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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,316 | OWR-11695867-001 | Lee–Rains–Warnaar Macdonald Integral Identities | Do the Lee–Rains–Warnaar vanishing-integral identities for Macdonald polynomials hold beyond the known Schur specialization $q=t$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-001",
"literature-status:partially-solved",
"owr-year:2022"
] | Albion proved the Schur specialization of the Lee--Rains--Warnaar identities, while the general Macdonald case in the extracted conjecture remains unresolved. | [
{
"url": "https://doi.org/10.1090/bproc/221",
"label": "Albion primary article"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Do the Lee–Rains–Warnaar vanishing-integral identities for Macdonald polynomials hold beyond the known Schur specialization $q=t$? | In [1], we were able to prove the Schur case of a particular pair of vanishing integrals conjectured by Lee, Rains and Warnaar [3, Conjecture 9.2]. Following the virtual Koornwinder integral approach to Littlewood identities of Rains and Warnaar [6], which he used to prove MacMahon’s conjecture for the generating funct... | 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 | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,317 | OWR-11695867-002 | Twenty-Vertex Models and Pachter-Triangle Tilings | Is the number of configurations of the twenty-vertex model with DWBC3 on an $n\times n$ grid equal to the number of domino tilings of Pachter's triangle of size $2n$, and does the analogous equality hold for the extended $(n+k)\times n$ model and enhanced triangle for every $k\geq 0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-002",
"literature-status:partially-solved",
"owr-year:2022"
] | The 20V--domino correspondence is proved for the maximal domain and the k=2,3 truncations, but the square-grid and all-k assertions in the record are not fully proved. | [
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p38/pdf",
"label": "Di Francesco primary article"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Is the number of configurations of the twenty-vertex model with DWBC3 on an $n\times n$ grid equal to the number of domino tilings of Pachter's triangle of size $2n$, and does the analogous equality hold for the extended $(n+k)\times n$ model and enhanced triangle for every $k\geq 0$? | Conjecture 3. The number of configurations of the 20V model with DWBC3 on an n \times n grid is equal to that of domino tilings of Pachter’s triangle of size 2n. In fact an extension of the 20V domain to a rectangle (n + k) \times n with horizon- tal outgoing edge orientations was also considered in [10]. Parallelly, t... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,318 | OWR-11695867-003 | Graded Analogues of Parking-Space Enumeration | Find a graded, or $q$-, analogue of the parking-space enumeration theorem, for example via Cherednik-algebra shift functors, Lie-theoretic $q$-Kreweras numbers, or the freeness conjecture. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-003",
"literature-status:open",
"owr-year:2022"
] | The requested q-version is still presented as future work; existing results provide related q-Catalan and Hecke-algebra formulas but not the requested theorem. | [
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Find a graded, or $q$-, analogue of the parking-space enumeration theorem, for example via Cherednik-algebra shift functors, Lie-theoretic $q$-Kreweras numbers, or the freeness conjecture. | Give a q-version of Theorem 2, for instance via Rouquier’s shift functors for Cherednik algebras, or by generalizing the Lie-theoretic q-Kreweras numbers of [12], or via the freeness conjecture of [9]. Future directions. The two previous theorems are very suggestive of further research. Our proof of Theorem 2 did not m... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,319 | OWR-11695867-006 | Fixed-Occurrence Permutation Pattern Asymptotics | For permutations with exactly $r$ occurrences of a fixed pattern, is $\psi_r(n)\sim C_r n^r\psi_0(n)$, with the conjectured algebraic form for the generating function $\Psi_r(x)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-006",
"literature-status:open",
"owr-year:2022"
] | The 2025 primary study still labels the asymptotic formula as a conjecture supported by computation, and no proof was located by the cutoff date. | [
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i1p3/pdf",
"label": "Conway--Guttmann primary article"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | For permutations with exactly $r$ occurrences of a fixed pattern, is $\psi_r(n)\sim C_r n^r\psi_0(n)$, with the conjectured algebraic form for the generating function $\Psi_r(x)$? | Accordingly, we conjecture that \psir (n) \sim Cr \cdot nr \cdot \psi0 (n). The general situation seems to be Q2r (n)(2n − r)! Cr \cdot 4n \psir (n) = \sim \sqrt{ } (n + 2r + 1)!(n − r)! n n\pi where Q2r (n) is a polynomial with integer coefficients of degree 2r. The amplitude coefficient Cr appears to increase exponential... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,320 | OWR-11695867-007 | Wilf Class Asymptotics with Fixed Pattern Occurrences | For each Wilf class with exactly $r$ occurrences of the pattern, is $\psi_r(n)\sim C_r n^r\psi_0(n)$, and what moment-sequence properties do the corresponding occurrence generating functions have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-007",
"literature-status:open",
"owr-year:2022"
] | The corresponding asymptotic for both length-four Wilf classes is explicitly conjectural in the 2025 study and remains open. | [
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i1p3/pdf",
