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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,916 | OWR-14298371-007 | Unconditionally Ruling Out Heuristica | Can the complexity-theoretic world Heuristica be ruled out unconditionally? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298371-007",
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"owr-year:2024"
] | Hirahara and Nanashima obtain conditional consequences from zero knowledge, but unconditional exclusion of Heuristica remains open; later work still describes the related average-hardness-to-one-way-function question as unresolved. | [
{
"url": "https://eccc.weizmann.ac.il/report/2024/063/download/",
"label": "Hirahara--Nanashima"
},
{
"url": "https://eccc.weizmann.ac.il/report/2026/052/",
"label": "ECCC 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Can the complexity-theoretic world Heuristica be ruled out unconditionally? | One-way functions and zero knowledge Although it remains open whether Heuristica can be ruled out unconditionally, Hirahara and Nanashima [HN24] ruled out Heuristica and Pessiland if NP has zero knowledge systems, which provides new worst-case characterizations of one- way functions. The report passage is retained verb... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,917 | OWR-14298371-009 | Abelian Embeddings and Gap-CSP Integrality Gaps | Can the complexity of $\operatorname{gap-CSP}\text{-}P[1,s]$ differ from that of $\operatorname{gap-CSP}\text{-}P[1-\varepsilon,s]$ only when $P$ admits a nontrivial Abelian embedding? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298371-009",
"literature-status:open",
"owr-year:2024"
] | The record presents the Abelian-embedding criterion as a conjectural explanation for an integrality-gap dichotomy; no authoritative proof or counterexample establishing that criterion was found, so the claim remains open. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/55937c4f-e831-4c4d-b8ee-73369eb5d131/content",
"label": "OWR 2024/27"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Can the complexity of $\operatorname{gap-CSP}\text{-}P[1,s]$ differ from that of $\operatorname{gap-CSP}\text{-}P[1-\varepsilon,s]$ only when $P$ admits a nontrivial Abelian embedding? | We conjecture that, in some sense, there could only be a difference between the complexity of the problems gap-CSP-P [1, s] and gap-CSP- P [1 − \varepsilon, s] if P admits non-trivial Abelian embeddings.1 In the talk we discussed 1The precise formulation has to do with the structure of integrality gaps for the natural ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,918 | OWR-14298371-010 | Output Length and Error of Seedless Extractors | Improve the output length and error parameters of seedless extractors. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 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-14298371-010",
"literature-status:open",
"owr-year:2024"
] | Seedless extractor constructions achieve strong parameters in restricted regimes, but improving output length together with negligible or exponentially small error remains an explicit open direction. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC9321789/",
"label": "Recent Advances in Randomness Extraction"
},
{
"url": "https://ems.press/content/serial-article-files/49481",
"label": "OWR 2024/27"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Improve the output length and error parameters of seedless extractors. | There are still interesting and important open problems left. For example, one natural open question is to improve the output length and error of the seedless extractors constructed. 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 | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,919 | OWR-14298372-001 | Isomorphism of Free Group Factors | Are the free group factors $L(\mathbb F_2)$ and $L(\mathbb F_3)$ isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 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-14298372-001",
"literature-status:open",
"owr-year:2024"
] | The isomorphism problem for the free group factors LF2 and LF3 remains unresolved; current operator-algebra references continue to treat the isomorphism question for different finite ranks as open. | [
{
"url": "https://arxiv.org/abs/funct-an/9211012",
"label": "Dykema"
},
{
"url": "https://www.math.ucla.edu/~popa/Talks/wFC_uclaNov2024.pdf",
"label": "Popa 2024 lecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | Are the free group factors $L(\mathbb F_2)$ and $L(\mathbb F_3)$ isomorphic? | It is an open problem whether LF2 is isomorphic to LF3 , where Fn is the free non- commutative group with n generators. ϕ(a1 b1 )ϕ(a2 b2 ) − ϕ(a1 a2 b1 b2 ) = (ϕ(a1 b1 ) − ϕ(a1 )ϕ(b1 )) (ϕ(a2 b2 ) − ϕ(a2 )ϕ(b2 )) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,920 | OWR-14298372-002 | Quantum-Channel Interpolation Characterization | Given (A1 , . . . , Am ), (B1 , . . . , Bm ) \in (Mn )m sa , when does there exist a unital quantum channel Φ : Mn \to Mn such that Φ(Bk ) = Ak for all k? Non-commutative Function Theory and Free Probability 1257 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 3 | partially_solved | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 poses this interpolation question and then gives a necessary-and-sufficient characterization as Theorem 5.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298372-002",
"literature-status:partially-solved",
"owr-year:2024"
] | The interpolation question has Choi-matrix and operator-system criteria and substantial results for structured or commuting families, but a general classification for arbitrary self-adjoint tuples is not known. | [
{
"url": "https://arxiv.org/abs/1012.1675",
"label": "Li--Poon"
},
{
"url": "https://people.wm.edu/~cklixx/cpafinal.pdf",
"label": "Li--Poon full paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | null | Given (A1 , . . . , Am ), (B1 , . . . , Bm ) \in (Mn )m sa , when does there exist a unital quantum channel Φ : Mn \to Mn such that Φ(Bk ) = Ak for all k? Non-commutative Function Theory and Free Probability 1257 | unrecoverable | The official report poses this interpolation question and then gives a necessary-and-sufficient characterization as Theorem 5. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,921 | OWR-14298372-004 | Setup for Noncommutative Stability Conjectures | To state the conjectured generalizations of (3) and (4), we first introduce (what we conjecture is) the correct notion of stability, which is compatible with an appro- priate determinantal representation, via the following lemma. where \alpha = (\alpha1 , . . . , \alphad ) \in Nd is the usual multi-index notation and c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 3 | open | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 is introductory setup for Conjectures 10 and 12, both preserved in the following records.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298372-004",
"literature-status:open",
"owr-year:2024"
] | The extracted record is an incomplete transition to a conjectured stability notion rather than a self-contained claim; known determinantal-representation theorems do not identify or settle the later conjectures, so this record is conservatively open. | [
{
"url": "https://arxiv.org/abs/1807.05645",
"label": "Volcic"
},
{
"url": "https://doi.org/10.4171/owr/2024/22",
"label": "OWR 2024/22"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | null | To state the conjectured generalizations of (3) and (4), we first introduce (what we conjecture is) the correct notion of stability, which is compatible with an appro- priate determinantal representation, via the following lemma. where \alpha = (\alpha1 , . . . , \alphad ) \in Nd is the usual multi-index notation and c... | unrecoverable | The official report confirms that this extraction is introductory setup for Conjectures 10 and 12, both preserved in the following records. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,922 | OWR-14298372-005 | Unitary Integral Identity for Noncommutative Polynomials | Let $p$ and $q$ be stable polynomials in noncommuting variables with $p(0)=q(0)=1$ and determinantal representations $\det p(X)=\det(I-A\otimes X)$ and $\det q(X)=\det(I-B\otimes X)$. Prove $\lim_{N\to\infty}\int_{U(N)^d}\det(p(U))\overline{\det(q(U))}\,dU=\det((I-A\otimes\overline B)^{-1})$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 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"
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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-14298372-005",
"literature-status:open",
"owr-year:2024"
] | The unitary-integral identity in Conjecture 10 is not proved in the cited report or in the primary literature located; known stability representation results and special cases do not settle the general assertion. | [
{
"url": "https://doi.org/10.4171/owr/2024/22",
"label": "OWR 2024/22"
},
{
"url": "https://arxiv.org/abs/1807.05645",
"label": "Volcic"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | Let $p$ and $q$ be stable polynomials in noncommuting variables with $p(0)=q(0)=1$ and determinantal representations $\det p(X)=\det(I-A\otimes X)$ and $\det q(X)=\det(I-B\otimes X)$. Prove $\lim_{N\to\infty}\int_{U(N)^d}\det(p(U))\overline{\det(q(U))}\,dU=\det((I-A\otimes\overline B)^{-1})$. | Conjecture 10. Let p and q be polynomials in non-commuting indeterminates x1 , . . . , xd with p(0) = q(0) = 1, and suppose p and q are stable with determinantal representations det p(X) = det(I − A ⊗ X), det q(X) = det(I − B ⊗ X). Then Z (11) lim det(p(U ))det q(U ) dU d = det((I − A ⊗ B)−1 ). N \to\infty U (N )d One ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,923 | OWR-14298372-006 | Uniform Determinant Integrals for Row Contractions | For every $0\leq r<1$ and integer $k\geq 1$, prove that there is $C(r,k)$ such that, for every $d$-tuple $A=(A_1,\ldots,A_d)$ of $k\times k$ matrices with $\|A\|_{\mathrm{row}}\leq r$, one has $\sup_N\int_{U(N)^d}|\det(I-A\otimes U)|^2\,dU\leq C(r,k)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 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"
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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-14298372-006",
"literature-status:open",
"owr-year:2024"
] | The uniform determinant integral bound in Conjecture 12 is known in special cases, but no general proof or counterexample for arbitrary row contractions and dimensions was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/22",
"label": "OWR 2024/22"
},
{
"url": "https://arxiv.org/abs/2507.19453",
"label": "Noncommutative Szego-type theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | For every $0\leq r<1$ and integer $k\geq 1$, prove that there is $C(r,k)$ such that, for every $d$-tuple $A=(A_1,\ldots,A_d)$ of $k\times k$ matrices with $\|A\|_{\mathrm{row}}\leq r$, one has $\sup_N\int_{U(N)^d}|\det(I-A\otimes U)|^2\,dU\leq C(r,k)$. | One can give a formal argument for the conjecture in the spirit of the proof of the strong Szegő limit theorem given by Bump and Diaconis [1]. The formal argument can be made rigorous if the following weaker conjecture holds: Conjecture 12. For each 0 \leq r < 1 and each integer k \geq 1, there is a constant C = C(r, ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,924 | OWR-14298372-007 | Free-Conjugate-Variable Regularity Overview | So what kind of regularity can one obtain if one makes various regularity as- sumptions on the free conjugate variables? Central to L2 -homology is the question of when there are such 1-cycles with Tj belonging to finite-rank operators versus Hilbert–Schmidt operators. Let now Q be some non-commutative polynomial in in... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 3 | open | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | Unrecoverable OWR statement (The official report uses this broad question to organize a survey of several established regularity results; it does not isolate an unresolv) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298372-007",
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] | The cited free-probability results give regularity and homological information in important cases, but the broad regularity question for free conjugate variables stated in the record remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/22",
"label": "OWR 2024/22"
},
{
"url": "https://par.nsf.gov/servlets/purl/10432807",
"label": "Regularity results"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | null | So what kind of regularity can one obtain if one makes various regularity as- sumptions on the free conjugate variables? Central to L2 -homology is the question of when there are such 1-cycles with Tj belonging to finite-rank operators versus Hilbert–Schmidt operators. Let now Q be some non-commutative polynomial in in... | unrecoverable | The official report uses this broad question to organize a survey of several established regularity results; it does not isolate an unresolved claim. | null | null | null | null | null | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,925 | OWR-14298372-008 | Free Polar Decomposition Under a Nondegeneracy Condition | Let $z$ be a $B$-valued circular element with a free bipolar decomposition, and suppose $\operatorname{span}\{E((z^*z)^k):k\geq 0\}$ is dense in $B$. Must $z$ admit a free polar decomposition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284](https://doi.org/10.4171/owr/2024/22)
## Literature review (checke... | 3 | open | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://arxiv.org/abs/2306.17133",
"label": "Dykema--Griffin"
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{
"url": "https://doi.org/10.4171/owr/2024/22",
"label": "OWR 2024/22"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/22 | null | null | null | Let $z$ be a $B$-valued circular element with a free bipolar decomposition, and suppose $\operatorname{span}\{E((z^*z)^k):k\geq 0\}$ is dense in $B$. Must $z$ admit a free polar decomposition? | If we assume the nondegeneracy condition that span\{E((z ∗ z)k ) | k \geq 0\} is dense in B, the question is open. 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 | Non-commutative Function Theory and Free Probability (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/22, pp. 1227--1284 |
30,005,926 | OWR-14298373-004 | Distance and Diameter Constants of High-Genus Triangulations | For random triangulations $T_{n,g}$ of high genus, are typical distances asymptotic to $D_\theta\log n$ and the diameter to $D'_\theta\log n$ with $D'_\theta=3D_\theta$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://doi.org/10.1214/24-AOP1746",
"label": "Budzinski--Chapuy--Louf"
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{
"url": "https://arxiv.org/abs/2606.27357",
"label": "Lions 2026"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | For random triangulations $T_{n,g}$ of high genus, are typical distances asymptotic to $D_\theta\log n$ and the diameter to $D'_\theta\log n$ with $D'_\theta=3D_\theta$? | We concluded with a few open questions on the optimal constants. In particular, we conjecture that the distance between two typical vertices of Tn,g is close to D\theta log n, whereas the diameter (i.e. the distance between the two furthest points) is close to D\theta′ log n with D\theta′ = 3D\theta . 2. Local limits i... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,927 | OWR-14298373-005 | Rigorous Construction of Conformal Field Theories | How can rigorous examples of conformal field theories be constructed, including rigorous path integrals and justification of the bootstrap hypothesis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14298373-005",
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{
"url": "https://arxiv.org/abs/1606.04493",
"label": "Huang open problems"
},
{
"url": "https://arxiv.org/abs/2102.11219",
"label": "Probabilistic Toda construction"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | How can rigorous examples of conformal field theories be constructed, including rigorous path integrals and justification of the bootstrap hypothesis? | How does one find examples of CFTs? Theories (CFT). A CFT is characterised by a minimal set of so-called primary random fields Vi defined on Rd and their correlation functions Yn h Vi (xi )i i=1 where S a local action functional. The challenge then is to find examples of S which give rise to a CFT, give a rigorous mean... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,928 | OWR-14298373-006 | Open Structures in Compactified Imaginary Liouville Theory | Are compactified imaginary Liouville models related to CILT, do they admit a path-integral formulation, are they logarithmic CFTs, and is there a probabilistic theory when $\beta^2\notin\mathbb{Q}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14298373-006",
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] | Compactified imaginary Liouville theory is constructed in rational parameter regimes with strong structural properties, but the listed questions for irrational parameters, path-integral and logarithmic-CFT structures, and the remaining probabilistic regimes are unresolved. | [
{
"url": "https://arxiv.org/abs/2310.18226",
"label": "Compactified Imaginary Liouville Theory"
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{
"url": "https://arxiv.org/abs/2112.14859",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | Are compactified imaginary Liouville models related to CILT, do they admit a path-integral formulation, are they logarithmic CFTs, and is there a probabilistic theory when $\beta^2\notin\mathbb{Q}$? | Open Questions 2 1. Are these models related to CILT? Is there a path integral formulation of G. Is it a logarithmic CFT? \sqrt{ } 4. Is there a probabilistc theory for \beta 2 \in / Q? Q Theorem. Let \beta 2 \in Q with \beta 2 < 2. The correlation functions h j Vej ,mj (zj , vj ))i are well defined if X mi = 0 and ei ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,929 | OWR-14298373-007 | Coulomb-Gas Asymptotics Beyond Weil–Petersson Quasicircles | What are the Coulomb-gas asymptotics when the boundary curve $\eta$ is not a Weil–Petersson quasicircle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
"url": "https://doi.org/10.1007/s00222-026-01417-5",
"label": "Coulomb gas with corners"
},
{
"url": "https://arxiv.org/abs/2110.11032",
