 analysis still identifies sufficient conditions for global optimality as an open problem. | [
{
"url": "https://doi.org/10.1007/s00211-023-01347-x",
"label": "Medina--Schmitzer--Bonafini, asymptotic analysis"
},
{
"url": "https://arxiv.org/abs/2001.10986",
"label": "Bonafini--Schmitzer, entropic domain decomposition"
},
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label":... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | For the limiting iterates of a domain-decomposition algorithm for optimal transport, what sufficient conditions on the cost function and transport data guarantee convergence to a globally optimal transport plan? | For the limiting iterates of the domain-decomposition optimal-transport algorithm, what sufficient conditions on the cost and the problem ensure convergence to a globally optimal transport plan? | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,633 | OWR-4990379-003 | Lagrangian Schemes for Irregular Porous-Medium Solutions | Does convergence of the Lagrangian discretization scheme remain valid for less regular porous-medium solutions, especially when $-\nabla U'(\rho)$ is nonzero on the boundary of the support of $\rho$, as for the Barenblatt solution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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-4990379-003",
"literature-status:open",
"owr-year:2021"
] | Convergence is proved under smoothness assumptions for the discrete Wasserstein-gradient-flow scheme, but convergence for less regular solutions with a nonzero boundary force at the Barenblatt support remains unresolved. | [
{
"url": "https://arxiv.org/abs/2106.08084",
"label": "Medina--Schmitzer--Bonafini, asymptotic analysis"
},
{
"url": "https://doi.org/10.1137/21M1422756",
"label": "Gallouet--Merigot--Natale, porous-media discretization"
},
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Ob... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | Does convergence of the Lagrangian discretization scheme remain valid for less regular porous-medium solutions, especially when $-\nabla U'(\rho)$ is nonzero on the boundary of the support of $\rho$, as for the Barenblatt solution? | Does the convergence result for the Lagrangian discretization scheme remain valid for less regular solutions, especially when -\nabla U'(\rho) is nonzero on the boundary of the support of \rho, as for the Barenblatt solution of the porous-media equation? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,634 | OWR-4990379-004 | Long-Time Relations between Mean-Field Games and Aggregation Equations | What is the relationship, if any, between the long-time behavior of mean-field-game systems and that of the associated aggregation or kinetic equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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-4990379-004",
"literature-status:open",
"owr-year:2021"
] | The report identifies a fast algorithm for the branching Brownian optimal transport problem as an open question; no general Sinkhorn-type complexity result resolves it. | [
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Oberwolfach Report 10/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | What is the relationship, if any, between the long-time behavior of mean-field-game systems and that of the associated aggregation or kinetic equation? | What is the relationship, if any, between the long-time behavior of mean-field-game systems and that of the associated aggregation or kinetic equation? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,635 | OWR-4990379-005 | Monge Minimizers for Multimarginal Coulomb Transport | Do Monge-type minimizers always exist for the multimarginal optimal-transport problem with Coulomb cost? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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-4990379-005",
"literature-status:open",
"owr-year:2021"
] | Monge minimizers are known for two marginals or one dimension, while the multimarginal Coulomb problem has non-Monge minimizers and general Monge existence remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Oberwolfach Report 10/2021"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7010387/",
"label": "Infinite-body optimal transport with Coulomb cost"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | Do Monge-type minimizers always exist for the multimarginal optimal-transport problem with Coulomb cost? | Do Monge-type minimizers always exist for the multimarginal optimal-transport problem with Coulomb cost? | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,636 | OWR-4990379-006 | Polynomial-Time Point Optimization and Abrikosov Crystallization | How can one construct, in polynomial time, $N$-point configurations on a prescribed submanifold of $\mathbb R^d$ that are optimal to high accuracy, and how can large-$N$ Abrikosov crystallization, especially in two dimensions, be understood mathematically? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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-4990379-006",
"literature-status:open",
"owr-year:2021"
] | Smale's polynomial-time near-minimization problem and the large-system Abrikosov crystallization problem have substantial asymptotic and numerical progress but remain unresolved in the stated generality. | [
{
"url": "https://www.fim.uni-passau.de/fileadmin/dokumente/fakultaeten/fim/lehrstuhl/muller/SmaleProblems1998.pdf",
"label": "Smale's Mathematical Problems for the Next Century"
},
{
"url": "https://doi.org/10.1016/j.jco.2015.02.003",
"label": "Distributing many points on spheres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | How can one construct, in polynomial time, $N$-point configurations on a prescribed submanifold of $\mathbb R^d$ that are optimal to high accuracy, and how can large-$N$ Abrikosov crystallization, especially in two dimensions, be understood mathematically? | Determine how to construct, in polynomial time, N-point configurations on a prescribed submanifold of R^d that are optimal to high accuracy, and develop a mathematical understanding of large-N Abrikosov crystallization phenomena, especially in two dimensions. | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,637 | OWR-4990379-007 | Fast Algorithms for Branching Brownian Unbalanced Transport | Can one design a fast algorithm for the regularized unbalanced optimal-transport problem associated with branching Brownian motion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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"
} | {
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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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990379-007",
"literature-status:open",
"owr-year:2021"
] | The extracted question concerns a fast algorithm for the branching Brownian transport problem; the cited report gives no algorithmic resolution and the general problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Oberwolfach Report 10/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | Can one design a fast algorithm for the regularized unbalanced optimal-transport problem associated with branching Brownian motion? | Can one design a fast algorithm for the regularized unbalanced optimal-transport problem associated with branching Brownian motion? | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,638 | OWR-4990379-008 | Gradient Flows for Network Transport Metrics | Analyze gradient flows for the network optimal-transport metrics $W_\kappa^2$ and their limiting Wasserstein and Fisher–Rao metrics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587](https://doi.org/10.4171/owr/2021/10)
## Literature review... | 3 | open | null | 2,021 | 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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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-4990379-008",
"literature-status:open",
"owr-year:2021"
] | The report explicitly leaves gradient flows for the resulting graph transport and Fisher--Rao type metrics as an interesting open problem; related metric theories do not settle this general question. | [
{
"url": "https://doi.org/10.4171/owr/2021/10",
"label": "Oberwolfach Report 10/2021"
},
{
"url": "https://doi.org/10.1007/s13373-017-0101-1",
"label": "Metric gradient flows overview"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/10 | null | null | null | Analyze gradient flows for the network optimal-transport metrics $W_\kappa^2$ and their limiting Wasserstein and Fisher–Rao metrics. | Analyze gradient flows for the network optimal-transport metrics W_\kappa^2 and their limiting Wasserstein and Fisher--Rao metrics. | 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 | Applications of Optimal Transportation in the Natural Sciences (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/10, pp. 507--587 |
30,004,639 | OWR-4990380-001 | Admissibility and Prediction for Multidimensional Hyperbolic Balance Laws | Find suitable admissibility criteria for physically reasonable solutions of multidimensional hyperbolic balance laws, especially the Euler system, determine how these criteria affect multiphase-flow models, random systems, and structure-preserving numerical schemes, and assess whether such laws can predict pandemic evo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661](https://doi.org/10.4171/owr/2021/11)
## Literature review (che... | 3 | open | null | 2,021 | 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"
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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-4990380-001",
"literature-status:open",
"owr-year:2021"
] | No universal admissibility criterion or well-posedness theory is known for multidimensional hyperbolic balance laws and Euler systems across the models listed in the record. | [
{
"url": "https://doi.org/10.4171/owr/2021/11",
"label": "Oberwolfach Report 11/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/11 | null | null | null | Find suitable admissibility criteria for physically reasonable solutions of multidimensional hyperbolic balance laws, especially the Euler system, determine how these criteria affect multiphase-flow models, random systems, and structure-preserving numerical schemes, and assess whether such laws can predict pandemic evo... | Find suitable admissibility criteria for physically reasonable solutions of multidimensional hyperbolic balance laws, especially the Euler system, determine how these criteria affect multiphase-flow models, random systems, and structure-preserving numerical schemes, and assess whether such laws can predict pandemic evo... | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661 |
30,004,640 | OWR-4990380-002 | Convergence of Fully Discrete Hyperbolic Balance-Law Schemes | Prove convergence of fully discrete approximations of hyperbolic balance laws, including Lax–Friedrichs and Godunov schemes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661](https://doi.org/10.4171/owr/2021/11)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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-4990380-002",
"literature-status:partially-solved",
"owr-year:2021"
] | Convergence is known for selected two by two systems, semidiscrete schemes, and classes with total-variation bounds, but general fully discrete Lax--Friedrichs or Godunov convergence remains open. | [
{
"url": "https://par.nsf.gov/servlets/purl/10249103",
"label": "Bressan--Chiri--Shen"
},
{
"url": "https://doi.org/10.4171/owr/2021/11",
"label": "Oberwolfach Report 11/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/11 | null | null | null | Prove convergence of fully discrete approximations of hyperbolic balance laws, including Lax–Friedrichs and Godunov schemes. | Prove convergence of fully discrete approximations of hyperbolic balance laws, including Lax--Friedrichs and Godunov schemes. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661 |
30,004,641 | OWR-4990380-003 | Convergence Without Continuous or TVD Numerical Fluxes | Determine whether a finite-volume flux that satisfies neither the usual continuity condition nor a TVD condition can nevertheless yield a convergent scheme, in particular for VOF–machine-learning solvers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661](https://doi.org/10.4171/owr/2021/11)
## Literature review (che... | 3 | open | null | 2,021 | 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-4990380-003",
"literature-status:open",
"owr-year:2021"
] | The extracted record contains only the words `An open problem' and a consequence, so no complete mathematical claim can be verified; under the stated rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/11",
"label": "Oberwolfach Report 11/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/11 | null | null | null | Determine whether a finite-volume flux that satisfies neither the usual continuity condition nor a TVD condition can nevertheless yield a convergent scheme, in particular for VOF–machine-learning solvers. | Determine whether a finite-volume flux that satisfies neither the usual continuity condition nor a TVD condition can nevertheless yield a convergent scheme, in particular for VOF--machine-learning solvers. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661 |
30,004,642 | OWR-4990380-005 | Higher-Order Entropy-Conservative Finite-Volume Methods | Generalize the entropy-conservative finite-volume discretization to higher-order methods. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661](https://doi.org/10.4171/owr/2021/11)
## Literature review (che... | 3 | open | null | 2,021 | 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-4990380-005",
"literature-status:open",
"owr-year:2021"
] | Higher-order extensions of the reported finite-volume construction remain unresolved in the generality stated, despite convergence and entropy results for selected lower-order schemes and systems. | [
{
"url": "https://doi.org/10.4171/owr/2021/11",
"label": "Oberwolfach Report 11/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/11 | null | null | null | Generalize the entropy-conservative finite-volume discretization to higher-order methods. | Generalize the entropy-conservative finite-volume discretization to higher-order methods. | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Hyperbolic Balance Laws: modeling, analysis, and numerics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/11, pp. 589--661 |
30,004,643 | OWR-4990381-001 | Density of Specializations of High-Genus Galois Covers | Let $E/\mathbb Q(T)$ be a $\mathbb Q$-regular Galois extension with group $G$ and function-field genus $g\geq2$. Does
$$
\frac{|\operatorname{Sp}(E)\cap S(G,x)|}{|S(G,x)|}\longrightarrow0
$$
as $x\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Density zero is proved conditionally for sufficiently many branch points and in several unconditional families, but the genus at least two question for a general cover remains unresolved. | [
{
"url": "https://doi.org/10.1017/S1474748019000537",
"label": "Density results for specialization sets"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $E/\mathbb Q(T)$ be a $\mathbb Q$-regular Galois extension with group $G$ and function-field genus $g\geq2$. Does
$$
\frac{|\operatorname{Sp}(E)\cap S(G,x)|}{|S(G,x)|}\longrightarrow0
$$