"label": "Conway--Guttmann primary article"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | For each Wilf class with exactly $r$ occurrences of the pattern, is $\psi_r(n)\sim C_r n^r\psi_0(n)$, and what moment-sequence properties do the corresponding occurrence generating functions have? | Accordingly, we conjecture that \psir (n) \sim Cr \cdot nr \cdot \psi0 (n) for both classes. 6. Stieltjes moment sequences Bostan, Elvey Price, Guttmann and Maillard showed that for all known PAP generating functions, the coefficients were Stieltjes moment sequences (SMS), and for Av(1324) the Hankel determinants were mo... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,321 | OWR-11695867-008 | Borwein Sign Conjectures | Do the Second and Cubic Borwein conjectures hold: for every positive integer $n$, do the coefficients of $P_n(q)^2$ and $P_n(q)^3$ have the repeating sign pattern $+,-,-$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-008",
"literature-status:partially-solved",
"owr-year:2022"
] | The first and second Borwein sign conjectures are proved, but the cubic statement is only partially proved and the further modulus claims remain conjectural. | [
{
"url": "https://arxiv.org/abs/2201.12415",
"label": "Wang--Krattenthaler"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Do the Second and Cubic Borwein conjectures hold: for every positive integer $n$, do the coefficients of $P_n(q)^2$ and $P_n(q)^3$ have the repeating sign pattern $+,-,-$? | Conjecture 1. It took almost 30 years until Chen Wang succeeded in proving this conjecture in [6], using saddle point approximation techniques. As I already indicated, “the” Borwein Conjecture (Conjecture 1) is actually the first of three conjectures made by Peter Borwein. The Second Borwein Conjecture from [1] predicts... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,322 | OWR-11695867-009 | Cubic and Higher Modulus Borwein Conjectures | Can the remaining cubic and higher-modulus Borwein sign conjectures be proved, including the modulus-$5$ and modulus-$7$ cases? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-009",
"literature-status:partially-solved",
"owr-year:2022"
] | The reported saddle-point program proves the first and second cases and substantial parts of the cubic case, but the full cubic and additional modulus conjectures are not established. | [
{
"url": "https://arxiv.org/abs/2201.12415",
"label": "Wang--Krattenthaler"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Can the remaining cubic and higher-modulus Borwein sign conjectures be proved, including the modulus-$5$ and modulus-$7$ cases? | (dominant) saddle points located at complex points. This makes the estimations that have to be performed more delicate. On the positive side, it allows one to proceed in a more streamlined fashion. In fact, it allows us to provide a uniform proof of the First and Second Borwein Conjecture (Conjectures 1 and 2), as well... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,323 | OWR-11695867-010 | Bijective Proof of a Hurwitz Number Identity | Let $H_{n,\ell}$ count ordered ℓ-tuples of transpositions in $S_n$ whose product is the identity. For $\lambda\vdash n$, let $f_\lambda$ count standard Young tableaux and let $C_\lambda=\sum_{(i,j)\in\lambda}(j-i)$. Give a bijective proof, for all ℓ≥0, of $n!H_{n,\ell}=\sum_{\lambda\vdash n}f_\lambda^2 C_\lambda^\ell$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-010",
"literature-status:open",
"owr-year:2022"
] | Louf asks for a bijective proof of the full Hurwitz identity for every ℓ. The former extraction retained only ℓ=0, the classical Robinson–Schensted identity. The source explicitly distinguishes this known special case.
**What remains.** A bijection for general ℓ is the open target. | [
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status ... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Let $H_{n,\ell}$ count ordered ℓ-tuples of transpositions in $S_n$ whose product is the identity. For $\lambda\vdash n$, let $f_\lambda$ count standard Young tableaux and let $C_\lambda=\sum_{(i,j)\in\lambda}(j-i)$. Give a bijective proof, for all ℓ≥0, of $n!H_{n,\ell}=\sum_{\lambda\vdash n}f_\lambda^2 C_\lambda^\ell$. | Open problem 1. Since Hn,0 = 1, the case ℓ = 0 boils down to showing bijectively that X (3) f\lambda2 = n! \lambda⊢n | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,324 | OWR-11695867-011 | Joint Genus and Degree Asymptotics for Connected Hurwitz Numbers | Determine asymptotic formulas for connected Hurwitz numbers when both genus and degree tend to infinity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-011",
"literature-status:open",
"owr-year:2022"
] | The requested simultaneous asymptotics for connected Hurwitz numbers and the proposed combinatorial understanding of the relevant coefficients remain unresolved in the identified literature. | [
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Determine asymptotic formulas for connected Hurwitz numbers when both genus and degree tend to infinity. | Finally, it is also an important question to obtain asymptotic enumeration for connected Hurwitz numbers (that is, with a definition similar to the geometric definition of Hn,ℓ , but requiring the surface above to be connected), both as the genus (of the surface above) and the size (here, the degree of the cover) go to 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 | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,325 | OWR-11695867-013 | Closed Sets Supporting Permutons | Which closed subsets of $[0,1]^2$ can occur as the support of a permuton? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-013",
"literature-status:partially-solved",
"owr-year:2022"
] | Recent work gives necessary and sufficient conditions in the discrete setting and a partial characterization for continuous supports, but not a complete characterization of all closed subsets of the square. | [