"label": "Strong Szego on a Jordan curve"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | What are the Coulomb-gas asymptotics when the boundary curve $\eta$ is not a Weil–Petersson quasicircle? | What happens if η is not a Weil-Petersson quasicircle? The expression on the right could be considered universal and appears for in- stance in small-t heat-trace formulas, see, e.g., [2, 5]. The proof of Theorem 2 starts from Proposition 1 and is based on careful asymptotic analysis of the Grunsky coefficients. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,930 | OWR-14298373-008 | Scaling Limits of Random High-Dimensional Dimer Tilings | What are the scaling limits and limit shapes of random dimer tilings of regions in $\mathbb{R}^n$ as $n\to\infty$, especially beyond two dimensions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://arxiv.org/abs/2304.08468",
"label": "Chandgotia--Sheffield--Wolfram"
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{
"url": "https://arxiv.org/abs/2506.12171",
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"label": "OWR 2024/25"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | What are the scaling limits and limit shapes of random dimer tilings of regions in $\mathbb{R}^n$ as $n\to\infty$, especially beyond two dimensions? | What does a random dimer tiling of Rn look like as n \to \infty? This vague question is made precise using the correspondence with divergence- free discrete vector fields f\tau , whose scaling limits are measurable divergence-free vector fields (in a suitable topology). 3. Differences between 2D and 3D The large deviat... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,931 | OWR-14298373-009 | Chemical Distance in Critical Percolation | Obtain stronger results for chemical distance in critical percolation and its relation to nonsimple CLE metrics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444](https://doi.org/10.4171/owr/2024/25)
## Literature review (checked 2026-08-22)... | 3 | partially_solved | null | 2,024 | 19 | 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 | [
"owr",
"oberwolfach-reports",
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"literature-status:partially-solved",
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] | Bounds and a 2026 intrinsic-metric scaling-limit result substantially advance critical chemical distance, but the exact chemical-distance exponent and stronger identification requested in the record remain open. | [
{
"url": "https://arxiv.org/abs/2604.14122",
"label": "Intrinsic metric scaling limit"
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{
"url": "https://arxiv.org/abs/1708.03643",
"label": "Damron--Hanson--Sosoe"
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{
"url": "https://doi.org/10.4171/owr/2024/25",
"label": "OWR 2024/25"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/25 | null | null | null | Obtain stronger results for chemical distance in critical percolation and its relation to nonsimple CLE metrics. | Proving anything stronger for the chemical distance in critical percolation remains an open question. (This problem was asked by O. The chemical distance metric for non-simple CLE Yizheng Yuan (joint work with Valeria Ambrosio and Jason Miller) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistical Physics and Random Surfaces (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/25, pp. 1387--1444 |
30,005,932 | OWR-14298374-001 | Random-Surface Modeling Motivation | What are possible ways to model this difference and to efficiently generate many such similar shapes that are possibly changing over time? Stochastic partial differential equations on surfaces and evolving random surfaces: a computational approach Annika Lang (joint work with David Cohen, Erik Jansson, Mike Pereira and... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 3 | partially_solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this question to introduce the stochastic surface models developed in the remainder of the abstract; it is not a de) | null | null | null | [
"owr",
"oberwolfach-reports",
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] | SPDE and Gaussian random-field constructions on fixed and evolving surfaces, together with convergent numerical schemes, provide efficient models for many shape families; a general method for generating arbitrary similar time-varying shapes remains open. | [
{
"url": "https://doi.org/10.1137/21M1400717",
"label": "Spherical Whittle--Matern fields"
},
{
"url": "https://arxiv.org/abs/1208.5958",
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},
{
"url": "https://doi.org/10.1016/j.spasta.2026.101013",
"label": "Surface spatio-temporal SPDEs"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | null | What are possible ways to model this difference and to efficiently generate many such similar shapes that are possibly changing over time? Stochastic partial differential equations on surfaces and evolving random surfaces: a computational approach Annika Lang (joint work with David Cohen, Erik Jansson, Mike Pereira and... | unrecoverable | The official report uses this question to introduce the stochastic surface models developed in the remainder of the abstract; it is not a delimited open problem. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,933 | OWR-14298374-002 | Infinite-Resolution Random-Surface Question | A natural question is if the obtained surfaces make sense when taking L to infinity. Figure 2. Random surfaces generated by the transformation (2) with different truncation levels L. (a) \alpha = 1/2 (b) \alpha = 1 (c) \alpha = 3/2 (d) \alpha = 2 (e) \alpha = 5/2 (f) \alpha = 3 (g) \alpha = 7/2 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 3 | partially_solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks whether the limit surface is well defined and immediately answers it through continuity and differentiability crite) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298374-002",
"literature-status:partially-solved",
"owr-year:2024"
] | The report reduces the limit question to continuity of the weighted spherical random field and gives a continuous modification for smoothness parameter alpha greater than 1, but the extracted question is broader than this established regime. | [
{
"url": "https://doi.org/10.4171/owr/2024/26",
"label": "Oberwolfach Report 26/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | null | A natural question is if the obtained surfaces make sense when taking L to infinity. Figure 2. Random surfaces generated by the transformation (2) with different truncation levels L. (a) \alpha = 1/2 (b) \alpha = 1 (c) \alpha = 3/2 (d) \alpha = 2 (e) \alpha = 5/2 (f) \alpha = 3 (g) \alpha = 7/2 | unrecoverable | The official report asks whether the limit surface is well defined and immediately answers it through continuity and differentiability criteria for the random field. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,934 | OWR-14298374-003 | Wishart Processes with Noninjective Semigroups | For the infinite-dimensional Wishart stochastic differential equation with injective diffusion operator $Q$, does there exist an unbounded semigroup generator $A$ for which a solution exists with $\alpha\notin\mathbb N$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 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-14298374-003",
"literature-status:open",
"owr-year:2024"
] | The 2024 report states this exact unbounded-generator, noninteger-parameter existence question as an open problem; the subsequent infinite-dimensional Wishart-process literature does not establish the requested case. | [
{
"url": "https://doi.org/10.4171/owr/2024/26",
"label": "Oberwolfach Report 26/2024"
},
{
"url": "https://doi.org/10.1214/24-EJP1173",
"label": "Infinite-dimensional Wishart processes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | For the infinite-dimensional Wishart stochastic differential equation with injective diffusion operator $Q$, does there exist an unbounded semigroup generator $A$ for which a solution exists with $\alpha\notin\mathbb N$? | Does there exist an unbounded operator A such that (1) allows for a solution for some \alpha \in / N? in S(Rn ) that are of rank at most k is only known when A ≡ 0 and Q = idRn see [5, Theorem 3.10]. Moreover, in the infinite-dimensional setting under the condition that rank(Q) = \infty, this result implies that finite... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,935 | OWR-14298374-004 | Positivity and Convergence of a Splitting Scheme | For the Lie-Trotter splitting scheme applied to $du=\Delta u\,dt+g(u)\,d\beta(t)$ with homogeneous Dirichlet data and the non-globally Lipschitz nonlinearity $g(v)=v^{1.25}$, prove positivity and mean-square convergence of order $1/2$. Also establish a weak convergence rate. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 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-14298374-004",
"literature-status:open",
"owr-year:2024"
] | The exact record is only a fragment saying that proving the stated numerical-SPDE properties remains open, so no later resolution is identifiable from the extracted claim. | [
{
"url": "https://doi.org/10.4171/owr/2024/26",
"label": "Oberwolfach Report 26/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | For the Lie-Trotter splitting scheme applied to $du=\Delta u\,dt+g(u)\,d\beta(t)$ with homogeneous Dirichlet data and the non-globally Lipschitz nonlinearity $g(v)=v^{1.25}$, prove positivity and mean-square convergence of order $1/2$. Also establish a weak convergence rate. | To prove this remains an open question. where G(t, x, y) is the fundamental solution to the deterministic heat equation. The time integrator (2) satisfies the following, see [3] for precise statements: • Almost surely, uLT m (x) ⩾ 0 for all x \in D and m \in \{0, . . . , M \}, • It is exact when applied to the SPDE (1)... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,936 | OWR-14298374-005 | Splitting Schemes for Rough Stochastic Heat Equations | For the fully discrete Lie-Trotter scheme applied to $\partial_tu=\partial_{xx}u+g(u)\dot W$ on $[0,1]$ with homogeneous Dirichlet data, extend positivity and mean-square convergence of order $1/4$ to rougher nonlinearities $g$, and determine a weak convergence rate. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298374-005",
"literature-status:open",
"owr-year:2024"
] | The source explicitly leaves positivity and convergence for the less regular nonlinearity open, and no authoritative subsequent result resolving that generalization was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/26",
"label": "Oberwolfach Report 26/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | For the fully discrete Lie-Trotter scheme applied to $\partial_tu=\partial_{xx}u+g(u)\dot W$ on $[0,1]$ with homogeneous Dirichlet data, extend positivity and mean-square convergence of order $1/4$ to rougher nonlinearities $g$, and determine a weak convergence rate. | To prove these properties for the SPDE (3) with g less regular than in [2] remains an open question. where ∆m,n W = WnN (tm+1 ) − WnN (tm ). Under some technical assumptions, the fully-discrete numerical scheme (4) sat- isfies the following, see [2] for precise statements: • Almost surely, uLT m,n ⩾ 0 for all m \in \{0... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,937 | OWR-14298374-006 | Autoencoder Optimization Perspectives | In particular, there is some duality in the way the minimization over f \in F is performed, as one can decide to either (i) simultaneously minimize over fenc and fdec , which is the standard way to proceed when training neural networks; (ii) minimize first over the encoder part, which allows to reformulate the min- imi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516](https://doi.org/10.4171/owr/2024... | 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 describes three equivalent optimization viewpoints and their modeling consequences; it does not state an unresolved math) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298374-006",
"literature-status:open",
"owr-year:2024"
] | The extracted record is an interpretive paragraph about autoencoder minimization rather than a complete theorem or question, so its mathematical status is unclear and is classified open under the triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2024/26",
"label": "Oberwolfach Report 26/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/26 | null | null | null | null | In particular, there is some duality in the way the minimization over f \in F is performed, as one can decide to either (i) simultaneously minimize over fenc and fdec , which is the standard way to proceed when training neural networks; (ii) minimize first over the encoder part, which allows to reformulate the min- imi... | unrecoverable | The official report describes three equivalent optimization viewpoints and their modeling consequences; it does not state an unresolved mathematical problem. | null | null | null | null | null | Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/26, pp. 1445--1516 |
30,005,938 | OWR-14298375-001 | Unspecified Hyperplane Arrangement Conjecture | conjecture. More recently and along the same lines, another arrangement construction, the matroid Schubert variety, was shown by Braden et al. [2] to give another matroid invariant, in this case its intersection cohomology. This was a key part in their celebrated proof of the top-heaviness conjecture, and gave an inter... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arrangements, Matroids and Logarithmic Vector Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/29, pp. 1615--1676](https://doi.org/10.4171/owr/2024/29)
## Literature review (checke... | 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 | Answered in the source or not an open problem (solved (not a problem; retire)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (not a problem; retire)**. The record is a fragment of the organizers' introduction (OWR 29/2024, p. 1616): its first word ends the sentence saying that Adiprasito–Huh–Katz used the Chow ring of a matroid to prove the Rota–Heron–Welsh conjecture ([Ann. of Math. 188... | [
"owr",
"oberwolfach-reports",
"OWR-14298375-001",
"literature-status:open",
"owr-year:2024"
] | The record contains only the word conjecture followed by workshop context and does not identify a mathematical claim that can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2024/29",
"label": "Oberwolfach Report 29/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/29 | null | null | null | null | conjecture. More recently and along the same lines, another arrangement construction, the matroid Schubert variety, was shown by Braden et al. [2] to give another matroid invariant, in this case its intersection cohomology. This was a key part in their celebrated proof of the top-heaviness conjecture, and gave an inter... | unrecoverable | The extraction is a table-of-contents and workshop-introduction fragment referring to already proved matroid conjectures rather than posing a new problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Arrangements, Matroids and Logarithmic Vector Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/29, pp. 1615--1676 |
30,005,939 | OWR-14298375-006 | Homotopy Classes from Elliptic Artin Monoids | Are the $\Pi$-classes associated with twins of non-cancellative elements in elliptic Artin monoids nontrivial, and are their inertia groups trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arrangements, Matroids and Logarithmic Vector Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/29, pp. 1615--1676](https://doi.org/10.4171/owr/2024/29)
## Literature review (checke... | 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-14298375-006",
"literature-status:open",
"owr-year:2024"
] | The record is only the fragment Finaly, we conjecture Conjecture and supplies no identifiable proposition whose truth can be checked. | [
{
"url": "https://doi.org/10.4171/owr/2024/29",
"label": "Oberwolfach Report 29/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/29 | null | null | null | Are the $\Pi$-classes associated with twins of non-cancellative elements in elliptic Artin monoids nontrivial, and are their inertia groups trivial? | Finaly, we conjecture Conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arrangements, Matroids and Logarithmic Vector Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/29, pp. 1615--1676 |
30,005,940 | OWR-14298376-001 | Unspecified Real Enumerative Geometry Conjecture | conjecture . . . . . . . . . . . . . . . . . . . . . 1306 Pierrick Bousseau (joint with Hülya Argüz) Generalized Block-Göttsche polynomials and Welschinger invariants . . . . 1309 Jake Solomon Towards quadratically enriched Gromov-Witten theory . . . . . . . . . . . . . . . . 1311 Thomas Guidoni Givental reconstruct... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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"
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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 extraction is a table-of-contents fragment ending in a contribution title, not a mathematical statement. No separate clean statement is ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298376-001",
"literature-status:open",
"owr-year:2024"
] | The record is a truncated table-of-contents fragment ending in conjecture, so the underlying mathematical assertion is unclear and cannot be classified as resolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . 1306 Pierrick Bousseau (joint with Hülya Argüz) Generalized Block-Göttsche polynomials and Welschinger invariants . . . . 1309 Jake Solomon Towards quadratically enriched Gromov-Witten theory . . . . . . . . . . . . . . . . 1311 Thomas Guidoni Givental reconstruct... | unrecoverable | The extraction is a table-of-contents fragment ending in a contribution title, not a mathematical statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,941 | OWR-14298376-004 | Welschinger Specialization of Generalized Block–Göttsche Polynomials | For a surface $S$ and curve class $\beta_S$, does the generalized Block–Göttsche polynomial specialize at $q=-1$ to the real Welschinger invariant, so that $\operatorname{BPS}_{\beta_S}^S(-1)=W_{\beta_S}^S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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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"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-14298376-004",
"literature-status:partially-solved",
"owr-year:2024"
] | Arguez and Bousseau prove the q equals minus 1 specialization for blowups of the projective plane at at most six general points, while the all-n conjecture remains stated and unproved. | [
{
"url": "https://arxiv.org/abs/2506.02770",
"label": "BPS polynomials and Welschinger invariants"
