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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,016 | OWR-14298589-001 | Bijections for Self-Overlapping Polygons in Other Topologies | Extend the known bijective approach to self-overlapping polygons from its present topological setting to other surface topologies, and characterize the resulting enumerative formulas. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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-14298589-001",
"literature-status:open",
"owr-year:2024"
] | The report presents extension of the self-overlapping-polygon bijection beyond the stated topology as an open question, and no later primary result located here resolves that general extension. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://epubs.siam.org/doi/10.1137/1.9781611973068.19",
"label": "Shor--van Wyk"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Extend the known bijective approach to self-overlapping polygons from its present topological setting to other surface topologies, and characterize the resulting enumerative formulas. | Whether our bijective approach can be extended to other topologies remains an intriguing open question. Wn(g) (x(z1 ), . . . , x(zn ))x′ (z1 ) . . . x′ (zn ) = X (g) \partial \partial Tℓ1 ,...,ℓn − \cdot\cdot\cdot − . \partialz1 \partialzn (\gammaz1 )ℓ1 \cdot \cdot \cdot (\gammazn )ℓn ℓ1 ,...,ℓn \geq1 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,017 | OWR-14298589-002 | Limiting Area Distribution of Random Self-Overlapping Polygons | For a uniformly random $n$-sided self-overlapping polygon with fixed generic side set, prove that its area minus $\frac{1}{2\pi}\log n$ converges in distribution as $n\to\infty$, and identify the limiting law. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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-14298589-002",
"literature-status:open",
"owr-year:2024"
] | The expectation has an established logarithmic asymptotic, but the centered distributional convergence is still stated as an open problem and no proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | For a uniformly random $n$-sided self-overlapping polygon with fixed generic side set, prove that its area minus $\frac{1}{2\pi}\log n$ converges in distribution as $n\to\infty$, and identify the limiting law. | Numerical experiments suggest that this random area, upon subtraction of 1 2\pi log n, converges in distribution as n \to \infty, but this remains an open problem. properties of uniformly sampled such disks, hinting at the existence of a universal scaling limit. For the first family, we consider n-sided self-overlappin... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,018 | OWR-14298589-003 | Mixed Square-Tiled-Surface Talk Transition | What we do not know (yet) about square-tiled surfaces in large genus? Given a positive integral partition µ = (m1 , . . . , mn ) of 2g − 2, let H(µ) be the stratum of holomorphic differentials on smooth complex curves whose orders of ∗ zeros are prescribed by the signature µ. Up to scaling of CP , the stratum H(µ) pa- ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 | Unrecoverable OWR statement (The official report confirms that this extraction joins the end of one contribution to the title and opening sentence of the next and contai) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-003",
"literature-status:open",
"owr-year:2024"
] | This is an agenda-level record collecting unresolved questions about square-tiled surfaces and large-genus strata; the cited surrounding results do not settle the extracted program. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | null | What we do not know (yet) about square-tiled surfaces in large genus? Given a positive integral partition µ = (m1 , . . . , mn ) of 2g − 2, let H(µ) be the stratum of holomorphic differentials on smooth complex curves whose orders of ∗ zeros are prescribed by the signature µ. Up to scaling of CP , the stratum H(µ) pa- ... | unrecoverable | The official report confirms that this extraction joins the end of one contribution to the title and opening sentence of the next and contains no standalone problem; the concrete square-tiled-surface questions are represented by the following records. No separate clean statement is promoted; the original record remains... | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,019 | OWR-14298589-004 | Large-Genus Cylinder Decompositions of Square-Tiled Surfaces | Determine the large-genus behavior of the limiting cylinder-area measure $\nu_{k,\mu}$ for every stratum of Abelian, quadratic, and higher-order differentials, extending the known principal-stratum results and the work in progress for quartic differentials. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | partially_solved | null | 2,024 | 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-14298589-004",
"literature-status:partially-solved",
"owr-year:2024"
] | The fixed-stratum counting limit is proved, and large-genus behavior is understood for principal quadratic strata, but the stated all-strata and quartic-differential program is incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2007.04740",
"label": "Delecroix--Goujard--Zograf--Zorich"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Determine the large-genus behavior of the limiting cylinder-area measure $\nu_{k,\mu}$ for every stratum of Abelian, quadratic, and higher-order differentials, extending the known principal-stratum results and the work in progress for quartic differentials. | Problem 1: cylinder decompositions in large genus We consider limits of square-tiled surfaces when the number of squares N and the genus g tend to infinity. In this first problem we first let N tend to infinity and then let g tend to infinity. When letting N tend to infinity, we have the following result which is very ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,020 | OWR-14298589-005 | Intermediate-Area Cylinders on Large-Genus Square-Tiled Surfaces | Determine the full cylinder-area spectrum for random square-tiled surfaces in large genus. In particular, estimate the number of cylinders whose normalized area lies between $1/\sqrt{g}$ and $2/\sqrt{g}$, between the known microscopic and macroscopic regimes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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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"id": 3,
"level": 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-14298589-005",
"literature-status:open",
"owr-year:2024"
] | Macroscopic and microscopic cylinder regimes have partial asymptotic descriptions, but the intermediate-area spectrum asked for in the record remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2007.04740",
"label": "large-genus square-tiled surfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Determine the full cylinder-area spectrum for random square-tiled surfaces in large genus. In particular, estimate the number of cylinders whose normalized area lies between $1/\sqrt{g}$ and $2/\sqrt{g}$, between the known microscopic and macroscopic regimes. | Problem 2: cylinders of intermediate area As stated in Theorem 2, in the large genus asymptotics we have a good under- standing of macroscopic cylinders (the ones with an area proportional to the area of the surface) and the microscopic ones (the ones with an area proportional to the area of the surface divided by g). ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,021 | OWR-14298589-006 | Diagonal Large-Genus Limits of Square-Tiled Surfaces | Fix $\alpha>0$. Determine the limiting behavior of random square-tiled surfaces with $N=\lfloor\alpha g\rfloor$ squares as $g\to\infty$, rather than first sending $N$ to infinity at fixed genus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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-14298589-006",
"literature-status:open",
"owr-year:2024"
] | The diagonal regime with the number of squares proportional to genus is explicitly posed as future work, and no primary result located here establishes its limiting behavior. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Fix $\alpha>0$. Determine the limiting behavior of random square-tiled surfaces with $N=\lfloor\alpha g\rfloor$ squares as $g\to\infty$, rather than first sending $N$ to infinity at fixed genus. | Problem 3: diagonal limit N = ⌊\alphag⌋ In Theorem 2 the limit in N (the number of squares) is taken first and then the limit in g is considered. It is highly interesting to try to understand the behavior of random square-tiled surfaces with N = ⌊\alphag⌋ squares where \alpha is some parameters and g tends to infinity.... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,022 | OWR-14298589-007 | Resolved Averaged Twist-Torus Distribution Lead-In | How do twist tori TP (et L) distribute in Mg as t \to \infty? 1. Twist tori Given a pants decomposition P of a closed oriented surface S of genus g \geq 2 and a positive length vector L \in RP >0 , we consider the twist torus | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | partially_solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | Duplicate/merged OWR extraction (The official report poses this broad question as a lead-in and immediately gives the authors’ averaged equidistribution theorem; the remaini) | [
"OWR-14298589-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Equidistribution results are known for broad families of expanding twist tori along almost all sequences or under structural hypotheses, but the unrestricted distribution question in the record is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2405.12106",
"label": "Calderon--Farre"
},
{
"url": "https://arxiv.org/abs/2507.09775",
"label": "Chaika--Khalil"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | null | How do twist tori TP (et L) distribute in Mg as t \to \infty? 1. Twist tori Given a pants decomposition P of a closed oriented surface S of genus g \geq 2 and a positive length vector L \in RP >0 , we consider the twist torus | unrecoverable | The official report poses this broad question as a lead-in and immediately gives the authors’ averaged equidistribution theorem; the remaining unaveraged conjecture is represented canonically by OWR-14298589-008. No separate clean statement is promoted; the original record remains publicly visible and retained for prov... | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,023 | OWR-14298589-008 | Masur-Veech Equidistribution of Individual Twist Tori | Prove that each expanding twist torus, without averaging, converges in the weak-star topology to the Masur–Veech–Smillie measure on the component of the stratum containing it. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | partially_solved | null | 2,024 | 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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"id": 3,
"level": 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... | [
"OWR-14298589-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Later work proves convergence outside a zero-density set for broad twist-torus families and identifies several limiting measures, but the all-time Masur--Veech--Smillie convergence conjectured here remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2405.12106",
"label": "Calderon--Farre"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Prove that each expanding twist torus, without averaging, converges in the weak-star topology to the Masur–Veech–Smillie measure on the component of the stratum containing it. | Pushing this down to Mg , we recover the equidistribution result from Theorem 2. The only thing left to do is identify ν. This is achieved by applying recent work of Apisa–Wright [1] that high rank affine invariant submanifolds are large. We estimate the rank of the support of ν using certain cylinder deformations [8].... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,024 | OWR-14298589-009 | Spines and One-Face Maps of Random Hyperbolic Surfaces | Determine the limiting law of the spine of a random hyperbolic surface as the genus tends to infinity, and find other natural geometric constructions of one-face maps on hyperbolic surfaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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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"id": 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-009",
"literature-status:open",
"owr-year:2024"
] | The law of the spine and a geometric one-face-map construction are posed as questions; existing bijections and random-surface results do not answer these requests in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1710.09727",
"label": "Mirzakhani--Petri"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Determine the limiting law of the spine of a random hyperbolic surface as the genus tends to infinity, and find other natural geometric constructions of one-face maps on hyperbolic surfaces. | What is the law of the spine of a random hyperbolic surface as g \to \infty ? What are other nice ways to construct a one face map on a hyperbolic surface ? Is there a nice geometric adaptation of Chapuy’s bijection to con- struct random surfaces ? Riemann Surfaces: Random, Flat, and Hyperbolic Geometry 2405 One of the... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,025 | OWR-14298589-010 | Geometric Chapuy Bijections for Random Surfaces | Construct a geometric adaptation of Chapuy’s bijection between one-face maps and decorated trees that directly produces random surfaces, and explain the associated enumerative identities geometrically. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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-14298589-010",
"literature-status:open",
"owr-year:2024"
] | The requested geometric adaptation of Chapuy's bijection is explicitly left open, and no primary construction resolving it was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Construct a geometric adaptation of Chapuy’s bijection between one-face maps and decorated trees that directly produces random surfaces, and explain the associated enumerative identities geometrically. | Is there a nice geometric adaptation of Chapuy’s bijection to con- struct random surfaces ? One of the key tools of the proof of [6] is Chapuy’s bijection between one faced maps and decorated trees [4]. Enumerative questions. A more modest question would be to find a better explanation of the following enumerative fact... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,026 | OWR-14298589-011 | Poisson Laws across Boundary Regimes of Random Hyperbolic Surfaces | Find a unified proof of the known volume identities and determine further volumes for which they hold. Prove a Poisson-limit interpolation for simple closed geodesics on random genus-$g$ hyperbolic surfaces with one boundary of length $L_g$ across the regimes $L_g=o(g)$, $L_g/g\to c$, and $L_g\gg g$, including existenc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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... | [
"OWR-14298589-012"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-011",
"literature-status:open",
"owr-year:2024"
] | The proposed Poisson interpolation across boundary-length regimes is stated as a conjecture; known Poisson laws for closed or restricted regimes do not establish the full three-regime statement. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1710.09727",
"label": "Mirzakhani--Petri"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Find a unified proof of the known volume identities and determine further volumes for which they hold. Prove a Poisson-limit interpolation for simple closed geodesics on random genus-$g$ hyperbolic surfaces with one boundary of length $L_g$ across the regimes $L_g=o(g)$, $L_g/g\to c$, and $L_g\gg g$, including existenc... | Question 6. Find a unified proof of these identities, and more volumes for which this is true. Interpolating between Theorems 1 and 2. Since metric maps can be seen as hyperbolic surfaces with a very large boundary [5], we make the following conjec- ture that, in some sense, interpolates betweens Theorems 1 and 2. L Co... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,027 | OWR-14298589-012 | Duplicate Boundary-Regime Poisson-Limit Conjecture | Interpolating between Theorems 1 and 2. Since metric maps can be seen as hyperbolic surfaces with a very large boundary [5], we make the following conjec- ture that, in some sense, interpolates betweens Theorems 1 and 2. L Conjecture 7. Let Ng g (x, y) be the number of simple closed geodesics of length \in [x, y] in a ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this overlapping extraction repeats the volume-identity question and boundary-regime Poisson-limit conject) | [
"OWR-14298589-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-012",
"literature-status:open",
"owr-year:2024"
] | The extracted conjecture remains unresolved in its full boundary-length interpolation, including the existence and identification of the universal rescaling function. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1710.09727",
"label": "Mirzakhani--Petri"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | null | Interpolating between Theorems 1 and 2. Since metric maps can be seen as hyperbolic surfaces with a very large boundary [5], we make the following conjec- ture that, in some sense, interpolates betweens Theorems 1 and 2. L Conjecture 7. Let Ng g (x, y) be the number of simple closed geodesics of length \in [x, y] in a ... | unrecoverable | The official report confirms that this overlapping extraction repeats the volume-identity question and boundary-regime Poisson-limit conjecture represented canonically by OWR-14298589-011. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,028 | OWR-14298589-013 | Uniform Bounds across Strata of Flat Surfaces | Extend the known lower bound to every hyperelliptic stratum. Establish corresponding upper and lower bounds for all strata. Determine whether the almost-everywhere qualification in the lower bound can be removed, or exhibit counterexamples. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | partially_solved | null | 2,024 | 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-14298589-013",
"literature-status:partially-solved",
"owr-year:2024"
] | Upper bounds and lower bounds in genus two, together with recent restricted hyperelliptic results, provide partial progress, while the all-hyperelliptic and all-strata questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2601.15993",
"label": "Aulicino--Masur--Pan--Su"
},
{
"url": "https://arxiv.org/abs/1810.05227",