{
"url": "https://arxiv.org/abs/2608.04135",
"label": "Coscia--Tassy--Winkler"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Which closed subsets of $[0,1]^2$ can occur as the support of a permuton? | We address the fundamental question of what can happen when two random variables with given real distributions interact. We ask: given a closed set in [0, 1], when is it the support of a permuton? Sets that Support a Joint Distribution Peter Winkler (joint work with Chris Coscia and Martin Tassy) Figure 1. Which of 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 | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,326 | OWR-11695867-014 | Bijection Between Symmetric Walk Families | Find a bijection between the symmetric walk families $X(\widehat S)$ and $Y(\widehat S)$ for every multiset $\widehat S$ of small steps. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-014",
"literature-status:open",
"owr-year:2022"
] | The equality of the two counted sets is known, but the requested direct bijection has not been established in the authoritative sources located by the cutoff. | [
{
"url": "https://arxiv.org/abs/2204.06847",
"label": "Elvey Price"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Find a bijection between the symmetric walk families $X(\widehat S)$ and $Y(\widehat S)$ for every multiset $\widehat S$ of small steps. | Theorem 1 (A. Elvey Price). For any multiset Sb of small steps, |X(S)| b = |Y (S)|. b The existing proof of this surprising fact uses elliptic functions. Problem 1. Find a bijection between X(S) b and Y (S).b Figure 1. A walk in X( b S) for Sb = \{ր, 2\times ↓, 2\times տ, 3\times ↑, 3\times ← , 4\times ւ, 5\times \to\}... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,327 | OWR-11695867-015 | Generating Functions for Parity Restricted 321 Avoiding Permutations | Is the generating function $\sum_{n\geq 1}P_{321}(n)q^n$ algebraic, D-finite, or D-algebraic, and what are the asymptotics of $P_{321}(n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-015",
"literature-status:open",
"owr-year:2022"
] | The algebraicity, D-finiteness, D-algebraicity, and asymptotics asked for the parity-restricted 321-avoiding permutation generating function remain unresolved in the identified literature. | [
{
"url": "https://personal.utdallas.edu/~nxw170830/docs/Papers/Misc/Oberwolfach_EC_2022_problem_session.pdf",
"label": "problem-session paper"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Is the generating function $\sum_{n\geq 1}P_{321}(n)q^n$ algebraic, D-finite, or D-algebraic, and what are the asymptotics of $P_{321}(n)$? | Is the generating function P n 321 n=1 P (n)q n algebraic, D-finite, or D-algebraic? What are the asymptotics 321 of P (n)? Figure 2. The letters in each of the 42 subwords in P3 are in- dicated by a gray background. For example, the subword in the top left should be read as (e, s1 , s2 , e, e, e, s2 , s3 , e, s1 , 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 | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,328 | OWR-11695867-016 | Log-Concavity of q-Stirling Polynomials | Are the $q$-Stirling polynomials $S_q[n,k]$ log-concave for all $n$ and $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-016",
"literature-status:open",
"owr-year:2022"
] | The stated log-concavity and asymptotic-normality questions for q-Stirling numbers are presented as conjectural, and no proof of the extracted claims was found by the cutoff. | [
{
"url": "https://arxiv.org/abs/2205.14078",
"label": "q-Stirling numbers in type B"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Are the $q$-Stirling polynomials $S_q[n,k]$ log-concave for all $n$ and $k$? | P i Definition 4. A polynomial i\geq0 ai q is log-concave if a2i \geq ai−1 ai+1 for all i \geq 1. Conjecture 3 ([3, Conjecture 7.4]). The polynomials Sq [n, k] are log-concave. • Have checked by computer all n, k \leq 50. • For k \geq 2, have confirmed that the coefficients of Sq [n, k] are asymptoti- cally normal as n \t... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,329 | OWR-11695867-017 | Parity Log-Concavity of Type-B q-Stirling Polynomials | Are the type-$B$ $q$-Stirling polynomials $S_q^B[n,k]$ parity log-concave for all $n$ and $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-017",
"literature-status:open",
"owr-year:2022"
] | The type-B q-Stirling parity-log-concavity conjecture remains explicitly unresolved in the primary treatment located by the cutoff. | [
{
"url": "https://arxiv.org/abs/2205.14078",
"label": "q-Stirling numbers in type B"
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Are the type-$B$ $q$-Stirling polynomials $S_q^B[n,k]$ parity log-concave for all $n$ and $k$? | Conjecture 4 ([3, Conjecture 7.5]). The polynomials SqB [n, k] are parity log- concave. 5. Theo Douvropoulos: Deformations of braid arrangements Figure 3 displays the braid arrangement, the Shi arrangement, and the Catalan ar- rangement for the symmetric group S3 , along with their defining set of hyperplanes and their ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,330 | OWR-11695867-020 | Rigorous Asymptotics for Hamiltonian Cycles in Random Maps | Can the predicted asymptotics for Hamiltonian cycles in random maps be proved by probabilistic or combinatorial methods? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305](https://doi.org/10.4171/owr/2022/57)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695867-020",
"literature-status:open",
"owr-year:2022"
] | Physics analyses predict the Hamiltonian-cycle growth and critical exponent and provide numerical evidence, but a rigorous mathematical proof of the requested asymptotics remains unavailable. | [
{
"url": "https://arxiv.org/abs/2305.02188",
"label": "Di Francesco et al."