},
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | For a surface $S$ and curve class $\beta_S$, does the generalized Block–Göttsche polynomial specialize at $q=-1$ to the real Welschinger invariant, so that $\operatorname{BPS}_{\beta_S}^S(-1)=W_{\beta_S}^S$? | We propose to view the polynomials BP S\betaS (q) as generalizations of Block- Göttsche polynomials. We conjecture that we also recovers the real Welschinger counts at q = −1: Conjecture [Argüz–Bousseau]. tropical curves in R2 with appropriate multiplicities [7, 8] – see also [1]. Accord- ing to Block-Göttsche, the ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,942 | OWR-14298376-005 | Refined Donaldson–Thomas Meaning of Block–Göttsche Polynomials | Do the generalized Block–Göttsche polynomials $\operatorname{BPS}_{\beta_S}^S(q)$ admit an interpretation in refined Donaldson–Thomas theory for the Calabi–Yau threefold $K_S$, the total space of the canonical bundle of $S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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"
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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-14298376-005",
"literature-status:open",
"owr-year:2024"
] | The proposed identification with refined BPS invariants of the canonical-line-bundle Calabi--Yau remains a conjecture in the latest primary treatment; only related special evidence is established. | [
{
"url": "https://arxiv.org/abs/2506.02770",
"label": "BPS polynomials and Welschinger invariants"
},
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | Do the generalized Block–Göttsche polynomials $\operatorname{BPS}_{\beta_S}^S(q)$ admit an interpretation in refined Donaldson–Thomas theory for the Calabi–Yau threefold $K_S$, the total space of the canonical bundle of $S$? | Finally, we conjecture that the polynomials BP S\betaS (q) have an alternative de- sciption in terms of refined Donaldson–Thomas theory of the Calabi–Yau 3-fold KS given by the total space of the canonical line bundle of the surface S. Using degeneration arguments, we prove this conjecture when S is a del Pezzo surface... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,943 | OWR-14298376-006 | Reconstruction of Real Gromov-Witten Invariants for Semisimple Targets | Does the real Gromov–Witten theory of every real-orientable target with semisimple quantum cohomology satisfy the proposed reconstruction formula for a suitable series $U_{t,q}(\psi)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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-14298376-006",
"literature-status:partially-solved",
"owr-year:2024"
] | The report proves the reconstruction identity for the real projective targets with the stated involution, but the extracted conjecture asserts it for every real-orientable target with semisimple quantum cohomology. | [
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | Does the real Gromov–Witten theory of every real-orientable target with semisimple quantum cohomology satisfy the proposed reconstruction formula for a suitable series $U_{t,q}(\psi)$? | for 1 − g − n < 0 at any point t such that \tau (t) = t. The right-hand side involves only integrals of \psi-classes over the moduli spaces of curves and the genus 0 complex and real Gromov-Witten theory of the target. Conjecture 1. The real Gromov-Witten of every real-orientable target whose quantum coholomogy is semi... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,944 | OWR-14298376-007 | Degeneration and Moduli of Logarithmic Linear Series | When a smooth curve $C$ degenerates to a nodal curve $C_0$, how do the line bundle $L$ and subspace $V$ of a linear series $(L,V)$ degenerate? Describe the moduli space of linear series on $C_0$. How can one detect whether a linear series on $C_0$ is the limit of linear series on smooth curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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-14298376-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Logarithmic linear-series constructions answer the degeneration questions in important cases and extend limit-linear-series methods beyond compact type, but the 2026 foundational work still describes the full moduli problem as developing. | [
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
},
{
"url": "https://arxiv.org/abs/2602.05685",
"label": "Vector bundles on Olsson fans"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | When a smooth curve $C$ degenerates to a nodal curve $C_0$, how do the line bundle $L$ and subspace $V$ of a linear series $(L,V)$ degenerate? Describe the moduli space of linear series on $C_0$. How can one detect whether a linear series on $C_0$ is the limit of linear series on smooth curves? | It is then natural to ask: Question 1. (1) How does the data of a linear series degenerate when C degenerate to a nodal curve C0 , i.e.: How does the line bundle L degenerate and how does V degenerate ? (2) What can we say about the moduli space of linear series on C0 ? (3) How can we detect when a linear series on C0 ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,945 | OWR-14298376-009 | Fano Varieties with Maximal Log-Smooth Degenerations | Characterize the smooth complex projective Fano varieties $Y$ for which there exist a smooth anticanonical divisor $D\in|-K_Y|$ and a maximal log-smooth degeneration $f:(\mathcal Y,\mathcal D)\to(S,0)$ with generic fiber $(Y,D)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338](https://doi.org/10.4171/owr/2024/23)
## Literature review (checked 2026-08-2... | 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-14298376-009",
"literature-status:open",
"owr-year:2024"
] | The source explicitly calls the restrictiveness of the existence of a maximal log-smooth degeneration an open question, with no resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2024/23",
"label": "Oberwolfach Report 23/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/23 | null | null | null | Characterize the smooth complex projective Fano varieties $Y$ for which there exist a smooth anticanonical divisor $D\in|-K_Y|$ and a maximal log-smooth degeneration $f:(\mathcal Y,\mathcal D)\to(S,0)$ with generic fiber $(Y,D)$. | Given Y , it is an open question of how restrictive the existence of (Y, D, f) is. Enumerative intrinsic mirror symmetry Michael van Garrel | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Real and Logarithmic Enumerative Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/23, pp. 1285--1338 |
30,005,946 | OWR-14298377-001 | Optimal Noiseless Rates for Max-Average-Margin Classifiers | Why can max-$\ell_p$ margins with $p>1$ improve noiseless recovery, and can the regularized max-average-margin estimator achieve the optimal $O(1/n)$ rate rather than $O(1/\sqrt n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistics and Learning Theory in the Era of Artificial Intelligence (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/30, pp. 1677--1718](https://doi.org/10.4171/owr/2024/30)
## Literatur... | 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-14298377-001",
"literature-status:open",
"owr-year:2024"
] | The source presents the mechanism and optimal noiseless rate for the regularized max-average-margin estimator as open problems; later work cited there does not prove the proposed O of one over n result. | [
{
"url": "https://doi.org/10.4171/owr/2024/30",
"label": "Oberwolfach Report 30/2024"
},
{
"url": "https://arxiv.org/abs/2212.03783",
"label": "Tight bounds for maximum l1-margin classifiers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/30 | null | null | null | Why can max-$\ell_p$ margins with $p>1$ improve noiseless recovery, and can the regularized max-average-margin estimator achieve the optimal $O(1/n)$ rate rather than $O(1/\sqrt n)$? | Together, these two results suggest a number of new open problems for future work: What is the underlying mechanism that p > 1 can lead to a better noiseless recovery? Could this regularized max-average-margin estimator achieve the optimal O(1/n) rate in the noiseless \sqrt{ } case, while interpolating max- margin inte... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistics and Learning Theory in the Era of Artificial Intelligence (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/30, pp. 1677--1718 |
30,005,947 | OWR-14298377-002 | Semi-Supervised Sparse Gaussian Classification | Characterize the statistical and computational regimes in which unlabeled data provably improve sparse Gaussian classification. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistics and Learning Theory in the Era of Artificial Intelligence (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/30, pp. 1677--1718](https://doi.org/10.4171/owr/2024/30)
## Literatur... | 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-14298377-002",
"literature-status:open",
"owr-year:2024"
] | The exact record ends before the claimed parameter regime and conclusion, so it is an incomplete result fragment rather than a triageable resolved proposition. | [
{
"url": "https://arxiv.org/abs/2409.03335",
"label": "Semi-Supervised Sparse Gaussian Classification"
},
{
"url": "https://doi.org/10.4171/owr/2024/30",
"label": "Oberwolfach Report 30/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/30 | null | null | null | Characterize the statistical and computational regimes in which unlabeled data provably improve sparse Gaussian classification. | The premise of semi-supervised learning (SSL) is that combining labeled and unla- beled data yields significantly more accurate models. Despite empirical successes, the theoretical understanding of SSL is still far from complete. In our work, we study SSL for high dimensional sparse Gaussian classification. To construct ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Statistics and Learning Theory in the Era of Artificial Intelligence (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/30, pp. 1677--1718 |
30,005,948 | OWR-14298580-002 | Unspecified Low-Dimensional Topology Conjecture | conjecture. 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:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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 extraction consists only of the trailing word 'conjecture' from the workshop introduction and contains no recoverable target at that loc) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298580-002",
"literature-status:open",
"owr-year:2024"
] | The record contains only the word conjecture and no mathematical statement, so its truth value is unclear and is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "Oberwolfach Report 34/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The extraction consists only of the trailing word 'conjecture' from the workshop introduction and contains no recoverable target at that location. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,949 | OWR-14298580-004 | L-Space Conjecture for Rational Homology Spheres | For every irreducible rational homology sphere $Y$, are the following equivalent: $Y$ supports no taut foliation, $Y$ is an L-space, and $\pi_1(Y)$ is not left-orderable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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... | [
"OWR-14298580-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298580-004",
"literature-status:open",
"owr-year:2024"
] | The L-space conjecture versus the proposed Heegaard Floer geography alternative remains unresolved; Alfieri--Binns prove only a wide class of cases. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.00490",
"label": "Alfieri--Binns primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | For every irreducible rational homology sphere $Y$, are the following equivalent: $Y$ supports no taut foliation, $Y$ is an L-space, and $\pi_1(Y)$ is not left-orderable? | Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false? A foliation of a three-manifold Y is a decomposition of Y into a disjoint union of immersed surfaces (leaves) that locally looks like the decomposition of R3 into horizontal planes. A foliation is called taut if there is a simple... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,950 | OWR-14298580-005 | Taut Foliations on Rational Homology Spheres | Deciding what rational homology spheres (b1 = 0) admit a taut foliation is one of the largest open questions of three-manifold topology today. Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false? Antonio Alfieri | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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 | Duplicate/merged OWR extraction (The extraction repeats the taut-foliation and geography context for the L-space conjecture retained in OWR-14298580-004. No separate clean s) | [
"OWR-14298580-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298580-005",
"literature-status:open",
"owr-year:2024"
] | The classification of rational homology spheres admitting taut foliations remains an open problem, as stated in the current report. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | null | Deciding what rational homology spheres (b1 = 0) admit a taut foliation is one of the largest open questions of three-manifold topology today. Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false? Antonio Alfieri | unrecoverable | The extraction repeats the taut-foliation and geography context for the L-space conjecture retained in OWR-14298580-004. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,951 | OWR-14298580-006 | Strong Geography Restrictions in Heegaard Floer Homology | The L-space conjecture is known to be true for graph manifolds, some families of knot surgeries, and some branched coverings . This statement puts us at a bifurcation: either the L-space conjecture is false, or the geography of the Heegaard Floer invariant is restricted, that is: not all modules can show up as torsion ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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 | Duplicate/merged OWR extraction (The extraction supplies context and a theorem before introducing the strong-geography question, which is retained completely in OWR-14298580) | [
"OWR-14298580-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298580-006",
"literature-status:open",
"owr-year:2024"
] | The record gives known cases and a logical alternative, but neither the universal L-space conjecture nor the universal geography restriction is settled. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.00490",
"label": "Alfieri--Binns primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | null | The L-space conjecture is known to be true for graph manifolds, some families of knot surgeries, and some branched coverings . This statement puts us at a bifurcation: either the L-space conjecture is false, or the geography of the Heegaard Floer invariant is restricted, that is: not all modules can show up as torsion ... | unrecoverable | The extraction supplies context and a theorem before introducing the strong-geography question, which is retained completely in OWR-14298580-008. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,952 | OWR-14298580-008 | Strong Geography for Rational Homology Spheres | For every rational homology sphere $Y$, does $HF^-(Y)$ contain a direct summand $\mathbb F[U]/U^\ell\oplus\mathbb F[U]/U^{\ell-1}\oplus\cdots\oplus\mathbb F[U]/U$, where $\ell$ is the least integer satisfying $U^\ell HF^-_{\mathrm{red}}(Y)=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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... | [
"OWR-14298580-006"
] | {
"source_url": "https://zenodo.org/records/23063072",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **A Negative Answer to the Strong Geography Question of Alfieri and Binns** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23063072) | [
"owr",
"oberwolfach-reports",
"OWR-14298580-008",
"literature-status:open",
"owr-year:2024"
] | The record is a truncated table-of-contents fragment ending in conjecture and contains no identifiable mathematical claim to verify. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | For every rational homology sphere $Y$, does $HF^-(Y)$ contain a direct summand $\mathbb F[U]/U^\ell\oplus\mathbb F[U]/U^{\ell-1}\oplus\cdots\oplus\mathbb F[U]/U$, where $\ell$ is the least integer satisfying $U^\ell HF^-_{\mathrm{red}}(Y)=0$? | Does HF− (Y ) satisfy the strong geography restriction for every rational homology sphere Y ? The stable chain rule for orthogonal calculus Connor Malin (joint work with Niall Taggart) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,953 | OWR-14298580-009 | Triviality of the Parametrized-Surgery Class on $S^4$ | Is the at-most-two-torsion class $\operatorname{ps}\circ r([c])=\operatorname{wat}(\Theta)=\operatorname{impl}(yx)=G(\nu T_c)$ in $\pi_0\operatorname{Diff}(S^4)$ trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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-14298580-009",
"literature-status:open",
"owr-year:2024"
] | The cited report explicitly says that whether the indicated class is trivial remains open; no later primary resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | Is the at-most-two-torsion class $\operatorname{ps}\circ r([c])=\operatorname{wat}(\Theta)=\operatorname{impl}(yx)=G(\nu T_c)$ in $\pi_0\operatorname{Diff}(S^4)$ trivial? | It remains open if the class from the theorem is in fact trivial. Figure 3. Parameterised surgery on depicted families of circles gives: (i) Watanabe’s wat(Θ) and (ii) Budney–Gabai’s impl(yx ). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,954 | OWR-14298580-010 | Motivic Generalization of Milnor Product Formulas | A natural question to ask is if one can do the same in the motivic case. Motivic Milnor formulas Hana Jia Kong (joint work with Weinan Lin) 2. Main results In this work, we compute explicit formulas for taking products using the motivic Milnor basis. For simplification, we work with base field R. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974](https://doi.org/10.4171/owr/2024/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 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 | Answered in the source or not an open problem (solved (answered in the source; the general case is a preprint)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source; the general case is a preprint)**. H. J. Kong (joint with W. Lin; OWR 34/2024, pp. 1965–1969) asks whether Milnor's product formulas, which make the Adams E₂-page computable, have motivic analogues, and gives explicit product formulas for t... | [
"owr",
"oberwolfach-reports",
"OWR-14298580-010",