as $x\to\infty$? | Let E/Q(T) be a Q-regular Galois extension of group G whose function-field genus satisfies g\geq2. Does the specialization set Sp(E) have density zero in S(G), that is, does |Sp(E)\cap S(G,x)|/|S(G,x)| tend to 0 as x tends to infinity? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,644 | OWR-4990381-002 | Local-Global Density of Galois Cover Specializations | Let $E/\mathbb Q(T)$ be a $\mathbb Q$-regular Galois extension with group $G$ and genus $g\geq2$. Does
$$
\frac{|\operatorname{Sp}(E)\cap S(G,x)|}{|\operatorname{Sp}(E)^{\mathrm{loc}}\cap S(G,x)|}\longrightarrow0
$$
as $x\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The local-global density ratio is proved to tend to zero conditionally for abelian groups with sufficiently many branch points, while the general genus at least two formulation remains open. | [
{
"url": "https://doi.org/10.1017/S1474748019000537",
"label": "Density results for specialization sets"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $E/\mathbb Q(T)$ be a $\mathbb Q$-regular Galois extension with group $G$ and genus $g\geq2$. Does
$$
\frac{|\operatorname{Sp}(E)\cap S(G,x)|}{|\operatorname{Sp}(E)^{\mathrm{loc}}\cap S(G,x)|}\longrightarrow0
$$
as $x\to\infty$? | For a Q-regular Galois extension E/Q(T) of group G with genus g\geq2, does |Sp(E)\cap S(G,x)|/|Sp(E)^{loc}\cap S(G,x)| tend to 0 as x tends to infinity? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,645 | OWR-4990381-005 | Rationality of Quasi-Monomial Fixed Fields | Let $K/k$ be a finite field extension and let $G$ act on $K(x_1,\ldots,x_n)$ by quasi-monomial $k$-automorphisms. Under what conditions is $K(x_1,\ldots,x_n)^G$ rational over $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,021 | 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-4990381-005",
"literature-status:open",
"owr-year:2021"
] | The quasi-monomial rationality question contains Noether's problem and rationality of algebraic tori; many cases are classified, but no general necessary and sufficient criterion is known. | [
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
},
{
"url": "https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/232901/1/B51-14.pdf",
"label": "Rationality problem for quasi-monomial actions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $K/k$ be a finite field extension and let $G$ act on $K(x_1,\ldots,x_n)$ by quasi-monomial $k$-automorphisms. Under what conditions is $K(x_1,\ldots,x_n)^G$ rational over $k$? | Let K/k be a finite field extension and let G act on K(x_1,\ldots,x_n) by quasi-monomial k-automorphisms. Under what conditions is the fixed field K(x_1,\ldots,x_n)^G k-rational? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,646 | OWR-4990381-007 | Motivic Realization of Rigid Local Systems | Let $X$ be a connected smooth quasi-projective variety over $\mathbb C$ with a smooth projective normal-crossing compactification, and let $\rho:\pi_1^{\mathrm{top}}(X,x)\to\operatorname{GL}_n(\mathbb C)$ be irreducible, rigid, and quasi-unipotent along the boundary. After restriction to a dense open subset $U\subseteq... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Katz and later work settle important curve and cohomologically rigid cases, and Færgeman proves the stated motivic realization for rigid reductive-group local systems on curves; the general smooth quasi-projective variety case remains open. | [
{
"url": "https://arxiv.org/abs/2405.18268",
"label": "Motivic realization of rigid G-local systems on curves"
},
{
"url": "https://arxiv.org/abs/1711.06436",
"label": "Cohomologically rigid local systems and integrality"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "O... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $X$ be a connected smooth quasi-projective variety over $\mathbb C$ with a smooth projective normal-crossing compactification, and let $\rho:\pi_1^{\mathrm{top}}(X,x)\to\operatorname{GL}_n(\mathbb C)$ be irreducible, rigid, and quasi-unipotent along the boundary. After restriction to a dense open subset $U\subseteq... | Let X be a connected smooth quasi-projective variety over C, with a smooth projective normal-crossings compactification, and let rho:pi_1^{top}(X,x)\to GL_n(C) be irreducible, quasi-unipotent along the boundary, and rigid. Must rho, after restriction to a dense open U, occur as a summand of the monodromy representation... | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,647 | OWR-4990381-008 | Integrality of Rigid Irreducible Local Systems | Let $X$ be a connected smooth quasi-projective variety over $\mathbb C$ with a normal-crossing compactification. Is every rigid irreducible representation $\rho:\pi_1^{\mathrm{top}}(X,x)\to\operatorname{GL}_n(\mathbb C)$ with quasi-unipotent local monodromies conjugate to a representation in $\operatorname{GL}_n(\mathc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,021 | 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-4990381-008",
"literature-status:open",
"owr-year:2021"
] | This record is a citation fragment beginning with `conjecture' and gives no complete claim; the missing statement cannot be resolved reliably, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $X$ be a connected smooth quasi-projective variety over $\mathbb C$ with a normal-crossing compactification. Is every rigid irreducible representation $\rho:\pi_1^{\mathrm{top}}(X,x)\to\operatorname{GL}_n(\mathbb C)$ with quasi-unipotent local monodromies conjugate to a representation in $\operatorname{GL}_n(\mathc... | Simpson's integrality conjecture: every rigid irreducible representation rho:pi_1^{top}(X,x)\to GL_n(C) with quasi-unipotent local monodromies as above is, up to conjugation, valued in GL_n(O_K) for the ring of integers O_K of some number field K. | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,648 | OWR-4990381-010 | Minimal Ramification over Rational Function Fields | For $q=p^\nu$ and a finite group $G$, is
$$
r_{\mathbb F_q(T)}(G)=\max\{1,d((G/p(G))^{\mathrm{ab}})\},
$$
where $r_{\mathbb F_q(T)}(G)$ is the minimum number of ramified primes and $G/p(G)$ is the maximal quotient of order prime to $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-010",
"literature-status:partially-solved",
"owr-year:2021"
] | The conjectural minimal-ramification formula is proved for abelian groups and many symmetric and alternating cases, including broad 2023 refinements, but not for arbitrary finite groups and q. | [
{
"url": "https://doi.org/10.1093/imrn/rnac370",
"label": "Minimal ramification over finite fields"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | For $q=p^\nu$ and a finite group $G$, is
$$
r_{\mathbb F_q(T)}(G)=\max\{1,d((G/p(G))^{\mathrm{ab}})\},
$$
where $r_{\mathbb F_q(T)}(G)$ is the minimum number of ramified primes and $G/p(G)$ is the maximal quotient of order prime to $p$? | For q=p^nu and a finite group G, prove or disprove the conjecture r_{F_q(T)}(G)=max\{1,d(((G/p(G))^{ab}))\}, where r_{F_q(T)}(G) is the minimal number of ramified primes and G/p(G) is the maximal quotient of order prime to 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,649 | OWR-4990381-011 | Sections and Rational Points of Hyperbolic Curves | Let $k$ be a finitely generated extension of $\mathbb Q$ and let $X/k$ be a proper hyperbolic curve. Is every section of $\pi_1(X)\to G_k$ induced by a unique point of $X(k)$? For a smooth nonproper hyperbolic curve $U$ with compactification $X$, is every section of $\pi_1(U)\to G_k$ likewise induced by a unique point ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-011",
"literature-status:partially-solved",
"owr-year:2021"
] | The section conjecture has p-adic, birational, and several conditional or special-case results, but the stated conjecture for proper hyperbolic curves over finitely generated fields of characteristic zero remains open. | [
{
"url": "https://doi.org/10.2140/ant.2021.15.435",
"label": "On the birational section conjecture over finitely generated fields"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $k$ be a finitely generated extension of $\mathbb Q$ and let $X/k$ be a proper hyperbolic curve. Is every section of $\pi_1(X)\to G_k$ induced by a unique point of $X(k)$? For a smooth nonproper hyperbolic curve $U$ with compactification $X$, is every section of $\pi_1(U)\to G_k$ likewise induced by a unique point ... | Section conjecture: if k is a finitely generated extension of Q and X/k is a proper hyperbolic curve, then every section of pi_1(X)\to G_k is induced by a unique k-rational point of X; for a smooth nonproper hyperbolic curve U with compactification X, every section of pi_1(U)\to G_k is likewise induced by a unique k-ra... | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,650 | OWR-4990381-012 | Birational Sections and Rational Points of Hyperbolic Curves | Let $K$ be the function field of a proper hyperbolic curve $X/k$. Is every section of $G_K\to G_k$ induced by a unique point of $X(k)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-012",
"literature-status:partially-solved",
"owr-year:2021"
] | Koenigsmann proves the p-adic birational case and Saïdi--Tyler reduce finitely generated fields over Q to number fields, but the number-field and hence general birational conjecture remains open. | [
{
"url": "https://doi.org/10.2140/ant.2021.15.435",
"label": "Saïdi--Tyler birational section conjecture"
},
{
"url": "https://doi.org/10.1007/s00222-023-01220-6",
"label": "Birational section conjecture with strong assumptions"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Let $K$ be the function field of a proper hyperbolic curve $X/k$. Is every section of $G_K\to G_k$ induced by a unique point of $X(k)$? | Birational section conjecture: for the function field K of a proper hyperbolic curve X/k, every section of the natural map G_K\to G_k is induced by a unique k-rational point of X. | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,651 | OWR-4990381-015 | Exceptional Reducibility Sets in Polynomial Specialization | For an irreducible polynomial $F(t,X)\in\mathbb Q[t,X]$, determine, up to a finite set,
$$
R_F=\{t_0\in\mathbb Q:F(t_0,X)\text{ is reducible}\},
$$
and find analogous descriptions over number fields and for integral parameters. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-015",
"literature-status:partially-solved",
"owr-year:2021"
] | The exceptional reducibility set is explicitly described for substantial classes, including many decomposable polynomials, but the general arbitrary-polynomial Hilbert--Siegel problem still has exceptional low-degree solvable cases open. | [
{
"url": "https://arxiv.org/abs/2001.03630",
"label": "K\\\"onig--Neftin, Reducible Fibers of Polynomial Maps"
},
{
"url": "https://arxiv.org/abs/2603.27728",
"label": "Behajaina--K\\\"onig--Neftin, DLS problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | For an irreducible polynomial $F(t,X)\in\mathbb Q[t,X]$, determine, up to a finite set,
$$
R_F=\{t_0\in\mathbb Q:F(t_0,X)\text{ is reducible}\},
$$
and find analogous descriptions over number fields and for integral parameters. | For an irreducible polynomial F(t,X)\in Q[t,X], determine the exceptional set R_F=\{t_0\in Q:F(t_0,X) is reducible\} up to a finite set, and investigate analogous descriptions over number fields and for integral parameters. | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,652 | OWR-4990381-016 | Anabelian Reconstruction of Genus-Zero Configuration Spaces | In genus zero, does an isomorphism of étale fundamental groups between a hyperbolic polycurve and a configuration space of a hyperbolic curve imply that the varieties are isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-016",
"literature-status:partially-solved",
"owr-year:2021"
] | Grothendieck-type reconstruction is proved for several classes of hyperbolic polycurves and configuration spaces, but the genus-zero configuration-space case in the full generality stated remains unresolved. | [
{
"url": "https://arxiv.org/abs/2407.09906",
"label": "Mochizuki, refined genus-zero Grothendieck conjecture"
},
{
"url": "https://arxiv.org/abs/1902.02058",
"label": "Mochizuki, hyperbolic polycurves"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | In genus zero, does an isomorphism of étale fundamental groups between a hyperbolic polycurve and a configuration space of a hyperbolic curve imply that the varieties are isomorphic? | In genus zero, does an isomorphism of etale fundamental groups between a hyperbolic polycurve and a configuration space of a hyperbolic curve imply that the two varieties are isomorphic? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,653 | OWR-4990381-017 | Local-Global Principles for Torsors over Semi-Global Fields | For a semi-global field $F$ and a linear algebraic group $G$, when does the local-global principle for $G$-torsors hold, and what is an explicit description of its obstruction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,021 | 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-4990381-017",
"literature-status:open",
"owr-year:2021"
] | The extracted question gives no identifiable obstruction or mathematical claim beyond an unspecified request for an explicit description; the cited report context does not determine a resolved target, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/12",
"label": "Oberwolfach Report 12/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | For a semi-global field $F$ and a linear algebraic group $G$, when does the local-global principle for $G$-torsors hold, and what is an explicit description of its obstruction? | For a semi-global field F and a linear algebraic group G, under what circumstances does the local-global principle for G-torsors hold, and what is an explicit description of its obstruction? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,654 | OWR-4990381-018 | Integral Universality of Goodwillie-Weiss Knot Invariants | Does the $n$th Goodwillie–Weiss approximation give the universal type-$(n-1)$ invariant of classical knots in $\mathbb R^3$ integrally, without inverting any primes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744](https://doi.org/10.4171/owr/2021/12)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,021 | 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-4990381-018",
"literature-status:partially-solved",
"owr-year:2021"
] | Goodwillie--Weiss stages are universal after localization at suitable primes and the integral conjecture is supported by finite-type calculations, but universality over the integers is not proved in full. | [
{
"url": "https://arxiv.org/abs/1411.1832",
"label": "Turchin--Willwacher, Embedding calculus knot invariants"
},
{
"url": "https://arxiv.org/abs/2010.05120",
"label": "Goodwillie--Klein--Weiss, embedding calculus and grope cobordism"
},
{
"url": "https://doi.org/10.4171/owr/2021/12",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/12 | null | null | null | Does the $n$th Goodwillie–Weiss approximation give the universal type-$(n-1)$ invariant of classical knots in $\mathbb R^3$ integrally, without inverting any primes? | Does the Goodwillie--Weiss n-th approximation give the universal type-(n-1) invariant of classical knots in R^3 integrally, without inverting any primes? | 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 | Homotopic and Geometric Galois Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/12, pp. 663--744 |