},
{
"url": "https://doi.org/10.4171/owr/2022/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/57 | null | null | null | Can the predicted asymptotics for Hamiltonian cycles in random maps be proved by probabilistic or combinatorial methods? | Is there some mathematical (probabilistic or even combinatorial) approach to proving this prediction? Figure 5. Left: an example of a vertex bicolored trivalent map of genus zero—here F − E + V = 3 − 3 + 2 = 2 = 2 − 2g, so that g = 0. Right: A redrawn map, where the path is the given Hamiltonian cycle and the rooted ed... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/57, pp. 3215--3305 |
30,005,331 | OWR-12697684-001 | Ryser-Brualdi-Stein Latin Square Transversal Conjecture | conjecture. A Latin square of order n is an n-by-n grid filled with n symbols in such a way that every symbol appears exactly once in each column and each row. A transversal of a Latin square is a collection of cells that share no column, no row, and are filled with distinct symbols. Interesting examples of Latin squares... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (The extraction is workshop context for the Ryser–Brualdi–Stein conjecture, whose complete formulation is retained in OWR-12697684-020. No se) | [
"OWR-12697684-020"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Contextual prose combines other topics without a distinct recoverable problem.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | null | conjecture. A Latin square of order n is an n-by-n grid filled with n symbols in such a way that every symbol appears exactly once in each column and each row. A transversal of a Latin square is a collection of cells that share no column, no row, and are filled with distinct symbols. Interesting examples of Latin squares... | unrecoverable | The extraction is workshop context for the Ryser–Brualdi–Stein conjecture, whose complete formulation is retained in OWR-12697684-020. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,332 | OWR-12697684-002 | Unspecified Extremal Combinatorics Conjecture | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Noam Lifshitz (joint with Peter Keevash and Dor Minzer) Product free sets in groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Uli Wagner (joint with Anna Lubiw, Zuzana Masárowá, and... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Unrecoverable OWR statement (The official report shows that this is an incomplete table-of-contents fragment without a mathematical statement. No separate clean statemen) | [] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-002",
"literature-status:open",
"owr-year:2023"
] | Table-of-contents text, not an open problem.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Noam Lifshitz (joint with Peter Keevash and Dor Minzer) Product free sets in groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Uli Wagner (joint with Anna Lubiw, Zuzana Masárowá, and... | unrecoverable | The official report shows that this is an incomplete table-of-contents fragment without a mathematical statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,333 | OWR-12697684-003 | Unspecified Random Function Root Problem | Van Vu Roots of random functions: Recent progress and open questions . . . . . . . . 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:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (The extraction is only the title of a contribution; its specific random-root questions are retained in OWR-12697684-016 and OWR-12697684-017) | [
"OWR-12697684-016",
"OWR-12697684-017"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-003",
"literature-status:open",
"owr-year:2023"
] | Table-of-contents text; the corresponding problems are retained separately.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | null | Van Vu Roots of random functions: Recent progress and open questions . . . . . . . . The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The extraction is only the title of a contribution; its specific random-root questions are retained in OWR-12697684-016 and OWR-12697684-017. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,334 | OWR-12697684-008 | Largest Product-Free Subsets of Alternating Groups | For a product-free subset $A\subset A_n$, determine the largest possible value of $|A|$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-008",
"literature-status:partially-solved",
"owr-year:2023"
] | The extremal size and dictator structure of product-free subsets of A_n are determined for sufficiently large n, but the extracted all-orders question is not completely settled. | [
{
"url": "https://arxiv.org/abs/2205.15191",
"label": "Keevash--Lifshitz--Minzer"
},
{
"url": "https://doi.org/10.1007/s00222-024-01273-1",
"label": "published paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For a product-free subset $A\subset A_n$, determine the largest possible value of $|A|$. | What’s the largest possible value of |A|? What are dictators in An ? By analogy from Boolean functions and set systems it makes sense to define A Ď An to be a dictator if there exists x P rns, such that the question whether \sigma belongs to A or not depends only on \sigma pxq . The Erdős–Ko–Rado theorem opened a whol... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,335 | OWR-12697684-010 | Hamiltonicity of Cayley and Vertex-Transitive Graphs | Is every connected Cayley graph Hamiltonian? More generally, which connected vertex-transitive graphs fail to have a Hamiltonian path or cycle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-010",
"literature-status:partially-solved",
"owr-year:2023"
] | The random-Cayley-graph instance is proved via spectral expansion, but the full Lovász conjecture for all Cayley or vertex-transitive graphs remains open. | [
{
"url": "https://arxiv.org/abs/2402.06603",
"label": "Draganić et al."
},
{
"url": "https://doi.org/10.1016/j.disc.2009.02.018",
"label": "Pak--Radoičić"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Is every connected Cayley graph Hamiltonian? More generally, which connected vertex-transitive graphs fail to have a Hamiltonian path or cycle? | One application is an important special case of a famous open question of Lovász [17] from 1969 concerning the Hamiltonicity of a certain class of well-behaved graphs (see e.g., [10] and its references for more background on the problem). Since Cayley graphs are vertex-transitive and none of the five known exceptions i... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,336 | OWR-12697684-011 | Erdős–Hajnal Clique-or-Independent-Set Conjecture | For every fixed graph $H$, does there exist $c(H)>0$ such that every $H$-free graph on $n$ vertices contains a clique or an independent set of size at least $n^{c(H)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12697684-012"
] | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-011",
"literature-status:open",
"owr-year:2023"
] | Corrected the original-report reference to OWR 01/2023. The previous literature-source link incorrectly pointed to OWR 57/2022.