"literature-status:open",
"owr-year:2024"
] | The motivic analogue is posed as a natural question; formulas are known over the real base field, but the extracted general question remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/34",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2411.12890",
"label": "Kong--Lin primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/34 | null | null | null | null | A natural question to ask is if one can do the same in the motivic case. Motivic Milnor formulas Hana Jia Kong (joint work with Weinan Lin) 2. Main results In this work, we compute explicit formulas for taking products using the motivic Milnor basis. For simplification, we work with base field R. | unrecoverable | The motivating question asks whether classical Milnor product formulas can be developed motivically, and the same contribution immediately presents the resulting explicit motivic formulas over the real base field. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Topologie (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/34, pp. 1913--1974 |
30,005,955 | OWR-14298581-001 | Calabi-Yau Torelli Table-of-Contents Fragment | conjecture . . . . 1840 Nicolas Addington (joint with Benjamin Tighe) On the Torelli problem for Calabi–Yau 3-folds, and the integral cohomology of the Fermat quintic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1843 Lie Fu (joint with Salvatore Floccari) Hyper-Kummer construction . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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 table-of-contents fragment and contains no mathematical conjecture.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298581-001",
"literature-status:open",
"owr-year:2024"
] | The record is only a truncated table-of-contents fragment ending in conjecture and does not identify a mathematical claim for verification. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | null | conjecture . . . . 1840 Nicolas Addington (joint with Benjamin Tighe) On the Torelli problem for Calabi–Yau 3-folds, and the integral cohomology of the Fermat quintic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1843 Lie Fu (joint with Salvatore Floccari) Hyper-Kummer construction . . . . . . . .... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment and contains no mathematical conjecture. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,956 | OWR-14298581-003 | Cohomological Dimension of Meromorphic Function Fields | Let $S$ be a connected normal Stein space of complex dimension $n$. Is the cohomological dimension of its field of meromorphic functions equal to $n$, that is, does $\operatorname{cd}(\mathcal M(S))=n$ hold? The question remains open in dimensions $n\geq 3$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-003",
"literature-status:partially-solved",
"owr-year:2024"
] | The equality is proved for connected normal Stein spaces of dimension two, while the general dimension at least three case remains open, already for complex affine space. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2410.16809",
"label": "Benoist primary paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Let $S$ be a connected normal Stein space of complex dimension $n$. Is the cohomological dimension of its field of meromorphic functions equal to $n$, that is, does $\operatorname{cd}(\mathcal M(S))=n$ hold? The question remains open in dimensions $n\geq 3$. | Is it true that cd(M(S)) = n? Wall Crossing and Moduli Spaces, Varieties and Derived Categories 1807 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,957 | OWR-14298581-004 | Isolated Complex-Geometry Question Label | Question 1. 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:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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 extraction contains only the label “Question 1.” The official report has no additional standalone problem at this position beyond the co) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298581-004",
"literature-status:open",
"owr-year:2024"
] | The record contains only Question 1 without its mathematical content, so the extracted problem is unresolved and cannot be more precisely classified. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | null | Question 1. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The extraction contains only the label “Question 1.” The official report has no additional standalone problem at this position beyond the complete questions preserved in neighboring records. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,958 | OWR-14298581-005 | Uniform Primary Brauer Bounds for K3 Surfaces | Let $K$ be a number field and $p$ a prime. Is there a uniform upper bound, depending only on $K$ and $p$, for $|\operatorname{Br}'(X)[p^\infty]|$ as $X$ ranges over all K3 surfaces over $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Uniform p-primary bounds are proved for K3 surfaces with a fixed lattice polarization, but the question for all K3 surfaces over the number field remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
},
{
"url": "https://indico.sns.it/event/98/contributions/794/",
"label": "Brakkee--Bragg--Varilly-Alvarado research summary"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Let $K$ be a number field and $p$ a prime. Is there a uniform upper bound, depending only on $K$ and $p$, for $|\operatorname{Br}'(X)[p^\infty]|$ as $X$ ranges over all K3 surfaces over $K$? | Is there an upper bound for the size of the p-primary torsion Br′ (X)[p\infty ], for all K3 surfaces X over K? Gong talk Bounding Brauer groups using moduli spaces Emma Brakkee (joint work with D. Bragg, A. Várilly-Alvarado) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,959 | OWR-14298581-006 | Kähler Shafarevich-Tate Twists | Let $\pi:X\to B$ be a Lagrangian fibration on an irreducible holomorphic symplectic manifold, and let $X^\phi\to B$ be the Shafarevich-Tate twist associated with a class $\phi$. Characterize the classes $\phi$ for which $X^\phi$ is Kähler. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-006",
"literature-status:partially-solved",
"owr-year:2024"
] | Kahlerness is established for broad torsion and related classes of twists, while the current primary literature still leaves the infinite-order component question open. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
},
{
"url": "https://link.springer.com/article/10.1007/s00209-025-03776-w",
"label": "Shafarevich--Tate twists primary paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Let $\pi:X\to B$ be a Lagrangian fibration on an irreducible holomorphic symplectic manifold, and let $X^\phi\to B$ be the Shafarevich-Tate twist associated with a class $\phi$. Characterize the classes $\phi$ for which $X^\phi$ is Kähler. | Question 1. When is a Shafarevich–Tate twist of a hyperkähler manifold Kähler? I partially answer this question in my upcoming work. Theorem 2. Pick a class \phi \in X such that r\phi lies in X0 for some positive integer r. Then the twist X \phi is Kähler. For the next theorem note that the differential d2 on the se... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,960 | OWR-14298581-007 | Stability Conditions from Surface Degenerations | Construct new Bridgeland stability conditions on surfaces by degenerating the geometric stability conditions associated with ample classes, particularly when contracting several rational curves or passing to mildly singular surfaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-007",
"literature-status:open",
"owr-year:2024"
] | The question of producing further stability conditions by studying surface degenerations is stated as a future direction and remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Construct new Bridgeland stability conditions on surfaces by degenerating the geometric stability conditions associated with ample classes, particularly when contracting several rational curves or passing to mildly singular surfaces. | A natural question is to produce more stability conditions for some surfaces, by studying degenerations of the examples above. 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 | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,961 | OWR-14298581-008 | Positive-Entropy Automorphisms of Strict Calabi-Yau Threefolds | Construct further smooth strict Calabi-Yau threefolds admitting primitive biregular automorphisms of positive entropy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Primitive positive-entropy automorphisms are explicitly constructed on some strict Calabi--Yau threefolds, but the request for many examples is not a classification theorem. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1306.1590",
"label": "Oguiso--Truong primary paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Construct further smooth strict Calabi-Yau threefolds admitting primitive biregular automorphisms of positive entropy. | Throughout this report, X is a normal projective variety of dimension d over C and f \in Bir X. This report consists of more speculations, rather than definite results, on automorphisms of strict Calabi–Yau threefolds in view of the following question after Dinh, Sibony and D.-Q. Zhang (See [6], [7] and [8] and referen... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,962 | OWR-14298581-009 | Strict Calabi-Yau Automorphism Preamble | Question 1. However, by now, we have only two such SCY3 ([11] for X3 and [9, Lemma 4.6] for X7 ; it is easy to check d2 (f ) > d1 (f ) for f \in Aut (X7 ) there): Theorem 5. Two rigid SCY3 Xk (k = 3, 7) have a primitive fk \in Aut (Xk ) of positive entropy. (See [10] for explicit definitions of Xk ). We have the follow... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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 stops immediately before the actual questions, which are preserved in the following record) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298581-009",
"literature-status:open",
"owr-year:2024"
] | The record ends before stating the question following the established examples and therefore supplies no fully specified claim beyond an unresolved research prompt. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | null | Question 1. However, by now, we have only two such SCY3 ([11] for X3 and [9, Lemma 4.6] for X7 ; it is easy to check d2 (f ) > d1 (f ) for f \in Aut (X7 ) there): Theorem 5. Two rigid SCY3 Xk (k = 3, 7) have a primitive fk \in Aut (Xk ) of positive entropy. (See [10] for explicit definitions of Xk ). We have the follow... | unrecoverable | The official report confirms that this extraction stops immediately before the actual questions, which are preserved in the following record. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,963 | OWR-14298581-010 | Second-Chern Orthogonality and Calabi-Yau Automorphisms | Let $X$ be a strict Calabi-Yau threefold with infinite automorphism group. Must $c_2(X)^\perp\cap\operatorname{Amp}(X)_{\mathbb Q}$ contain a nonzero class? Also, does any such threefold other than the known examples $X_3$ and $X_7$ admit a primitive automorphism of positive entropy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-010",
"literature-status:open",
"owr-year:2024"
] | The two stated questions about rational ample classes orthogonal to the second Chern class and further strict Calabi--Yau examples remain open in the cited primary discussion. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2407.17297",
"label": "Oguiso primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Let $X$ be a strict Calabi-Yau threefold with infinite automorphism group. Must $c_2(X)^\perp\cap\operatorname{Amp}(X)_{\mathbb Q}$ contain a nonzero class? Also, does any such threefold other than the known examples $X_3$ and $X_7$ admit a primitive automorphism of positive entropy? | Is c2 (X)⊥ \capAmp (X)(Q)\\{0\} 6= \varnothing for a SCY3 X of |Aut (X)| = \infty? Is there a SCY3 with primitive automorphism of positive entropy other than Xk (k = 3 and 7)? Wall Crossing and Moduli Spaces, Varieties and Derived Categories 1823 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,964 | OWR-14298581-011 | Deformation Equivalence of Categorical Hyperkähler Constructions | Let $g\geq 0$ and let $w\in\mathbb Z$ be coprime to $v$. Prove that the reduced category $T_S(v)_w^{\mathrm{red}}$ is deformation equivalent to $D^b(\operatorname{Hilb}(S,g'))$, where $g'=(\langle v,v\rangle+2)/2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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-14298581-011",
"literature-status:open",
"owr-year:2024"
] | The proposed deformation-equivalence statement for the categorical construction is explicitly labelled Conjecture 6 and no primary proof or disproof was located. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | Let $g\geq 0$ and let $w\in\mathbb Z$ be coprime to $v$. Prove that the reduced category $T_S(v)_w^{\mathrm{red}}$ is deformation equivalent to $D^b(\operatorname{Hilb}(S,g'))$, where $g'=(\langle v,v\rangle+2)/2$. | We do not expect the categories T\sigmaS (v)w to produce new examples of IHS va- rieties, but we believe they are related to known examples of IHS varieties by in- teresting derived equivalences, more precisely by compactifications of the Fourier- Mukai derived equivalence between a (relative) abelian variety and its d... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,965 | OWR-14298581-012 | Equivariant Fukaya-Cohomology Discussion | Can we fill in the other parts of this story? I.e. (1) Is there a G-equivariant Fukaya category FukG (X)? (2) If so, is HH• (FukG (X)) equal to QH•G (X)? (3) What is the mirror structure? 2This space is really a spectrum, constructed from Floer homotopy theory. 3Since X̆ is just the dual torus to the torus in X, the 1-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 3 | partially_solved | 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 poses these questions to motivate the talk, immediately rejects the naive first two formulations, and develops a more el) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298581-012",
"literature-status:partially-solved",
"owr-year:2024"
] | For the U(1) case the talk reports negative or more complicated answers to the proposed equivariant Fukaya and Hochschild-equals-quantum-cohomology formulations, while the broad multi-part question remains unsettled. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | null | Can we fill in the other parts of this story? I.e. (1) Is there a G-equivariant Fukaya category FukG (X)? (2) If so, is HH• (FukG (X)) equal to QH•G (X)? (3) What is the mirror structure? 2This space is really a spectrum, constructed from Floer homotopy theory. 3Since X̆ is just the dual torus to the torus in X, the 1-... | unrecoverable | The official report poses these questions to motivate the talk, immediately rejects the naive first two formulations, and develops a more elaborate categorical framework; it does not present a standalone unresolved conjecture. | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,966 | OWR-14298581-013 | Isolated Hyperkähler Conjecture Label | conjecture. 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:** [Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854](https://doi.org/10.4171/owr/2024/... | 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 an isolated table-of-contents fragment containing only the word “conjecture.”) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298581-013",
"literature-status:open",
"owr-year:2024"
] | The record consists only of the word conjecture, so no mathematical claim can be identified; under the stated rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/32 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is an isolated table-of-contents fragment containing only the word “conjecture.” | null | null | null | null | null | Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/32, pp. 1787--1854 |
30,005,967 | OWR-14298582-001 | Moment-SOS Convergence for PDE-Constrained Variational Problems | Extend the convergence analysis of finite-element moment-sum-of-squares relaxations beyond variational problems with a unique global minimizer and boundary constraints, to variational problems subject to partial differential equation constraints. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/35, pp. 1975--2032](https://doi.org/10.4171/owr/2024/35... | 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-14298582-001",
"literature-status:open",
"owr-year:2024"
] | The report explicitly identifies extending convergence analysis from boundary-only variational problems to PDE-constrained problems as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/35",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/35 | null | null | null | Extend the convergence analysis of finite-element moment-sum-of-squares relaxations beyond variational problems with a unique global minimizer and boundary constraints, to variational problems subject to partial differential equation constraints. | It remains an open problem to remove this restrictive assumption and extend the convergence analysis to variational problems with PDE constraints. 1.2. Null Lagrangians and occupation measures. A key limitation of the discretize-and-relax approach reviewed above is that it does not give certified lower bounds on f ∗ . F... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Polynomial Optimization for Nonlinear Dynamics: Theory, Algorithms and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/35, pp. 1975--2032 |
30,005,968 | OWR-14298583-001 | Tail-Dependence Estimators Under Long-Range Dependence | Determine the asymptotic distribution of the empirical tail-dependence estimator $\widehat\rho_{B,n}(T)$ for a long-range-dependent max-stable stationary time series, in the regime $u_n\to\infty$ and $n\mathbb P(X_0>u_n)\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics, Statistics, and Geometry of Extreme Events in High Dimensions (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/38, pp. 2179--2250](https://doi.org/10.4171/owr/2024/38)
## Lit... | 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-14298583-001",
"literature-status:partially-solved",
"owr-year:2024"
] | The short-range case has variance bounds and asymptotic normality, whereas the limiting distribution in the long-range case is explicitly left open. | [
{