30,004,655 | OWR-4990383-001 | Sharp-Interface Limits of Periodic Phase-Transition Equations | Let $a$ be a $\mathbb Z^d$-periodic uniformly elliptic matrix field, let $W$ be a double-well potential with global minima at $\pm1$, and let $u_\varepsilon$ solve
$$
\partial_tu_\varepsilon-\operatorname{div}\!\bigl(a(\varepsilon^{-1}x)Du_\varepsilon\bigr)+\varepsilon^{-2}W'(u_\varepsilon)=0
$$
on $\mathbb R^d\times(0... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogenization Theory: Periodic and Beyond (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/14, pp. 791--852](https://doi.org/10.4171/owr/2021/14)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,021 | 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-4990383-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Homogenized interface laws and sharp-interface limits are proved for laminar media, restricted initial data, and periodic mobility/dissipation models, but the full periodic uniformly elliptic phase-transition problem as stated is not resolved in all dimensions and data. | [
{
"url": "https://doi.org/10.6082/uchicago.4837",
"label": "Morfe, Homogenization of Interface Motions"
},
{
"url": "https://arxiv.org/abs/2011.15012",
"label": "Morfe, Allen--Cahn with periodic mobility"
},
{
"url": "https://doi.org/10.4171/owr/2021/14",
"label": "Oberwolfach Report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/14 | null | null | null | Let $a$ be a $\mathbb Z^d$-periodic uniformly elliptic matrix field, let $W$ be a double-well potential with global minima at $\pm1$, and let $u_\varepsilon$ solve
$$
\partial_tu_\varepsilon-\operatorname{div}\!\bigl(a(\varepsilon^{-1}x)Du_\varepsilon\bigr)+\varepsilon^{-2}W'(u_\varepsilon)=0
$$
on $\mathbb R^d\times(0... | For the stated Z^d-periodic uniformly elliptic phase-transition equations with double-well potential W, and for the stated periodic mean-curvature-type equation, determine the limiting behavior of u_epsilon as epsilon tends to 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 | Homogenization Theory: Periodic and Beyond (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/14, pp. 791--852 |
30,004,656 | OWR-4990384-001 | Robustness-Driven Overparameterization in Two-Layer Neural Networks | Does interpolation by a two-layer neural network with few parameters necessarily force the represented function to have a large Lipschitz constant, thereby making overparameterization necessary for robustness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Foundations of Machine Learning (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/15, pp. 853--894](https://doi.org/10.4171/owr/2021/15)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 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-4990384-001",
"literature-status:partially-solved",
"owr-year:2021"
] | The robustness lower bound is proved in undercomplete regimes and for polynomially bounded weights, and recent work gives near-conjectural bounds for piecewise-linear activations with arbitrary weights; the stated broad conjecture remains unproved. | [
{
"url": "https://arxiv.org/abs/2009.14444",
"label": "Bubeck--Li--Nagaraj, law of robustness"
},
{
"url": "https://arxiv.org/abs/2202.11592",
"label": "Wu--Sahai, law beyond isoperimetry"
},
{
"url": "https://arxiv.org/abs/2607.07778",
"label": "Shmalo, arbitrary weights"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/15 | null | null | null | Does interpolation by a two-layer neural network with few parameters necessarily force the represented function to have a large Lipschitz constant, thereby making overparameterization necessary for robustness? | Conjecture that interpolation by a two-layer neural network using few parameters automatically forces the represented function to have a large Lipschitz constant, thereby making overparameterization a law of robustness. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mathematical Foundations of Machine Learning (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/15, pp. 853--894 |
30,004,657 | OWR-7155438-002 | High-Order Variational Integrators for Degenerate Lagrangians | For general degenerate Lagrangians, can degenerate variational integrators be generalized to arbitrary order using Galerkin or Runge–Kutta discretizations; can they and symplectic Runge–Kutta methods be obtained without assuming any component of the symplectic potential vanishes; and do symplectic Runge–Kutta methods f... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Numerical Integration (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/17, pp. 943--999](https://doi.org/10.4171/owr/2021/17)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,021 | 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-7155438-002",
"literature-status:open",
"owr-year:2021"
] | Variational and symplectic constructions exist for important degenerate or velocity-linear classes, but the three questions ask for a general construction and equivalence result that are not established in the stated generality. | [
{
"url": "https://arxiv.org/abs/1401.7904",
"label": "Leok--Ohsawa--Sosa, variational partitioned Runge--Kutta methods"
},
{
"url": "https://arxiv.org/abs/2001.07185",
"label": "Sanz-Serna, discrete variational methods"
},
{
"url": "https://doi.org/10.4171/owr/2021/17",
"label": "Obe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/17 | null | null | null | For general degenerate Lagrangians, can degenerate variational integrators be generalized to arbitrary order using Galerkin or Runge–Kutta discretizations; can they and symplectic Runge–Kutta methods be obtained without assuming any component of the symplectic potential vanishes; and do symplectic Runge–Kutta methods f... | For general degenerate Lagrangians, can degenerate variational integrators be generalized to arbitrary order using Galerkin or Runge--Kutta discretizations; can they and symplectic Runge--Kutta methods be obtained without assuming any component of the symplectic potential vanishes; and do symplectic Runge--Kutta method... | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Geometric Numerical Integration (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/17, pp. 943--999 |
30,004,658 | OWR-7155439-003 | Galois Representations from Hecke Maximal Ideals | For every maximal ideal $\mathfrak m$ of the Hecke algebra $\mathbb T_S(K)$, does there exist a continuous semisimple Galois representation $\bar\rho_{\mathfrak m}$ with the prescribed Hecke characteristic polynomials, maximally odd complex conjugation, and Fontaine–Laffaille Hodge–Tate weights? If $\mathfrak m$ is non... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/18, pp. 1001--1046](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,021 | 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-7155439-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Hecke-eigensystem-valued residual Galois representations and many characteristic-zero or automorphic cases are constructed, but the full universal statement including all listed local and lift properties is not known in the stated generality. | [
{
"url": "https://arxiv.org/abs/1506.04144",
"label": "Scholze, torsion in locally symmetric cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2021/18",
"label": "Oberwolfach Report 18/2021"
},
{
"url": "https://arxiv.org/abs/1209.6293",
"label": "Calegari--Geraghty, modularity be... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/18 | null | null | null | For every maximal ideal $\mathfrak m$ of the Hecke algebra $\mathbb T_S(K)$, does there exist a continuous semisimple Galois representation $\bar\rho_{\mathfrak m}$ with the prescribed Hecke characteristic polynomials, maximally odd complex conjugation, and Fontaine–Laffaille Hodge–Tate weights? If $\mathfrak m$ is non... | Conjecture: for every maximal ideal m of the Hecke algebra T_S(K), there is a continuous semisimple Galois representation rho-bar_m with the prescribed Hecke characteristic polynomials, maximally odd complex conjugation, and Fontaine--Laffaille Hodge--Tate weights. If m is non-Eisenstein, this representation has a lift... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/18, pp. 1001--1046 |
30,004,659 | OWR-7155439-004 | Taylor–Wiles Deformation Maps to Augmented Hecke Algebras | Does there exist an $\mathcal O[\Delta_Q]$-algebra homomorphism from $R_{S\cup Q}$ to the $Q$-augmented Hecke algebra $\mathbb T_{S\cup Q,Q\text{-aug}}(K_0(Q)/K_1(Q))$ localized at the maximal ideal $\mathfrak m_{\bar\rho}$ determined by the residual representation $\bar\rho$, carrying the characteristic polynomial of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/18, pp. 1001--1046](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,021 | 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-7155439-004",
"literature-status:open",
"owr-year:2021"
] | The displayed Taylor--Wiles-level deformation-to-Hecke algebra map is posed as a conjectural input; derived patching develops consequences conditional on such inputs, but no general proof of this exact statement was found. | [
{
"url": "https://doi.org/10.4171/owr/2021/18",
"label": "Oberwolfach Report 18/2021"
},
{
"url": "https://arxiv.org/abs/1608.07236",
"label": "Galatius--Venkatesh, derived Galois deformation rings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/18 | null | null | null | Does there exist an $\mathcal O[\Delta_Q]$-algebra homomorphism from $R_{S\cup Q}$ to the $Q$-augmented Hecke algebra $\mathbb T_{S\cup Q,Q\text{-aug}}(K_0(Q)/K_1(Q))$ localized at the maximal ideal $\mathfrak m_{\bar\rho}$ determined by the residual representation $\bar\rho$, carrying the characteristic polynomial of ... | Conjecture: there exists an O[Delta_Q]-algebra homomorphism from R_{S union Q} to the Q-augmented Hecke algebra T_{S union Q,Q-aug}(K_0(Q)/K_1(Q)) localized at the relevant maximal ideal, carrying the characteristic polynomial of rho_{S union Q}(Fr_v) to P_v(X) for every v not in S union Q. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/18, pp. 1001--1046 |
30,004,660 | OWR-7155441-001 | Langlands-Dual Parametrization of Shifted Quantum Affine Modules | Are the simple modules of a truncated shifted quantum affine algebra of non-simply-laced type parametrized by monomials in the Langlands-dual q-character of a finite-dimensional representation of the Langlands-dual quantum affine algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,021 | 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-7155441-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Baxter polynomiality proves the predicted descent and finiteness consequences and gives substantial evidence, but the proposed Langlands-dual parametrization of all non-simply-laced simple truncation modules remains conjectural. | [
{
"url": "https://arxiv.org/abs/2010.06996",
"label": "Hernandez, representations of shifted quantum affine algebras"
},
{
"url": "https://arxiv.org/abs/2501.16859",
"label": "Hernandez--Zhang, Jordan--H\\\"older property"
},
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Are the simple modules of a truncated shifted quantum affine algebra of non-simply-laced type parametrized by monomials in the Langlands-dual q-character of a finite-dimensional representation of the Langlands-dual quantum affine algebra? | Conjecture: the simple modules of a truncation of a shifted quantum affine algebra in non-simply-laced type are explicitly parametrized by monomials in the Langlands-dual q-character of a finite-dimensional representation of the Langlands-dual quantum affine algebra. | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,661 | OWR-7155441-002 | Rigidity of Morphisms to Wound Unipotent Groups | Let $U$ be a wound unipotent group over $k$, let $x$ be a closed point of $\mathbb P_k^1$, put $X=\mathbb P_k^1\setminus\{x\}$, and choose $y_1,y_2\in X(k)$. Is every $k$-morphism $f:X\times X\to U$ that is trivial on $\{y_1\}\times X$ and $X\times\{y_2\}$ the constant morphism $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,021 | 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-7155441-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The rigidity conjecture is proved in characteristic different from two and yields the stated structural applications there; the characteristic-two case and full all-characteristic assertion remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://hal.science/hal-02358528/document",
"label": "Achet, Unirational Algebraic Groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Let $U$ be a wound unipotent group over $k$, let $x$ be a closed point of $\mathbb P_k^1$, put $X=\mathbb P_k^1\setminus\{x\}$, and choose $y_1,y_2\in X(k)$. Is every $k$-morphism $f:X\times X\to U$ that is trivial on $\{y_1\}\times X$ and $X\times\{y_2\}$ the constant morphism $1$? | Conjecture: let U be a wound unipotent group over k, let x be a closed point of P^1_k, let X=P^1_k minus x, and let y_1,y_2 be k-points of X. Every k-morphism f:X times X to U that is trivial on {y_1} times X and on X times {y_2} is the constant morphism 1. | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,662 | OWR-7155441-003 | Higher Product Rigidity for Wound Unipotent Targets | Let $U$ be a wound unipotent group over $k$, let $X_1,\ldots,X_n$ be nonempty open subschemes of $\mathbb P_k^1$ with chosen points $x_i\in X_i(k)$, and let $D$ be the union of their complementary divisors. If $n$ exceeds the degree of primitivity of $D$, is every $k$-morphism $\prod_iX_i\to U$ that is trivial whenever... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,021 | 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-7155441-003",
"literature-status:open",
"owr-year:2021"
] | The higher degree-of-primitivity rigidity statement is presented as a conjectural strengthening of the characteristic-one case; no proof of the general assertion or its descending-central-series consequence was found. | [
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://hal.science/hal-02358528/document",
"label": "Achet, Unirational Algebraic Groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Let $U$ be a wound unipotent group over $k$, let $X_1,\ldots,X_n$ be nonempty open subschemes of $\mathbb P_k^1$ with chosen points $x_i\in X_i(k)$, and let $D$ be the union of their complementary divisors. If $n$ exceeds the degree of primitivity of $D$, is every $k$-morphism $\prod_iX_i\to U$ that is trivial whenever... | Conjecture: let U be a wound unipotent group over k, let X_1,...,X_n be nonempty open subschemes of P^1_k with chosen k-points x_i, and let D be the union of their complementary divisors. If n is greater than the degree of primitivity of D, then every k-morphism from the product of the X_i to U that is trivial when any... | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,663 | OWR-7155441-004 | Discrete-Valuation Local-Global Principle for Homogeneous Varieties and Torsors | For a projective homogeneous variety or torsor $V$ over $F$, is $V(F)$ nonempty if and only if $V(M_x)$ is nonempty for every $x$ in the set $S$ of points corresponding to discrete valuations of $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,021 | 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-7155441-004",
"literature-status:partially-solved",
"owr-year:2021"