**What remains.** The mathematical question and its existing unresolved status are unchanged. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For every fixed graph $H$, does there exist $c(H)>0$ such that every $H$-free graph on $n$ vertices contains a clique or an independent set of size at least $n^{c(H)}$? | A graph G contains a graph H if H is isomorphic to an induced subgraph of G, and G is H-free otherwise. Erdős and Hajnal [6, 7] proposed in 1977 the following well-known conjecture, stating that unlike in arbitrary graphs where we can only guarantee a clique or a stable set of polylogarithmic size if we impose even a ... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,337 | OWR-12697684-012 | Repeated Erdős–Hajnal Conjecture Context | The one due to Gyárfás from the late ’90s [9] raised the question of trying to prove the conjecture for specific small graphs. The second is a classical result due to Alon, Pach and Solymosi [1] that the class of graphs satisfying the Erdős–Hajnal Conjecture is closed under the substitution operation, in particular, ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (The official report confirms that this is contextual repetition of the Erdős–Hajnal conjecture retained in OWR-12697684-011. No separate cle) | [
"OWR-12697684-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-012",
"literature-status:open",
"owr-year:2023"
] | Background on Erdős–Hajnal, already represented by the canonical conjecture.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | null | The one due to Gyárfás from the late ’90s [9] raised the question of trying to prove the conjecture for specific small graphs. The second is a classical result due to Alon, Pach and Solymosi [1] that the class of graphs satisfying the Erdős–Hajnal Conjecture is closed under the substitution operation, in particular, ... | unrecoverable | The official report confirms that this is contextual repetition of the Erdős–Hajnal conjecture retained in OWR-12697684-011. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,338 | OWR-12697684-014 | Unions of Linear Bases as Additive Bases | For every prime $p$, does there exist $k(p)$ such that every union of $k(p)$ linear bases of $\mathbb F_p^n$ is an additive basis of $\mathbb F_p^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-014",
"literature-status:partially-solved",
"owr-year:2023"
] | The full additive-basis conjecture is not settled for all primes; the weak form is proved, and the p=3 case has a 2026 revised preprint, while the remaining general-prime assertion remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2111.13658",
"label": "Nagy--Pach--Tomon, Additive Bases"
},
{
"url": "https://arxiv.org/abs/2510.01300",
"label": "Yu, Note on the Additive Basis Conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For every prime $p$, does there exist $k(p)$ such that every union of $k(p)$ linear bases of $\mathbb F_p^n$ is an additive basis of $\mathbb F_p^n$? | This conjecture is wide open for every p ě 3. This conjecture is implied by the statement fp pnq “ Ωpn log pq. Theorem 1. There exists c ą 0 such that fp pnq ě c logloglogp p ¨ n. Also, there exists \varepsilon ą 0 such that if p ě 5, then fp pnq ě p1 ` \varepsilonqn. | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,339 | OWR-12697684-016 | Real Zeros of General Random Functions | For broad classes of random functions, determine the mean, variance, and limiting distribution of the number of real zeros. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12697684-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-016",
"literature-status:partially-solved",
"owr-year:2023"
] | Classical and several structured coefficient models have asymptotic means, variances, and central limit theorems, but the stated general random-polynomial or random-function problem has no complete solution. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2303.05478",
"label": "Do--Nguyen, Real Roots of Random Polynomials"
},
{
"url": "https://arxiv.org/abs/1904.04347",
"label": "Random Polynomial Central Limit Theor... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For broad classes of random functions, determine the mean, variance, and limiting distribution of the number of real zeros. | What can we say about its mean, variance, and limiting distribution of this real random variable ? The series of papers by Kac and Littlewood-Offord in the 1940s on this question is the starting point of the theory of random functions. log n ď Nn,ξ ď log2 n. log log n In the proof of this theorem, Littlewood and Offord i... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,340 | OWR-12697684-017 | Expected Real Roots of General Random Polynomials | Determine the expected number $\mathbb{E}N_{n,\xi}$ of real roots for general random polynomials, or more generally for random functions, beyond the Gaussian coefficient case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12697684-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-017",
"literature-status:partially-solved",
"owr-year:2023"
] | Expectation formulas are known for Kac, Weyl, and broad coefficient classes, but no theorem determines the expectation for general random polynomials or arbitrary random functions. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2303.05478",
"label": "Do--Nguyen, Real Roots of Random Polynomials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Determine the expected number $\mathbb{E}N_{n,\xi}$ of real roots for general random polynomials, or more generally for random functions, beyond the Gaussian coefficient case. | Problem 3. Determine the expectation ENn,ξ for general random polynomials or even general random functions. A notable fact here is that Kac’s formula (or more advanced methods on Gauss- ian processes) allows us to obtain a precise answer in the case when ξ is Gaussian. Much less has been known for other variables. Unti... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,341 | OWR-12697684-018 | Enumeration and Sparsity of Growing-$k$ SAT Functions | Determine the asymptotic number of distinct $k$-SAT Boolean functions when $k$ grows with the number $n$ of variables. For which growth rates of $k$ are almost all such functions unate, and what are the corresponding sparse-formula thresholds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 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-12697684-018",