"url": "https://doi.org/10.4171/owr/2024/38",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/38 | null | null | null | Determine the asymptotic distribution of the empirical tail-dependence estimator $\widehat\rho_{B,n}(T)$ for a long-range-dependent max-stable stationary time series, in the regime $u_n\to\infty$ and $n\mathbb P(X_0>u_n)\to\infty$. | In the case of short-range dependence, we can further show asymptotic normal- ity, while the asymptotic distribution in the long-range dependent case remains an open problem. • If X is long-range dependent in the sense of Definition 1, then hp i Var nP(X0 > un )Pb n,un ((0, \infty)|T | ) = \infty. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mathematics, Statistics, and Geometry of Extreme Events in High Dimensions (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/38, pp. 2179--2250 |
30,005,969 | OWR-14298583-002 | Observed Extreme-Rainfall Trends | Is climate change making individual extreme rainfall events in northeastern United States more frequent, more intense, or both? Rainfall trends in the USA: data quality and prediction skill Holger Rootzén (joint work with Helga Olafsdottir, David Bolin, Richard Katz) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics, Statistics, and Geometry of Extreme Events in High Dimensions (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/38, pp. 2179--2250](https://doi.org/10.4171/owr/2024/38)
## Lit... | 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"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 poses this empirical question and then gives the study’s answer: events became more frequent, while their individual-siz) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298583-002",
"literature-status:partially-solved",
"owr-year:2024"
] | A peer-reviewed study of 333 northeastern U.S. gauges finds temperature-linked increases in event frequency and little evidence of an intensity-distribution trend; broader attribution remains scope-dependent. | [
{
"url": "https://journals.ametsoc.org/view/journals/clim/34/22/JCLI-D-20-0938.1.xml",
"label": "Olafsdottir--Rootzen--Bolin primary study"
},
{
"url": "https://doi.org/10.4171/owr/2024/38",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/38 | null | null | null | null | Is climate change making individual extreme rainfall events in northeastern United States more frequent, more intense, or both? Rainfall trends in the USA: data quality and prediction skill Holger Rootzén (joint work with Helga Olafsdottir, David Bolin, Richard Katz) | unrecoverable | The official report poses this empirical question and then gives the study’s answer: events became more frequent, while their individual-size distribution showed little evidence of increase. | null | null | null | null | null | Mathematics, Statistics, and Geometry of Extreme Events in High Dimensions (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/38, pp. 2179--2250 |
30,005,970 | OWR-14298584-001 | Exceptional Galois Points on Modular Curves | Extend the Khawaja–Siksek finiteness theorem for primitive algebraic points from symmetric and alternating Galois groups to other families of simple and almost simple groups. More specifically, let $N$ be large and let $j:X_0(N)\to X(1)$ be the usual map. Hilbert irreducibility gives a thin set $S\subset X(1)(\mathbb{Q... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,024 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
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"created_at": "2026-07-31T15:26:25.670Z"
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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-14298584-001",
"literature-status:open",
"owr-year:2024"
] | The finiteness of the thin exceptional set and the existence of a non-j-map family with the stated Galois group are posed as open problems in the current primary report. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Extend the Khawaja–Siksek finiteness theorem for primitive algebraic points from symmetric and alternating Galois groups to other families of simple and almost simple groups. More specifically, let $N$ be large and let $j:X_0(N)\to X(1)$ be the usual map. Hilbert irreducibility gives a thin set $S\subset X(1)(\mathbb{Q... | Open Problems It would be interesting (and probably not too difficult) to extend the proof of Theorem 3 to other families of simple and almost simple groups. Is the set S finite or infinite? More- over, is there an infinite family of algebraic points on X0 (N ) with Galois group PGL2 (Z/N Z) that is not arising from j?... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,971 | OWR-14298584-003 | Mod-p Automorphic Induction and p-Adic Regulators | Can one construct and characterize mod-$p$ automorphic induction without passing through mod-$p$ Galois representations? Can one predict the $p$-adic valuation of the relevant ratios of regulators or, when nonzero, of $\#H^i(M(\mathcal{O}_1),\mathbb{Z})/\#H^i(M(\mathcal{O}_2),\mathbb{Z})$? Can one define $p$-adic regul... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 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-14298584-003",
"literature-status:open",
"owr-year:2024"
] | The report states that mod-p automorphic induction, p-adic regulator ratios, and the associated valuation formulas remain questions; existing work gives exclusions and conditional mod-p results but no general solution. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
},
{
"url": "https://arxiv.org/abs/2407.07240",
"label": "Bartel--Page, Vigneras orbifolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Can one construct and characterize mod-$p$ automorphic induction without passing through mod-$p$ Galois representations? Can one predict the $p$-adic valuation of the relevant ratios of regulators or, when nonzero, of $\#H^i(M(\mathcal{O}_1),\mathbb{Z})/\#H^i(M(\mathcal{O}_2),\mathbb{Z})$? Can one define $p$-adic regul... | Can one bypass mod p Galois representations? More precisely, can one construct and characterise mod p automorphic induction? Can one predict the p-adic valuation of Regi (M (O1 ))2/Regi (M (O1 ))2 or of \#Hi (M (O1 ), Z)/\#Hi (M (O2 ), Z) when it is nonzero? Can one define a notion of p-adic regulators, whose ratios gi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,972 | OWR-14298584-004 | Explicit Semistable Reduction and Galois Actions for Curves | Given a smooth projective curve $Y$ over a discretely valued field $K$, compute a finite extension $L/K$, a semistable model of $Y_L$, and the action of $\operatorname{Gal}(L/K)$ on its special fiber. Develop an explicit method in arbitrary genus, beyond the classes for which such computations are already known. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 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-14298584-004",
"literature-status:partially-solved",
"owr-year:2024"
] | Semistable reduction guarantees existence after a finite extension, and explicit algorithms cover important classes including hyperelliptic and degree-p covers, but computation of the model and Galois action for arbitrary genus at this generality is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
},
{
"url": "https://arxiv.org/abs/2512.09082",
"label": "Dokchitser, A classification of reduction types of curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Given a smooth projective curve $Y$ over a discretely valued field $K$, compute a finite extension $L/K$, a semistable model of $Y_L$, and the action of $\operatorname{Gal}(L/K)$ on its special fiber. Develop an explicit method in arbitrary genus, beyond the classes for which such computations are already known. | problem. Problem 1. Compute a finite extension L/K, a semistable model Y of YL , and the action of the Galois group of L/K on the special fiber Ys . A solution to this problem is trivial for g = 0 and well known for g = 1. For genus g \geq 2 there are only partial solutions in special cases, some of which we review bel... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,973 | OWR-14298584-005 | Stable Reduction of Plane Quartics from Cayley Octads | Prove that the combinatorial data of the configuration of the eight points in a Cayley octad determines the stable reduction type of the associated smooth plane quartic, analogously to the way a cluster picture determines stable reduction in the hyperelliptic case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 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"
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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-14298584-005",
"literature-status:open",
"owr-year:2024"
] | The octad-picture criterion has extensive computational and theoretical evidence, but the 2025 primary paper still states the stable-reduction correspondence as a conjecture rather than a theorem. | [
{
"url": "https://doi.org/10.1007/s10208-025-09704-y",
"label": "van Bommel--Docking--Dokchitser--Lercier et al., Reduction of Plane Quartics and Cayley Octads"
},
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Prove that the combinatorial data of the configuration of the eight points in a Cayley octad determines the stable reduction type of the associated smooth plane quartic, analogously to the way a cluster picture determines stable reduction in the hyperelliptic case. | We propose to replace the eight Weierstraß points in the hyperelliptic case by a Cayley octad. We conjecture that combinatorial data about the configuration of these eight points fully determines the stable reduction type of the curve, analogously to the cluster picture in the hyperelliptic case. The report passage is ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,974 | OWR-14298584-007 | Field Extensions and Ordinarity in Arithmetic Specialization | In the arithmetic specialization result of Bright and Newton, when is the finite extension $k'/k$ necessary? Can the ordinarity hypothesis be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,024 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
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"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-14298584-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Bright--Newton prove existence of relevant primes after a finite extension at good ordinary reduction, but the necessity of that extension and whether ordinarity can be removed remain unresolved. | [
{
"url": "https://doi.org/10.1007/s00222-023-01210-8",
"label": "Bright--Newton, Evaluating the wild Brauer group"
},
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | In the arithmetic specialization result of Bright and Newton, when is the finite extension $k'/k$ necessary? Can the ordinarity hypothesis be removed? | At this point some natural questions arise: (1) When is the field extension k ′ /k appearing in Bright and Newton’s result needed? (2) Is the ordinary condition necessary? 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 | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,975 | OWR-14298584-008 | Brauer Groups of Tame Stacky Curves | Compute the Brauer group of an arbitrary tame stacky curve over an algebraically closed field. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,024 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
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"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298584-008",
"literature-status:partially-solved",
"owr-year:2024"
] | General tools now compute many tame stacky-curve Brauer groups, including broad algebraically closed-field and modular-curve cases, but the unrestricted question as stated is not a single completed classification. | [
{
"url": "https://arxiv.org/abs/2410.06217",
"label": "Achenjang, On Brauer groups of tame stacks"
},
{
"url": "https://arxiv.org/abs/2507.08780",
"label": "Bishop, Brauer groups of tame stacky curves"
},
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source re... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Compute the Brauer group of an arbitrary tame stacky curve over an algebraically closed field. | Can one compute the Brauer group of a tame stacky curve over an algebraically closed field? 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 | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,976 | OWR-14298584-009 | Quasilinear Finite-Field Polynomial Multiplication | For a prime $p$, let $M_p(d)$ denote the multitape-Turing-machine cost of multiplying polynomials of degree at most $d$ in $\mathbb{F}_p[x]$, and put $n=d\log p$. Prove that $M_p(d)=O(n\log n)$ uniformly in $p$ and $d$, including when $p=2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"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"
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"level": 3,
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14298584-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298584-009",
"literature-status:open",
"owr-year:2024"
] | The extracted record is a truncated introduction to the finite-field polynomial-multiplication conjecture, so it does not state a separate claim beyond the conjecture itself; the cited report identifies that conjecture as open. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1145/3505584",
"label": "Harvey--van der Hoeven, Polynomial multiplication over finite fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | For a prime $p$, let $M_p(d)$ denote the multitape-Turing-machine cost of multiplying polynomials of degree at most $d$ in $\mathbb{F}_p[x]$, and put $n=d\log p$. Prove that $M_p(d)=O(n\log n)$ uniformly in $p$ and $d$, including when $p=2$. | 1. Upper bounds Let M (n) denote the cost of multiplying n-bit integers. By “cost” we mean the number of steps performed by a multitape Turing machine [Pap94]. Theorem 1 ([HvdH21]). M (n) = O(n log n). Suprisingly, the “function field case” appears to be more difficult. For a prime p, let Mp (d) denote the cost (still ... | 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 | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,977 | OWR-14298584-010 | Duplicate Finite-Field Polynomial-Multiplication Conjecture | One case of this conjecture is easy: if log p ≫ log d, then we may lift the problem to Z[x], pack the coefficients into huge integers (this technique is known as Kronecker substitution, see [GG13, Cor. However, in general the conjecture is wide open, even for p = 2. 2. Lower bounds The upper bound in Theorem 1 is expec... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
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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 overlapping extraction repeats the finite-field polynomial-multiplication conjecture represented cano) | [
"OWR-14298584-009"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298584-010",
"literature-status:open",
"owr-year:2024"
] | The general O(n log n) finite-field multiplication bound remains open even for the binary field; unconditional results retain an iterated-logarithm factor, while the strongest O(n log n) result is conditional. | [
{
"url": "https://doi.org/10.1145/3505584",
"label": "Harvey--van der Hoeven, Polynomial multiplication over finite fields"
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{
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"label": "Oberwolfach source report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | null | One case of this conjecture is easy: if log p ≫ log d, then we may lift the problem to Z[x], pack the coefficients into huge integers (this technique is known as Kronecker substitution, see [GG13, Cor. However, in general the conjecture is wide open, even for p = 2. 2. Lower bounds The upper bound in Theorem 1 is expec... | unrecoverable | The official report confirms that this overlapping extraction repeats the finite-field polynomial-multiplication conjecture represented canonically by OWR-14298584-009. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,978 | OWR-14298584-011 | Density of Sums of Two Rational Cubes | Determine the asymptotic proportion of positive integers that can be expressed as a sum of two rational cubes. In particular, is the density equal to $1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | 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-14298584-011",
"literature-status:partially-solved",
"owr-year:2024"
] | Positive and negative proportions are proved and newer Selmer-group work improves the bounds, but the exact density, expected to be one half, is not established. | [
{
"url": "https://arxiv.org/abs/2210.10730",
"label": "Alpoge--Bhargava--Shnidman, Integers expressible as the sum of two rational cubes"
},
{
"url": "https://arxiv.org/abs/2405.09311",
"label": "Koymans--Smith, Sums of rational cubes and the 3-Selmer group"
},
{
"url": "https://doi.org/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Determine the asymptotic proportion of positive integers that can be expressed as a sum of two rational cubes. In particular, is the density equal to $1/2$? | What proportion of the positive integers can be expressed as the sum of two rational cubes? Sums of rational cubes and the 3-Selmer group Alexander Smith (joint work with Peter Koymans) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,979 | OWR-14298584-012 | Efficient Computation of Exceptional Galois Representations | Develop an efficient general algorithm for computing exceptional Galois representations, including their projective representations, with substantially better complexity than exhaustive class-field-theoretic or targeted number-field searches. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 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-14298584-012",
"literature-status:partially-solved",
"owr-year:2024"
] | Algorithms using class-field-theoretic and targeted-search methods handle many exceptional projective representations, including substantial A5 tables, but a uniformly efficient general method remains unavailable. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
},
{
"url": "https://arxiv.org/abs/math/0507502",
"label": "Booker, Artin's conjecture, Turing's method and the Riemann hypothesis"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Develop an efficient general algorithm for computing exceptional Galois representations, including their projective representations, with substantially better complexity than exhaustive class-field-theoretic or targeted number-field searches. | A natural question is how to compute efficiently such Galois representations in the exceptional case. 3. Computing the projective representation The first step is to compute the number field cut by the projective representation of the Galois group. There are known algorithms using computational class field theory to bu... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,980 | OWR-14298584-013 | Classification of Abelian-Surface L-Functions of Small Conductor | Prove the proposed classification of the $456$ $L$-functions of abelian surfaces over $\mathbb{Q}$ of conductor at most $1000$, including completeness of the list and the asserted division into products, quadratic-coefficient newforms, Weil restrictions, and generic abelian surfaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368](https://doi.org/10.4171/owr/2024/40)