"label": "Aggarwal--Delecroix--Goujard--Zograf--Zorich"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Extend the known lower bound to every hyperelliptic stratum. Establish corresponding upper and lower bounds for all strata. Determine whether the almost-everywhere qualification in the lower bound can be removed, or exhibit counterexamples. | There are some obvious questions that remain: (1) We would like to extend the lower bound to all hyperelliptic strata. (2) Can one find corresponding upper and lower bounds for all strata? (3) Can one remove the almost everywhere statement in the lower bound or are there examples where the given lower bound does not ho... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,029 | OWR-14298589-014 | Enumerative Meaning of k-Leaky Double Hurwitz Numbers | Find an enumerative interpretation of the $k$-leaky double Hurwitz numbers $H_g^k(A)$ for $k>0$. More broadly, formulate natural enumerative problems for $k$-differentials of arbitrary genus $g$ and zero-pole profile $A$, and determine whether their counts equal or otherwise relate to $H_g^k(A)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | open | null | 2,024 | 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-14298589-014",
"literature-status:open",
"owr-year:2024"
] | Intersection-theoretic and tropical formulas now give strong structural information about k-leaky numbers, but their enumerative meaning for positive k is still explicitly described as unclear. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1017/fms.2025.26",
"label": "Cavalieri--Markwig--Schmitt"
},
{
"url": "https://arxiv.org/abs/2509.04335",
"label": "one-part leaky covers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | Find an enumerative interpretation of the $k$-leaky double Hurwitz numbers $H_g^k(A)$ for $k>0$. More broadly, formulate natural enumerative problems for $k$-differentials of arbitrary genus $g$ and zero-pole profile $A$, and determine whether their counts equal or otherwise relate to $H_g^k(A)$. | Enumerative Meaning and Future Directions A major open question is to find an enumerative interpretation of the k-leaky double Hurwitz numbers for k > 0. where e = (e1 , . . . , en ) is a vector of non-negative integers and breg (A) is a variant of the branch class with codimension 2g − 3 + n − |e|. These numbers inter... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,030 | OWR-14298589-015 | k-Differential Interpretation of Leaky Double Hurwitz Numbers | For arbitrary genus $g$ and zero-pole profile $A$, formulate a natural enumerative problem for $k$-differentials with prescribed periods or residues. Determine its relationship to the $k$-leaky double Hurwitz number $H_g^k(A)$, extending the similarities observed in genus zero. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424](https://doi.org/10.4171/owr/2024/41)
## Literature review (che... | 3 | partially_solved | null | 2,024 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298589-015",
"literature-status:partially-solved",
"owr-year:2024"
] | Genus-zero residue-counting problems and structural comparisons with k-leaky numbers are known, but the arbitrary-genus enumerative problem and the proposed relationship remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2024/41",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1017/fms.2025.26",
"label": "Cavalieri--Markwig--Schmitt"
},
{
"url": "https://arxiv.org/abs/2509.04335",
"label": "one-part leaky covers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/41 | null | null | null | For arbitrary genus $g$ and zero-pole profile $A$, formulate a natural enumerative problem for $k$-differentials with prescribed periods or residues. Determine its relationship to the $k$-leaky double Hurwitz number $H_g^k(A)$, extending the similarities observed in genus zero. | Is there an interesting enumerative problems for k-differentials in arbitrary genus g and profile A of zeros and poles? Does it have some relationship to the number Hgk (A)? 6. Enumerative Meaning and Future Directions A major open question is to find an enumerative interpretation of the k-leaky double Hurwitz numbers ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Riemann Surfaces: Random, Flat, and Hyperbolic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/41, pp. 2369--2424 |
30,006,031 | OWR-14298590-001 | Little Three-Disks Actions on Operadic Homotopy Centers | Does the little three-disks operad act on the homotopy center of every nonsymmetric operad? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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-14298590-001",
"literature-status:open",
"owr-year:2024"
] | The proposed E3-action on the homotopy center of a non-symmetric operad is presented as a conjecture with a proof plan; the identified literature proves the analogous monoid case, not this stated operadic claim. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2012.04.011",
"label": "Batanin--Markl"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | Does the little three-disks operad act on the homotopy center of every nonsymmetric operad? | This conjecture is the analogue of the result from Batanin and Berger about the action of the little 2-disks operad on the homotopy center of a monoid [2]. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,032 | OWR-14298590-002 | Higher-Dimensional Categorical Nerves | How can categorical nerve constructions and their universal properties be extended to higher dimensions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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-14298590-002",
"literature-status:open",
"owr-year:2024"
] | The report presents reaching higher dimensions as future work; no complete higher-dimensional result resolving the extracted question was identified. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | How can categorical nerve constructions and their universal properties be extended to higher dimensions? | How do we reach higher dimensions? Theorem 1. [MOR22] All 2-categorical nerves are equivalent and satisfy the uni- versal property given by Gepner–Haugseng. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,033 | OWR-14298590-003 | Simpson’s Weak-Units Conjecture for Higher Categories | Are fair $n$-categories equivalent to weakly globular $n$-fold categories, as predicted by Simpson's weak-units conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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,
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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-14298590-003",
"literature-status:open",
"owr-year:2024"
] | The fair n-category formulation of Simpson's weak-units conjecture remains a proposed equivalence rather than a proved theorem in the cited report and current literature. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
},
{
"url": "https://arxiv.org/abs/1609.04072",
"label": "Paoli, Weakly globular N-fold categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | Are fair $n$-categories equivalent to weakly globular $n$-fold categories, as predicted by Simpson's weak-units conjecture? | Therefore one way to for- mulate the Simspon’s conjecture is that fair n-categories are equivalent to weakly globular n-fold categories. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,034 | OWR-14298590-004 | Geometric Fixed Points for Poincaré Infinity-Categories | How should geometric fixed-point constructions such as $\Phi^{C_2}\mathrm{THR}(R)$ extend to Poincaré $\infty$-categories? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298590-004",
"literature-status:open",
"owr-year:2024"
] | The report states the extension of the geometric-fixed-point formula from ring spectra to Poincare infinity-categories as a natural question; no proof of the extracted extension was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
},
{
"url": "https://younghomseminar.github.io/posts/2023-04-13/",
"label": "Rasmusen, THR of Poincare infinity-categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | How should geometric fixed-point constructions such as $\Phi^{C_2}\mathrm{THR}(R)$ extend to Poincaré $\infty$-categories? | Using this C2 -action, it was shown in [2] that ΦC2 THR(R) ≃ ΦC2 R ⊗R ΦC2 R, A natural question is now, how one could extend this to the setting of Poincaré \infty-categories? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,035 | OWR-14298590-006 | Left-Exact Characterization of Enriched Topoi | Is a presentable enriched category $E$ a $V$-topos if and only if the colimit functor $\mathcal{P}(E)\to E$ is left exact? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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-14298590-006",
"literature-status:open",
"owr-year:2024"
] | The enriched V-topos characterization is stated as a conjecture in the report, and no subsequent proof of the full assertion was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | Is a presentable enriched category $E$ a $V$-topos if and only if the colimit functor $\mathcal{P}(E)\to E$ is left exact? | We conjecture that a presentable V-category E is a V-topos if and only if the colimit functor P (E) \to E is left exact. This conjecture is connected to the existence of a (pseudo) distributive law Q\omega P \to P Q\omega between the free cocompletion monad P : VCAT \to VCAT and the free finite completion monad Q\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 | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,036 | OWR-14298590-007 | Distributivity of Compact Weight Scales | Do the $\omega$-compact weight-scale constructions in enriched higher category theory satisfy the required distributivity law? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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"
} | {
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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-14298590-007",
"literature-status:open",
"owr-year:2024"
] | The distributivity of the scale of omega-compact weights is explicitly presented as a conjecture; no resolution of the general statement was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | Do the $\omega$-compact weight-scale constructions in enriched higher category theory satisfy the required distributivity law? | We conjecture that if the smc \infty-category V is \omega-presentable, then the scale \omega(V) of \omega-compact weights is distributive. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,037 | OWR-14298590-008 | Higher Algebra Structures on Graph-Cooperad Deformations | Does the deformation complex of the chain cooperad $\mathrm{EGraphs}_n^c$ carry a natural $E_{n+2}$-algebra structure, with the action of the $L_\infty$-algebra $\mathrm{EGC}_{2n}$ inducing a quasi-isomorphism
$$U_{E_{n+2}}(\mathrm{EGC}_{2n})\xrightarrow{\sim}\operatorname{Def}(\mathrm{EGraphs}_n^c,\mathrm{EGraphs}_n^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308](https://doi.org/10.4171/owr/2024/39)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,024 | 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"
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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-14298590-008",
"literature-status:open",
"owr-year:2024"
] | The claimed natural En+2-structure and enveloping-algebra quasi-isomorphism are explicitly conjectural in the primary report, with no later proof identified. | [
{
"url": "https://doi.org/10.4171/owr/2024/39",
"label": "Oberwolfach Report 39 (2024)"
},
{
"url": "https://pro.univ-lille.fr/fileadmin/user_upload/pages_pros/benoit_fresse/Manuscripts/owr-BFresse-2024.pdf",
"label": "Fresse, Homotopical Algebra and Higher Structures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/39 | null | null | null | Does the deformation complex of the chain cooperad $\mathrm{EGraphs}_n^c$ carry a natural $E_{n+2}$-algebra structure, with the action of the $L_\infty$-algebra $\mathrm{EGC}_{2n}$ inducing a quasi-isomorphism
$$U_{E_{n+2}}(\mathrm{EGC}_{2n})\xrightarrow{\sim}\operatorname{Def}(\mathrm{EGraphs}_n^c,\mathrm{EGraphs}_n^... | We conjecture that the deformation complex of the object EGraphscn (in the category of chain cooperads) is equipped with a natural En+2 -algebra structure and that the action of the L\infty -algebra EGC2n on EGraphscn \sim gives rise to a quasi-isomorphism UEn+2 (EGC2n ) − \to Dfm(EGraphscn , EGraphscn ), where UEn+2 (... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/39, pp. 2251--2308 |
30,006,038 | OWR-14298591-001 | Workshop Summary on Mathematical General Relativity | problem. Sung-Jin Oh explained a very flexible and promising newly-developed method of generating initial data sets with good localisation and fall off properties, gener- alising and complementing existing gluing results. Considering asymptotically hyperbolic instead of asymptotically Euclidean ini- tial data sets, Ann... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is workshop-summary prose covering several talks and contains no standalone problem. No se) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-001",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a contextual report fragment rather than an identifiable mathematical assertion; its status is therefore unresolved and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | null | problem. Sung-Jin Oh explained a very flexible and promising newly-developed method of generating initial data sets with good localisation and fall off properties, gener- alising and complementing existing gluing results. Considering asymptotically hyperbolic instead of asymptotically Euclidean ini- tial data sets, Ann... | unrecoverable | The official report confirms that this extraction is workshop-summary prose covering several talks and contains no standalone problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,039 | OWR-14298591-002 | Global Dynamics of the Vlasov–Maxwell System | Do arbitrary sufficiently regular initial data for the relativistic Vlasov–Maxwell system generate global-in-time classical solutions, beyond the known perturbative and symmetry-restricted regimes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
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"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-14298591-002",
"literature-status:open",
"owr-year:2024"
] | The source explicitly says that the underlying Vlasov-Maxwell problem remains open beyond special cases; 2025 work proves only a small-data global-existence and scattering regime. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
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},
{
"url": "https://msp.org/apde/2025/18-3/apde-v18-n3-p03-s.pdf",
"label": "Bigorgne, Global existence and modified scattering"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Do arbitrary sufficiently regular initial data for the relativistic Vlasov–Maxwell system generate global-in-time classical solutions, beyond the known perturbative and symmetry-restricted regimes? | Although the problem remains open besides these specific cases, various continu- ation criteria have been obtained during the past decades (see for instance [7, 9]). Modified scattering for the small data solutions to the Vlasov-Maxwell system Léo Bigorgne | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,040 | OWR-14298591-003 | Reported Asymptotics for Silent Wave Equations | We study the asymptotics of solutions to systems of linear wave equations on cos- mological spacetimes. Here the asymptotics refer to the behavior of the solutions near a cosmological singularity, or near infinity in the expanding direction. The asymptotics correspond to the heuristics of the BKL conjecture. We present... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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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 | Unrecoverable OWR statement (The official report presents asymptotic estimates of all orders and a Maxwell-field application as results of the reported work; it does not) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-003",
"literature-status:open",
"owr-year:2024"
] | The extracted passage reports asymptotic estimates and an application, but does not state a definite problem whose full resolution can be assessed; unresolved or unclear claims are classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | null | We study the asymptotics of solutions to systems of linear wave equations on cos- mological spacetimes. Here the asymptotics refer to the behavior of the solutions near a cosmological singularity, or near infinity in the expanding direction. The asymptotics correspond to the heuristics of the BKL conjecture. We present... | unrecoverable | The official report presents asymptotic estimates of all orders and a Maxwell-field application as results of the reported work; it does not pose a separate open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,041 | OWR-14298591-004 | Incomplete Lorentzian-Geometry Result Fragment | Conjecture 3.4], this where (hǫ )µν \to 0 as ǫ \to 0 together with all derivatives along \partialt and 1 (ǫ2 + |x|2 ) 2 \partialx ; (iii) in the setting (II), we can moreover ensure that gǫ = g outside of the domain of influence of Ū . This also holds when (M, g) is a neighborhood of the domain of outer communications... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged fragment of a result and surrounding technical hypotheses, not a standalone o) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-004",
"literature-status:open",
"owr-year:2024"
] | The extracted text is an incomplete reference to Conjecture 3.4 and does not identify a complete claim; its unresolved status is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | null | Conjecture 3.4], this where (hǫ )µν \to 0 as ǫ \to 0 together with all derivatives along \partialt and 1 (ǫ2 + |x|2 ) 2 \partialx ; (iii) in the setting (II), we can moreover ensure that gǫ = g outside of the domain of influence of Ū . This also holds when (M, g) is a neighborhood of the domain of outer communications... | unrecoverable | The official report confirms that this extraction is a damaged fragment of a result and surrounding technical hypotheses, not a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,042 | OWR-14298591-006 | Einstein Boundary Regularity with Positive Cosmological Constant | Do the generic regularity and local-solvability properties of the Anderson boundary map for Ricci-flat and negative Einstein metrics extend to Einstein metrics with positive Einstein constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-006",
"literature-status:open",
"owr-year:2024"