"literature-status:open",
"owr-year:2023"
] | The fixed-k enumeration and unateness results do not resolve the Bollobas--Brightwell regime when k grows with n; the requested growing-k behavior remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2107.09233",
"label": "Dong--Mani--Zhao, Enumerating k-SAT Functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Determine the asymptotic number of distinct $k$-SAT Boolean functions when $k$ grows with the number $n$ of variables. For which growth rates of $k$ are almost all such functions unate, and what are the corresponding sparse-formula thresholds? | What happens when k grows with n? to consider the DNF version.) We call such a function unate if it is monotone after first negating some subset of variables, or equivalently, each variable xi appears only positively (as xi ) or only negatively (as xi ). For fixed k ě 2, an easy argument n shows that the number of unate ... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,342 | OWR-12697684-019 | Reed’s Chromatic-Number Conjecture | Does every graph $G$ satisfy $\chi(G)\leq\left\lceil(\Delta(G)+1+\omega(G))/2\right\rceil$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-019",
"literature-status:open",
"owr-year:2023"
] | The exact record contains only the label Conjecture and no identifiable mathematical assertion; under the stated rule the unresolved or unclear item is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Does every graph $G$ satisfy $\chi(G)\leq\left\lceil(\Delta(G)+1+\omega(G))/2\right\rceil$? | Conjecture. In particular this machinery was key in their proof of the best current bound for the general version of the problem. Typically a graph will have many Mozhan partitions, and the method involves a scheme called a move sequence for exploring the set of all such partitions to find one that is particularly favou... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,343 | OWR-12697684-020 | Ryser–Brualdi–Stein Transversal Conjecture | Does every Latin square of order $n$ have a transversal of size $n-1$, and a full transversal when $n$ is odd? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12697684-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-020",
"literature-status:partially-solved",
"owr-year:2023"
] | Montgomery proves the n-1-transversal conclusion for all sufficiently large orders, but the full Ryser--Brualdi--Stein assertion, including the odd-order transversal case, remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2310.19779",
"label": "Montgomery, Transversals in Latin Squares"
},
{
"url": "https://arxiv.org/abs/2406.19873",
"label": "Montgomery, Latin Square Transversal Sur... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Does every Latin square of order $n$ have a transversal of size $n-1$, and a full transversal when $n$ is odd? | Conjecture 1. To prove Theorem 2, we then use a combination of the semi-random method and the absorption method. We use an implementation of the semi-random method in this setting from work of the author with Pokrovskiy and Sudakov [9], and therefore all the main novelty occurs in our use of absorption. Since its codifi... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,344 | OWR-12697684-021 | Exact Thresholds for Rainbow Matchings in Hypergraphs | How large must $N$ be in terms of $t$ and $r$ to guarantee a rainbow matching of size $t$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-021",
"literature-status:partially-solved",
"owr-year:2023"
] | For fixed uniformity r at least 3 the threshold is known up to constants as Theta of t to the r and the linear conjecture is false, but the exact threshold asked for is not determined. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2212.07580",
"label": "Sharp Bounds for Rainbow Matchings"
},
{
"url": "https://doi.org/10.1112/jlms.70252",
"label": "Sharp Bounds for Rainbow Matchings, JLMS"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | How large must $N$ be in terms of $t$ and $r$ to guarantee a rainbow matching of size $t$? | How large does N need to be (in terms of t and r), such that it is always possible to find a rainbow matching of size t? Nevertheless, it turns out that the conjecture of Glebov–Sudakov–Szabó [10] is actually false: We showed that for any fixed uniformity r ě 3, the functions f pr, tq and F pr, tq are in fact on the or... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,345 | OWR-12697684-022 | Stable Algorithms and Overlap Gaps for Friendly Bisections | For $h>0$, is there a stable polynomial-time algorithm that finds an $h$-friendly bisection of $G(n,1/2)$? Does the overlap-gap property hold for every $h>0$, perhaps by transfer from random regular graphs to Erdős–Rényi graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 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-12697684-022",
"literature-status:open",
"owr-year:2023"
] | The cited FKN algorithm and overlap-gap framework leave the algorithmic stability question open; no primary result found by the checked date settles it. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2105.13337",
"label": "FKN, Friendly Bisections in Random Graphs"
},
{
"url": "https://arxiv.org/abs/2202.10379",
"label": "Overlap Gaps in Random Regular Graphs"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For $h>0$, is there a stable polynomial-time algorithm that finds an $h$-friendly bisection of $G(n,1/2)$? Does the overlap-gap property hold for every $h>0$, perhaps by transfer from random regular graphs to Erdős–Rényi graphs? | Whether the algorithm constructed in [FKN` 21] exhibits such stability remains an interesting open question. The existence of such a translation and in general the presence of the OGP for all h ą 0 is another interesting open question, which we leave for future research. The report passage is retained verbatim as the r... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,346 | OWR-12697684-024 | Chromatic Alternatives from Girth and Local Covers | Does a function $f:\mathbb N^2\to\mathbb N$ exist such that every finite graph $G$ with $\chi(G)\geq f(r,k)$ either has a subgraph of chromatic number at least $k$ and girth greater than $r$, or has an $r$-local cover of chromatic number at least $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-024",