] | The local--global principle is proved for projective homogeneous spaces and torsors over rational groups and for several strong-smoothness cases, including the quadratic-form application, but the full discrete-valuation conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://doi.org/10.1112/S0010437X19007632",
"label": "Patching over Berkovich curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | For a projective homogeneous variety or torsor $V$ over $F$, is $V(F)$ nonempty if and only if $V(M_x)$ is nonempty for every $x$ in the set $S$ of points corresponding to discrete valuations of $F$? | Conjecture: for a projective homogeneous variety or torsor V over F, V(F) is nonempty if and only if V(M_x) is nonempty for every x in the set S of points corresponding to discrete valuations of 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 | Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,664 | OWR-7155441-007 | Redundant Inequalities in String Cones | For an arbitrary reduced word $\mathbf i$, how many inequalities defining its string cone are redundant, and can the redundancies be classified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,021 | 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-7155441-007",
"literature-status:open",
"owr-year:2021"
] | The redundancy-classification question for recursively generated string-cone inequalities is not resolved in general; only structural reductions and special cases are established. | [
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://arxiv.org/abs/2109.14439",
"label": "Koshevoy--Schumann, redundancy in string-cone inequalities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | For an arbitrary reduced word $\mathbf i$, how many inequalities defining its string cone are redundant, and can the redundancies be classified? | For an arbitrary reduced word i, how many inequalities in the associated string cone are redundant, and can these redundancies be classified? | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,665 | OWR-7155441-008 | Exponent Criterion for Nonredundant String-Cone Inequalities | Are the inequalities defining the string cone $S_{\mathbf i}$ nonredundant if and only if the absolute value of the exponent of every variable in $W|_{T_{\mathbf i}^{\vee}}$ is at most $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,021 | 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-7155441-008",
"literature-status:partially-solved",
"owr-year:2021"
] | The exponent condition is proved sufficient for non-redundancy, but the converse equivalence remains a conjecture; the cited work reports only partial cases and evidence. | [
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://arxiv.org/abs/2109.14439",
"label": "Koshevoy--Schumann, redundancy in string-cone inequalities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Are the inequalities defining the string cone $S_{\mathbf i}$ nonredundant if and only if the absolute value of the exponent of every variable in $W|_{T_{\mathbf i}^{\vee}}$ is at most $1$? | Conjecture: the inequalities defining the string cone S_i are non-redundant if and only if the absolute value of the exponent of every variable in W restricted to T_i dual is at most 1. | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,666 | OWR-7155441-009 | Normal Schubert Varieties in Full Affine Flag Varieties | Let $G$ be absolutely simple over a Laurent-series field of characteristic $p>0$, with $p\mid|\pi_1(G)|$. Classify all normal Schubert varieties in the neutral component $\operatorname{Fl}_{G,a}^{\circ}$ of the full affine flag variety; equivalently, classify the corresponding affine Weyl-group elements or alcoves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,021 | 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-7155441-009",
"literature-status:partially-solved",
"owr-year:2021"
] | Normality criteria and complete classifications are now available in important cases, including adjoint groups in sufficiently large characteristic and semisimple-rank-one examples, but the requested full affine-flag classification for all listed pairs is not complete. | [
{
"url": "https://arxiv.org/abs/2508.04876",
"label": "Bieker, normality in the tamely ramified case"
},
{
"url": "https://arxiv.org/abs/2312.11154",
"label": "Bieker--Richarz, normality of affine Schubert varieties"
},
{
"url": "https://doi.org/10.4171/owr/2021/20",
"label": "Oberwo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Let $G$ be absolutely simple over a Laurent-series field of characteristic $p>0$, with $p\mid|\pi_1(G)|$. Classify all normal Schubert varieties in the neutral component $\operatorname{Fl}_{G,a}^{\circ}$ of the full affine flag variety; equivalently, classify the corresponding affine Weyl-group elements or alcoves. | Problem: for the relevant pairs (G,p), classify all Schubert varieties in the full affine flag variety Fl^circ_{G,a}, equivalently classify the corresponding affine Weyl-group elements or alcoves in the apartment. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,667 | OWR-7155441-010 | Elementary Proofs and Computations of Equivariant Multiplicities | Can the equivariant-multiplicity formula involving the Duistermaat–Heckman measure be proved without using such measures, and can concrete examples be computed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,021 | 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-7155441-010",
"literature-status:open",
"owr-year:2021"
] | The report records both questions as unresolved and says known computation methods are not completely algorithmic; only a rank-one example is given, with no general solution established. | [
{
"url": "https://ems.press/content/serial-article-files/46898",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://arxiv.org/abs/1911.05526",
"label": "Pădurariu, K-theoretic Hall algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Can the equivariant-multiplicity formula involving the Duistermaat–Heckman measure be proved without using such measures, and can concrete examples be computed? | Can the equivariant-multiplicity formula involving the Duistermaat--Heckman measure be proved without using Duistermaat--Heckman measures, and can concrete examples be computed? | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,668 | OWR-7155441-011 | Injectivity of the Quantum K-Theoretic Hall Homomorphism | Let $(Q, W)$ be the quiver with potential associated to a symmetric quiver (such as the tripled quiver with canonical cubic potential), let $K(Q, W)$ be its critical $K$-theoretic Hall algebra (KHA), and let $U^+$ be the positive half of the corresponding quantum affine algebra. Is the canonical graded algebra homomorp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148](https://doi.org/10.4171/owr/2021/20)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,021 | 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-7155441-011",
"literature-status:open",
"owr-year:2021"
] | Injectivity is explicitly stated as a conjecture in the report, and the subsequent K-theoretic Hall-algebra literature still describes recovery of the quantum affine algebra as conjectural rather than proving this map injective. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/f2f10f3f-72af-4586-9653-7e0b6b7e77c9/content",
"label": "Oberwolfach Report 20/2021"
},
{
"url": "https://arxiv.org/abs/1911.05526",
"label": "Pădurariu, K-theoretic Hall algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/20 | null | null | null | Let $(Q, W)$ be the quiver with potential associated to a symmetric quiver (such as the tripled quiver with canonical cubic potential), let $K(Q, W)$ be its critical $K$-theoretic Hall algebra (KHA), and let $U^+$ be the positive half of the corresponding quantum affine algebra. Is the canonical graded algebra homomorp... | Conjecture: the graded algebra homomorphism psi from U^+ to K(Q,W) is injective. | 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 Groups (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/20, pp. 1087--1148 |
30,004,669 | OWR-7155442-002 | Depth Relative to K-Trivial Oracles | For a $K$-trivial oracle $A$, is $A$-depth strictly stronger than depth, or does $A$-depth coincide with depth? More generally, which of these two cases occurs for $K$-trivial oracles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,021 | 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-7155442-002",
"literature-status:open",
"owr-year:2021"
] | Relativized depth has been developed and its basic preservation theorems proved, but for K-trivial oracles the central alternatives in the queued question are explicitly left open. | [
{
"url": "https://iris.uniroma1.it/bitstream/11573/1713789/1/relativized-depth.pdf",
"label": "Delle Rose, Bienvenu and Merkle, Relativized depth"
},
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | For a $K$-trivial oracle $A$, is $A$-depth strictly stronger than depth, or does $A$-depth coincide with depth? More generally, which of these two cases occurs for $K$-trivial oracles? | For a K-trivial oracle A, is A-depth strictly stronger than depth, or does A-depth coincide with depth? More generally, which of these two cases occurs for K-trivial oracles? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,670 | OWR-7155442-004 | Computable Multifunctions Between Effectively Hausdorff Spaces | Find and prove a characterization of computable multifunctions when both the domain $X$ and codomain $Y$ are effectively Hausdorff spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,021 | 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"
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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-7155442-004",
"literature-status:open",
"owr-year:2021"
] | The report introduces effectively Hausdorff spaces and leaves the characterization of computable multifunctions as an open problem; later surveys develop the framework but do not supply the requested general characterization. | [
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
},
{
"url": "https://arxiv.org/abs/2004.09450",
"label": "Schröder, Admissibly represented spaces and QCB-spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Find and prove a characterization of computable multifunctions when both the domain $X$ and codomain $Y$ are effectively Hausdorff spaces. | Find and prove a characterization of computable multifunctions when both the domain X and codomain Y are effectively Hausdorff spaces. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,671 | OWR-7155442-005 | Geometric Analogues of Finite Effective Complexity | Can one formulate and prove the geometric analogue of the finite effective-complexity statement for points and lines on the projective plane, together with the corresponding sphere-area inequality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,021 | 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-7155442-005",
"literature-status:open",
"owr-year:2021"
] | The source itself labels this as an open question and gives no precise theorem whose truth or falsity would settle it; no authoritative subsequent resolution was identified. | [
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Can one formulate and prove the geometric analogue of the finite effective-complexity statement for points and lines on the projective plane, together with the corresponding sphere-area inequality? | Can one formulate and prove the geometric analogue of the finite effective-complexity statement for points and lines on the projective plane, together with the corresponding sphere-area inequality? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,672 | OWR-7155442-006 | Long Binary Blocks in Uniformly Random Sequences | What can be said about the occurrence of binary blocks of length larger than $\log N$ when a length-$N$ sequence is sampled from the uniform distribution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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"
} | {
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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-7155442-006",
"literature-status:partially-solved",
"owr-year:2021"
] | The logarithmic critical regime is now described by Poisson genericity, with computable examples and metric results, but no general characterization of all block lengths larger than logarithmic size is established. | [
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
},
{
"url": "https://doi.org/10.1093/imrn/rnac234",
"label": "Álvarez, Becher and Mereb, Poisson generic sequences"
},
{
"url": "https://arxiv.org/abs/2411.04116",
"label": "Álvarez... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | What can be said about the occurrence of binary blocks of length larger than $\log N$ when a length-$N$ sequence is sampled from the uniform distribution? | What can be said about the occurrence of binary blocks of length larger than log N when a length-N sequence is sampled from the uniform distribution? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,673 | OWR-7155442-007 | Computability and Complexity Characterizations of Poisson Genericity | For Poisson-generic reals, does a computable example exist, is every Martin–Löf random real Poisson generic, can Poisson genericity be characterized by Kolmogorov complexity, and is Poisson genericity $\Pi^0_3$-complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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",
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"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-7155442-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Computable Poisson generic reals and the inclusion of all Martin-Löf random reals were proved, and the Π03-completeness question was settled, while the requested Kolmogorov-complexity characterization remains unresolved in this form. | [
{
"url": "https://doi.org/10.1093/imrn/rnac234",
"label": "Álvarez, Becher and Mereb, Poisson generic sequences"
},
{
"url": "https://arxiv.org/abs/2305.10529",
"label": "Becher, Jackson, Kwietniak and Mance, descriptive complexity"
},
{
"url": "https://ems.press/content/serial-article-f... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | For Poisson-generic reals, does a computable example exist, is every Martin–Löf random real Poisson generic, can Poisson genericity be characterized by Kolmogorov complexity, and is Poisson genericity $\Pi^0_3$-complete? | For Poisson-generic reals, is there a computable example, are all Martin--Lof random reals Poisson generic, can Poisson genericity be characterized by Kolmogorov complexity, and is the class of Poisson-generic reals Pi^0_3-complete? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,674 | OWR-7155442-008 | Embedding Locally Countable Orders into Turing Degrees | Does every locally countable partial order of cardinality continuum embed into the Turing degrees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,021 | 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"
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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-7155442-008",
"literature-status:open",
"owr-year:2021"
] | The queued item is Sacks' question on embedding every locally countable partial order of continuum size into the Turing degrees; it remains open in ZFC, with positive results under CH, MA, and for restricted heights. | [
{
"url": "https://home.iitk.ac.in/~krashu/tdst.pdf",
"label": "Kumar, Set theory and Turing degrees"