] | The source explicitly identifies the analogous regularity result for positive Einstein constants as an open question, with no later resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Do the generic regularity and local-solvability properties of the Anderson boundary map for Ricci-flat and negative Einstein metrics extend to Einstein metrics with positive Einstein constant? | It remains an open question whether a similar result holds for positive Einstein constants. Theorem 3. Let n \geq 4 and Ω be an n-dimensional manifold with smooth bound- ary Σ satisfying \pi1 (Ω, Σ) = 0. The boundary map Π : M ck,\alpha (Ω)/Dk+1,\alpha (Ω) \to − k,\alpha k−1,\alpha S1 (Σ) \times C (Σ) is regular on an ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,043 | OWR-14298591-007 | Dynamics Near Generic Spacetime Singularities | Give a rigorous dynamical description of generic solutions of the Einstein equations near spacetime singularities, including the extent to which Belinski–Khalatnikov–Lifshitz dynamics governs their asymptotic behavior. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-007",
"literature-status:open",
"owr-year:2024"
] | The report calls the dynamical description of generic spacetime behavior near singularities a wide open problem; the extracted claim remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Give a rigorous dynamical description of generic solutions of the Einstein equations near spacetime singularities, including the extent to which Belinski–Khalatnikov–Lifshitz dynamics governs their asymptotic behavior. | Due to the Hawking–Penrose singularity theorems, see for instance [1], it is known that “singularities” are a robust prediction of Einstein’s equations on a spacetime (M, g): 1 (1) Ricµν − R gµν = 2 Tµν 2 However, it remains a wide open problem to understand the dynamical description of spacetimes near their singularit... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,044 | OWR-14298591-008 | Classification of Static Near-Horizon Geometries | For cosmological constant $\Lambda\geq0$ and horizon dimension $n\geq3$, classify the compact static near-horizon geometries, equivalently the compact solutions of the near-horizon quasi-Einstein equation with closed dual one-form $X^\flat$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 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-14298591-008",
"literature-status:open",
"owr-year:2024"
] | The report explicitly says that the classification of static near-horizon geometries for nonnegative cosmological constant in the stated dimensions remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
},
{
"url": "https://doi.org/10.12942/lrr-2013-8",
"label": "Lucietti and Kunduri, Near-horizon geometries"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | For cosmological constant $\Lambda\geq0$ and horizon dimension $n\geq3$, classify the compact static near-horizon geometries, equivalently the compact solutions of the near-horizon quasi-Einstein equation with closed dual one-form $X^\flat$. | Interestingly, if Λ \geq 0 and n \geq 3, the classification of static near-horizon geometries remains an open problem. It has been an open problem to determine whether spherical topology of M together with the equations (1) imply the existence of a Killing vector field. Theorem 1 ([13]). Any n-dimensional compact Riema... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,045 | OWR-14298591-009 | Uniqueness of Spherical Schwarzschild–Anti-de Sitter Spacetimes | Prove a uniqueness theorem for spherical Schwarzschild–anti-de Sitter spacetimes among static Einstein spacetimes with negative cosmological constant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-009",
"literature-status:open",
"owr-year:2024"
] | The report identifies uniqueness of spherical Schwarzschild-AdS as a notable open problem, and current uniqueness literature still describes the general static asymptotically AdS statement as unproved. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
},
{
"url": "https://doi.org/10.12942/lrr-2008-6",
"label": "Emparan, Reall, and collaborators, Black holes in higher dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Prove a uniqueness theorem for spherical Schwarzschild–anti-de Sitter spacetimes among static Einstein spacetimes with negative cosmological constant. | On the other hand, for negative cosmological constant, the uniqueness of spherical Schwarzschild-AdS remains a notable open problem. Theorem 2 ([20]). Any d \geq 4-dimensional analytic Einstein spacetime with Λ > 0, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must b... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,046 | OWR-14298591-010 | Teukolsky Energy Decay on Extremal Kerr Spacetimes | On an extremal Kerr spacetime with $|a|=M$, prove energy boundedness and energy decay for fixed-azimuthal-mode solutions of the Teukolsky equations, with the predicted pointwise decay away from the future event horizon, decay of the outgoing component on the horizon, and generic growth of the ingoing component there. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-010",
"literature-status:partially-solved",
"owr-year:2024"
] | For subextremal Kerr the Teukolsky boundedness and decay statement is proved, while the extremal case in the extracted conjecture remains conditional and explicitly conjectural. | [
{
"url": "https://arxiv.org/abs/2512.08917",
"label": "Benomio and Teixeira da Costa, Maxwell equations on Kerr"
},
{
"url": "https://arxiv.org/abs/2007.07211",
"label": "Shlapentokh-Rothman and Teixeira da Costa, Teukolsky decay"
},
{
"url": "https://doi.org/10.4171/owr/2024/36",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | On an extremal Kerr spacetime with $|a|=M$, prove energy boundedness and energy decay for fixed-azimuthal-mode solutions of the Teukolsky equations, with the predicted pointwise decay away from the future event horizon, decay of the outgoing component on the horizon, and generic growth of the ingoing component there. | We direct the reader to [17, 18] for sharp pointwise decay results. In the case |a| = M , based on the heuristic works [8, 12] and the recent proof of scalar azimuthal instabilities by Gajic [10], one may conjecture: Conjecture 1 (Extremal components, |a| \leq M ). Fix M > 0 and let |a| \leq M . Solutions \alpha and \a... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,047 | OWR-14298591-011 | Stability of Extremal Critical Collapse | Does there exist a teleologically determined hypersurface in the moduli space of initial data that consists of asymptotically extremal black holes, contains the known critical family $D_{\lambda_*}$, and locally separates future-complete data from collapsing data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-011",
"literature-status:open",
"owr-year:2024"
] | The stability of extremal critical collapse is stated as a conjecture in the report; no theorem establishing the proposed moduli-space hypersurface was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Does there exist a teleologically determined hypersurface in the moduli space of initial data that consists of asymptotically extremal black holes, contains the known critical family $D_{\lambda_*}$, and locally separates future-complete data from collapsing data? | Despite this inherent instability of the critical solution, we expect extremal critical collapse itself to be a stable phenomenon: We conjecture that there exists a teleologically determined “hypersurface” in moduli space which con- sists of asymptotically extremal black holes, contains D\lambda∗ , and locally delimits... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,048 | OWR-14298591-012 | Global Stability and Asymptotics of Cosmological Spacetimes | For $\Lambda>0$, do sufficiently small perturbations of de Sitter or Kerr–de Sitter initial data yield global solutions of $\operatorname{Ric}(g)+\Lambda g=0$, and can those solutions be described asymptotically? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-012",
"literature-status:partially-solved",
"owr-year:2024"
] | Global nonlinear stability of slowly rotating Kerr-de Sitter was proved without symmetry assumptions, but the extracted question is broader than that parameter regime. | [
{
"url": "https://arxiv.org/abs/1606.04014",
"label": "Hintz and Vasy, Global nonlinear stability of Kerr-de Sitter"
},
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | For $\Lambda>0$, do sufficiently small perturbations of de Sitter or Kerr–de Sitter initial data yield global solutions of $\operatorname{Ric}(g)+\Lambda g=0$, and can those solutions be described asymptotically? | A fundamental question is whether (EVE) can be solved globally if we perturb the initial conditions of this spacetime and whether the global solution can be described asymptotically. Waves on Kerr–de Sitter space András Vasy (joint work with Peter Hintz, Oliver Petersen) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,049 | OWR-14298591-013 | Tensorial Mode Stability of Kerr–de Sitter Spacetimes | Prove ungauged tensorial Einstein mode stability throughout the full subextremal Kerr–de Sitter parameter range. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112](https://doi.org/10.4171/owr/2024/36)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298591-013",
"literature-status:open",
"owr-year:2024"
] | The extracted fragment only says that a mode-stability problem is important and notes expected tensorial extensions; it supplies no completed proof of the general claim. | [
{
"url": "https://doi.org/10.4171/owr/2024/36",
"label": "Oberwolfach Report 36 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/36 | null | null | null | Prove ungauged tensorial Einstein mode stability throughout the full subextremal Kerr–de Sitter parameter range. | is an important open problem. (Cf. recent work of Casals and Texeira da Costa [CTdC22], as well as of Hintz [Hin24]!) In particular, Hintz has shown mode sta- bility in the scalar setting (with a tensorial version expected) in the subextremal ‘physical regime’, i.e. when Λm2 is small. Theorem 1 (Hintz-Petersen-V., in p... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mathematical Aspects of General Relativity (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/36, pp. 2033--2112 |
30,006,050 | OWR-14298592-001 | Workshop Contents Listing for Low-Dimensional Topology | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2541 Paula Truöl Notions of braid positivity and knot concordance . . . . . . . . . . . . . . . . . . . . . 2543 Laura Wakelin The Dehn surgery characterisation problem . . . . . . . . . . . . . . . . . . . . . . . . . 2546 MATRIX-MFO Tandem Workshop... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298592-001",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a table-of-contents fragment containing only the word conjecture and no identifiable mathematical claim; its status is unresolved and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2541 Paula Truöl Notions of braid positivity and knot concordance . . . . . . . . . . . . . . . . . . . . . 2543 Laura Wakelin The Dehn surgery characterisation problem . . . . . . . . . . . . . . . . . . . . . . . . . 2546 MATRIX-MFO Tandem Workshop... | unrecoverable | The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,051 | OWR-14298592-002 | Completeness of Unzipped-Link Invariants for Spatial Theta Graphs | For a spatial theta-graph $\Gamma\subset S^3$, let $L_\Gamma$ consist of its three constituent knots and all two-component links obtained by unzipping one edge with every possible linking number. Does $L_\Gamma$ determine $\Gamma$ up to isotopy, and what minimal sublist of $L_\Gamma$ suffices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-002",
"literature-status:open",
"owr-year:2024"
] | The primary report poses completeness of the infinite list of constituent and unzipped links as an unanswered question and gives no proof; no later resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43 (2024)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | For a spatial theta-graph $\Gamma\subset S^3$, let $L_\Gamma$ consist of its three constituent knots and all two-component links obtained by unzipping one edge with every possible linking number. Does $L_\Gamma$ determine $\Gamma$ up to isotopy, and what minimal sublist of $L_\Gamma$ suffices? | Is LΓ a complete invariant of Γ? Invariants and Structures in Low-Dimensional Topology 2519 Skein module relations. Let K denote the free Q[a, a−1 ]–module generated by links in S 3 . Factoring out by the Conway skein relation ! − " = a \cdot a we obtain an extended version of the Alexander skein module—extended as we ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,052 | OWR-14298592-003 | Probabilities of Properties in Random-Knot Models | Fix a knot property $\mathcal P$ and a random-knot model $(K_n)$. Determine $\lim_{n\to\infty}\Pr[K_n\text{ has }\mathcal P]$, when this limit exists. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-003",
"literature-status:open",
"owr-year:2024"
] | The question is model-dependent and the report presents it as a direction for future probabilistic study; no general probability theorem for arbitrary knot properties was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43 (2024)"
},
{
"url": "https://doi.org/10.1007/s00454-024-00663-9",
"label": "Random Meander Model for Links"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | Fix a knot property $\mathcal P$ and a random-knot model $(K_n)$. Determine $\lim_{n\to\infty}\Pr[K_n\text{ has }\mathcal P]$, when this limit exists. | An alternative approach that could provide a weaker but still interesting answer is the study of the properties described by such open problems from a probabilistic point of view. What is the probability that a random knot K satisfies the property P ? Models for random knots Valentina Bais, Agnese Barbensi, Benjamin Bu... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,053 | OWR-14298592-004 | Realization and Classification of Poincaré Duality Four-Complexes | Given a fundamental triple $(T,w,b)$, determine whether it is realized by a Poincaré-duality $4$-complex or by a manifold. For a realizable triple, determine which classes $b'\in H_4(T;\mathbb Z)$ are realized, and identify the additional data needed beyond the symmetric $2$-type to recover the homotopy type. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-004",
"literature-status:open",
"owr-year:2024"
] | The report lists realization of arbitrary fundamental triples by PD4-complexes or manifolds and refinement of the symmetric 2-type as general problems; the cited realization theory does not settle them in full. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43 (2024)"
},
{
"url": "https://msp.org/agt/2008/8-4/agt-v8-n4-p18-s.pdf",
"label": "Baues and Bleile, Poincare duality complexes in dimension four"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | Given a fundamental triple $(T,w,b)$, determine whether it is realized by a Poincaré-duality $4$-complex or by a manifold. For a realizable triple, determine which classes $b'\in H_4(T;\mathbb Z)$ are realized, and identify the additional data needed beyond the symmetric $2$-type to recover the homotopy type. | We considered the following general problems. (1) Given a fundamental triple (T, w, b), does there exist a PD4 -complex which realises it? Does there exist a manifold that realises it? (2) Assuming that a fundamental triple (T, w, b) is realised by a PD4 -complex, for which b′ \in H4 (T ; Z) is the triple (T, w, b) rea... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,054 | OWR-14298592-005 | Ribbon-Clasp Obstruction Methods | Unfortunately, we have not yet succeeded in applying our methods to examples, so it remains to be seen whether Proposition 2 and Corollary 3 can be used to settle open questions about the ribbon clasp number. Definition 1. The ribbon clasp number c∗r (K) of a knot K \subset S3 is defined as the minimal number of clasp ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report describes attempted applications of proved propositions and says that no examples had yet been obtained; it does not for) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298592-005",
"literature-status:open",
"owr-year:2024"
] | The source report says the proposed ribbon-clasp obstruction had not yet been applied to examples and leaves its use for open ribbon-clasp questions unresolved; no later proof of the extracted problem was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | null | Unfortunately, we have not yet succeeded in applying our methods to examples, so it remains to be seen whether Proposition 2 and Corollary 3 can be used to settle open questions about the ribbon clasp number. Definition 1. The ribbon clasp number c∗r (K) of a knot K \subset S3 is defined as the minimal number of clasp ... | unrecoverable | The official report describes attempted applications of proved propositions and says that no examples had yet been obtained; it does not formulate a separate self-contained open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,055 | OWR-14298592-006 | Minimum-Volume Hyperbolic Knots in the Three-Torus | Is the topological volume of the three-torus equal to twice the volume $v_8$ of a regular ideal octahedron, with the minimum realized by the three-component link whose complement is homeomorphic to the Borromean-rings complement; that is, is $\operatorname{vol}_t(T^3)=2v_8$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-006",
"literature-status:open",
"owr-year:2024"
] | The report gives the candidate knot and proves structural constraints on any volume minimizer, but explicitly presents equality with the candidate volume as a conjecture and does not complete the finite-census or theoretical argument. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | Is the topological volume of the three-torus equal to twice the volume $v_8$ of a regular ideal octahedron, with the minimum realized by the three-component link whose complement is homeomorphic to the Borromean-rings complement; that is, is $\operatorname{vol}_t(T^3)=2v_8$? | We conjectured that this link L realises volt(T3 ), and that therefore the inequality volt(T3 ) \leq vol(S3 − B) = 2v8 is actually an equality. punctured sphere, and then by studying the guts of the resulting manifold [2] we argue that, if K ′ cannot be isotoped to be transverse to the fibration, then the volume of its... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,056 | OWR-14298592-008 | The L-Space and Left-Orderability Conjecture | For every irreducible rational homology $3$-sphere $M$, are the following equivalent: $M$ is not an L-space; $M$ admits a coorientable taut foliation; and $\pi_1(M)$ is left-orderable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-008",
"literature-status:open",
"owr-year:2024"