## Literature review (checked 2026-08-22)
**St... | 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-14298584-013",
"literature-status:open",
"owr-year:2024"
] | The count of 456 is still presented as provisional and conditional on the paramodular conjecture, with completeness and the proof of the stated classification not established in the source literature. | [
{
"url": "https://doi.org/10.4171/owr/2024/40",
"label": "Oberwolfach source report"
},
{
"url": "https://math.mit.edu/~drew/JA2025.pdf",
"label": "Booker--Sutherland, L-functions from nothing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/40 | null | null | null | Prove the proposed classification of the $456$ $L$-functions of abelian surfaces over $\mathbb{Q}$ of conductor at most $1000$, including completeness of the list and the asserted division into products, quadratic-coefficient newforms, Weil restrictions, and generic abelian surfaces. | conjecture. There are 456 L-functions of abelian surfaces A/Q with conductor N \leq 1000, of which • 360 arise from products of elliptic curves over Q; • 17 arise from weight-2 newforms with quadratic coefficients; • 2 arise from the Weil restriction of an elliptic curve over a quadratic field; • 77 arise from generic ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Explicit Methods in Number Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/40, pp. 2309--2368 |
30,005,981 | OWR-14298585-002 | Scaling Constants for Discrete Energies on Metric Spaces | Characterize the compact metric spaces that admit a proper scaling constant $\sigma_p$ for graph approximations whose renormalized discrete $p$-energies converge to a meaningful continuum energy. Give further examples beyond the known $p$-conductively homogeneous spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510](https://doi.org/10.4171/owr/2024/42)
## Literature rev... | 3 | partially_solved | 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-14298585-002",
"literature-status:partially-solved",
"owr-year:2024"
] | p-conductive homogeneity gives a sufficient structural criterion for a proper scaling constant and the literature supplies Sierpinski-carpet, nested-fractal, and other examples, but it is not a classification of all metric spaces. | [
{
"url": "https://ems.press/content/book-files/28253",
"label": "Kigami, Conductive homogeneity of compact metric spaces and construction of p-energy"
},
{
"url": "https://doi.org/10.4171/owr/2024/42",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.4171/JFG/156",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/42 | null | null | null | Characterize the compact metric spaces that admit a proper scaling constant $\sigma_p$ for graph approximations whose renormalized discrete $p$-energies converge to a meaningful continuum energy. Give further examples beyond the known $p$-conductively homogeneous spaces. | What kind of metric spaces does a proper scaling constant \sigmap exist? What are examples of such spaces? Our answer to the first question is the notion of p-conductive homogeneity introduced in [4]. where ∇f is the derivative of f . This says if f \in W 1,p (Rn ), then (2p−1 )n Epn (f ) converges as n \to \infty. One ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510 |
30,005,982 | OWR-14298585-004 | p-Energies on Nonsmooth Metric-Measure Spaces | Develop an intrinsic notion of $p$-energy for nonsmooth metric-measure spaces and characterize the geometric hypotheses under which the competing Sobolev, Dirichlet-form, upper-gradient, and discrete-approximation constructions agree. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510](https://doi.org/10.4171/owr/2024/42)
## Literature rev... | 3 | partially_solved | 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-14298585-004",
"literature-status:partially-solved",
"owr-year:2024"
] | Metric-measure analysis now has several rigorous notions of nonsmoothness and corresponding Sobolev, Dirichlet, and p-energy frameworks, but there is no universal structure or single theory for every metric-measure space. | [
{
"url": "https://doi.org/10.4171/owr/2024/42",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1007/s000390050094",
"label": "Cheeger, Differentiability of Lipschitz functions on metric measure spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/42 | null | null | null | Develop an intrinsic notion of $p$-energy for nonsmooth metric-measure spaces and characterize the geometric hypotheses under which the competing Sobolev, Dirichlet-form, upper-gradient, and discrete-approximation constructions agree. | What does it mean that your world is not smooth? Who is your p-energy when your world is not smooth? Patricia Alonso Ruiz (joint work with Fabrice Baudoin) and its associated p-energy functional Z (1) Ep (f ) = |∇f |p dx. Rn | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510 |
30,005,983 | OWR-14298585-005 | Construction of p-Energies without Classical Gradients | How can one construct a canonical $p$-energy on a space that has no classical gradient? Determine hypotheses under which graph-limit, upper-gradient, and Korevaar–Schoen constructions exist and yield the same energy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510](https://doi.org/10.4171/owr/2024/42)
## Literature rev... | 3 | partially_solved | 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-14298585-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Discrete graph limits, p-conductive homogeneity, upper gradients, and Korevaar--Schoen constructions provide workable p-energies under different hypotheses, but no general construction applies to every nonsmooth world. | [
{
"url": "https://ems.press/content/book-files/28253",
"label": "Kigami, Conductive homogeneity of compact metric spaces and construction of p-energy"
},
{
"url": "https://doi.org/10.4171/owr/2024/42",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1016/j.jfa.2026.1... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/42 | null | null | null | How can one construct a canonical $p$-energy on a space that has no classical gradient? Determine hypotheses under which graph-limit, upper-gradient, and Korevaar–Schoen constructions exist and yield the same energy. | how could I construct a p-energy if there is no classical ∇f in my world? Thankfully you are not alone in your question and many people have been thinking about it in the past years. During this workshop we have seen several ways to carry out this construction under different kinds of “non-smoothness” in your world. For... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510 |
30,005,984 | OWR-14298585-006 | Cheeger-Space Criteria for Metric-Measure Spaces | Characterize when a metric-measure space $(X,d,m)$ is a Cheeger space, and determine when the resulting metric-measure construction gives the appropriate $p$-energy on $X$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510](https://doi.org/10.4171/owr/2024/42)
## Literature rev... | 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-14298585-006",
"literature-status:open",
"owr-year:2024"
] | Cheeger spaces are a defined and well-studied class, but the record supplies no particular metric-measure space whose membership can be decided; membership and the relevant p-energy theory remain hypothesis-dependent. | [
{
"url": "https://doi.org/10.4171/owr/2024/42",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1007/s000390050094",
"label": "Cheeger, Differentiability of Lipschitz functions on metric measure spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/42 | null | null | null | Characterize when a metric-measure space $(X,d,m)$ is a Cheeger space, and determine when the resulting metric-measure construction gives the appropriate $p$-energy on $X$. | Is your world (X, d, m) a Cheeger space? In this talk you learn a further approach that relies solely on the metric measure structure of your world, when that is a Cheeger space. The construction is based on seminal work by Korevaar and Schoen in [5] and the construction of diffusion on d-sets by Kumagai and Sturm in [9... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Recent Developments in Dirichlet Form Theory and Related Fields (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/42, pp. 2425--2510 |
30,005,985 | OWR-14298586-001 | Robustness of Climate Models at Unresolved Scales | Determine whether reduced geophysical-flow models admit sufficiently rough solution spaces, whether their numerical approximations are robust under grid-scale perturbations, and which stochastic structures correctly represent unresolved processes. In particular, decide whether white-noise and Brownian-motion models suf... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786](https://doi.org/10.4171/owr/2024/31)
## Literature review... | 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-14298586-001",
"literature-status:open",
"owr-year:2024"
] | The record asks broad unresolved questions about robustness of numerical climate models and the appropriate stochastic treatment of unresolved scales; existing rough-path and regularity-structure theories do not settle model-specific adequacy. | [
{
"url": "https://doi.org/10.4171/owr/2024/31",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1007/s00222-014-0505-4",
"label": "Hairer, A theory of regularity structures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/31 | null | null | null | Determine whether reduced geophysical-flow models admit sufficiently rough solution spaces, whether their numerical approximations are robust under grid-scale perturbations, and which stochastic structures correctly represent unresolved processes. In particular, decide whether white-noise and Brownian-motion models suf... | Are numerical methods used in simulations sufficiently robust under grid-scale perturbations? Is it sufficient to consider the usual white noise–Brownian motion ansatz for stochastic effects in continuum me- chanics, or do the nonlinearity and space-time extent of the underlying processes call for advanced concepts suc... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786 |
30,005,986 | OWR-14298586-002 | Mechanisms and Scales of Tropical-Cyclone Edge Intensification | For edge-intensified tropical convection, determine (1) what sets the number and separation distance of convergence lines, including without a sea-surface-temperature gradient; (2) why convection does not occur over the highest sea-surface temperature and whether a predictive model of edge intensification can be derive... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786](https://doi.org/10.4171/owr/2024/31)
## Literature review... | 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",
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"OWR-14298586-002",
"literature-status:open",
"owr-year:2024"
] | The underlying simulations identify wind--surface-flux coupling and bottom-heavy ascent as mechanisms for edge intensification, but the separation distance, complete mechanism, and rotational dependence remain open research questions. | [
{
"url": "https://doi.org/10.4171/owr/2024/31",
"label": "Oberwolfach source report"
},
{
"url": "https://doi.org/10.1175/JCLI-D-22-0382.1",
"label": "Masunaga, The edge intensification of Eastern Pacific ITCZ convection"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/31 | null | null | null | For edge-intensified tropical convection, determine (1) what sets the number and separation distance of convergence lines, including without a sea-surface-temperature gradient; (2) why convection does not occur over the highest sea-surface temperature and whether a predictive model of edge intensification can be derive... | There are a number of open questions which we intend to pursue in future research. Even with no sea-surface temperature gradient imposed, convergence lines form (as in the well-known phemomenon of convective aggregation), and we are working on a theory for their separation distance. (2) What is the precise mechanism th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786 |
30,005,987 | OWR-14298586-003 | Entrainment-Mediated Tropical-Cyclone Intensification | Using three-dimensional high-resolution simulations, verify the asymptotically derived pathway in which cloud-tower entrainment produces a radial mean flow that transports angular momentum inward and intensifies a tropical cyclone. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786](https://doi.org/10.4171/owr/2024/31)
## Literature review... | 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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298586-003",
"literature-status:open",
"owr-year:2024"
] | The asymptotic analysis proposes an entrainment-mediated intensification pathway, but the source explicitly leaves its verification with three-dimensional high-resolution simulations for future work. | [
{
"url": "https://doi.org/10.4171/owr/2024/31",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/31 | null | null | null | Using three-dimensional high-resolution simulations, verify the asymptotically derived pathway in which cloud-tower entrainment produces a radial mean flow that transports angular momentum inward and intensifies a tropical cyclone. | It remains open, however, to verify the pathway as it was discovered by asymptotic analy- sis. Model Hierarchies in Atmosphere, Ocean, and Climate Sciences 1759 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786 |
30,005,988 | OWR-14298586-004 | Cloud-Organization Limit Cycles | Explain the mechanism producing limit cycles in shallow cumulus organization. Determine how external forcings affect their size, frequency, and amplitude; whether they respond quasi-statically to time-dependent forcing; how the diurnal radiative cycle and realistic open boundaries modify them; and how relevant they are... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786](https://doi.org/10.4171/owr/2024/31)
## Literature review... | 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"
} | {
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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-14298586-004",
"literature-status:open",
"owr-year:2024"
] | The reported cloud-organization limit cycles are preliminary model findings; their mechanism, forcing response, diurnal-radiative modification, boundary sensitivity, and climate relevance remain explicitly open. | [
{
"url": "https://doi.org/10.4171/owr/2024/31",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/31 | null | null | null | Explain the mechanism producing limit cycles in shallow cumulus organization. Determine how external forcings affect their size, frequency, and amplitude; whether they respond quasi-statically to time-dependent forcing; how the diurnal radiative cycle and realistic open boundaries modify them; and how relevant they are... | Obviously, these preliminary findings invoke many new questions such as • What is the precise mechanism that cause these limit cycles? • How do the different external forcings influence the limit cycles in size, frequency and amplitude? • How effective will the limit cycle behaviour respond to time-varying ex- ternal f... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Model Hierarchies in Atmosphere, Ocean, and Climate Sciences (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/31, pp. 1731--1786 |
30,005,989 | OWR-14298587-001 | Stable Phase-Transition Table-of-Contents Entry | 2144 Joaquim Serra (joint with Hardy Chan, Alessio Figalli, Xavier Fernández- Real) Stable phase transitions: open questions and new results . . . . . . . . . . . . . . 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:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,024 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is only a table-of-contents entry, not a mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-001",
"literature-status:open",
"owr-year:2024"
] | The extracted text is a table-of-contents fragment naming a talk on stable phase transitions and open questions, without a definite mathematical claim that can be verified or classified as solved. | [
{
"url": "https://doi.org/10.4171/owr/2024/37",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | null | 2144 Joaquim Serra (joint with Hardy Chan, Alessio Figalli, Xavier Fernández- Real) Stable phase transitions: open questions and new results . . . . . . . . . . . . . . The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is only a table-of-contents entry, not a mathematical problem. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,990 | OWR-14298587-002 | Boundary Frequency Gap for Optimal Partitions | For a boundary free-interface point in a spectral optimal-partition problem in dimension $d>2$, determine the exact frequency gap $\delta_d$ above frequency $2$. Prove or disprove that $\delta_d=5/2$, attained by three domains forming a collinear triple junction of $3/2$-points that meets the boundary orthogonally. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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-14298587-002",
"literature-status:open",
"owr-year:2024"
] | The boundary frequency gap is known only with a positive dimensional gap and the conjectural value five halves is not proved; the cited primary report still lists it as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2024/37",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | For a boundary free-interface point in a spectral optimal-partition problem in dimension $d>2$, determine the exact frequency gap $\delta_d$ above frequency $2$. Prove or disprove that $\delta_d=5/2$, attained by three domains forming a collinear triple junction of $3/2$-points that meets the boundary orthogonally. | We conjecture that \deltad = 5/2 and is achieved by three domains forming a triple junction of 3/2-points disposed on a line that reaches \partialD orthogonally. The analysis of F up to \partialD faces issues, of both technical and topological nature, which are not present inside D: first, the monotonicity of the frequ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,991 | OWR-14298587-003 | Regularity of Boundary Free Interfaces | For the boundary free interface $\mathcal F_{\partial D}$ of a spectral optimal partition, let $\operatorname{Reg}$ be the set of points whose limiting frequency is an integer. Is $\operatorname{Reg}$ a $C^1$ submanifold of codimension one in $\partial D$? Does $\mathcal F_{\partial D}\setminus\operatorname{Reg}$ have ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | 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"