"literature-status:open",
"owr-year:2023"
] | No primary theorem found resolving the stated chromatic and girth alternatives or the existence of f of r and k; the local-covering question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Does a function $f:\mathbb N^2\to\mathbb N$ exist such that every finite graph $G$ with $\chi(G)\geq f(r,k)$ either has a subgraph of chromatic number at least $k$ and girth greater than $r$, or has an $r$-local cover of chromatic number at least $k$? | Is there a function f : N2 Ñ N such that every finite graph G of chromatic number at least f pr, kq satisfies one of the following two conditions: (1) G has a subgraph of chromatic number at least k and girth greater than r; (2) The r-local covering Gr of G has chromatic number at least k. The report passage is retaine... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,347 | OWR-12697684-026 | Additive Dimension of Transpositions | Let $M_n$ be the least integer such that every family of $M_n$ transpositions in $S_n$ contains pairwise distinct transpositions that can be ordered to have product equal to the identity. Determine $M_n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-026",
"literature-status:partially-solved",
"owr-year:2023"
] | The transposition product parameter has lower bound Omega of n log n and current rainbow-cycle methods give a near-matching upper bound, but the exact value and remaining logarithmic factor are open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2309.04460",
"label": "Essentially Tight Bounds for Rainbow Cycles"
},
{
"url": "https://doi.org/10.1112/plms.70044",
"label": "Essentially Tight Bounds for Rainbow... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Let $M_n$ be the least integer such that every family of $M_n$ transpositions in $S_n$ contains pairwise distinct transpositions that can be ordered to have product equal to the identity. Determine $M_n$. | For the theorem above, a known lower bound is Ωpn log nq, and this result addresses a question of Keevash, Mubayi, Sudakov, and Ver- straete [1]. 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,348 | OWR-12697684-027 | Local Count Thresholds for Bounded-Degree Embeddings | Determine the least $f_k(\Delta)$ such that matching all local $k$-uniform homomorphism counts for every graph on at most $f_k(\Delta)$ vertices forces embeddings of all $n$-vertex graphs of maximum degree at most $\Delta$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-027",
"literature-status:open",
"owr-year:2023"
] | The exact dependence f of k and Delta is not known; the embedding theorem records only an Omega of Delta lower bound and gives no matching characterization. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://doi.org/10.1016/j.procs.2021.11.048",
"label": "Allen--Bottcher--Davies--Hng--Skokan, Approximate Blow-up Lemma"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Determine the least $f_k(\Delta)$ such that matching all local $k$-uniform homomorphism counts for every graph on at most $f_k(\Delta)$ vertices forces embeddings of all $n$-vertex graphs of maximum degree at most $\Delta$. | What is fk p∆q? 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,349 | OWR-12697684-028 | Biased Sub-Balanced Slices of Boolean Functions | For every indicator function $f$ on the balanced slice with $\mathbb E f=1/2$, must there be a sub-balanced slice of dimension $\log^*n$, or at least of dimension tending to infinity, on which $\mathbb E f>0.51$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-028",
"literature-status:open",
"owr-year:2023"
] | The proposed sub-balanced-slice strengthening is posed as an open question in the source report, and no primary resolution was found by the checked date. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For every indicator function $f$ on the balanced slice with $\mathbb E f=1/2$, must there be a sub-balanced slice of dimension $\log^*n$, or at least of dimension tending to infinity, on which $\mathbb E f>0.51$? | Can we find examples on a slice? For all indicator functions f on the slice with Ef “ 1\{2, does there exist a sub-balanced slice of dimension log˚ n (or growing) on which Ef ą 0.51?} Jacques Verstraete Let G be a graph of edge-density p P r0, 1s. The positive discrepancy of a graph G is defined by ! ˆ ˙ ) ` |X| disc pGq... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,350 | OWR-12697684-029 | Positive Discrepancy away from Multipartite Densities | For every $\varepsilon>0$, does there exist $a>0$ such that every $n$-vertex graph of density $p$ whose distance from every number $(i-1)/i$ is at least $\varepsilon$ satisfies $\operatorname{disc}^+(G)\geq a\sqrt{p(1-p)}\,n^{3/2}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-029",
"literature-status:open",
"owr-year:2023"
] | No primary result found proving or disproving the stated density-separated positive-discrepancy lower bound; the source conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For every $\varepsilon>0$, does there exist $a>0$ such that every $n$-vertex graph of density $p$ whose distance from every number $(i-1)/i$ is at least $\varepsilon$ satisfies $\operatorname{disc}^+(G)\geq a\sqrt{p(1-p)}\,n^{3/2}$? | We propose the following conjecture: Conjecture 8. Ehud Friedgut The parity set has the property that any subcube is half in the set and half out of the set. However, modulo 3 conditions will only work on sufficiently large subcubes. Can we find examples on a slice? Question 7. A sub-balanced slice of dimension 2k is 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,351 | OWR-12697684-030 | Heavy Cycles in Eulerian Digraphs | Let $D$ be an Eulerian weighted digraph in which the total weight of edges leaving each vertex is at least $1$. Must $D$ contain a directed cycle of weight at least a universal positive constant? What stronger bound follows if $D$ is strongly $2$-connected? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-030",
"literature-status:open",
"owr-year:2023"
] | The general weighted-digraph theorem gives only a vanishing lower bound, and the cited literature does not settle the Eulerian or strongly 2-connected Omega of 1 cycle question. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/1911.07778",