] | The L-space conjecture remains unresolved in general: current work still describes the equivalence with left-orderability and taut foliations as widely open, despite substantial verified classes. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
},
{
"url": "https://doi.org/10.1016/j.aim.2026.110956",
"label": "Boyer--Gordon--Hu, Slope detection and toroidal 3-manifolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | For every irreducible rational homology $3$-sphere $M$, are the following equivalent: $M$ is not an L-space; $M$ admits a coorientable taut foliation; and $\pi_1(M)$ is left-orderable? | In [1] the authors conjecture moreover that being an L-space is equivalent to the fundamental group of the manifold being left-orderable, meaning that it admits a total order that is invariant by left multiplication. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,057 | OWR-14298592-009 | Leaf Spaces of Explicit Taut Foliations | For explicit taut foliations constructed from knot diagrams, determine the leaf space of the lifted foliation well enough to decide whether the induced $\pi_1$-action descends to a nontrivial orientation-preserving action on $\mathbb R$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-009",
"literature-status:open",
"owr-year:2024"
] | The report poses understanding leaf spaces of explicit non-R-covered taut foliations as an unresolved question and explains that the needed quotient action is generally difficult to obtain; no general solution was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | For explicit taut foliations constructed from knot diagrams, determine the leaf space of the lifted foliation well enough to decide whether the induced $\pi_1$-action descends to a nontrivial orientation-preserving action on $\mathbb R$. | Can we understand the leaf space of some “explicit” taut foliations that have been constructed in the literature such as, for example, the ones con- structed in [12], in order to apply this technique? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,058 | OWR-14298592-012 | Finiteness of Fibered Strongly Quasipositive Knots in Concordance Classes | Does each smooth concordance class contain only finitely many fibered strongly quasipositive knots? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-012",
"literature-status:open",
"owr-year:2024"
] | The source report explicitly calls this finiteness question a weaker version of Baker's conjecture that remains open; later work gives finiteness for narrower positive-knot classes, not the stated fibered strongly quasipositive class. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
},
{
"url": "https://doi.org/10.1007/s00029-024-00996-6",
"label": "Krishna--Morton, Twist positivity, L-space knots, and concordance"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | Does each smooth concordance class contain only finitely many fibered strongly quasipositive knots? | Are there only finitely many strongly quasipositive, fibered knots in each smooth concordance class in C? As far as we know, the following question, which is a weaker version of Conjec- ture 1, remains open. Braid positive knots are those knots which are closures of positive braids, i.e. those braids that can be repres... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,059 | OWR-14298592-013 | Concordance Rigidity of Braid-Positive Knots | If two braid-positive knots are smoothly concordant, must they be isotopic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-013",
"literature-status:open",
"owr-year:2024"
] | Concordance-isotopy for all braid-positive knots is still posed as a question; positive three-braid results provide invariants and infinite distinct concordance families but do not settle the universal assertion. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
},
{
"url": "https://doi.org/10.1007/s00029-024-00996-6",
"label": "Krishna--Morton, Twist positivity, L-space knots, and concordance"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | If two braid-positive knots are smoothly concordant, must they be isotopic? | Are concordant braid positive knots isotopic? Braid positive knots are those knots which are closures of positive braids, i.e. those braids that can be represented in terms of the positive Artin generators \sigma1 , . . . , \sigman−1 of Bn for some n \geq 1. Braid positive knots are fibered [10] and strongly quasiposit... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,060 | OWR-14298592-014 | Concordance of an Explicit Pair of Positive Three-Braid Knots | Are the closures of the positive three-braids $\sigma_1^3\sigma_2^3\sigma_1^6\sigma_2^6$ and $\sigma_1^3\sigma_2^5\sigma_1^3\sigma_2^7$ smoothly concordant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550](https://do... | 3 | open | null | 2,024 | 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-14298592-014",
"literature-status:open",
"owr-year:2024"
] | The report records explicit non-isotopic positive three-braid pairs that available concordance invariants do not distinguish and states that further invariants were still needed; no concordance counterexample or proof was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/43",
"label": "Oberwolfach Report 43/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/43 | null | null | null | Are the closures of the positive three-braids $\sigma_1^3\sigma_2^3\sigma_1^6\sigma_2^6$ and $\sigma_1^3\sigma_2^5\sigma_1^3\sigma_2^7$ smoothly concordant? | However, there are still many pairs of examples of positive 3-braid knots that we cannot distinguish in concordance with these methods, although we know them to be non-isotopic from the work of Birman–Menasco [4, 5], e.g. the closures of \sigma13 \sigma23 \sigma16 \sigma26 and \sigma13 \sigma25 \sigma13 \sigma27 . In t... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants in Low-Dimensional Topology: Combinatorics, Geometry, and Computation (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/43, pp. 2511--2550 |
30,006,061 | OWR-14298593-001 | Exceptional Collections on Noncommutative Del Pezzo Surfaces | Prove the following conjectures for noncommutative del Pezzo surfaces: (1) an exceptional object is determined by its Grothendieck-group class and full exceptional collections are mutation-equivalent; (2) every pure helix deforms to the noncommutative surface; and (3) two marked surfaces are isomorphic exactly when the... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606](https://doi.org/10.4171/owr/2024/4... | 3 | open | null | 2,024 | 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-14298593-001",
"literature-status:open",
"owr-year:2024"
] | The report states three broad conjectures about exceptional objects, pure helices, and affine-Weyl classification on noncommutative del Pezzo surfaces; later mutation results for del Pezzo cones do not establish all three conjectures. | [
{
"url": "https://doi.org/10.4171/owr/2024/44",
"label": "Oberwolfach Report 44/2024"
},
{
"url": "https://arxiv.org/abs/2604.11319",
"label": "Nordskova--Van den Bergh, NCCRs of cones over del Pezzo surfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/44 | null | null | null | Prove the following conjectures for noncommutative del Pezzo surfaces: (1) an exceptional object is determined by its Grothendieck-group class and full exceptional collections are mutation-equivalent; (2) every pure helix deforms to the noncommutative surface; and (3) two marked surfaces are isomorphic exactly when the... | Conjecture 1. An exceptional object on a noncommutative del Pezzo surface is determined by its class in the Grothendieck group, so that a marking is equivalent to its image in the Grothendieck group. Any full exceptional collections on the derived category of a noncommutative del Pezzo surface are related by mutations.... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606 |
30,006,062 | OWR-14298593-002 | Maximal Modifying Algebras for Canonical Threefold Singularities | Prove that every local three-dimensional Gorenstein canonical singularity admits a maximal modifying algebra. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606](https://doi.org/10.4171/owr/2024/4... | 3 | open | null | 2,024 | 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-14298593-002",
"literature-status:open",
"owr-year:2024"
] | The extracted record is only an isolated conjecture label; its surrounding passage concerns the still-conjectural existence of maximal modifying algebras for all three-dimensional Gorenstein canonical singularities, with no general proof located. | [
{
"url": "https://doi.org/10.4171/owr/2024/44",
"label": "Oberwolfach Report 44/2024"
},
{
"url": "https://arxiv.org/abs/1007.1296",
"label": "Iyama--Wemyss, Maximal Modifications and Auslander--Reiten Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/44 | null | null | null | Prove that every local three-dimensional Gorenstein canonical singularity admits a maximal modifying algebra. | conjecture. Corollary 2. Let (R, mR ) be a local ring of 3-dimensional Gorenstein canonical singularity that admits a crepant resolution f : X \to Spec R. If the third Betti number b3 (f −1 (mR )) is non-zero, then R does not admit a noncommutative crepant resolution. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606 |
30,006,063 | OWR-14298593-003 | Compatible Feigin-Odesskii Poisson Brackets | For coprime integers $r,d$ with $r>0$, determine the maximal dimension of a vector space of compatible Poisson brackets on $\mathbb P^{d-1}$ that contains a fixed Feigin-Odesskii bracket of type $(d,r)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606](https://doi.org/10.4171/owr/2024/4... | 3 | open | null | 2,024 | 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-14298593-003",
"literature-status:open",
"owr-year:2024"
] | General maximal-dimension classification for compatible Feigin--Odesskii brackets remains a question; special cases determine dimensions such as 9 or 10, but the stated arbitrary type-(d,r) problem is not solved. | [
{
"url": "https://doi.org/10.4171/owr/2024/44",
"label": "Oberwolfach Report 44/2024"
},
{
"url": "https://doi.org/10.1007/s00229-023-01479-2",
"label": "Markarian--Polishchuk, Compatible Feigin--Odesskii Poisson brackets"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/44 | null | null | null | For coprime integers $r,d$ with $r>0$, determine the maximal dimension of a vector space of compatible Poisson brackets on $\mathbb P^{d-1}$ that contains a fixed Feigin-Odesskii bracket of type $(d,r)$. | A natural question is what is the maximal dimension of a space of compatible Poisson brackets on Pd−1 containing a given FO-bracket of type (d, r). Algebraic Geometry and Noncommutative Projective Varieties 2571 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606 |
30,006,064 | OWR-14298593-004 | Classification of Noncommutative Hypersurfaces | Classify noncommutative hypersurfaces $\operatorname{qgr}(A/(f))\subseteq\operatorname{qgr}A$, where $A$ is Artin-Schelter regular and $f\in Z(A)$ is homogeneous, and describe their singularities and derived categories beyond the known quadratic and finite-over-the-center cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606](https://doi.org/10.4171/owr/2024/4... | 3 | open | null | 2,024 | 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-14298593-004",
"literature-status:open",
"owr-year:2024"
] | Noncommutative hypersurfaces are treated in important special cases, especially quadrics and finite-over-the-center orders, but the general classification and derived-category problem stated in the record remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/44",
"label": "Oberwolfach Report 44/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/44 | null | null | null | Classify noncommutative hypersurfaces $\operatorname{qgr}(A/(f))\subseteq\operatorname{qgr}A$, where $A$ is Artin-Schelter regular and $f\in Z(A)$ is homogeneous, and describe their singularities and derived categories beyond the known quadratic and finite-over-the-center cases. | An important problem is to understand noncommutative hypersurfaces: subcate- gories of the form qgr(A/(f )) \subset qgr A, where f \in Z(A) is a homogeneous central element of some degree d. The case of quadrics (d = 2) has been studied extensively, starting with the introduction in [1] of a Koszul duality technique th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606 |
30,006,065 | OWR-14298593-005 | Ozone Groups of Calabi-Yau and PI AS-Regular Algebras | Classify the Calabi-Yau algebras whose ozone group $\operatorname{Oz}(A)=\operatorname{Gal}(A/Z(A))$ is trivial. Also classify the PI Artin-Schelter regular algebras whose ozone groups have maximal rank. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606](https://doi.org/10.4171/owr/2024/4... | 3 | partially_solved | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s00209-025-03777-9",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (one of two questions answered in the source). J. Gaddis (joint with K. Chan, R. Won and J. J. Zhang; OWR 44/2024, p. 2589) asks which Calabi–Yau algebras have trivial ozone group, and which PI Artin–Schelter regular algebras have ozone groups of maxima... | [
"owr",
"oberwolfach-reports",
"OWR-14298593-005",
"literature-status:open",
"owr-year:2024"
] | The maximal-rank PI AS-regular case is characterized by skew polynomial rings and the ozone-group abelianity question has since been answered, but the broader classification of Calabi--Yau algebras with trivial ozone group in the record remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/44",
"label": "Oberwolfach Report 44/2024"
},
{
"url": "https://doi.org/10.1007/s00209-025-03777-9",
"label": "Chan--Gaddis--Won--Zhang, Ozone groups of AS-regular algebras"
},
{
"url": "https://arxiv.org/abs/2512.21056",
"label": "Liu--Wu--... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/44 | null | null | null | Classify the Calabi-Yau algebras whose ozone group $\operatorname{Oz}(A)=\operatorname{Gal}(A/Z(A))$ is trivial. Also classify the PI Artin-Schelter regular algebras whose ozone groups have maximal rank. | This raises the question of which Calabi–Yau algebras have trivial ozone groups. This leaves the question of which PI AS regular algebras have ozone groups of maximal rank. Algebraic Geometry and Noncommutative Projective Varieties 2589 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Algebraic Geometry and Noncommutative Projective Varieties (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/44, pp. 2551--2606 |
30,006,066 | OWR-14298795-001 | Workshop Summary on Anabelian Geometry | conjecture. Tim Holzschuh used the étale homotopy type, for instance, for simply connected and possibly singular varieties over the reals to prove an analogue of the real section conjecture. The homotopical point of view was also present in Mair’s talk about condensed shapes. Furthermore, Lüdtke presented work connec... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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 | Unrecoverable OWR statement (The official report confirms that this extraction is workshop-summary prose covering many talks and contains no standalone conjecture. No se) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298795-001",
"literature-status:open",
"owr-year:2024"
] | The extracted statement is only the word conjecture in a workshop-report context and does not identify a definite mathematical claim; under the required treatment of unclear records it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | null | conjecture. Tim Holzschuh used the étale homotopy type, for instance, for simply connected and possibly singular varieties over the reals to prove an analogue of the real section conjecture. The homotopical point of view was also present in Mair’s talk about condensed shapes. Furthermore, Lüdtke presented work connec... | unrecoverable | The official report confirms that this extraction is workshop-summary prose covering many talks and contains no standalone conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,067 | OWR-14298795-002 | Workshop Contents Listing for Anabelian Geometry | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 2627 Wieslawa Niziol (joint with Pierre Colmez, Sally Gilles) Geometric duality for p-adic pro-étale cohomology of analytic varieties . 2630 Daniel Litt (joint with Yeuk Hay Joshua Lam) On the converse to Eisenstein’s last theorem . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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 | Unrecoverable OWR statement (The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298795-002",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a fragment of a table of contents beginning with conjecture and contains no recoverable proposition to verify; under the required treatment of unclear records it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 2627 Wieslawa Niziol (joint with Pierre Colmez, Sally Gilles) Geometric duality for p-adic pro-étale cohomology of analytic varieties . 2630 Daniel Litt (joint with Yeuk Hay Joshua Lam) On the converse to Eisenstein’s last theorem . . . . . . . . . . . . .... | unrecoverable | The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,068 | OWR-14298795-003 | Degeneration and Purity of Local-Field Adic Systems | Let $X$ be a smooth variety over a $p$-adic local field $K$, and let $\ell\neq p$. For pure $\mathbb Q_\ell$-adic local systems on $X$, do the systems degenerate to limiting mixed structures at ramification points, and is their cohomology pure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-003",
"literature-status:open",
"owr-year:2024"
] | The source report explicitly identifies both degeneration to a limiting mixed structure at ramification and purity of cohomology as basic open problems for these pure l-adic local systems. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Let $X$ be a smooth variety over a $p$-adic local field $K$, and let $\ell\neq p$. For pure $\mathbb Q_\ell$-adic local systems on $X$, do the systems degenerate to limiting mixed structures at ramification points, and is their cohomology pure? | The two most basic open problems about such local systems are: (1) Whether they degenerate to a limiting mixed structure at a ramification point, and (2) Whether their cohomology is pure. Pure ℓ-adic local systems over local fields Moritz Kerz (joint work with Hélène Esnault) Anabelian Geometry and Representations of ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,069 | OWR-14298795-004 | Grothendieck’s Section Conjecture | Let $X$ be a proper hyperbolic curve over a finitely generated extension $k/\mathbb Q$. Is the canonical map from $X(k)$ to the conjugacy classes of sections of