},
{
"url": "https://arxiv.org/abs/2309.01876",
"label": "Higuchi and Lutz, A note on a conjecture of Sacks"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Does every locally countable partial order of cardinality continuum embed into the Turing degrees? | Does every locally countable partial order of cardinality continuum embed into the Turing degrees? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,675 | OWR-7155442-009 | Computable Characterizations of Hausdorff Packing Regularity | For $A\subset 2^\omega$, can computability partially characterize regularity defined by $\dim_H(A)=\dim_P(A)$? Can the point-to-set principles give an alternative proof of the closed-subset result for regular analytic sets, and can the analyticity assumption be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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"
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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-7155442-009",
"literature-status:partially-solved",
"owr-year:2021"
] | Point-to-set principles and optimal-oracle results settle substantial analytic and regular-set cases, and determinacy-based work extends closed-subset conclusions beyond analytic sets under extra axioms, but the full computability characterization and unconditional analyticity removal remain open. | [
{
"url": "https://arxiv.org/abs/2101.11152",
"label": "Stull, Optimal oracles for point-to-set principles"
},
{
"url": "https://doi.org/10.1017/jsl.2023.29",
"label": "Peng, Wu and Yu, Some consequences of TD and sTD"
},
{
"url": "https://ems.press/content/serial-article-files/46899",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | For $A\subset 2^\omega$, can computability partially characterize regularity defined by $\dim_H(A)=\dim_P(A)$? Can the point-to-set principles give an alternative proof of the closed-subset result for regular analytic sets, and can the analyticity assumption be removed? | For A contained in 2^omega, can computability partially characterize regularity defined by dim_H(A)=dim_P(A)? Can the point-to-set principles give an alternative proof of the closed-subset result for regular analytic sets, and can the analyticity assumption be removed? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,676 | OWR-7155442-010 | Admissible Sets and Their Jump Structures | For every admissible set $A$, is $A$ $\Sigma$-equivalent to its jump structure $J(A)$ if and only if every structure $B$ that is $\Sigma$-definable in $A$ satisfies $B\leq_\Sigma A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,021 | 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-7155442-010",
"literature-status:open",
"owr-year:2021"
] | The equivalence for admissible sets is presented as a conjecture; fixed-point results for the jump operator establish context and examples, not the stated equivalence for every admissible set. | [
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
},
{
"url": "https://old.math.nsc.ru/conference/malmeet/11/plenary/2011MM_Puzarenko.pdf",
"label": "Puzarenko, Fixed points of the Sigma jump operator"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | For every admissible set $A$, is $A$ $\Sigma$-equivalent to its jump structure $J(A)$ if and only if every structure $B$ that is $\Sigma$-definable in $A$ satisfies $B\leq_\Sigma A$? | Conjecture: for every admissible set A, A is Sigma-equivalent to its jump structure J(A) if and only if every structure B that is Sigma-definable in A satisfies B less-than-or-equal-to-Sigma A. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,677 | OWR-7155442-011 | Zigzagging Skips of Arithmetical Degrees | Does there exist an arithmetical degree $\mathbf a$ such that, for every $n$, the $n$th skip of $\mathbf a$ is not below the $(n+1)$st skip, equivalently every $n$th skip is nontotal? Can the HYP degrees be characterized as the degrees bounded by all skip $2$-cycles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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-7155442-011",
"literature-status:partially-solved",
"owr-year:2021"
] | Skip 2-cycles were constructed and the HYP-degree characterization was answered affirmatively by Goh, but the separate existence question for one degree with the required zig-zag behavior is not settled by those results. | [
{
"url": "https://people.math.wisc.edu/~slempp/papers/cototal.pdf",
"label": "Andrews et al., On cototality and the skip operator"
},
{
"url": "https://people.math.wisc.edu/~soskova/talks/WDCM2021Soskova.pdf",
"label": "Soskova, The e-verse"
},
{
"url": "https://ems.press/content/serial-... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Does there exist an arithmetical degree $\mathbf a$ such that, for every $n$, the $n$th skip of $\mathbf a$ is not below the $(n+1)$st skip, equivalently every $n$th skip is nontotal? Can the HYP degrees be characterized as the degrees bounded by all skip $2$-cycles? | Does there exist an arithmetical degree a such that, for every n, the n-th skip of a is not below the (n+1)-st skip, equivalently every n-th skip is nontotal? Can the HYP degrees be characterized as the degrees bounded by all skip 2-cycles? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,678 | OWR-7155442-012 | Positive Degrees Within Truth Table and Many One Degrees | Can odd numbers other than $1$ occur as the number of positive degrees inside a truth-table degree? Does every many-one degree that is not recursive either consist of one one-one degree or contain an infinite antichain of one-one degrees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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-7155442-012",
"literature-status:partially-solved",
"owr-year:2021"
] | The finite odd-number phenomenon for positive degrees inside truth-table degrees remains incomplete, while the many-one subquestion on infinite antichains of one-one degrees was resolved positively in 2026 for every nonrecursive nonirreducible degree. | [
{
"url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/92D4726C02642E1CA649BE1B8AEDAB2C/S0022481200010987a.pdf",
"label": "Stephan, On the structures inside truth-table degrees"
},
{
"url": "https://arxiv.org/abs/2607.06218",
"label": "Richter, Stephan and Zhang, Chain... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Can odd numbers other than $1$ occur as the number of positive degrees inside a truth-table degree? Does every many-one degree that is not recursive either consist of one one-one degree or contain an infinite antichain of one-one degrees? | Can odd numbers other than 1 occur as the number of positive degrees inside a truth-table degree? Does every many-one degree that is not recursive either consist of one one-one degree or contain an infinite antichain of one-one degrees? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,679 | OWR-7155442-013 | Weihrauch Reductions for Paths Through Ill-Founded Trees | Let $\mathrm{CNN}$ denote the task of computing a path through an ill-founded subtree of $\mathbb N^{\mathbb N}$. Is $\mathrm{CNN}$ uniformly Weihrauch-reducible to $\Sigma^0_1\text{-RT}$ or to $\mathrm{wFindHS}\text{-}\Pi^0_1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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-7155442-013",
"literature-status:partially-solved",
"owr-year:2021"
] | The 2024 primary paper proves that KL is not Weihrauch reducible to DS or BS, but the queued CNN reductions and the broader Gamma-presented hierarchy questions are not fully characterized. | [
{
"url": "https://arxiv.org/abs/2401.11807",
"label": "Goh, Pauly and Valenti, weakness of DS"
},
{
"url": "https://doi.org/10.1017/jsl.2021.10",
"label": "Marcone and Valenti, open and clopen Ramsey theorems"
},
{
"url": "https://ems.press/content/serial-article-files/46899",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | Let $\mathrm{CNN}$ denote the task of computing a path through an ill-founded subtree of $\mathbb N^{\mathbb N}$. Is $\mathrm{CNN}$ uniformly Weihrauch-reducible to $\Sigma^0_1\text{-RT}$ or to $\mathrm{wFindHS}\text{-}\Pi^0_1$? | Can the problem CNN of computing a path through an ill-founded subtree of N^N be uniformly Weihrauch-reduced to Sigma^0_1-RT or to wFindHS-Pi^0_1? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,680 | OWR-7155442-014 | Weihrauch Determinacy and Degree Structure Questions | What are the exact Weihrauch relations among $\Sigma^0_1\text{-DS}$, $\Sigma^0_1\text{-BSLQO}$, $\Sigma^0_1\text{-BSPO}$, $\Sigma^0_1\text{-BS}$, and $\Delta^0_2\text{-DS}$? Does Turing determinacy imply dependent choice for reals, and does Turing determinacy together with dependent choice imply strong Turing determina... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190](https://doi.org/10.4171/owr/2021/21)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,021 | 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-7155442-014",
"literature-status:partially-solved",
"owr-year:2021"
] | The bundled questions remain open in their full forms: the DS and BS relations, determinacy implications, and Turing-degree definability are not jointly settled, although the report records partial results and solved easier cases. | [
{
"url": "https://ems.press/content/serial-article-files/46899",
"label": "Oberwolfach Report 21/2021"
},
{
"url": "https://doi.org/10.1134/S1995080218050037",
"label": "Arslanov and Yamaleev, definability in the difference hierarchy"
},
{
"url": "https://arxiv.org/abs/2401.11807",
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/21 | null | null | null | What are the exact Weihrauch relations among $\Sigma^0_1\text{-DS}$, $\Sigma^0_1\text{-BSLQO}$, $\Sigma^0_1\text{-BSPO}$, $\Sigma^0_1\text{-BS}$, and $\Delta^0_2\text{-DS}$? Does Turing determinacy imply dependent choice for reals, and does Turing determinacy together with dependent choice imply strong Turing determina... | What are the exact Weihrauch relations among Sigma^0_1-DS, Sigma^0_1-BSLQO, Sigma^0_1-BSPO, Sigma^0_1-BS, and Delta^0_2-DS? Does Turing determinacy imply dependent choice for reals, and does Turing determinacy together with dependent choice imply strong Turing determinacy? Given a properly 2-c.e. degree D, does there e... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computability Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/21, pp. 1149--1190 |
30,004,681 | OWR-7155444-001 | Comparative Advantages of Physics-Based and Machine-Learned Models | Is a physics-based model always advantageous when the underlying system obeys physical laws, and which modelling or controller-design problems can be solved better with machine learning? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257](https://doi.org/10.4171/owr/2021/23)
## Literature review (chec... | 3 | open | null | 2,021 | 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-7155444-001",
"literature-status:open",
"owr-year:2021"
] | The question asks for a general comparative theory of physics-based and machine-learning models in control; current work supplies model-specific guarantees and tradeoffs, not a universal advantage criterion. | [
{
"url": "https://doi.org/10.4171/owr/2021/23",
"label": "Oberwolfach Report 23/2021"
},
{
"url": "https://arxiv.org/abs/2306.13867",
"label": "Physics-informed machine learning for modeling and control"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/23 | null | null | null | Is a physics-based model always advantageous when the underlying system obeys physical laws, and which modelling or controller-design problems can be solved better with machine learning? | Is a physics-based model always advantageous when the underlying system obeys physical laws, and which modelling or controller-design problems can be solved better with machine learning? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257 |
30,004,682 | OWR-7155444-003 | High-Dimensional Regression and PDE Learning Without Dimensional Curse | What error bounds can be obtained for regression of high-dimensional nonsmooth functions, how can PDEs be solved without the curse of dimensionality, and what training and validation data sizes and distributions are efficient and effective for deep learning? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257](https://doi.org/10.4171/owr/2021/23)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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-7155444-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Compositional approximation theory now gives polynomial complexity bounds for important classes of functions, differential equations, and control problems, but the broad regression, PDE, and training-distribution questions in the extracted statement remain open. | [
{
"url": "https://epubs.siam.org/doi/10.1137/21M1391596",
"label": "Jentzen et al., feedforward networks and compositional functions"
},
{
"url": "https://arxiv.org/abs/2304.07947",
"label": "Duan et al., deep neural network approximation of composition functions"
},
{
"url": "https://do... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/23 | null | null | null | What error bounds can be obtained for regression of high-dimensional nonsmooth functions, how can PDEs be solved without the curse of dimensionality, and what training and validation data sizes and distributions are efficient and effective for deep learning? | What error bounds can be obtained for regression of high-dimensional nonsmooth functions, how can PDEs be solved without the curse of dimensionality, and what training and validation data sizes and distributions are efficient and effective for deep learning? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257 |
30,004,683 | OWR-7155444-004 | Computable Coherent Sets in Stochastic Dynamics | Can coherent families of sets for a time-dependent stochastic dynamical system be characterized in a way that permits numerical computation, and can the resulting problem be solved efficiently in higher dimensions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257](https://doi.org/10.4171/owr/2021/23)
## Literature review (chec... | 3 | open | null | 2,021 | 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-7155444-004",
"literature-status:open",
"owr-year:2021"
] | Spectral and transfer-operator methods compute coherent families in important finite-dimensional settings, but a general characterization supporting efficient computation in higher dimensions remains unavailable. | [
{
"url": "https://doi.org/10.4171/owr/2021/23",
"label": "Oberwolfach Report 23/2021"
},
{
"url": "https://doi.org/10.3934/jcd.2016008",
"label": "Denner, Junge and Matthes, computing coherent sets"
},
{
"url": "https://doi.org/10.1137/19M1261791",
"label": "Froyland, Koltai and Stah... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/23 | null | null | null | Can coherent families of sets for a time-dependent stochastic dynamical system be characterized in a way that permits numerical computation, and can the resulting problem be solved efficiently in higher dimensions? | Can coherent families of sets for a time-dependent stochastic dynamical system be characterized in a way that permits numerical computation, and can the resulting problem be solved efficiently in higher dimensions? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257 |