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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-14298587-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Boundary regularity has been proved on the frequency-two regular set, but the full C1-submanifold and codimension-two description remains unresolved; in dimension two the report also gives a counterexample to the analogous codimension claim for the broader nonregular set. | [
{
"url": "https://doi.org/10.4171/owr/2024/37",
"label": "Oberwolfach source report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | For the boundary free interface $\mathcal F_{\partial D}$ of a spectral optimal partition, let $\operatorname{Reg}$ be the set of points whose limiting frequency is an integer. Is $\operatorname{Reg}$ a $C^1$ submanifold of codimension one in $\partial D$? Does $\mathcal F_{\partial D}\setminus\operatorname{Reg}$ have ... | Is it true that Reg is a C 1 submanifold of codimension 1 in \partialD? Is it true that the remaining set F\partialD \ Reg has codimension 2 in \partialD? 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 | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,992 | OWR-14298587-005 | Regularity of Stationary Constraint Maps and Their Heat Flow | Extend the regularity theory for energy-minimizing maps constrained to a target domain to stationary constraint maps, and develop the corresponding regularity theory for their parabolic heat flow. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-005",
"literature-status:open",
"owr-year:2024"
] | The extension of regularity from energy-minimizing constraint maps to stationary maps and the corresponding heat-flow theory remain unresolved; current surveys still present these as open directions. | [
{
"url": "https://link.springer.com/article/10.1007/s44007-026-00209-w",
"label": "Constraint Maps, 2026"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Extend the regularity theory for energy-minimizing maps constrained to a target domain to stationary constraint maps, and develop the corresponding regularity theory for their parabolic heat flow. | Here, we propose a few open problems: • What can be said beyond energy-minimality? Can we address the same regularity issue, for example, in the case of stationary constraint maps? • Related to the previous point, what can be said about the corresponding heat flow problem? The report passage is retained verbatim as the... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,993 | OWR-14298587-006 | Regularity of Fractional Multiphase Interfaces | Develop a regularity theory for fractional multiphase minimal partitions with general surface-tension coefficients, whether or not those coefficients satisfy the triangle inequality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-006",
"literature-status:open",
"owr-year:2024"
] | The report identifies regularity for general coefficients, including coefficients that need not satisfy the triangle inequality, as open; no later primary result located here closes that general question. | [
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Develop a regularity theory for fractional multiphase minimal partitions with general surface-tension coefficients, whether or not those coefficients satisfy the triangle inequality. | The regularity theory for general coefficients, satisfying or not the triangle inequality, is still 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 | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,994 | OWR-14298587-009 | Gradient-Constrained Ginzburg-Landau Minimizers | For $2\leq N\leq 6$, let $u_\varepsilon(x)=f_\varepsilon(|x|)x/|x|$ be the radial vortex solution on $B^N$. Is $u_\varepsilon$ the unique minimizer of the Ginzburg-Landau energy $G_\varepsilon$ over the gradient fields $\mathcal V=\{u=\nabla\phi:\phi\in H^2(B^N),\ \nabla\phi=\operatorname{Id}\text{ on }\partial B^N\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,024 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
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"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-009",
"literature-status:partially-solved",
"owr-year:2024"
] | The unique-minimizer statement over gradient fields is proved in dimensions N\geq 4, but the unrestricted question as stated for all N\geq 2 is not fully settled. | [
{
"url": "https://arxiv.org/abs/2310.11384",
"label": "Ignat--Nahon--Nguyen, gradient fields"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | For $2\leq N\leq 6$, let $u_\varepsilon(x)=f_\varepsilon(|x|)x/|x|$ be the radial vortex solution on $B^N$. Is $u_\varepsilon$ the unique minimizer of the Ginzburg-Landau energy $G_\varepsilon$ over the gradient fields $\mathcal V=\{u=\nabla\phi:\phi\in H^2(B^N),\ \nabla\phi=\operatorname{Id}\text{ on }\partial B^N\}$? | Is u\varepsilon the (unique) minimizer of G\varepsilon over gradient fields V = \{u = ∇\phi : \phi \in H 2 (B N , R), ∇\phi = Id on \partialB N \}? SN −1 where ∇/ \cdot v ◦ (r, \cdot) = 0 in SN −1 and \psi is a scalar function. The spectral decomposition of s(r, \cdot) and \psi(r, \cdot) in L2 (SN −1 ) yields a decompo... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,995 | OWR-14298587-010 | Continuity of Gradient Distance for Monotone Equations | Let $G\in C^0(\mathbb R^2;\mathbb R^2)$ be strictly monotone, and let $u$ be a Lipschitz solution of $\operatorname{div}G(\nabla u)=0$. If $\mathcal B$ is the set where ellipticity degenerates simultaneously from below and above, is $x\mapsto\operatorname{dist}(\nabla u(x),\mathcal B)$ continuous? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,024 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
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"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-14298587-010",
"literature-status:open",
"owr-year:2024"
] | The continuity of x\mapsto\operatorname{dist}(\nabla u(x),B) for arbitrary continuous strictly monotone vector fields remains a conjectural regularity statement; no primary proof or counterexample was located. | [
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Let $G\in C^0(\mathbb R^2;\mathbb R^2)$ be strictly monotone, and let $u$ be a Lipschitz solution of $\operatorname{div}G(\nabla u)=0$. If $\mathcal B$ is the set where ellipticity degenerates simultaneously from below and above, is $x\mapsto\operatorname{dist}(\nabla u(x),\mathcal B)$ continuous? | We conjecture that, for any general strictly monotone vector fields G \in C 0 (R2 ; R2 ) and any Lipschitz solution u of div G(∇u) = 0, the function x 7\to dist(∇u(x), B) is continuous. 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 | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,996 | OWR-14298587-012 | Pointwise Quadratic Bounds for Extremal Solutions | For an extremal solution $u^\star$ of a semilinear elliptic equation near an isolated singularity, prove or disprove the pointwise estimate $\limsup_{x\to 0} f'(u^\star(x))|x|^2<\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-012",
"literature-status:open",
"owr-year:2024"
] | Low-dimensional regularity is proved, but the pointwise finiteness of limsup_{x\to 0} f'(u^*(x))|x|^2 remains unresolved; recent work gives averaged bounds and a limsup lower-bound mechanism, not the requested upper bound. | [
{
"url": "https://arxiv.org/abs/2606.21546",
"label": "Figalli--Franceschini, 2026"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | For an extremal solution $u^\star$ of a semilinear elliptic equation near an isolated singularity, prove or disprove the pointwise estimate $\limsup_{x\to 0} f'(u^\star(x))|x|^2<\infty$. | Size of the singular set Concerning the regularity of u⋆ , in [1], Brezis also asked: “Open problem 1: Is there something “sacred” about dimension 10? Alternatively, can one prove in “low” dimension that u⋆ is smooth for every f and every Ω?” After many partial results ([12, 7, 4, 6, 14, 8, 5]), Cabré, Figalli, Serra ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,997 | OWR-14298587-013 | Rigidity of Stable One-Phase Solutions | Let $u$ be a global stable solution of the one-phase free-boundary problem in $\mathbb R^n$. Prove that $u$ is one-dimensional when $n\leq 6$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-013",
"literature-status:partially-solved",
"owr-year:2024"
] | The stable one-phase rigidity conjecture is proved in some low-dimensional or restricted settings, including dimension 3, while the general dimensions 5 and 6 remain open. | [
{
"url": "https://arxiv.org/abs/2503.21245",
"label": "Chan--Fernandez-Real--Figalli--Serra"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Let $u$ be a global stable solution of the one-phase free-boundary problem in $\mathbb R^n$. Prove that $u$ is one-dimensional when $n\leq 6$. | Conjecture 6. Let u be a global stable solution to the one-phase problem in Rn . Then, if n \leq 6, u is one-dimensional. In fact, our results are a bit more general, and also apply to the Alt–Phillips free boundary problem. We finish the talk by stating an important conjecture for the one-phase problem, whose minimal ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,998 | OWR-14298587-014 | Classification of Stable Allen-Cahn Configurations | Classify the global stable critical points of the Allen-Cahn energy in $\mathbb R^3$. In particular, determine whether all stable configurations have the macroscopic regularity and minimal-surface behavior known for absolute minimizers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-014",
"literature-status:open",
"owr-year:2024"
] | Results for minimizers and selected stable configurations do not classify all stable configurations; the requested extension remains an open problem. | [
{
"url": "https://arxiv.org/abs/2503.21245",
"label": "Chan--Fernandez-Real--Figalli--Serra"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Classify the global stable critical points of the Allen-Cahn energy in $\mathbb R^3$. In particular, determine whether all stable configurations have the macroscopic regularity and minimal-surface behavior known for absolute minimizers. | However, extending these results to encompass all stable configurations —i.e. those ‘observable’ in nature— remains a significant and challenging open question. Stable phase transitions: open questions and new results Joaquim Serra (joint work with Hardy Chan, Alessio Figalli, Xavier Fernández-Real) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,005,999 | OWR-14298587-016 | Continuum Laws for Dislocation Motion | Derive continuum evolution laws for dislocation-density fields and their associated elastoplastic effects from the physical laws governing individual dislocations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-016",
"literature-status:partially-solved",
"owr-year:2024"
] | Bonicatto and Rindler rigorously homogenize a prototypical rate-independent model from discrete dislocations to dislocation fields, but this does not settle general constitutive laws for dislocation-field motion and elasto-plastic effects. | [
{
"url": "https://arxiv.org/abs/2410.02906",
"label": "Bonicatto--Rindler, dislocation homogenization"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Derive continuum evolution laws for dislocation-density fields and their associated elastoplastic effects from the physical laws governing individual dislocations. | While much consensus exists on what the physical laws are for the individual dislocations, it is not clear - and in fact one of the most pressing open problems of solid mechanics - how to formulate laws for the movement of dislocation fields and the corresponding elasto-plastic effects. On the homogenization problem fo... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,006,000 | OWR-14298587-018 | Two-Dimensionality of Low-Energy Abelian Higgs Fields | For the abelian Higgs energy in dimension $n\geq 5$, prove that every critical pair in the low-energy, nearly flat regime is gauge-equivalent to a two-dimensional solution. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-018",
"literature-status:partially-solved",
"owr-year:2024"
] | The low-energy two-dimensionality conjecture is proved for critical points in dimensions 2\leq n\leq 4 and for local minimizers in every dimension, but remains open for general critical points in higher dimensions. | [
{
"url": "https://poisson.phc.dm.unipi.it/~pigati/papers/ymh-savin.pdf",
"label": "Pigati--De Philippis--Halavati, abelian Higgs"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | For the abelian Higgs energy in dimension $n\geq 5$, prove that every critical pair in the low-energy, nearly flat regime is gauge-equivalent to a two-dimensional solution. | We conjecture that it is always true in this low-energy regime, up to change of gauge. Savin’s approach uses viscosity techniques, resembling the Krylov–Safanov the- ory in spirit. In particular, it is not always clear how one can extend these tech- niques to the vectorial setting, where the maximum principle does not ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,006,001 | OWR-14298587-019 | Boundary Uniqueness on Lipschitz Domains | Let $\Omega\subset\mathbb R^n$ be an arbitrary Lipschitz domain, let $u\in C(\overline\Omega)$ be harmonic in $\Omega$, and suppose that $u$ vanishes on a relatively open boundary patch $\Sigma$. If $\mathcal H^{n-1}(\{x\in\Sigma:\nabla u(x)=0\})>0$, must $u\equiv 0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298587-019",
"literature-status:open",
"owr-year:2024"
] | Tolsa's boundary uniqueness theorem requires a sufficiently small Lipschitz slope; removing that smallness assumption for arbitrary Lipschitz domains remains open. | [
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
},
{
"url": "https://ems.press/content/serial-article-files/46973",
"label": "Oberwolfach Report 37/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Let $\Omega\subset\mathbb R^n$ be an arbitrary Lipschitz domain, let $u\in C(\overline\Omega)$ be harmonic in $\Omega$, and suppose that $u$ vanishes on a relatively open boundary patch $\Sigma$. If $\mathcal H^{n-1}(\{x\in\Sigma:\nabla u(x)=0\})>0$, must $u\equiv 0$? | It is still an open question whether the same statement holds if we only assume Ω is a Lipschitz domain (and remove the smallness assumption on the Lipschitz constant). 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 | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,006,002 | OWR-14298587-020 | Sharp Bianchi-Egnell Stability Constant | Determine the optimal constant $c_{\mathrm{BE}}$ in the Bianchi-Egnell quantitative stability inequality for the Sobolev inequality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 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"
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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-14298587-020",
"literature-status:open",
"owr-year:2024"
] | The best Bianchi--Egnell constant is known to be positive and has improved bounds, but no exact value is known for the classical Sobolev inequality. | [
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/blms.12837",
"label": "Konig, sharp Bianchi--Egnell constant"
},
{
"url": "https://ems.press/content/serial-article-files/50045",
"label": "Oberwolfach Report 37/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Determine the optimal constant $c_{\mathrm{BE}}$ in the Bianchi-Egnell quantitative stability inequality for the Sobolev inequality. | On the other hand, it is a major open question to determine the value of the best constant cBE . The stability of Sobolev’s inequality: best constants and optimizers Tobias König The Sobolev inequality Z Z n−2 n 2n 2 (1) |∇u| dx \geq Sn |u| n−2 dx , Rn Rn with optimal constant Sn > 0, is optimized precisely by constan... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,006,003 | OWR-14298587-021 | Bianchi-Egnell Optimizers | Characterize the optimizers of the sharp Bianchi-Egnell stability constant $c_{\mathrm{BE}}$. In particular, determine whether optimizers are radial and whether they can change sign. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178](https://doi.org/10.4171/owr/2024/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | 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-14298587-021",
"literature-status:partially-solved",
"owr-year:2024"
] | Existence of a minimizer attaining c_{BE} is proved in every classical dimension d\geq 3, but characterization and qualitative properties of all sharp-constant optimizers remain open. | [
{
"url": "https://ems.press/content/serial-article-files/49782",
"label": "Konig, existence of a minimizer"
},
{
"url": "https://arxiv.org/abs/2210.08482",
"label": "Konig, sharp-constant bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/37 | null | null | null | Characterize the optimizers of the sharp Bianchi-Egnell stability constant $c_{\mathrm{BE}}$. In particular, determine whether optimizers are radial and whether they can change sign. | It remains an open problem to characterize the optimizers of cBE and even to determine their basic qualitative properties. 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 | Calculus of Variations (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/37, pp. 2113--2178 |
30,006,004 | OWR-14298588-001 | Mod-p Reductions of Crystalline Galois Representations | Let $\rho:\operatorname{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)\to\mathrm{GL}_n(\overline{\mathbb{Q}}_p)$ be crystalline with Hodge–Tate weights $h_1\geq\cdots\geq h_n$. Classify the possible semisimplified reductions $\overline{\rho}:\operatorname{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)\to\mathrm{GL}_n(\overline... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | 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-14298588-001",
"literature-status:partially-solved",
"owr-year:2024"
] | Theorem 1 gives strong inertial-weight constraints for direct sums of crystalline characters and is best possible for n=2, while the general classification and sharpness for n>2 remain unresolved; 2026 work adds further constraints but not a full classification. | [
{
"url": "https://ems.press/content/serial-article-files/50046",
"label": "Gee--Kisin, crystalline Breuil--Kisin reductions"
},
{
"url": "https://arxiv.org/abs/2607.08660",