$$1\to\pi_1^{\mathrm{et}}(X_{\bar k})\to\pi_1^{\mathrm{et}}(X)\to\operatorname{Gal}(\bar k/k)\to1$$
a bijection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-004",
"literature-status:open",
"owr-year:2024"
] | Grothendieck's Section Conjecture for proper hyperbolic curves over arbitrary finitely generated extensions of Q remains one of the major open problems; recent work proves only broad conditional or special-case results. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://doi.org/10.1002/mana.70049",
"label": "Bresciani, On the section conjecture over fields of finite type"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Let $X$ be a proper hyperbolic curve over a finitely generated extension $k/\mathbb Q$. Is the canonical map from $X(k)$ to the conjugacy classes of sections of
$$1\to\pi_1^{\mathrm{et}}(X_{\bar k})\to\pi_1^{\mathrm{et}}(X)\to\operatorname{Gal}(\bar k/k)\to1$$
a bijection? | Conjecture. To this end, we fix the following situation: Setup. Let k be a field with separable closure k̄ \supset k, and let X be a geometri- cally connected quasi-compact and quasi-separated scheme over k. Write Galk := Gal(k̄/k) for the absolute Galois group of k with respect to k̄, Xk̄ for the base change of X to k̄... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,070 | OWR-14298795-005 | The Generalized Étale-Homotopy Section Conjecture | Determine the classes of varieties $X/k$ for which the canonical map $X(k)\to\Gamma^{\mathrm{et}}(X/k)$ is a bijection, where $\Gamma^{\mathrm{et}}(X/k)$ is the set of homotopy classes of sections of the étale-homotopy fibration $\Pi^{\mathrm{et}}(X)\to\Pi^{\mathrm{et}}(k)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-005",
"literature-status:open",
"owr-year:2024"
] | The generalized Section Conjecture for higher etale homotopy types is proved in restricted real and nilpotent settings, but the record's general bijectivity assertion is not established. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Determine the classes of varieties $X/k$ for which the canonical map $X(k)\to\Gamma^{\mathrm{et}}(X/k)$ is a bijection, where $\Gamma^{\mathrm{et}}(X/k)$ is the set of homotopy classes of sections of the étale-homotopy fibration $\Pi^{\mathrm{et}}(X)\to\Pi^{\mathrm{et}}(k)$. | Conjecture. The canonical map X(k) \to Γét (X/k), a 7\to [a∗ ] is a bijection. Remark. (1) Of course, one still has to determine for which varieties X/k the above conjecture should hold, as it clearly does not hold in general (e.g. X = A1k ). (2) One can check that if X is aspherical, i.e. if \pinét (X) = 0 for n > 1... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,071 | OWR-14298795-008 | The Grothendieck–Katz p-Curvature Conjecture | Let $A$ be a matrix with entries in $\mathbb Q(z)$. Are all solutions of $(\partial/\partial z-A)\mathbf f(z)=0$ algebraic if and only if the reduction of $(\partial/\partial z-A)^p$ vanishes for almost all primes $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-008",
"literature-status:open",
"owr-year:2024"
] | The Grothendieck--Katz p-curvature conjecture and the stronger nonlinear Eisenstein-integrality conjecture in the record remain open in general, with proofs only for substantial special classes. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2501.13175",
"label": "Lam--Litt, Algebraicity and integrality of solutions to differential equations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Let $A$ be a matrix with entries in $\mathbb Q(z)$. Are all solutions of $(\partial/\partial z-A)\mathbf f(z)=0$ algebraic if and only if the reduction of $(\partial/\partial z-A)^p$ vanishes for almost all primes $p$? | Considering some basic examples shows that this a priori algebraic question is actually of an arithmetic nature; for example, the differential equation \partial a − f (z) = 0, a \in C \partialz z has solutions of the form cz a , which are algebraic if and only if a is a rational number. This conjecture is widely open; t... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,072 | OWR-14298795-009 | Incomplete Nonlinear Eisenstein-Conjecture Continuation | conjecture is (at least a priori) much stronger than the p-curvature conjecture. Anabelian Geometry and Representations of Fundamental Groups 2633 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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 | Unrecoverable OWR statement (The official report confirms that this extraction is only a dangling sentence continuing a preceding nonlinear differential-equation conject) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298795-009",
"literature-status:open",
"owr-year:2024"
] | The fragment refers to the Lam--Litt algebraicity and integrality conjecture, a strengthening of the classical p-curvature conjecture; later work proves special cases and a non-abelian analogue, but not the general conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2501.13175",
"label": "Lam--Litt, Algebraicity and integrality"
},
{
"url": "https://arxiv.org/abs/2601.07933",
"label": "Lam--Litt, p-Curvature and non-Abelian co... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | null | conjecture is (at least a priori) much stronger than the p-curvature conjecture. Anabelian Geometry and Representations of Fundamental Groups 2633 | unrecoverable | The official report confirms that this extraction is only a dangling sentence continuing a preceding nonlinear differential-equation conjecture and contains no independently recoverable statement. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,073 | OWR-14298795-011 | Index Divisibility in p-Power Pullbacks of Curves | Let $X$ be a smooth projective curve of genus at least $2$ embedded in an abelian variety $A$ over a finite extension $k/\mathbb Q_p$, and assume that $X$ contains no torsion point of order prime to $p$. For all sufficiently large $n$, is the index of the inverse image of $X$ under $[p^n]:A\to A$ divisible by $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-011",
"literature-status:open",
"owr-year:2024"
] | The p-power pullback index-divisibility assertion remains a conjecture; the source makes the downstream section results conditional on it, and no proof or counterexample was found in the current primary-literature check. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Let $X$ be a smooth projective curve of genus at least $2$ embedded in an abelian variety $A$ over a finite extension $k/\mathbb Q_p$, and assume that $X$ contains no torsion point of order prime to $p$. For all sufficiently large $n$, is the index of the inverse image of $X$ under $[p^n]:A\to A$ divisible by $p$? | Conjecture 1. Let X be a smooth projective curve of genus \geq 2 embedded in an abelian variety A over a field k finite over Qp . Assume that X \subset A contains no torsion points of order prime with p. For n >> 0 large enough, the inverse image Xn of X along pn : A \to A has index divisible by p. We remark that part of... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,074 | OWR-14298795-012 | Outer Automorphisms of p-Adic Absolute Galois Groups | Determine the structure of the outer automorphism group $\operatorname{Out}(G_K)$ of the absolute Galois group of a $p$-adic field $K$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-012",
"literature-status:open",
"owr-year:2024"
] | The full structure of Out of the absolute Galois group of a p-adic field is not known; current work constructs and studies arithmetic Dehn twists in the maximal pro-p quotient but does not classify the whole outer automorphism group. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2303.04309",
"label": "Gropper, Surfaces and p-adic fields I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Determine the structure of the outer automorphism group $\operatorname{Out}(G_K)$ of the absolute Galois group of a $p$-adic field $K$. | What is the structure of the group Out(GK )? 2. Main Results In the talk we outline the ideas and tools used [7] to study Out(GK ). These ideas are highly influenced by the philosophy of arithmetic topology. Arithmetic Topology, first pioneered in [9] by Mazur, draws analogies between number theory and low dimensional to... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,075 | OWR-14298795-013 | Finite Index of Arithmetic Dehn-Twist Subgroups | For a $p$-adic field $K$, does the profinite subgroup generated by all arithmetic Dehn twists have finite index in $\operatorname{Out}(G_K(p))$, where $G_K(p)$ is the maximal pro-$p$ quotient of the absolute Galois group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-013",
"literature-status:open",
"owr-year:2024"
] | Arithmetic Dehn twists are known to have infinite order in the relevant outer automorphism groups, but whether their profinite subgroup has finite index in Out of the maximal pro-p Galois group remains unanswered. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2303.04309",
"label": "Gropper, Surfaces and p-adic fields I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | For a $p$-adic field $K$, does the profinite subgroup generated by all arithmetic Dehn twists have finite index in $\operatorname{Out}(G_K(p))$, where $G_K(p)$ is the maximal pro-$p$ quotient of the absolute Galois group? | Does the profinite group, generated by all Dehn twists, have finite index in Out(GK (p))? Anabelian Geometry and Representations of Fundamental Groups 2641 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,076 | OWR-14298795-014 | Kim’s Nonabelian Chabauty Conjecture | For a hyperbolic curve $X/\mathbb Q$ and a prime $p$ of good reduction, do the refined Chabauty–Kim sets eventually equal the rational points; that is, is $X(\mathbb Q_p)_n=X(\mathbb Q)$ for all sufficiently large $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-014",
"literature-status:open",
"owr-year:2024"
] | Kim's equality of the non-abelian Chabauty--Kim sets with the rational points for all sufficiently large levels is still a general conjecture; finiteness and equality are proved only in restricted families and levels. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2305.09462",
"label": "Betts--Kumpitsch--Litt, Chabauty--Kim and the Section Conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | For a hyperbolic curve $X/\mathbb Q$ and a prime $p$ of good reduction, do the refined Chabauty–Kim sets eventually equal the rational points; that is, is $X(\mathbb Q_p)_n=X(\mathbb Q)$ for all sufficiently large $n$? | Conjecture 3. X(Qp )n is finite for n ≫ 0. The finiteness of X(Qp )n for sufficiently large n is implied by the Bloch–Kato conjecture [4]. It is conjectured that the sets X(Qp )n not only become finite but eventually coincide exactly with the set of rational points [7, Conj. 3.1]. Conjecture 4 (Kim’s Conjecture). X(Qp )n =... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,077 | OWR-14298795-017 | Holomorphic Convexity of Universal Covers | Is the universal cover of every smooth projective variety holomorphically convex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-017",
"literature-status:open",
"owr-year:2024"
] | The general Shafarevich holomorphic-convexity question remains open; the linear-fundamental-group case is proved, including recent quasiprojective extensions, but non-linear fundamental groups are not covered. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://arxiv.org/abs/2408.16441",
"label": "Bakker--Brunebarbe--Tsimerman, Linear Shafarevich conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Is the universal cover of every smooth projective variety holomorphically convex? | A more precise question was asked by Shafarevich [3, IX.4.3]: is the universal cover X̃ of a smooth projective complex variety X always holomorphically convex, i.e. does X̃ admit a proper holomorphic map to a Stein space? Constructing holomorphic functions on universal covers of complex algebraic varieties Yohan Bruneb... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,078 | OWR-14298795-018 | Characteristic Classes of Hodge–Tate Local Systems | Let $X$ be a smooth algebraic variety over a finite extension $K/\mathbb Q_p$, and let $L$ be a Hodge–Tate local system on $X$. Is
$$\alpha_X(\ell_i(L))=(i-1)!\sum_{m\in\mathbb Z}m\,\operatorname{ch}_{i-1}(\operatorname{gr}_mD_{\mathrm{HT}}(L))?$$
This asks for the expected Hodge–Tate characteristic-class identity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-018",
"literature-status:open",
"owr-year:2024"
] | The displayed identity for characteristic classes of Hodge--Tate local systems is posed as an unresolved question in the primary report; the cited characteristic-class literature does not establish this general p-adic comparison. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://math.mit.edu/~apetrov/papers/pdf/ow_2024.pdf",
"label": "Ge, Characteristic-class question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Let $X$ be a smooth algebraic variety over a finite extension $K/\mathbb Q_p$, and let $L$ be a Hodge–Tate local system on $X$. Is
$$\alpha_X(\ell_i(L))=(i-1)!\sum_{m\in\mathbb Z}m\,\operatorname{ch}_{i-1}(\operatorname{gr}_mD_{\mathrm{HT}}(L))?$$
This asks for the expected Hodge–Tate characteristic-class identity. | For a Hodge-Tate local system L on X, is it true that the image 2i−1 of the characteristic class ℓi (L) \in Hét (X, Qp ) under the map \alphaX equals X (i − 1)! m \cdot chi−1 (grm DHT (L))? m\inZ Here chi−1 denotes the degree 2(i − 1) component of the Chern character in de Rham cohomology. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,079 | OWR-14298795-019 | Lang–Vojta and Shafarevich Finiteness Conjectures | Does every hyperbolic variety over a number field have only finitely many integral points? More generally, for which classes of canonically polarized varieties are there only finitely many isomorphism classes with good reduction outside a fixed finite set of places? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | open | null | 2,024 | 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-14298795-019",
"literature-status:open",
"owr-year:2024"
] | The extracted passage invokes the still-unresolved Lang--Vojta finiteness conjecture and notes that the Shafarevich finiteness problem is known only in restricted classes; recent results remain partial. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://annals.math.princeton.edu/2025/202-3/p01",
"label": "Lawrence--Sawin, Shafarevich for hypersurfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Does every hyperbolic variety over a number field have only finitely many integral points? More generally, for which classes of canonically polarized varieties are there only finitely many isomorphism classes with good reduction outside a fixed finite set of places? | In fact such finiteness results are expected in much greater generality: The Lang-Vojta conjecture, one of the major open problems in Diophantine geometry, predicts the finiteness of integral points on any hyperbolic variety over a number field. Even 40 years later, the Shafarevich conjecture is known only in very few cas... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,080 | OWR-14298795-020 | Finiteness for Subvarieties of Abelian Varieties | Extend arithmetic-finiteness and big-monodromy results from high-codimension subvarieties with ample normal bundle to smaller-codimension subvarieties of abelian varieties and, more generally, to varieties admitting a finite morphism to an abelian variety. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670](https://doi.org/10.4171/owr/2024/45)
## Literature review... | 3 | partially_solved | null | 2,024 | 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-14298795-020",
"literature-status:partially-solved",
"owr-year:2024"
] | The report proves substantial low-dimensional and ample-normal-bundle cases, and recent work proves finiteness for smooth hypersurfaces in fixed ample classes in suitable abelian varieties; the broader smaller-codimension and finite-to-abelian question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/45",
"label": "Oberwolfach Report 45/2024"
},
{
"url": "https://annals.math.princeton.edu/2025/202-3/p01",
"label": "Lawrence--Sawin, Shafarevich for hypersurfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/45 | null | null | null | Extend arithmetic-finiteness and big-monodromy results from high-codimension subvarieties with ample normal bundle to smaller-codimension subvarieties of abelian varieties and, more generally, to varieties admitting a finite morphism to an abelian variety. | How about subvarieties of smaller codimension in abelian varieties, or more generally varieties with a finite morphism to an abelian variety? Theorem 4. Let X \subset A be a smooth irreducible subvariety with ample normal bundle and dimension < g/2. Then the following are equivalent: (a) X \subset A is nondivisible with... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Anabelian Geometry and Representations of Fundamental Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/45, pp. 2621--2670 |
30,006,081 | OWR-14298796-001 | Adjoint-Free Approximation of Nonsymmetric Low-Rank Matrices | Determine when and with what sample complexity a nonsymmetric low-rank matrix or nonselfadjoint compact operator can be approximated using only forward sketches, without querying its adjoint. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900](https://doi.org/10.4171/owr/2024/48)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,024 | 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-14298796-001",
"literature-status:partially-solved",
"owr-year:2024"
] | Adjoint-free approximation is proved for a family of non-self-adjoint compact operators and elliptic PDE solution operators, with sample-complexity bounds; the unrestricted non-symmetric low-rank matrix problem is not fully resolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/48",
"label": "Oberwolfach Report 48/2024"
},
{
"url": "https://www.jmlr.org/papers/v25/24-0162.html",
"label": "Boullé et al., Operator learning without the adjoint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/48 | null | null | null | Determine when and with what sample complexity a nonsymmetric low-rank matrix or nonselfadjoint compact operator can be approximated using only forward sketches, without querying its adjoint. | There is a mystery at the heart of operator learning: how can one recover a non- self-adjoint operator from data without probing its adjoint? This motivates a fundamental question in numerical linear algebra: can one approximate a non-symmetric low-rank matrix without sketching its ad- joint? Operator learning without ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900 |