30,004,684 | OWR-7155444-005 | Reduced Variables Preserving Dominant Dynamical Timescales | Given only a high-dimensional description of a dynamical system, how can one construct a low-dimensional collective variable that reproduces its dominant dynamical timescales? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257](https://doi.org/10.4171/owr/2021/23)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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,
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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 | [
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"OWR-7155444-005",
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] | Constructive transition-density and manifold-learning procedures, variational slow-coordinate methods, and reweighted data-driven approaches now find collective variables under structural assumptions, but no general method works from arbitrary high-dimensional descriptions. | [
{
"url": "https://doi.org/10.4171/owr/2021/23",
"label": "Oberwolfach Report 23/2021"
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{
"url": "https://doi.org/10.1016/j.sbi.2017.02.006",
"label": "Husic and Pande, collective variables"
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{
"url": "https://pubs.acs.org/doi/10.1021/acs.jctc.2c00873",
"label": "Rydzewski et al.,... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/23 | null | null | null | Given only a high-dimensional description of a dynamical system, how can one construct a low-dimensional collective variable that reproduces its dominant dynamical timescales? | Given only a high-dimensional description of a dynamical system, how can one construct a low-dimensional collective variable that reproduces its dominant dynamical timescales? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257 |
30,004,685 | OWR-7155444-006 | State Reconstruction and Reduced Coordinates from Sparse Sensors | What are the mathematical limits and possibilities of sensor placement, measurement-map discovery, time-delay methods, and multimodal data fusion for reconstructing the full state of a complex dynamical system and producing useful reduced coordinates? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257](https://doi.org/10.4171/owr/2021/23)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "dynamical_systems",
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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 | [
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"OWR-7155444-006",
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] | Takens-type embeddings, observability-Gramian placement, and nonlinear network reconstruction provide rigorous or constructive results in restricted settings, but general limits for recovering full states from multimodal noisy measurements remain open. | [
{
"url": "https://doi.org/10.1016/0167-2789(91)90222-U",
"label": "Casdagli et al., state reconstruction with noise"
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{
"url": "https://doi.org/10.1016/j.compchemeng.2012.07.014",
"label": "Serpas et al., sensor location for nonlinear systems"
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{
"url": "https://doi.org/10.1063/5.009... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/23 | null | null | null | What are the mathematical limits and possibilities of sensor placement, measurement-map discovery, time-delay methods, and multimodal data fusion for reconstructing the full state of a complex dynamical system and producing useful reduced coordinates? | What are the mathematical limits and possibilities of sensor placement, measurement-map discovery, time-delay methods, and multimodal data fusion for reconstructing the full state of a complex dynamical system and producing useful reduced coordinates? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mini-Workshop: Analysis of Data-driven Optimal Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/23, pp. 1209--1257 |
30,004,686 | OWR-7155445-001 | Unified Analysis of Higher-Dimensional Evolution Equations | Can there be a unifying theory for the analytical and numerical treatment of evolution equations on higher-dimensional domains? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/24, pp. 1259--1289](https://doi.org/10.4171/owr/2021/24)
## Literat... | 3 | open | null | 2,021 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "PDEs and their applications in physics and geometry.",
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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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"OWR-7155445-001",
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{
"url": "https://doi.org/10.4171/owr/2021/24",
"label": "Oberwolfach Report 24/2021"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/24 | null | null | null | Can there be a unifying theory for the analytical and numerical treatment of evolution equations on higher-dimensional domains? | Can there be a unifying theory for the analytical and numerical treatment of evolution equations on higher-dimensional domains? | 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: Mathematics of Dissipation – Dynamics, Data and Control (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/24, pp. 1259--1289 |
30,004,687 | OWR-7155446-002 | Green–Griffiths–Lang Conjecture for General-Type Varieties | If $X$ is a complex projective variety of general type, does there exist a proper algebraic subvariety $Y$ of $X$ containing every nonconstant holomorphic map $f:\mathbb{C}\to X$, with the smallest such $Y$ expected over number fields to coincide with the Mordell locus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
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"slug": "algebraic-geometry",
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"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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems 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-7155446-002",
"literature-status:partially-solved",
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] | The Green-Griffiths-Lang conjecture remains open for arbitrary varieties of general type, while major partial results prove it for broad classes such as sufficiently positive generic hypersurfaces and varieties with additional positivity or group-theoretic hypotheses. | [
{
"url": "https://doi.org/10.1007/s00222-023-01219-z",
"label": "Cadorel, Demailly and collaborators, hyperbolicity"
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{
"url": "https://arxiv.org/abs/1801.04765",
"label": "Demailly, recent results on GGL"
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{
"url": "https://doi.org/10.4171/owr/2021/25",
"label": "Oberwolfach Rep... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | If $X$ is a complex projective variety of general type, does there exist a proper algebraic subvariety $Y$ of $X$ containing every nonconstant holomorphic map $f:\mathbb{C}\to X$, with the smallest such $Y$ expected over number fields to coincide with the Mordell locus? | If X is a complex projective variety of general type, does there exist a proper algebraic subvariety Y of X containing every nonconstant holomorphic map f from C to X, with the smallest such Y expected over number fields to coincide with the Mordell locus? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,688 | OWR-7155446-003 | Directed Green–Griffiths–Lang Conjecture Beyond Rank One | Does the generalized Green–Griffiths–Lang conjecture hold for directed manifolds of general type beyond rank one, perhaps after imposing a suitable semistability condition on the directed subbundle $V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
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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-7155446-003",
"literature-status:open",
"owr-year:2021"
] | The generalized directed Green--Griffiths--Lang statement is proved only under strong general-type or jet-stability hypotheses; the unrestricted rank->1 formulation remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/25",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1412.2986",
"label": "Demailly, partial GGL theorem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | Does the generalized Green–Griffiths–Lang conjecture hold for directed manifolds of general type beyond rank one, perhaps after imposing a suitable semistability condition on the directed subbundle $V$? | Does the generalized Green--Griffiths--Lang conjecture hold for directed manifolds of general type beyond rank one, perhaps after imposing a suitable semistability condition on the directed subbundle V? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,689 | OWR-7155446-004 | Jet-Differential Base Loci for Green–Griffiths–Lang | Can one prove the Green–Griffiths–Lang conjecture by showing that the projection to $X$ of the base locus of Green–Griffiths jet differentials is a proper subvariety, using further differential equations from sections on that base locus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,021 | 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,
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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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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155446-004",
"literature-status:open",
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] | The cited jet-differential constructions give sections in important cases, but the required base-locus control needed for the full generalized GGL conjecture is still not established. | [
{
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"label": "Oberwolfach report"
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{
"url": "https://arxiv.org/abs/1412.2986",
"label": "Demailly, partial GGL theorem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | Can one prove the Green–Griffiths–Lang conjecture by showing that the projection to $X$ of the base locus of Green–Griffiths jet differentials is a proper subvariety, using further differential equations from sections on that base locus? | Can one prove the Green--Griffiths--Lang conjecture by showing that the projection to X of the base locus of Green--Griffiths jet differentials is a proper subvariety, using further differential equations from sections on that base locus? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,690 | OWR-7155446-005 | Nonsmooth Homogeneous Complex Monge–Ampère Solutions | How can one construct a solution $u$ of the homogeneous complex Monge–Ampère equation on $\mathbb{P}^1$ times the unit disc that fails to be $C^2$, including at an interior point? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
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"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-7155446-005",
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] | The 2021 report leaves the explicit construction of a solution outside C^2 on P^1\times D unresolved; later work constructs non-maximal-rank solutions but states that the precise regularity failure is not determined. | [
{
"url": "https://doi.org/10.4171/owr/2021/25",
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{
"url": "https://doi.org/10.2140/apde.2019.12.493",
"label": "Ross--Witt Nystr\\\"om, maximal rank"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | How can one construct a solution $u$ of the homogeneous complex Monge–Ampère equation on $\mathbb{P}^1$ times the unit disc that fails to be $C^2$, including at an interior point? | How can one construct a solution u of the homogeneous complex Monge--Ampere equation on P^1 times the unit disc that fails to be C^2, including at an interior point? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,691 | OWR-7155446-008 | Uniform Bounded Solutions of the d-Bar Equation | Given a bounded $(0,1)$-form $f$ on a domain $\Omega\subset\mathbb{C}^n$ with $\bar\partial f=0$, does there exist a bounded function $u$ such that $\bar\partial u=f$ and $\|u\|_\infty\leq C(\Omega)\|f\|_\infty$, where $C(\Omega)$ depends only on the domain? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,021 | 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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"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-7155446-008",
"literature-status:open",
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] | Uniform sup-norm solvability is known for C^2 finite-type domains and for broad classes including real-analytic boundaries, but the stated general problem for arbitrary pseudoconvex finite-type domains in C^n, n\geq3, is not fully resolved. | [
{
"url": "https://arxiv.org/abs/1909.04080",
"label": "Grundmeier--Simon--Stens\\\"ones"
},
{
"url": "https://doi.org/10.1007/s42543-025-00096-0",
"label": "Yuan, uniform estimates"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | Given a bounded $(0,1)$-form $f$ on a domain $\Omega\subset\mathbb{C}^n$ with $\bar\partial f=0$, does there exist a bounded function $u$ such that $\bar\partial u=f$ and $\|u\|_\infty\leq C(\Omega)\|f\|_\infty$, where $C(\Omega)$ depends only on the domain? | Given a bounded (0,1)-form f on a domain Omega in C^n with partial-bar f=0, does there exist a bounded function u such that partial-bar u=f and ||u||_infinity is at most C(Omega)||f||_infinity, where C(Omega) depends only on the domain? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,692 | OWR-7155446-010 | Smooth Interior Regularity for Complex Monge–Ampère Equations | If $\Omega$ is a bounded hyperconvex domain in $\mathbb{C}^n$ and $u$ solves $(dd^c u)^n=f\,d\lambda$ with $u=0$ on the boundary, does $f\in C^\infty(\Omega)$ and $f>0$ imply $u\in C^\infty(\Omega)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345](https://doi.org/10.4171/owr/2021/25)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,021 | 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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"id": 3,
"level": 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-7155446-010",
"literature-status:open",
"owr-year:2021"
] | The interior smooth-regularity conjecture for positive smooth density on arbitrary bounded domains remains open; existing results cover special domains and give a priori estimates, not the full assertion. | [
{
"url": "https://doi.org/10.4171/owr/2021/25",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1002.4825",
"label": "He, complex Monge--Amp\\`ere regularity"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/25 | null | null | null | If $\Omega$ is a bounded hyperconvex domain in $\mathbb{C}^n$ and $u$ solves $(dd^c u)^n=f\,d\lambda$ with $u=0$ on the boundary, does $f\in C^\infty(\Omega)$ and $f>0$ imply $u\in C^\infty(\Omega)$? | If Omega is a bounded hyperconvex domain in C^n and u solves (dd^c u)^n=f d lambda with u=0 on the boundary, does f in C-infinity(Omega) and f>0 imply u in C-infinity(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 | Geometric Methods of Complex Analysis (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/25, pp. 1291--1345 |
30,004,693 | OWR-7155447-001 | Reading Practices and Arguments in Mathematical Classics | For mathematical classics in different cultural traditions, how were the texts made available to readers, how were they read, and what can these reading practices teach about the nature of mathematical argument and practice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this workshop-level overview merges availability, reading-practice, and mathematical-argument themes that are) | [