"label": "Bhatt--Gee--Kisin, mod p reductions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Let $\rho:\operatorname{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)\to\mathrm{GL}_n(\overline{\mathbb{Q}}_p)$ be crystalline with Hodge–Tate weights $h_1\geq\cdots\geq h_n$. Classify the possible semisimplified reductions $\overline{\rho}:\operatorname{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)\to\mathrm{GL}_n(\overline... | question (which is in turn motivated by ques- tions about congruences between modular forms of different weights): Let ρ : Gal(Qp /Qp ) −\to GLn (Qp ) be a crystalline Galois representation, of Hodge– Tate weights h1 \geq h2 \geq \cdot \cdot \cdot \geq hn . Then what are the possibilities for ρ : Gal(Qp /Qp ) −\to GLn ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,005 | OWR-14298588-003 | Higgs Bundles Arising from p-Adic Galois Representations | Under the stated $p$-adic Simpson equivalence, characterize the Higgs bundles that correspond to $p$-adic Galois representations through the designated embedding, beyond the known cases of line bundles and abeloid varieties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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-14298588-003",
"literature-status:open",
"owr-year:2024"
] | The essential image of representations inside the p-adic Simpson category is understood in rank one and for abeloids, but the general Higgs-bundle characterization asked here remains open. | [
{
"url": "https://arxiv.org/abs/2207.13657",
"label": "Heuer, rank-one image"
},
{
"url": "https://arxiv.org/abs/2107.09403",
"label": "Heuer--Mann--Werner, abeloids"
},
{
"url": "https://link.springer.com/article/10.1007/s00222-025-01321-4",
"label": "Heuer, p-adic Simpson correspon... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Under the stated $p$-adic Simpson equivalence, characterize the Higgs bundles that correspond to $p$-adic Galois representations through the designated embedding, beyond the known cases of line bundles and abeloid varieties. | Question 5. Under the equivalence S of Theorem 4, which Higgs bundles corre- spond to representations via the embedding described in Example 2? This is expected to be a very difficult question. The answer is known in the case of line bundles [6] and abeloid varieties [8], where it is already quite subtle. In fact, 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 | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,006 | OWR-14298588-006 | Categorical Local Langlands Program Summary | This talk is a report on joint work in progress with Lucas Mann. Our goal is to formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues–Scholze [3] for many groups. We begin by briefly recalling the setup for this conjecture. Fix a finite extension E/Qp and a connected reductive quasis... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction is introductory programmatic exposition; the categorical local Langlands conjecture itself) | [
"OWR-14298588-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-006",
"literature-status:partially-solved",
"owr-year:2024"
] | The categorical local Langlands program has substantial conditional and unconditional results for GL-type, generic, and inductively accessible groups, but the full conjecture for every connected reductive quasisplit G is not proved. | [
{
"url": "https://arxiv.org/abs/2606.00983",
"label": "Hansen--Mann, categorical local Langlands"
},
{
"url": "https://arxiv.org/abs/2606.10149",
"label": "Helm--Solleveld--Xu, generic categorical LLC"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | null | This talk is a report on joint work in progress with Lucas Mann. Our goal is to formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues–Scholze [3] for many groups. We begin by briefly recalling the setup for this conjecture. Fix a finite extension E/Qp and a connected reductive quasis... | unrecoverable | The official report confirms that this extraction is introductory programmatic exposition; the categorical local Langlands conjecture itself is stated formally in OWR-14298588-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,007 | OWR-14298588-007 | Equivalent Categorical Local Langlands Formulation | Conjecture 1. The functor a\psi is fully faithful, and extends to an equivalence of categories L\psi : D(BunG ) ≃ IndCoh(ParG ) such that the diagram a\psi QCoh(ParG ) / D(BunG ) ◗◗◗ ◗◗◗Ξ ◗◗◗ ≀ L\psi ◗◗◗ ( IndCoh(ParG ) commutes. In fact, this conjecture can be sharpened quite a bit. Proposition 2. The equivalence L\ps... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** partia... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms that this extraction gives an equivalent functorial formulation of the categorical local Langlands conjecture r) | [
"OWR-14298588-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-007",
"literature-status:partially-solved",
"owr-year:2024"
] | The proposed equivalence remains a conjecture in general; 2026 work proves major cases or conditional implications, including GL-type and broad generic or inductive settings, but not the full stated equivalence for all quasisplit groups. | [
{
"url": "https://arxiv.org/abs/2606.00983",
"label": "Hansen--Mann, categorical local Langlands"
},
{
"url": "https://arxiv.org/abs/2606.10149",
"label": "Helm--Solleveld--Xu, generic categorical LLC"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | null | Conjecture 1. The functor a\psi is fully faithful, and extends to an equivalence of categories L\psi : D(BunG ) ≃ IndCoh(ParG ) such that the diagram a\psi QCoh(ParG ) / D(BunG ) ◗◗◗ ◗◗◗Ξ ◗◗◗ ≀ L\psi ◗◗◗ ( IndCoh(ParG ) commutes. In fact, this conjecture can be sharpened quite a bit. Proposition 2. The equivalence L\ps... | unrecoverable | The official report confirms that this extraction gives an equivalent functorial formulation of the categorical local Langlands conjecture represented canonically by OWR-14298588-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,008 | OWR-14298588-008 | Fargues-Scholze Categorical Local Langlands Equivalence | Let $E/\mathbb{Q}_p$ be finite and let $G/E$ be quasisplit reductive. Construct the conjectural equivalence between $D_{\mathrm{lis}}(\operatorname{Bun}_G,\overline{\mathbb{Q}}_\ell)$ and the ind-coherent sheaves on the stack of $L$-parameters, normalized by a Whittaker datum, and prove that it intertwines Hecke operat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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... | [
"OWR-14298588-006",
"OWR-14298588-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-008",
"literature-status:open",
"owr-year:2024"
] | The Fargues--Scholze categorical equivalence remains conjectural for general quasi-split groups; recent work gives substantial reductions and cases but not a general proof. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2102.13459",
"label": "Fargues--Scholze"
},
{
"url": "https://arxiv.org/abs/2606.00983",
"label": "Hansen--Mann"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Let $E/\mathbb{Q}_p$ be finite and let $G/E$ be quasisplit reductive. Construct the conjectural equivalence between $D_{\mathrm{lis}}(\operatorname{Bun}_G,\overline{\mathbb{Q}}_\ell)$ and the ind-coherent sheaves on the stack of $L$-parameters, normalized by a Whittaker datum, and prove that it intertwines Hecke operat... | Fix distinct prime numbers p, ℓ. Let E be a finite extension of Qp , and G a quasi-split reductive group over E. The most refined form of the categorical local Langlands conjecture has been proposed in the work of Fargues–Scholze [5, Conjecture I.10.2]. Technically speak- ing, we also fix a square root of q (the cardin... | 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 | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,009 | OWR-14298588-009 | Hecke Eigensheaves for Discrete L-Parameters | For every discrete $L$-parameter $\phi$ of $G$, construct a perverse Hecke eigensheaf $F_\phi\in D_{\mathrm{lis}}(\operatorname{Bun}_G,\overline{\mathbb{Q}}_\ell)$ whose restriction to each basic stratum realizes the local Langlands packet of the corresponding inner form with the predicted multiplicities. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** partia... | 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-14298588-009",
"literature-status:partially-solved",
"owr-year:2024"
] | The Hecke eigensheaf and packet properties are proved in important cases, including cuspidal parameters for general linear groups and special low-rank cases, but the stated general discrete-parameter conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1608.07446",
"label": "Hamann--Imai--Yang"
},
{
"url": "https://arxiv.org/abs/2102.13459",
"label": "Fargues--Scholze"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | For every discrete $L$-parameter $\phi$ of $G$, construct a perverse Hecke eigensheaf $F_\phi\in D_{\mathrm{lis}}(\operatorname{Bun}_G,\overline{\mathbb{Q}}_\ell)$ whose restriction to each basic stratum realizes the local Langlands packet of the corresponding inner form with the predicted multiplicities. | Before the joint work with Scholze, Fargues [4] has originated the geometrization of the local Langlands with his conjecture on Hecke eigensheaves for discrete L- parameters. Here is a slightly modified version of (a part of) the conjecture: Conjecture (Fargues). Let \phi be a discrete L-parameter of G. There exists 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 | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,010 | OWR-14298588-010 | Hecke Eigensheaves for Arthur Parameters | For every Arthur parameter $\psi$, construct an associated perverse eigensheaf $F_\psi$ on $\operatorname{Bun}_G$ with the predicted Hecke eigenproperty and, when $G$ is semisimple, the predicted decomposition over basic strata into the Arthur packets of the pure inner forms of $G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** partia... | 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... | [
"OWR-14298588-012"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-010",
"literature-status:partially-solved",
"owr-year:2024"
] | Candidate sheaves are constructed on the spectral side for arbitrary A-parameters, but the expected perverse, packet, and automorphic-side properties are not established in general. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.06006",
"label": "Bertoloni Meli--Koshikawa--Leake"
},
{
"url": "https://arxiv.org/abs/2606.00983",
"label": "Hansen--Mann"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | For every Arthur parameter $\psi$, construct an associated perverse eigensheaf $F_\psi$ on $\operatorname{Bun}_G$ with the predicted Hecke eigenproperty and, when $G$ is semisimple, the predicted decomposition over basic strata into the Arthur packets of the pure inner forms of $G$. | We propose that a variant of the conjecture should hold for A-parameters, also known as Arthur parameters: Definition. We conjecture that a variant of eigensheaf exists for any A-parameter: Conjecture. (2) F\psi is perverse. (3) Assume G is semisimple, in which case Gb is a pure inner form of G for any basic b. There e... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,011 | OWR-14298588-012 | Arthur-Eigensheaf Spectral-Side Continuation | In particular, the categorical local Langlands conjecture would imply that there exists a nonzero F\psi \in Dlis (BunG , Qℓ ) satisfying the property (1). If \psi is tempered, i.e., trivial on the second SL2 , the construction of the above ind-coherent sheaf is not difficult, and it is essentially obtained from the reg... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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 | Duplicate/merged OWR extraction (The official report confirms that this extraction is discussion and evidence following the Arthur-parameter eigensheaf conjecture represente) | [
"OWR-14298588-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-012",
"literature-status:open",
"owr-year:2024"
] | The record is contextual commentary about consequences and constructions rather than a standalone proved claim; the general categorical realization it invokes remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2606.00983",
"label": "Hansen--Mann"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | null | In particular, the categorical local Langlands conjecture would imply that there exists a nonzero F\psi \in Dlis (BunG , Qℓ ) satisfying the property (1). If \psi is tempered, i.e., trivial on the second SL2 , the construction of the above ind-coherent sheaf is not difficult, and it is essentially obtained from the reg... | unrecoverable | The official report confirms that this extraction is discussion and evidence following the Arthur-parameter eigensheaf conjecture represented canonically by OWR-14298588-010, not a separate conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,012 | OWR-14298588-013 | Algebraicity of Tate Classes on GSp4 Shimura Varieties | Determine when the Tate classes in the relevant degree-three etale cohomology of the Shimura threefold $S_K(\mathrm{GSp}_4)$ arise from algebraic cycles, as predicted by the Tate conjecture. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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-14298588-013",
"literature-status:open",
"owr-year:2024"
] | The Tate-cycle question for the indicated GSp4 Shimura cohomology has substantial results for endoscopic and generic cases, but no general algebraicity theorem for all extracted classes is known. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2211.10838",
"label": "Sweeting"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Determine when the Tate classes in the relevant degree-three etale cohomology of the Shimura threefold $S_K(\mathrm{GSp}_4)$ arise from algebraic cycles, as predicted by the Tate conjecture. | The main question of this talk is when these classes arise from algebraic cycles, as predicted by the Tate conjecture. Let g be a classical cuspidal eigenform of weight two for GL2 ; then g has a Galois representation, constructed by Deligne as a quotient H 1 (X1 (N )Q , Qℓ ) ։ ρg for some sufficiently large level N . ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,013 | OWR-14298588-014 | Cyclic Lifting Property for Moduli Stacks | Characterize the algebraic stacks that satisfy the cyclic lifting property. Extend the associated $p$-adic volume formula to moduli spaces with non-quotient singularities, including moduli of Higgs bundles, coherent sheaves, and quiver representations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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-14298588-014",
"literature-status:open",
"owr-year:2024"
] | The cyclic lifting property is verified in the examples used for the volume formula, but the class of stacks for which it holds is explicitly left open. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Characterize the algebraic stacks that satisfy the cyclic lifting property. Extend the associated $p$-adic volume formula to moduli spaces with non-quotient singularities, including moduli of Higgs bundles, coherent sheaves, and quiver representations. | It is an open problem to understand for which class of stacks the cyclic lifting property is satisfied. In [6] this p-adic volume formula was applied to the moduli DM-stack of G- Higgs bundles (with additional assumptions to guarantee smoothness) M f♥ . In F G f♥ this case, the twisted inertia stack can be shown to be ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,014 | OWR-14298588-015 | Reported Height Theorem for Abelian Isogeny Classes | As the Mumford-Tate conjecture is known for many abelian varieties, our theorem is unconditional in those cases. Heights in the isogeny class of an abelian variety Mark Kisin (joint work with Lucia Mocz) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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 states the bounded-height finiteness result as a theorem conditional on the Mumford–Tate conjecture and notes the cases ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298588-015",
"literature-status:open",
"owr-year:2024"
] | The extracted sentence records a conditionality observation about the Mumford--Tate conjecture, not a resolution of that conjecture or of the associated height problem; the general issue remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | null | As the Mumford-Tate conjecture is known for many abelian varieties, our theorem is unconditional in those cases. Heights in the isogeny class of an abelian variety Mark Kisin (joint work with Lucia Mocz) | unrecoverable | The official report states the bounded-height finiteness result as a theorem conditional on the Mumford–Tate conjecture and notes the cases where it is already unconditional; it does not pose the unconditional extension as an open problem. No separate clean statement is promoted; the original record remains publicly vi... | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
30,006,015 | OWR-14298588-016 | Fontaine-Mazur Conjecture for Unramified Galois Representations | Prove the Fontaine–Mazur conjecture for the indicated unramified Galois representations, extending the known special unramified Tate results to the general setting. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912](https://doi.org/10.4171/owr/2024/33)
## Literature review (checked 2026-08-22)
**Status:** open
... | 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-14298588-016",
"literature-status:open",
"owr-year:2024"
] | The passage uses the Fontaine--Mazur conjecture and recovers only a special unramified Tate statement; the general Fontaine--Mazur claim remains open despite many special cases. | [
{
"url": "https://doi.org/10.4171/owr/2024/33",
"label": "OWR report"
},
{
"url": "https://annals.math.princeton.edu/2015/182-3/p03",
"label": "Scholze"
},
{
"url": "https://arxiv.org/abs/2404.18967",
"label": "Luo"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/33 | null | null | null | Prove the Fontaine–Mazur conjecture for the indicated unramified Galois representations, extending the known special unramified Tate results to the general setting. | Fontaine-Mazur conjecture (consider any faithful representation of GGal /Gur ). On the other hand, by combing the theorem with an argument of Faltings, one can recover a case of the unramified Mazur conjecture: Let K ur /K be the maximal extension unramified at all primes w|p. Then the analogue of Faltings’ theorem on ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Arithmetic Geometry (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/33, pp. 1855--1912 |
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