30,006,082 | OWR-14298796-002 | Linear Error Growth for Large Operator Perturbations | Prove that the approximation-error bound for the adjoint-free operator-learning method continues to grow linearly with the perturbation size beyond the small-perturbation regime. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900](https://doi.org/10.4171/owr/2024/48)
## Literature review (checked 2026-0... | 3 | open | null | 2,024 | 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-14298796-002",
"literature-status:open",
"owr-year:2024"
] | The source proves linear error growth only for small perturbations and explicitly leaves the extension to large perturbations as a conjecture; current literature supplies no general proof of that extension. | [
{
"url": "https://doi.org/10.4171/owr/2024/48",
"label": "Oberwolfach Report 48/2024"
},
{
"url": "https://www.jmlr.org/papers/v25/24-0162.html",
"label": "Boullé et al., Operator learning without the adjoint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/48 | null | null | null | Prove that the approximation-error bound for the adjoint-free operator-learning method continues to grow linearly with the perturbation size beyond the small-perturbation regime. | We show that for small perturbations, our bound on the approximation error grows linearly with the size of the perturbation, and we conjecture that this linear growth continues for large perturbations as well. An adjoint-free operator learning approach. To provide an operator learn- ing approach that does not need acce... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900 |
30,006,083 | OWR-14298796-004 | Improved Error Rates for QMC Slicing | Prove the improved convergence rates observed numerically when quasi-Monte Carlo designs replace independent random directions in sliced approximations of kernel sums. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900](https://doi.org/10.4171/owr/2024/48)
## Literature review (checked 2026-0... | 3 | open | null | 2,024 | 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-14298796-004",
"literature-status:open",
"owr-year:2024"
] | The extracted statement is an unspecified formal proof of numerically observed improved QMC-slicing rates; the primary account explicitly says that this proof remains open, with later work still presenting the improvement as numerical evidence. | [
{
"url": "https://doi.org/10.4171/owr/2024/48",
"label": "Oberwolfach Report 48/2024"
},
{
"url": "https://openreview.net/pdf?id=iNmVX9lx9l",
"label": "Hertrich--Jahn--Quellmalz, Fast summation by QMC slicing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/48 | null | null | null | Prove the improved convergence rates observed numerically when quasi-Monte Carlo designs replace independent random directions in sliced approximations of kernel sums. | While we numerically observe better error rates, a formal proof of this remains an open question. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900 |
30,006,084 | OWR-14298796-005 | Wasserstein Velocities for Boltzmann Curves | Given a family $f_t:\mathbb R^d\to\mathbb R$ and the Boltzmann densities $\rho_t=e^{-f_t}/Z_t$, find general conditions ensuring a globally integrable velocity field $v_t$ satisfying $\partial_t\rho_t+\nabla\cdot(\rho_t v_t)=0$. Equivalently, determine when the Fisher-Rao curve $(\rho_t)$ is absolutely continuous in Wa... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900](https://doi.org/10.4171/owr/2024/48)
## Literature review (checked 2026-0... | 3 | open | null | 2,024 | 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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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298796-005",
"literature-status:open",
"owr-year:2024"
] | The fragment asks for existence of a Wasserstein velocity field for a general prescribed Boltzmann family; the current primary paper gives sufficient conditions and specific well-behaved interpolations, not a general existence theorem. | [
{
"url": "https://doi.org/10.4171/owr/2024/48",
"label": "Oberwolfach Report 48/2024"
},
{
"url": "https://proceedings.iclr.cc/paper_files/paper/2025/hash/1d1cea122b9ec9f78acc21510659e500-Abstract-Conference.html",
"label": "Chemseddine et al., Neural sampling from Boltzmann densities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/48 | null | null | null | Given a family $f_t:\mathbb R^d\to\mathbb R$ and the Boltzmann densities $\rho_t=e^{-f_t}/Z_t$, find general conditions ensuring a globally integrable velocity field $v_t$ satisfying $\partial_t\rho_t+\nabla\cdot(\rho_t v_t)=0$. Equivalently, determine when the Fisher-Rao curve $(\rho_t)$ is absolutely continuous in Wa... | An important question is, whether for a given family of functions ft , such velocity Neural sampling from Boltzmann densities: Fisher-Rao curves in the Wasserstein geometry Gabriele Steidl (joint work with Jannis Chemseddine, Christian Wald, Richard Duong) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Deep Learning for PDE-based Inverse Problems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/48, pp. 2805--2900 |
30,006,085 | OWR-14298797-001 | Brownian Loop Measure for Stochastic Geometric Heat Flow | For the renormalized stochastic geometric heat equation in the full subcritical regime, prove the expected connection between its invariant measure and Brownian loop measure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Directions in Rough Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/49, pp. 2901--2948](https://doi.org/10.4171/owr/2024/49)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,024 | 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"
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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-14298797-001",
"literature-status:open",
"owr-year:2024"
] | For the stochastic geometric heat equation, the invariant measure is expected to be Brownian loop measure, while the primary source explicitly identifies the connection as an open problem; no later proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/49",
"label": "Oberwolfach Report 49/2024"
},
{
"url": "https://anr.fr/Project-ANR-23-ERCS-0011",
"label": "ANR project on low-regularity dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/49 | null | null | null | For the renormalized stochastic geometric heat equation in the full subcritical regime, prove the expected connection between its invariant measure and Brownian loop measure. | The connection with the Brownian loop measure remains an open problem. We consider the stochastic geometric heat equation given by (1) \partialt u\alpha = \partialx2 u\alpha + Γ\alpha \beta \gamma \alpha \alpha \beta\gamma (u) \partialx u \partialx u + h (u) + \sigmai (u) ξi , The main problem is to find suitable counte... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Directions in Rough Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/49, pp. 2901--2948 |
30,006,086 | OWR-14298797-002 | Algebraic Generators and Equivalence of Loop Invariants | Prove that every loop invariant is a shuffle combination of trivial loop invariants, signed areas, and conjugation invariants. Also characterize the equivalence relation $X\sim X'$ defined by equality of all loop-invariant signature coordinates. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Directions in Rough Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/49, pp. 2901--2948](https://doi.org/10.4171/owr/2024/49)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,024 | 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-14298797-002",
"literature-status:open",
"owr-year:2024"
] | The primary preprint proves infinitely many algebraically independent loop invariants but leaves both the proposed shuffle-generation conjecture and the signature-based equivalence relation unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/49",
"label": "Oberwolfach Report 49/2024"
},
{
"url": "https://arxiv.org/abs/2412.19670",
"label": "Diehl--Preiß--Reizenstein, Conjugation, loop and closure invariants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/49 | null | null | null | Prove that every loop invariant is a shuffle combination of trivial loop invariants, signed areas, and conjugation invariants. Also characterize the equivalence relation $X\sim X'$ defined by equality of all loop-invariant signature coordinates. | We conjecture that all loop invariants can be written as shuffles of trivial loop invariants (shuffles of anything with letters), signed areas (ij−ji) and conjugation invariants. Another open problem that remains is to characterize the equivalence relation X \sim X ′ defined by hS(X), ui = hS(X ′ ), ui for all loop-invarian... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Directions in Rough Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/49, pp. 2901--2948 |
30,006,087 | OWR-14298798-001 | Resolved Equilibration-Time Lead-In for Open-Boundary ASEP | A natural question is to ask how long it takes to reach equilibrium. Theorem 1 ([1, Theorem 1.1]). Assume that \beta < \alpha. Then depending on ρ, as t \to \infty, h (t, 0) − µt (ρ > 12 ) P − \leq s \to FGSE (s), \sigmat1/3 h (t, 0) − µt (ρ = 12 ) P − \leq s \to FGOE (s), \sigmat1/3 h (t, 0) − µρ t (ρ < 21 ) P − \leq ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mixing Times in the Kardar–Parisi–Zhang Universality Class (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/51, pp. 3001--3020](https://doi.org/10.4171/owr/2024/51)
## Lite... | 3 | open | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report raises the equilibration-time question only as a lead-in and immediately states that the reported joint work obtains the) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298798-001",
"literature-status:open",
"owr-year:2024"
] | The record asks for a general equilibration or mixing-time theory in the KPZ class; current work establishes model-specific asymptotics and cutoff results but not a general answer to this broad question. | [
{
"url": "https://doi.org/10.4171/owr/2024/51",
"label": "Oberwolfach Report 51/2024"
},
{
"url": "https://ems.press/journals/owr/articles/14298798",
"label": "Busani et al., KPZ mixing-times workshop report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/51 | null | null | null | null | A natural question is to ask how long it takes to reach equilibrium. Theorem 1 ([1, Theorem 1.1]). Assume that \beta < \alpha. Then depending on ρ, as t \to \infty, h (t, 0) − µt (ρ > 12 ) P − \leq s \to FGSE (s), \sigmat1/3 h (t, 0) − µt (ρ = 12 ) P − \leq s \to FGOE (s), \sigmat1/3 h (t, 0) − µρ t (ρ < 21 ) P − \leq ... | unrecoverable | The official report raises the equilibration-time question only as a lead-in and immediately states that the reported joint work obtains the sharp cutoff profile, so it is not presented as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Mixing Times in the Kardar–Parisi–Zhang Universality Class (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/51, pp. 3001--3020 |
30,006,088 | OWR-14298799-001 | Two-Loop SLE and Loop-Model Measures | Relate the two-loop Schramm-Loewner evolution measure to concrete statistical-mechanics measures, such as the $O(n)$ loop model, and to the counting measure on conformal loop ensembles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Critical phenomena of the XY model (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/52, pp. 3021--3054](https://doi.org/10.4171/owr/2024/52)
## Literature review (checked 2... | 3 | open | null | 2,024 | 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-14298799-001",
"literature-status:open",
"owr-year:2024"
] | A two-loop SLE measure is now constructed and characterized through Brownian-loop and CFT formulations, but its relation to O(n) loop models and CLE counting measures is explicitly left as an open comparison problem. | [
{
"url": "https://doi.org/10.4171/owr/2024/52",
"label": "Oberwolfach Report 52/2024"
},
{
"url": "https://arxiv.org/abs/2411.02232",
"label": "Luo--Maibach, Two-loop Loewner potentials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/52 | null | null | null | Relate the two-loop Schramm-Loewner evolution measure to concrete statistical-mechanics measures, such as the $O(n)$ loop model, and to the counting measure on conformal loop ensembles. | By Möbius invariance, we reduce our question of finding the minimizer to the concentric circles S 1 and e−2\pi\tau S 1 , where \tau is the modulus of the annulus enclosed by the circles. How does the two-loop SLE measure relate to specific models such as the O(n) loop model or to the counting measure on CLE as in [7]?... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Critical phenomena of the XY model (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/52, pp. 3021--3054 |
30,006,089 | OWR-14298800-001 | Sensor-Actuator Co-Design and Distributed Controllability Algorithms | Given a sensing or actuation budget and a control-cost functional, how should sensors or actuators be selected to minimize cost? Is there a local distributed algorithm for the rank or controllability-volume problem? Characterize when adding or removing links from the system dynamics or communication network improves se... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254](https:/... | 3 | open | null | 2,024 | 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-14298800-001",
"literature-status:open",
"owr-year:2024"
] | The cited work supplies closed forms and rank tests for particular constrained controllability problems, but the listed co-design, distributed-algorithm, network-link, and PDE-ADMM questions remain unresolved as a collection. | [
{
"url": "https://doi.org/10.4171/owr/2024/56",
"label": "Oberwolfach Report 56/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/56 | null | null | null | Given a sensing or actuation budget and a control-cost functional, how should sensors or actuators be selected to minimize cost? Is there a local distributed algorithm for the rank or controllability-volume problem? Characterize when adding or removing links from the system dynamics or communication network improves se... | Related open questions include: (1) Co-design: given a sensing or actuation budget and a control cost function, how can sensors or actuators be selected to minimize control cost? (2) Is there a local and distributed algorithm that can solve the rank or con- trollability volume problem? (3) When links are added or remov... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254 |
30,006,090 | OWR-14298800-002 | Continuous-Time Limits of Stochastic Bures-Wasserstein Consensus | Derive the continuous-time limit as $\Delta t\to0$ of the stochastic multi-agent consensus dynamics on Bures–Wasserstein space, including the limiting stochastic differential equation and conditions for well-posedness and consensus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254](https:/... | 3 | open | null | 2,024 | 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-14298800-002",
"literature-status:open",
"owr-year:2024"
] | The source formulates the continuous-time limit of the stochastic Bures--Wasserstein multi-agent update as an open problem; existing barycenter and consensus results do not derive this specific stochastic limit. | [
{
"url": "https://doi.org/10.4171/owr/2024/56",
"label": "Oberwolfach Report 56/2024"
},
{
"url": "https://arxiv.org/abs/2407.06389",
"label": "Borghi--Herty--Stavitskiy, Dynamics of measure-valued agents"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/56 | null | null | null | Derive the continuous-time limit as $\Delta t\to0$ of the stochastic multi-agent consensus dynamics on Bures–Wasserstein space, including the limiting stochastic differential equation and conditions for well-posedness and consensus. | An open problem is to consider the limit ∆t \to 0 and derive a time-continuous description of the stochastic multi-agent system in Bures–Wasserstein space. We consider below a perturbed version of the update where we introduce a ran- i,Σ dom tangent vector W(k) \in Sym component-wise normally distributed. To ensure the... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254 |
30,006,091 | OWR-14298800-003 | Nash Equilibria over Unbounded Measure Spaces | Establish general conditions for existence of Nash equilibria for games whose strategies are probability measures on unbounded sets. Under those conditions, determine whether gradient descent–ascent converges to an equilibrium, beyond the known displacement-convex–concave cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254](https:/... | 3 | partially_solved | null | 2,024 | 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-14298800-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Recent primary work proves existence and exponential Wasserstein convergence for a broad displacement convex--concave class on unbounded measure spaces, but the unrestricted Nash-equilibrium and gradient-descent-ascent problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/56",
"label": "Oberwolfach Report 56/2024"
},
{
"url": "https://arxiv.org/abs/2411.07403",
"label": "Conger et al., Coupled Wasserstein gradient flows"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/56 | null | null | null | Establish general conditions for existence of Nash equilibria for games whose strategies are probability measures on unbounded sets. Under those conditions, determine whether gradient descent–ascent converges to an equilibrium, beyond the known displacement-convex–concave cases. | Theoretical contributions: From an optimization perspective, the existence of a Nash equilibrium over measures on unbounded sets has been an open question. Since existence is unknown, there are no systematic tools for computing equilibria and in particular, convergence of gradient descent-ascent to an equilibrium is an... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/56, pp. 3211--3254 |
30,006,092 | OWR-14298801-003 | Query Complexity and Achievable Functions in Multivariable Quantum Signal Processing | For multivariable quantum signal processing, lower-bound the query complexity required to realize a prescribed function class when ancillary space, intermediate measurements, or different oracle types are allowed. Identify a nontrivial, simply described subclass of achievable functions with improved numerical propertie... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantum Signal Processing and Nonlinear Fourier Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/46, pp. 2671--2750](https://doi.org/10.4171/owr/2024/46)
## ... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298801-003",
"literature-status:open",
"owr-year:2024"
] | The M-QSP paper gives a characterization only up to an explicit conjecture and leaves query lower bounds and restricted achievable subclasses as future directions; no definitive resolution of these extracted problems was found. | [