"OWR-7155447-003",
"OWR-7155447-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-001",
"literature-status:open",
"owr-year:2021"
] | This is an unresolved historiographical question about access to and reading of ancient mathematical texts; the workshop literature offers discussion rather than a settled explanatory result. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | null | For mathematical classics in different cultural traditions, how were the texts made available to readers, how were they read, and what can these reading practices teach about the nature of mathematical argument and practice? | unrecoverable | The official report shows that this workshop-level overview merges availability, reading-practice, and mathematical-argument themes that are retained separately in OWR-7155447-003 and OWR-7155447-004. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,694 | OWR-7155447-002 | The Persistence of Ancient Mathematical Classics | Why does mathematics, a discipline that values progress, have classics, especially classics from Antiquity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-002",
"literature-status:open",
"owr-year:2021"
] | The question asks for a broad historical explanation of why mathematics has classics, especially from Antiquity; no unique, settled answer is established in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | Why does mathematics, a discipline that values progress, have classics, especially classics from Antiquity? | Why does mathematics, a discipline that values progress, have classics, especially classics from Antiquity? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,695 | OWR-7155447-003 | Mathematical Classics across Scholarly Traditions | What do mathematical classics mean in different scholarly traditions, how were they made available and used differently, and what did it mean for works to be deemed classics in the Arabic world? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-7155447-001"
] | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-003",
"literature-status:open",
"owr-year:2021"
] | The comparative questions about what counts as a classic and how Arabic traditions used and read such works remain active historiographical research questions rather than solved propositions. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What do mathematical classics mean in different scholarly traditions, how were they made available and used differently, and what did it mean for works to be deemed classics in the Arabic world? | What do mathematical classics mean in different scholarly traditions, how were they made available and used differently, and what did it mean for works to be deemed classics in the Arabic world? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,696 | OWR-7155447-004 | Classical Authority in Mathematical Innovation and Argument | What can the use of classical works to legitimize mathematical innovation teach us about the nature of mathematical argument and, more generally, mathematical practice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-7155447-001"
] | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-004",
"literature-status:open",
"owr-year:2021"
] | The question seeks a general account of mathematical argument and practice across historical traditions; the cited workshop material frames it as an open interpretive program. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What can the use of classical works to legitimize mathematical innovation teach us about the nature of mathematical argument and, more generally, mathematical practice? | What can the use of classical works to legitimize mathematical innovation teach us about the nature of mathematical argument and, more generally, mathematical practice? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,697 | OWR-7155447-005 | Yang Hui's Reclassification of Problems from The Nine Chapters | Why did Yang Hui and Jia Xian add nine problems to The Nine Chapters, why did Yang Hui choose the added rather than the original problems in his Reclassification, and why did he change their order? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-005",
"literature-status:open",
"owr-year:2021"
] | The motivations for Yang Hui's additions, selections, and reordering of problems are historical questions without a definitive explanation in the cited primary scholarship. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | Why did Yang Hui and Jia Xian add nine problems to The Nine Chapters, why did Yang Hui choose the added rather than the original problems in his Reclassification, and why did he change their order? | Why did Yang Hui and Jia Xian add nine problems to The Nine Chapters, why did Yang Hui choose the added rather than the original problems in his Reclassification, and why did he change their order? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,698 | OWR-7155447-006 | Mathematical Work in Commentarial Readings of Classics | How do different commentaries on mathematical classics read the underlying texts, and what kinds of mathematical work are involved in those readings? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-006",
"literature-status:open",
"owr-year:2021"
] | The question asks for a comparative analysis of commentarial reading practices and the mathematical work involved; it remains an open historiographical inquiry. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | How do different commentaries on mathematical classics read the underlying texts, and what kinds of mathematical work are involved in those readings? | How do different commentaries on mathematical classics read the underlying texts, and what kinds of mathematical work are involved in those readings? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,699 | OWR-7155447-007 | Meanings and Purposes in Mathematical Commentaries | What meanings and purposes, or artha, do commentaries give to mathematical treatises, and what mathematical work is required to establish them? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-007",
"literature-status:open",
"owr-year:2021"
] | The proposed comparison of the meanings and purposes assigned by commentaries is an interpretive research question, not a claim with a settled yes-or-no resolution. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What meanings and purposes, or artha, do commentaries give to mathematical treatises, and what mathematical work is required to establish them? | What meanings and purposes, or artha, do commentaries give to mathematical treatises, and what mathematical work is required to establish them? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,700 | OWR-7155447-008 | Reading Mathematical Classics from Lost Traditions | What does it mean to read a mathematical classic from an alien tradition or one that is irretrievably lost, and what distance or otherness and interpretive methods does that imply? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-008",
"literature-status:open",
"owr-year:2021"
] | The question of reading classics from alien or irretrievably lost traditions is a continuing methodological and historiographical problem with no definitive resolution. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What does it mean to read a mathematical classic from an alien tradition or one that is irretrievably lost, and what distance or otherness and interpretive methods does that imply? | What does it mean to read a mathematical classic from an alien tradition or one that is irretrievably lost, and what distance or otherness and interpretive methods does that imply? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,701 | OWR-7155447-009 | Chasles's Reconstruction of Brahmagupta and Euclid | How did Michel Chasles envision a common framework for reconstructing Brahmagupta's theory of rational cyclic quadrilaterals and Euclid's lost porisms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-009",
"literature-status:open",
"owr-year:2021"
] | The extracted question is an underspecified historical question about a scholar's intended common framework; the available workshop record does not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | How did Michel Chasles envision a common framework for reconstructing Brahmagupta's theory of rational cyclic quadrilaterals and Euclid's lost porisms? | How did Michel Chasles envision a common framework for reconstructing Brahmagupta's theory of rational cyclic quadrilaterals and Euclid's lost porisms? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,702 | OWR-7155447-010 | Mathematical Knowledge Transferred to Practitioners and Craftsmen | What exactly was transferred when mathematical classics were appropriated by practitioners and craftsmen—demonstrations, methods, practical results, or ideas of good mathematics—and can such works qualify as classics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-010",
"literature-status:open",
"owr-year:2021"
] | The transfer of mathematical content or practice and the classification of practitioners' works as classics remain open historical questions in the cited discussion. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What exactly was transferred when mathematical classics were appropriated by practitioners and craftsmen—demonstrations, methods, practical results, or ideas of good mathematics—and can such works qualify as classics? | What exactly was transferred when mathematical classics were appropriated by practitioners and craftsmen—demonstrations, methods, practical results, or ideas of good mathematics—and can such works qualify as classics? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,703 | OWR-7155447-011 | Material Forms and Reading of Mathematical Classics | What are the relationships among mathematical texts, marginalia, layouts, diagrams, and other material components, and how do different writing materials shape the process of reading and appropriating classics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406](https://doi.org/10... | 3 | open | null | 2,021 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | History of Mathematical Classics and Marginalia workshop report (historiography, not a mathematical research problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155447-011",
"literature-status:open",
"owr-year:2021"
] | The relationships among the components of mathematical textual production and the effects of writing materials are treated as an open roundtable research question. | [
{
"url": "https://doi.org/10.4171/owr/2021/26",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/26 | null | null | null | What are the relationships among mathematical texts, marginalia, layouts, diagrams, and other material components, and how do different writing materials shape the process of reading and appropriating classics? | What are the relationships among mathematical texts, marginalia, layouts, diagrams, and other material components, and how do different writing materials shape the process of reading and appropriating classics? | 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 | Mathematics and its Ancient Classics Worldwide: Translations, Appropriations, Reconstructions, Roles (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/26, pp. 1347--1406 |
30,004,704 | OWR-7155448-001 | Simpler Quantization of Weil-Petersson Iterated Fibrations | Is there a simpler construction and quantization of the iterated fibration structure used for the Weil–Petersson metric and its associated pseudodifferential calculus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Singular PDE (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/27, pp. 1407--1461](https://doi.org/10.4171/owr/2021/27)
## Literature review (checked 202... | 3 | open | null | 2,021 | 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-7155448-001",
"literature-status:open",
"owr-year:2021"
] | The extracted request for a simpler method is underspecified and the report presents techniques rather than a definitive simplification; it therefore remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/27",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/27 | null | null | null | Is there a simpler construction and quantization of the iterated fibration structure used for the Weil–Petersson metric and its associated pseudodifferential calculus? | Is there a simpler way to construct and quantize the iterated fibration structure used for the Weil--Petersson metric and its associated pseudodifferential calculus? | 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 | Analysis, Geometry and Topology of Singular PDE (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/27, pp. 1407--1461 |
30,004,705 | OWR-7155448-003 | Exact Flat Choir Numbers and Dimension-Sixteen Tori | What is the exact flat choir number $b_n$ in each dimension $n$, and in particular what is the largest collection of mutually isospectral, nonisometric flat tori in dimension $16$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Singular PDE (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/27, pp. 1407--1461](https://doi.org/10.4171/owr/2021/27)
## Literature review (checked 202... | 3 | open | null | 2,021 | 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-7155448-003",
"literature-status:open",
"owr-year:2021"
] | Finiteness of each flat choir number is known and new lower-bound constructions exist, but the exact value for every dimension, including dimension 16, is not determined. | [
{
"url": "https://arxiv.org/abs/2110.09457",
"label": "Nilsson--Rowlett--Rydell, flat tori"
},
{
"url": "https://arxiv.org/abs/2412.16709",
"label": "M\\\"ardby--Rowlett--Rydell, six dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/27 | null | null | null | What is the exact flat choir number $b_n$ in each dimension $n$, and in particular what is the largest collection of mutually isospectral, nonisometric flat tori in dimension $16$? | What is the precise flat choir number b_n for each dimension n, and in particular what is the largest collection of mutually isospectral non-isometric flat tori in dimension 16? | 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 | Analysis, Geometry and Topology of Singular PDE (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/27, pp. 1407--1461 |
30,004,706 | OWR-7155449-005 | Quasi-Jacobi Structure of K3 Hilbert-Scheme Invariants | For the enumerative series $F_{g,m}(\alpha;\gamma_1,\ldots,\gamma_N)$ associated with Hilbert schemes of points on a K3 surface, prove the conjectured quasi-Jacobi-form structure with its predicted index and weight, the multiple-cover formula via formal Hecke operators, and the holomorphic-anomaly equation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,021 | 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-7155449-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155449-005",
"literature-status:partially-solved",
"owr-year:2021"
] | The quasi-Jacobi, multiple-cover, and holomorphic-anomaly assertions have proofs in genus zero and in low-marking cases, but the stated general conjectures remain open. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://people.kth.se/~georgo/note/HilbHAE.pdf",
"label": "Oberdieck"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | For the enumerative series $F_{g,m}(\alpha;\gamma_1,\ldots,\gamma_N)$ associated with Hilbert schemes of points on a K3 surface, prove the conjectured quasi-Jacobi-form structure with its predicted index and weight, the multiple-cover formula via formal Hecke operators, and the holomorphic-anomaly equation. | For the enumerative series F_{g,m}(α;γ_1, …, γ_N) associated with Hilbert schemes of points on a K3 surface, Conjectures 2–4 assert quasi-Jacobi-form structure with the stated index and weight, the multiple-cover formula via formal Hecke operators, and the stated holomorphic-anomaly equation. | corrected_verified | The series notation was repaired and the three conjectural components were recast as a direct task without changing their content. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,707 | OWR-7155449-006 | Duplicate K3 Hilbert-Scheme Conjecture Suite | For the same enumerative series, the multiple-cover conjecture and the holomorphic-anomaly equation are conjectured to hold, with the resulting F_{g,m} being quasi-Jacobi forms of the predicted index and weight. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official Oberwolfach report confirms that Conjectures 2–4 form one contiguous suite on quasi-Jacobi structure, multiple covers, and the ) | [
"OWR-7155449-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155449-006",
"literature-status:partially-solved",
"owr-year:2021"
] | The continuation of the multiple-cover and holomorphic-anomaly conjectures is known in genus zero and selected low-complexity cases, while the unrestricted statement remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://people.kth.se/~georgo/note/HilbHAE.pdf",
"label": "Oberdieck"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | null | For the same enumerative series, the multiple-cover conjecture and the holomorphic-anomaly equation are conjectured to hold, with the resulting F_{g,m} being quasi-Jacobi forms of the predicted index and weight. | unrecoverable | The official Oberwolfach report confirms that Conjectures 2–4 form one contiguous suite on quasi-Jacobi structure, multiple covers, and the holomorphic-anomaly equation. This shorter extraction repeats the full suite already preserved in OWR-7155449-005. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,708 | OWR-7155449-010 | Extremal Invariants of Bounded-Volume Hyperbolic Manifolds | For connected closed hyperbolic $n$-manifolds of volume at most $v$, determine or maximize the systole, kissing number, first positive Laplace eigenvalue, and multiplicity of that eigenvalue; in dimension two, volume is equivalent to fixing the genus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,021 | 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-7155449-010",
"literature-status:open",
"owr-year:2021"
] | General optimization of systole, kissing number, first Laplace eigenvalue, and eigenvalue multiplicity at fixed genus and volume remains unresolved; current work supplies bounds and isolated cases rather than a full classification. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2302.02540",
"label": "Fortier Bourque--Petri"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | For connected closed hyperbolic $n$-manifolds of volume at most $v$, determine or maximize the systole, kissing number, first positive Laplace eigenvalue, and multiplicity of that eigenvalue; in dimension two, volume is equivalent to fixing the genus. | For connected closed hyperbolic n-manifolds of volume at most v, determine or maximize the systole, kissing number, first positive Laplace eigenvalue, and multiplicity of that eigenvalue; in dimension two, volume is equivalent to fixing the genus. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,709 | OWR-7155449-011 | Low-Volume and Asymptotic Hyperbolic-Invariant Maximizers | For connected oriented closed hyperbolic $n$-manifolds of volume at most $v$, determine the low-volume maximizers and large-$v$ asymptotics of the maximal systole, kissing number, first positive Laplace eigenvalue, and its multiplicity. In dimension two, does the Bolza surface maximize the first positive eigenvalue and... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,021 | 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-7155449-011",
"literature-status:open",
"owr-year:2021"
] | For genus two the Bolza surface is known to optimize the systolic quantities in the stated context, but its expected optimality for the first eigenvalue and multiplicity, and the requested asymptotics, remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2302.02540",
"label": "Fortier Bourque--Petri"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | For connected oriented closed hyperbolic $n$-manifolds of volume at most $v$, determine the low-volume maximizers and large-$v$ asymptotics of the maximal systole, kissing number, first positive Laplace eigenvalue, and its multiplicity. In dimension two, does the Bolza surface maximize the first positive eigenvalue and... | Determine the maximizers of these hyperbolic invariants for low volumes and their asymptotic behavior as v tends to infinity; in particular, is the Bolza surface the maximizer of the first eigenvalue and its multiplicity among genus-two hyperbolic surfaces? | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,710 | OWR-7155449-014 | Completed Masur–Veech Volumes of Odd Strata | Prove the conjectural identities expressing completed Masur–Veech volumes of odd quadratic-differential strata as their actual volumes plus weighted contributions from adjacent strata. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,021 | 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-7155449-014",
"literature-status:partially-solved",
"owr-year:2021"
] | Completed-volume formulas and the technically difficult two-singularity case have been proved, but the full conjectural equality and all stated adjacent-stratum weights are not established in general. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2502.13121",
"label": "Duryev--Goujard--Yakovlev"
},
{
"url": "https://arxiv.org/abs/2605.27611",
"label": "Möller--Prado"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | Prove the conjectural identities expressing completed Masur–Veech volumes of odd quadratic-differential strata as their actual volumes plus weighted contributions from adjacent strata. | Conjecture: for every admissible odd quadratic-differential stratum, the completed Masur–Veech volume equals the actual volume plus the displayed weighted contributions from adjacent strata, including the listed coefficients for the first strata. | corrected_verified | The repaired standalone statement was checked against the official Oberwolfach report. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,711 | OWR-7155449-015 | Completed $\Theta$-Twisted Volumes of Bordered-Curve Moduli | Prove the identity $\widehat V_{g,n}(L_1,\ldots,L_n)=V^\Theta_{g,n}(L_1,\ldots,L_n)$ between the completed super Weil–Petersson volume polynomial and the $\Theta$-twisted volume polynomial of bordered-curve moduli. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518](https://doi.org/10.4171/owr/2021/28)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,021 | 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-7155449-015",
"literature-status:open",
"owr-year:2021"
] | Later work constructs super Weil--Petersson measures and proves finiteness and recursion properties, but the specific natural Euler-class identity and equality of volumes in the record remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2021/28",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2312.14558",
"label": "Norbury"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/28 | null | null | null | Prove the identity $\widehat V_{g,n}(L_1,\ldots,L_n)=V^\Theta_{g,n}(L_1,\ldots,L_n)$ between the completed super Weil–Petersson volume polynomial and the $\Theta$-twisted volume polynomial of bordered-curve moduli. | For the Θ-twisted volume polynomials of the moduli spaces of bordered curves, conjecture that the completed polynomial V̂_{g,n}(L_1,…,L_n) equals the polynomial V^Θ_{g,n}(L_1,…,L_n) defined using the natural extension of the relevant bundle. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Enumerative Geometry of Surfaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/28, pp. 1463--1518 |
30,004,712 | OWR-7155450-003 | Hyperkähler Compactification of Projective Fibrations | Given a smooth projective fibration $M_U\to U$, where $U\subseteq\mathbb{P}^n$, when does there exist a smooth hyper-Kähler compactification $M$ of $M_U$ with a regular morphism $\pi:M\to\mathbb{P}^n$ extending $\pi_U$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577](https://doi.org/10.4171/owr/2021/29)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-7155450-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Compactification criteria and broad classes of torsors and group schemes are now known, including smooth hyper-Kähler examples, but no necessary-and-sufficient criterion for the general question is established. | [
{
"url": "https://doi.org/10.4171/owr/2021/29",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2411.06505",
"label": "Saccà"
},
{
"url": "https://arxiv.org/abs/2002.01420",
"label": "Saccà"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/29 | null | null | null | Given a smooth projective fibration $M_U\to U$, where $U\subseteq\mathbb{P}^n$, when does there exist a smooth hyper-Kähler compactification $M$ of $M_U$ with a regular morphism $\pi:M\to\mathbb{P}^n$ extending $\pi_U$? | Given a smooth projective fibration M_U → U with U contained in P^n, when does there exist a smooth hyper-Kähler compactification M of M_U with a regular morphism π:M → P^n extending π_U? | corrected_verified | The projective-space inclusions and morphisms were consistently dollar-delimited without changing the question. | null | null | null | null | null | Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577 |
30,004,713 | OWR-7155450-004 | Kodaira Dimensions of Abelian-Differential Moduli Spaces | Determine the behavior of the Kodaira dimension of moduli spaces of Abelian differentials as the genus $g$ becomes large, especially for strata with few marked points, including the subcanonical case $n=1$ with $\mu=(2g-2)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577](https://doi.org/10.4171/owr/2021/29)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-7155450-004",
"literature-status:partially-solved",
"owr-year:2021"
] | General type is proved for many few-zero strata and for the large-genus odd and even minimal spin components, but the broad few-point Kodaira-dimension question remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/29",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2204.11943",
"label": "Chen--Costantini--Möller"
},
{
"url": "https://arxiv.org/abs/2410.18719",
"label": "Bud--Chen--Möller"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/29 | null | null | null | Determine the behavior of the Kodaira dimension of moduli spaces of Abelian differentials as the genus $g$ becomes large, especially for strata with few marked points, including the subcanonical case $n=1$ with $\mu=(2g-2)$. | Determine the behavior of the Kodaira dimension of moduli spaces of Abelian differentials as the genus g becomes large, especially in cases with few marked points, including the subcanonical case n=1 with μ=(2g−2). | corrected_verified | The genus, marking, and stratum parameters were normalized as LaTeX without changing the problem. | null | null | null | null | null | Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577 |
30,004,714 | OWR-7155450-006 | Flag-Variety Line-Bundle Cohomology in Positive Characteristic | Over a field of positive characteristic, determine the cohomology groups of line bundles on the complete flag variety $\operatorname{Flag}(V)$ as $\operatorname{GL}(V)$-representations, or at least characterize which such cohomology groups vanish. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577](https://doi.org/10.4171/owr/2021/29)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,021 | 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-7155450-006",
"literature-status:partially-solved",
"owr-year:2021"
] | Gao--Raicu characterize vanishing and nonvanishing and obtain character formulas for restricted families, while later work adds recursions and characteristic-two formulas; the full GL(V)-representation problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/29",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2210.03656",
"label": "Gao--Raicu"
},
{
"url": "https://arxiv.org/abs/2411.13450",
"label": "Kyomuhangi--Raicu--Reed"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/29 | null | null | null | Over a field of positive characteristic, determine the cohomology groups of line bundles on the complete flag variety $\operatorname{Flag}(V)$ as $\operatorname{GL}(V)$-representations, or at least characterize which such cohomology groups vanish. | Over a field of positive characteristic, determine the cohomology groups of line bundles on the complete flag variety Flag(V) as GL(V)-representations, or at least characterize which such cohomology groups vanish. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Classical Algebraic Geometry (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/29, pp. 1519--1577 |
30,004,715 | OWR-7155451-004 | Scalar-Curvature Rigidity on Wrapped Sphere Complements | Let $\Sigma$ be a subset of the standard unit sphere $S^n$ with the wrapping property, and let $X=S^n\setminus\Sigma$ with its standard metric $g_0$. If a possibly incomplete metric $g$ on $X$ satisfies $g\geq g_0$ and $\operatorname{Sc}(g)\geq n(n-1)=\operatorname{Sc}(g_0)$, must $g=g_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 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-7155451-004",
"literature-status:partially-solved",
"owr-year:2021"
] | Rigidity is proved in restricted singular-set and codimension settings, including wrapping hypotheses, but the stated general rigidity problem on a punctured sphere remains unresolved. | [
{
"url": "https://www.ihes.fr/~gromov/wp-content/uploads/2019/08/scalar-lectures-IHES-2019-4.pdf",
"label": "Gromov, scalar curvature lectures"
},
{
"url": "https://arxiv.org/abs/2306.06906",
"label": "Li, Su and Wang, scalar curvature rigidity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Let $\Sigma$ be a subset of the standard unit sphere $S^n$ with the wrapping property, and let $X=S^n\setminus\Sigma$ with its standard metric $g_0$. If a possibly incomplete metric $g$ on $X$ satisfies $g\geq g_0$ and $\operatorname{Sc}(g)\geq n(n-1)=\operatorname{Sc}(g_0)$, must $g=g_0$? | Let Σ be a subset of the standard unit sphere S^n with the wrapping property, and let X=S^n∖Σ with its standard metric g_0. If a possibly incomplete metric g on X satisfies g≥g_0 and Sc(g)≥n(n−1)=Sc(g_0), must g equal g_0? | corrected_verified | Set difference, scalar-curvature, and comparison notation were normalized without changing the rigidity question. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
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