{
"url": "https://quantum-journal.org/papers/q-2022-09-20-811/",
"label": "Rossi and Chuang, Multivariable QSP"
},
{
"url": "https://arxiv.org/abs/2205.06261",
"label": "M-QSP primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/46 | null | null | null | For multivariable quantum signal processing, lower-bound the query complexity required to realize a prescribed function class when ancillary space, intermediate measurements, or different oracle types are allowed. Identify a nontrivial, simply described subclass of achievable functions with improved numerical propertie... | Discussion and open problems Having reviewed some of the main statements of the original instantiation of M- QSP, as well as works since published addressing, extending, or circumventing its methods, we enumerate some open problems/promising avenues. (a) Adding abilities to the computing party: To enable the recovery o... | 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: Quantum Signal Processing and Nonlinear Fourier Analysis (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/46, pp. 2671--2750 |
30,006,093 | OWR-14298802-003 | Workshop Contents Listing for Algebraic K-Theory | conjecture . . . . . . . . . . . . . . . . . . . 2755 Shai Keidar Ambidexterity and Chromatic Cyclotomic Extensions . . . . . . . . . . . . . . . . 2759 Qingyuan Bai Cyclotomic and polygonic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2761 Turner McLaurin, Kirsten Wickelgren K-Theory, La... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804](https://doi.org/10.4171/owr/2024/47)
## Liter... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298802-003",
"literature-status:open",
"owr-year:2024"
] | The extracted record is only a table-of-contents fragment and does not state a determinate mathematical claim; its status is therefore unresolved. | [
{
"url": "https://doi.org/10.4171/OWR/2024/47",
"label": "Oberwolfach Report 47"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/47 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . 2755 Shai Keidar Ambidexterity and Chromatic Cyclotomic Extensions . . . . . . . . . . . . . . . . 2759 Qingyuan Bai Cyclotomic and polygonic spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2761 Turner McLaurin, Kirsten Wickelgren K-Theory, La... | unrecoverable | The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804 |
30,006,094 | OWR-14298802-004 | Expository Telescope-Conjecture Fragment | 2.3. Enter the telescope conjecture. Recall the cofiber sequence wn Σ|vn | V (n − 1) / V (n − 1) / V (n) 2.2. The chromatic filtration. Later we learned that the stable homotopy cate- gory itself is similarly organized. The key tool here is Bousfield localization, which conveniently appeared in 1978, just in time for u... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804](https://doi.org/10.4171/owr/2024/47)
## Liter... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "topology",
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is background exposition on the telescope conjecture, whose higher-height form is discusse) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298802-004",
"literature-status:open",
"owr-year:2024"
] | The record is an incomplete cofiber-sequence fragment rather than a complete question or conjecture, so no determinate solved or disproved status can be assigned. | [
{
"url": "https://doi.org/10.4171/OWR/2024/47",
"label": "Oberwolfach Report 47"
},
{
"url": "https://doi.org/10.2307/120991",
"label": "Hopkins and Smith, Periodicity theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/47 | null | null | null | null | 2.3. Enter the telescope conjecture. Recall the cofiber sequence wn Σ|vn | V (n − 1) / V (n − 1) / V (n) 2.2. The chromatic filtration. Later we learned that the stable homotopy cate- gory itself is similarly organized. The key tool here is Bousfield localization, which conveniently appeared in 1978, just in time for u... | unrecoverable | The official report confirms that this extraction is background exposition on the telescope conjecture, whose higher-height form is discussed there as disproved, not a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804 |
30,006,095 | OWR-14298802-005 | Existence of the Smith–Toda Complex $V(4)$ | Does the Smith–Toda complex $V(4)$ exist at any prime? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804](https://doi.org/10.4171/owr/2024/47)
## Liter... | 3 | partially_solved | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
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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-14298802-005",
"literature-status:partially-solved",
"owr-year:2024"
] | The Hopkins-Smith periodicity theorem generalizes the self-map construction to every finite type, but the specific Smith-Toda construction does not: the report states that V(4) has not been constructed and higher V(n) can fail to exist. | [
{
"url": "https://doi.org/10.4171/OWR/2024/47",
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"url": "https://doi.org/10.2307/120991",
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{
"url": "https://doi.org/10.4007/annals.2010.171.491",
"label": "Nave, Nonexistence of a Smith-Toda com... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/47 | null | null | null | Does the Smith–Toda complex $V(4)$ exist at any prime? | Can we generalize this to n > 3? 2.4. The Hopkins-Smith periodicity theorem. wn Σ|vn | V (n − 1) / V (n − 1) / V (n) Periodicity Theorem. Let X be a p-local type n finite spectrum, meaning that K(n)∗ X 6= 0 and K(m)∗ X = 0 for m < n. Then for some d > 0 (and divisible by |vn |) there is a map | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804 |
30,006,096 | OWR-14298802-007 | Reported Structure of Circle-Cochain THH | THH of cochains on the circle Neil P. Strickland Given a space X we write D+ (X) for the mapping spectrum from X to the sphere spectrum S. This might also be denoted by F (X+ , S) or S X , and called the spherical cochain ring for X. The spectrum A = D+ (S 1 ) = D+ (BZ) = S BZ can also be regarded as the homotopy fixed... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804](https://doi.org/10.4171/owr/2024/47)
## Liter... | 3 | open | null | 2,024 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
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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 | Unrecoverable OWR statement (The official report discusses structural results for the topological Hochschild homology of spherical cochains on the circle and does not po) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298802-007",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a title and descriptive THH setup, not a complete mathematical question or falsifiable claim; its literature status is consequently unresolved. | [
{
"url": "https://doi.org/10.4171/OWR/2024/47",
"label": "Oberwolfach Report 47"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/47 | null | null | null | null | THH of cochains on the circle Neil P. Strickland Given a space X we write D+ (X) for the mapping spectrum from X to the sphere spectrum S. This might also be denoted by F (X+ , S) or S X , and called the spherical cochain ring for X. The spectrum A = D+ (S 1 ) = D+ (BZ) = S BZ can also be regarded as the homotopy fixed... | unrecoverable | The official report discusses structural results for the topological Hochschild homology of spherical cochains on the circle and does not pose a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Algebraic \$K\$-Theory and the Telescope Conjecture (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/47, pp. 2751--2804 |
30,006,097 | OWR-14298803-001 | Efficient Nonlinear Balanced-Truncation Model Reduction | Develop more efficient balanced reduced-order models for nonlinear systems and compare them systematically with other nonlinear model-reduction methods. Use scalable approximations of the associated Hamilton–Jacobi–Bellman equations to enable real-time output-feedback control. Determine whether iterative solvers and al... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300](https://doi.org/10.4171/owr/2024/57)
#... | 3 | open | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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 | [
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"OWR-14298803-001",
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] | The workshop explicitly leaves open problems for nonlinear balanced truncation, and the extracted record does not specify a single resolved conjecture or estimate. | [
{
"url": "https://doi.org/10.4171/OWR/2024/57",
"label": "Oberwolfach Report 57"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/57 | null | null | null | Develop more efficient balanced reduced-order models for nonlinear systems and compare them systematically with other nonlinear model-reduction methods. Use scalable approximations of the associated Hamilton–Jacobi–Bellman equations to enable real-time output-feedback control. Determine whether iterative solvers and al... | Open Problems In this talk, we will also highlight open problems that remain for nonlinear bal- anced truncation. transformation approach (sometimes referred to balance-and-reduce as opposed to balance-then-reduce) for the nonlinear case. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300 |
30,006,098 | OWR-14298803-002 | Neural Networks for High-Dimensional Optimal Feedback Control | Determine when neural networks can solve high-dimensional infinite-horizon optimal feedback-control problems with rigorous accuracy, stability, and complexity guarantees that avoid the curse of dimensionality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300](https://doi.org/10.4171/owr/2024/57)
#... | 3 | partially_solved | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
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"slug": "computer-science",
"order_index": 15,
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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-14298803-002",
"literature-status:partially-solved",
"owr-year:2024"
] | Neural-network and HJB methods compute candidate feedback laws for selected high-dimensional deterministic, stochastic, and robust systems, including examples up to dimension thirty, but no general exact or curse-free solution is known. | [
{
"url": "https://doi.org/10.1137/19M1288802",
"label": "Nakamura-Zimmerer et al., Adaptive deep learning for HJB"
},
{
"url": "https://doi.org/10.1016/j.cnsns.2025.109196",
"label": "Space-time neural HJB method"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/57 | null | null | null | Determine when neural networks can solve high-dimensional infinite-horizon optimal feedback-control problems with rigorous accuracy, stability, and complexity guarantees that avoid the curse of dimensionality. | Can neural networks solve high dimensional optimal feedback control problems? Optimal feedback control. This talk concerns infinite horizon optimal control problems, which in continuous time are given by Z \infty minimize J(x0 , u) := \beta t ℓ(x(t), u(t)) dt u\inU 0 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300 |
30,006,099 | OWR-14298803-003 | Data-Driven Estimation of Maximal Time Averages | Given sampled trajectory data but no explicit governing vector field, estimate the maximal long-time average of an observable by approximating the Koopman generator. Establish convergence beyond polynomial ODEs and characterize the required data, dictionary, and sampling assumptions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300](https://doi.org/10.4171/owr/2024/57)
#... | 3 | partially_solved | null | 2,024 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14298803-003",
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] | Auxiliary-function duality solves the model-based maximal-average problem in the limiting sense, and EDMD data methods prove convergence under polynomial-ODE assumptions; a general non-polynomial data-driven theory remains open. | [
{
"url": "https://doi.org/10.1016/j.physleta.2017.12.023",
"label": "Tobasco et al., Optimal bounds for time averages"
},
{
"url": "https://arxiv.org/abs/2405.00539",
"label": "Llamazares-Elias et al., EDMD convergence bounds"
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{
"url": "https://doi.org/10.4171/OWR/2024/57",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/57 | null | null | null | Given sampled trajectory data but no explicit governing vector field, estimate the maximal long-time average of an observable by approximating the Koopman generator. Establish convergence beyond polynomial ODEs and characterize the required data, dictionary, and sampling assumptions. | Can one estimate maximal time averages in this case? The maximum time average as x0 is varied can be calculated by solving a convex optimization problem over continuously differentiable “auxiliary functions” [5], (1) max g(x0 ) = inf U s.t. U − g(x) − f (x) \cdot ∇v(x) \geq 0 \forallx \in X. x0 \inX U\inR v\inC 1 (X) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300 |
30,006,100 | OWR-14298803-004 | Finite-Sample Error Bounds for EDMD Time-Average Optimization | Derive explicit bounds for the gap between the exact auxiliary-function optimum and its EDMD-based approximation as a function of the number $N$ of data points, the dictionary degree $m$, and the sampling step $\tau$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300](https://doi.org/10.4171/owr/2024/57)
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"name": "oberwolfach_reports_open_problems",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298803-004",
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] | The requested explicit optimal-value gap as a function of data count, dictionary degree, and sampling step is explicitly identified as open; existing EDMD bounds do not supply this complete estimate. | [
{
"url": "https://doi.org/10.4171/OWR/2024/57",
"label": "Fantuzzi and Bramburger in Oberwolfach Report 57"
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{
"url": "https://arxiv.org/abs/2405.00539",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/57 | null | null | null | Derive explicit bounds for the gap between the exact auxiliary-function optimum and its EDMD-based approximation as a function of the number $N$ of data points, the dictionary degree $m$, and the sampling step $\tau$. | Another key open problem is to derive explicit estimates for the difference between the optimal values of problems (2) and (1) as a function of the number N of data points, the degree m of the approximating dictionary Ψ, and the data sampling step \tau . We wonder if recent advances in the quantitative error analysis f... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/57, pp. 3255--3300 |
30,006,101 | OWR-14298804-001 | Strongly Polynomial Algorithms for Linear Programming | Does linear programming admit a strongly polynomial-time algorithm? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14298804-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-001",
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] | Recent work gives strongly polynomial algorithms for important restricted LP classes such as two variables per inequality, while the existence of a strongly polynomial algorithm for general linear programming remains explicitly outstanding. | [
{
"url": "https://ir.cwi.nl/pub/34290/34290.pdf",
"label": "Dadush et al., Strongly polynomial LP for a restricted class"
},
{
"url": "https://doi.org/10.4171/OWR/2024/50",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Does linear programming admit a strongly polynomial-time algorithm? | Zhuan Khye Koh presented some groundbreaking progress toward resolving the long-standing open problem of finding a strongly polynomial algorithm for linear programming. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,102 | OWR-14298804-002 | Duplicate Strongly Polynomial Linear-Programming Lead-In | This achievement goes beyond previous results, which were limited to feasibility problems, marking a major step toward the aforementioned outstanding open problem. We conclude with mentioning that the workshop included an open problem session, during which six problems were discussed and compiled in this report to guid... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
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"slug": "computer-science",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction is contextual commentary about progress toward the strongly polynomial linear-programming ) | [
"OWR-14298804-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-002",
"literature-status:open",
"owr-year:2024"
] | The reported achievement concerns restricted feasibility or sparse-row and sparse-column LP classes; it does not resolve the outstanding strongly polynomial algorithm problem for general LP. | [
{
"url": "https://ir.cwi.nl/pub/34290/34290.pdf",
"label": "Dadush et al., Strongly polynomial LP for a restricted class"
},
{
"url": "https://doi.org/10.4171/OWR/2024/50",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | This achievement goes beyond previous results, which were limited to feasibility problems, marking a major step toward the aforementioned outstanding open problem. We conclude with mentioning that the workshop included an open problem session, during which six problems were discussed and compiled in this report to guid... | unrecoverable | The official report confirms that this extraction is contextual commentary about progress toward the strongly polynomial linear-programming problem represented canonically by OWR-14298804-001. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,103 | OWR-14298804-003 | Workshop Contents Listing for Combinatorial Optimization | 2987 Martin Skutella Open Problem: Is Zonotope Containment fixed-parameter tractable with respect to the dimension d? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2988 Sophie Huiberts Open Problem: The \delta-distance Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2989... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report confirms that this extraction is a contents listing of six open-problem contributions, not a standalone problem. No sepa) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-003",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a table-of-contents list of several distinct open problems rather than one determinate claim, so no single solved or disproved status can be assigned. | [
{
"url": "https://doi.org/10.4171/OWR/2024/50",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | 2987 Martin Skutella Open Problem: Is Zonotope Containment fixed-parameter tractable with respect to the dimension d? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2988 Sophie Huiberts Open Problem: The \delta-distance Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2989... | unrecoverable | The official report confirms that this extraction is a contents listing of six open-problem contributions, not a standalone problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,104 | OWR-14298804-004 | Integer Feasibility with Bounded Subdeterminants | Let $P=\{x\in\mathbb R^n:Ax\leq b\}$, where $A$ is integral and the absolute values of its full-rank subdeterminants are bounded by $\Delta$. For arbitrary $\Delta\geq3$, can one decide in polynomial time whether $P$ contains an integer vector? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 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-14298804-004",
"literature-status:open",
"owr-year:2024"
] | The source explicitly states that polynomial-time integer-feasibility testing for bounded full-rank subdeterminants with general Delta at least three remains open; later structural results do not resolve that general question. | [
{
"url": "https://doi.org/10.4171/OWR/2024/50",
"label": "Kuhlmann et al. in Oberwolfach Report 50"
},
{
"url": "https://doi.org/10.1016/j.jcta.2024.106003",
"label": "Celaya et al., Bounded non-vanishing subdeterminants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Let $P=\{x\in\mathbb R^n:Ax\leq b\}$, where $A$ is integral and the absolute values of its full-rank subdeterminants are bounded by $\Delta$. For arbitrary $\Delta\geq3$, can one decide in polynomial time whether $P$ contains an integer vector? | It remains an open problem whether one can determine in polynomial time if P contains an integer vector for general values of ∆ \geq 3. On integer feasibility of polyhedra with bounded subdeterminants Stefan Kuhlmann (joint work with Marcel Celaya, Martin Henk, Joseph Paat, Robert Weismantel) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,105 | OWR-14298804-007 | Fixed-Parameter Tractability of Zonotope Containment | Given $G\in\mathbb R^{d\times n}$ and $H\in\mathbb R^{d\times m}$, can one decide whether the zonotope $Z(G)$ is contained in $Z(H)$ in time $f(d)\operatorname{poly}(n+m)$ for some computable function $f$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 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... | [
"OWR-14298804-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-007",
"literature-status:open",
"owr-year:2024"
] | Zonotope containment is co-NP-complete and polynomial for some fixed parameters, but fixed-parameter tractability in the dimension remains explicitly open in current primary work. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0947358021000856",
"label": "Kulmburg and Althoff, Zonotope containment"
},
{
"url": "https://mlanthology.org/colt/2025/froese2025colt-open/",
"label": "Froese et al., Open problem on zonotope FPT"
},
{
"url": "https://doi.org/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Given $G\in\mathbb R^{d\times n}$ and $H\in\mathbb R^{d\times m}$, can one decide whether the zonotope $Z(G)$ is contained in $Z(H)$ in time $f(d)\operatorname{poly}(n+m)$ for some computable function $f$? | Open Problem: Is Zonotope Containment fixed-parameter tractable with respect to the dimension d? We ask if the Zonotope Containment Problem is fixed-parameter tractable with respect to the dimension d. In other words: Is there an algorithm that decides Zonotope Containment with running time poly(n + m) \cdot f (d) for ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,106 | OWR-14298804-008 | Duplicate Dimension-Parameterized Zonotope Containment | We ask if the Zonotope Containment Problem is fixed-parameter tractable with respect to the dimension d. In other words: Is there an algorithm that decides Zonotope Containment with running time poly(n + m) \cdot f (d) for an arbitrary function f ? The report passage is retained verbatim as the relevant context for thi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the fixed-parameter tractability question represented canonically by OWR-14298804-) | [
"OWR-14298804-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-008",
"literature-status:open",
"owr-year:2024"
] | This duplicates the dimension-parameterized zonotope-containment question; current literature records co-NP-completeness and special-case algorithms but no fixed-parameter algorithm in the dimension. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0947358021000856",
"label": "Kulmburg and Althoff, Zonotope containment"
},
{
"url": "https://mlanthology.org/colt/2025/froese2025colt-open/",
"label": "Froese et al., Open problem on zonotope FPT"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | We ask if the Zonotope Containment Problem is fixed-parameter tractable with respect to the dimension d. In other words: Is there an algorithm that decides Zonotope Containment with running time poly(n + m) \cdot f (d) for an arbitrary function f ? The report passage is retained verbatim as the relevant context for thi... | unrecoverable | The official report confirms that this extraction repeats the fixed-parameter tractability question represented canonically by OWR-14298804-007. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,107 | OWR-14298804-009 | Finite Strategies in the Distance Game | In the $\delta$-distance game, Peter chooses a leaving vertex of a simplex in the unit ball, and Roland chooses a replacement vertex that preserves the $\delta$-distance property and crosses the opposite face; the game ends when the simplex contains the origin. Does Peter have a strategy that always terminates, and can... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 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... | [
"OWR-14298804-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-009",
"literature-status:open",
"owr-year:2024"
] | The OWR report still poses the finite-strategy and polynomial-round questions for the delta-distance game. Related shadow-simplex and smoothed-simplex analyses do not settle this adversarial two-player game. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.345",
"label": "Shadow simplex method"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | In the $\delta$-distance game, Peter chooses a leaving vertex of a simplex in the unit ball, and Roland chooses a replacement vertex that preserves the $\delta$-distance property and crosses the opposite face; the game ends when the simplex contains the origin. Does Peter have a strategy that always terminates, and can... | Open Problem: The \delta-distance Game Sophie Huiberts We say that a full-dimensional simplex conv(a1 , . . . , ad+1 ) \subset Rd has the \delta-distance property if for each i = 1, . . . , d + 1 the Euclidean distance between vertex ai and the supporting hyperplane of the opposite face affhull(a1 , . . . , ai−1 , ai+1 ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,108 | OWR-14298804-010 | Duplicate Finite-Strategy Question for the Distance Game | Does Peter have a finite strategy? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the finite-strategy question represented canonically by OWR-14298804-009. No separ) | [
"OWR-14298804-009"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-010",
"literature-status:open",
"owr-year:2024"
] | The extracted finite-strategy question is the same unresolved delta-distance game problem; existing simplex-method results concern different probabilistic or geometric models and do not provide a strategy. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.345",
"label": "Shadow simplex method"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | Does Peter have a finite strategy? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction repeats the finite-strategy question represented canonically by OWR-14298804-009. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,109 | OWR-14298804-012 | Approximating Fare-Zone Assignment on Trees | Given a tree $G=(V,E)$ and weighted commodity paths $(P_i,w_i,u_i)$, choose $y_e\in\{0,1\}$ to maximize $\sum_{e\in E}y_e\sum_{i:e\in P_i}w_i$ subject to $\sum_{e\in P_i}y_e\leq u_i$ for every $i$. What approximation guarantees are achievable on trees, particularly when the maximum number of paths sharing an edge is bo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,024 | 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... | [
"OWR-14298804-013"
] | null | null | null | null | [Discussion #4 unrefereed claim, 2026-10-15] I have released an unrefereed preprint, **Fare Zone Assignment with Hard Cut Budgets under Bounded Congestion** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23391140) | [
"owr",
"oberwolfach-reports",
"OWR-14298804-012",
"literature-status:partially-solved",
"owr-year:2024"
] | A 2025 primary paper gives O(log n) and O(log n/log log n) approximations on trees and exact rooted cases, but the broader optimal approximation and bounded-congestion questions remain open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2512.19493",
"label": "Hoefer--Kauther--Pabst--Peis--Tran"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Given a tree $G=(V,E)$ and weighted commodity paths $(P_i,w_i,u_i)$, choose $y_e\in\{0,1\}$ to maximize $\sum_{e\in E}y_e\sum_{i:e\in P_i}w_i$ subject to $\sum_{e\in P_i}y_e\leq u_i$ for every $i$. What approximation guarantees are achievable on trees, particularly when the maximum number of paths sharing an edge is bo... | Open Problem: Fare Zone Assignment Britta Peis (joint work with Britta Peis, Philipp Pabst, Lennart Kauther, and Sam Fiorini) We are given a tree G = (V, E) and a set of commodities (Pi , wi , ui ), where each Pi \subseteq E is a path in G, wi denotes the weight of Pi and ui denotes the “maximum number of allowed cuts ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,110 | OWR-14298804-013 | Duplicate Fare-Zone Approximation Question | What else can we say about approximation results on trees? Open Problem: Fare Zone Assignment Britta Peis (joint work with Britta Peis, Philipp Pabst, Lennart Kauther, and Sam Fiorini) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the tree fare-zone approximation question represented canonically by OWR-14298804-) | [
"OWR-14298804-012"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-013",
"literature-status:partially-solved",
"owr-year:2024"
] | Recent work substantially advances the requested tree approximation results, including sublogarithmic guarantees and exact rooted instances, but does not close the full approximation frontier posed in the OWR extract. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2512.19493",
"label": "Recent FZA results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | What else can we say about approximation results on trees? Open Problem: Fare Zone Assignment Britta Peis (joint work with Britta Peis, Philipp Pabst, Lennart Kauther, and Sam Fiorini) | unrecoverable | The official report confirms that this extraction repeats the tree fare-zone approximation question represented canonically by OWR-14298804-012. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,111 | OWR-14298804-014 | Two-Coloring Light Tournaments | Is there a polynomial-time algorithm that partitions every two-colorable light tournament into two acyclic vertex sets, or is deciding two-colorability NP-hard even for light tournaments? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 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... | [
"OWR-14298804-015"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-014",
"literature-status:open",
"owr-year:2024"
] | The exact two-coloring question remains unresolved: published algorithms give constant-color upper bounds for 2-colorable or light tournaments, not a polynomial-time two-color algorithm. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://epubs.siam.org/doi/abs/10.1137/23M1602127",
"label": "Klingelhoefer--Newman"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Is there a polynomial-time algorithm that partitions every two-colorable light tournament into two acyclic vertex sets, or is deciding two-colorability NP-hard even for light tournaments? | Open Problem: Complexity of 2-coloring light tournaments Alantha Newman (joint work with Felix Klingehoefer) A tournament T = (V, A) is an orientation of a complete graph: for each pair of vertices u, v \in V , either arc (u, v) or arc (v, u) belongs to the arc set A. The open question is to determine the complexity of... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,112 | OWR-14298804-015 | Duplicate Light-Tournament Two-Coloring Question | The open question is to determine the complexity of 2-coloring light tournaments: Is there a polynomial-time algorithm to color a 2-colorable light tournament with two colors? Open Problem: Complexity of 2-coloring light tournaments Alantha Newman (joint work with Felix Klingehoefer) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the complexity question represented canonically by OWR-14298804-014. No separate c) | [
"OWR-14298804-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-015",
"literature-status:open",
"owr-year:2024"
] | The extracted question is not settled by the current light-tournament coloring literature; the known polynomial algorithms use more than two colors and leave the exact two-color complexity open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.71",
"label": "ESA paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | The open question is to determine the complexity of 2-coloring light tournaments: Is there a polynomial-time algorithm to color a 2-colorable light tournament with two colors? Open Problem: Complexity of 2-coloring light tournaments Alantha Newman (joint work with Felix Klingehoefer) | unrecoverable | The official report confirms that this extraction repeats the complexity question represented canonically by OWR-14298804-014. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,113 | OWR-14298804-016 | Half-Integral Extreme Points for a Feedback-Vertex-Set Relaxation | Does every basic feasible solution of the Chudak–Goemans–Hochbaum–Williamson linear-programming relaxation for a nontrivial feedback vertex set instance have a variable of value at least $1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 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... | [
"OWR-14298804-017"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-016",
"literature-status:open",
"owr-year:2024"
] | Polynomial-size FVS relaxations with integrality gap at most two are known, but the Fiorini extreme-point rounding question identified in the OWR report is explicitly not resolved. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://chekuri.cs.illinois.edu/papers/fvs-polyhedral-mpa.pdf",
"label": "FVS polyhedral results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | Does every basic feasible solution of the Chudak–Goemans–Hochbaum–Williamson linear-programming relaxation for a nontrivial feedback vertex set instance have a variable of value at least $1/2$? | Open Problem: Rounding Algorithms for Feedback Vertex Set and Subset Feedback Vertex Set Chandra Chekuri The Feedback Vertex Set problem (FVS) in undirected graphs is the following: given a graph G = (V, E) with vertex weights w : V \to Z+ , find a min-weight vertex subset S \subseteq V such that G − S is acyclic. In Ob... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,114 | OWR-14298804-017 | Duplicate Fiorini Feedback-Vertex-Set Question | The paper also showed that a previous LP relaxation suggested by Chekuri and Madan [4] also has integrality gap of 2 and this resolved an open problem. In particular, the original question of Fiorini is not yet resolved. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000](https://doi.org/10.4171/owr/2024/50)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction is commentary on the still-open Fiorini question represented canonically by OWR-14298804-0) | [
"OWR-14298804-016"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298804-017",
"literature-status:open",
"owr-year:2024"
] | The cited work resolves an integrality-gap question for a prior LP, but it states that Fiorini's original rounding or extreme-point question remains unresolved. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/706cca58-da6b-4d8c-a979-ebf6e92658f0/download",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2303.12850",
"label": "Chandrasekaran et al., FVS"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/50 | null | null | null | null | The paper also showed that a previous LP relaxation suggested by Chekuri and Madan [4] also has integrality gap of 2 and this resolved an open problem. In particular, the original question of Fiorini is not yet resolved. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is commentary on the still-open Fiorini question represented canonically by OWR-14298804-016. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/50, pp. 2949--3000 |
30,006,115 | OWR-14298805-001 | Survey of Smooth Modular Representations | What is known and what is not known? (with the convolution product), is isomorphic to the opposite algebra. If indG K (1R ) is projective, the K-invariants functor V 7\to V K gives a bijection \{V \in IrrR (G), V K 6= 0\} ≃ \{M \in Mod(HR (G, K)) simple\} and a category equivalence from the category ModR (G, K) of V \i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 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 | Unrecoverable OWR statement (The official report presents “what is known and what is not known?” as the heading of a broad survey, not as a standalone mathematical probl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298805-001",
"literature-status:open",
"owr-year:2024"
] | The extracted text is an open-ended survey prompt asking what is known and unknown about smooth modular representations and Hecke algebras; it is not a resolved mathematical assertion. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "Vigneras survey report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | null | What is known and what is not known? (with the convolution product), is isomorphic to the opposite algebra. If indG K (1R ) is projective, the K-invariants functor V 7\to V K gives a bijection \{V \in IrrR (G), V K 6= 0\} ≃ \{M \in Mod(HR (G, K)) simple\} and a category equivalence from the category ModR (G, K) of V \i... | unrecoverable | The official report presents “what is known and what is not known?” as the heading of a broad survey, not as a standalone mathematical problem. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
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