"label": "Knierim--Kupavskii--Mubayi--Verstraete, Heavy Cycles"
},
{
"url": "https://doi.org/10.1016/j.jctb.2020.12.008",
"label": "Heavy Cycles, Journ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Let $D$ be an Eulerian weighted digraph in which the total weight of edges leaving each vertex is at least $1$. Must $D$ contain a directed cycle of weight at least a universal positive constant? What stronger bound follows if $D$ is strongly $2$-connected? | What happens if D is Eulerian? What happens if D is strongly 2-connected? Concretely, if D is Eulerian, is there a cycle of weight Ωp1q? 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,352 | OWR-12697684-031 | Monochromatic Subspaces in Binary Vector Spaces | Let $f(n)$ be the largest number such that every two-coloring of $\mathbb F_2^n\setminus\{0\}$ contains a monochromatic set of $f(n)$ nonzero vectors forming a linear subspace together with $0$. Is $f(n)=O(n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-031",
"literature-status:open",
"owr-year:2023"
] | The specified F2-vector-space Ramsey problem still has only a logarithmic-factor upper bound in the cited record; recent almost-all-group results do not establish f of n equals O of n for every n. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2412.21194",
"label": "Conlon--Fox--Pham--Yepremyan, Random Cayley Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Let $f(n)$ be the largest number such that every two-coloring of $\mathbb F_2^n\setminus\{0\}$ contains a monochromatic set of $f(n)$ nonzero vectors forming a linear subspace together with $0$. Is $f(n)=O(n)$? | Is f pnq “ Opnq? Karim Adiprasito ř Question 12. Given a graph G and C a collection of cycles, let \C\}1 “ \gammaPC |\gamma| be the total length. Given a field F and C, glue in the corresponding 2-disks into the cell complex underlying the graph, and consider the homology over F . Let \alphaF pGq be the minimum \}C\}1 ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,353 | OWR-12697684-032 | Homotopical versus Homological Cycle-Filling Complexity | Over finite connected graphs, is the ratio between the minimum total cycle length needed to attach $2$-cells that kill the fundamental group and the minimum total cycle length needed to kill first homology over $\mathbb F_2$ unbounded? Does this remain true for bounded-degree graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 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-12697684-032",
"literature-status:open",
"owr-year:2023"
] | Known constructions give additive separation between alpha_pi1 and alpha_F2, but no result establishes an unbounded ratio, so the stated question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | Over finite connected graphs, is the ratio between the minimum total cycle length needed to attach $2$-cells that kill the fundamental group and the minimum total cycle length needed to kill first homology over $\mathbb F_2$ unbounded? Does this remain true for bounded-degree graphs? | Is it true that \alpha\pi1 pGq\{\alphaF2 pGq is unbounded?} Jacob Fox This question arises out of current work of Conlon, Fox, Pham, and Yepremyan. Question 11. Let f pnq be the maximum size (number of elements) of a monochro- matic (ignoring 0) linear subspace guaranteed in any 2-coloring of the nonzero elements of Fn... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,354 | OWR-12697684-033 | High-Chromatic Odd-Cycle-Free Graphs with Large Minimum Degree | For fixed $k$, do there exist $n$-vertex graphs containing no odd cycle of length less than $2k+1$, with chromatic number at least four and minimum degree at least $f(k)n$, where $f(k)$ is of order $1/k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-033",
"literature-status:open",
"owr-year:2023"
] | Known constructions are of order 1 over k squared, while minimum-degree theorems force 3-colorability above roughly 1 over 2k; existence of chi at least 4 examples at a constant over k remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://arxiv.org/abs/2302.01875",
"label": "Bottcher--Han--Kohayakawa--Person, Odd-Cycle-Free Graphs"
},
{
"url": "https://doi.org/10.1016/j.ejc.2025.104143",
"label": "Yuan--Peng, Euro... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For fixed $k$, do there exist $n$-vertex graphs containing no odd cycle of length less than $2k+1$, with chromatic number at least four and minimum degree at least $f(k)n$, where $f(k)$ is of order $1/k$? | Julia Böttcher Question 13. Do there exist n-vertex graphs Gn which is tC3 , C5 , . . . , C2k´1 u-free (as subgraphs) with chromatic number χpGn q ě 4 and minimum degree \deltapGn q ě f pkqn where f pkq is at least linear in 1\{k? It is known for f pkq “ 3\{p2k 2 `k`1q and it is known to be false for f pkq “ 1\{p2kq w... | 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,355 | OWR-12697684-034 | Equal Products from Disjoint Subsets of Finite Groups | For every $k\geq2$, does there exist $c(k)$ such that every subset $S$ of a finite group $G$ of order $n$, with $|S|\geq c(k)\log n$, contains pairwise disjoint subsets $T_1,\ldots,T_k$ that can each be ordered to give the same product? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89](https://doi.org/10.4171/owr/2023/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697684-034",
"literature-status:open",
"owr-year:2023"
] | The requested logarithmic threshold is not known even for general abelian groups; sunflower bounds give an additional log-logarithmic loss, so the assertion remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/1",
"label": "Oberwolfach Reports 2023/1"
},
{
"url": "https://doi.org/10.4007/annals.2021.194.3.5",
"label": "Alweiss--Lovett--Wu--Zhang, Improved Sunflower Bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/1 | null | null | null | For every $k\geq2$, does there exist $c(k)$ such that every subset $S$ of a finite group $G$ of order $n$, with $|S|\geq c(k)\log n$, contains pairwise disjoint subsets $T_1,\ldots,T_k$ that can each be ordered to give the same product? | For every k ě 2 does there exist cpkq so that for all groups G with |G| “ n and S Ď G with |S| ě cpkq log n, there are T1 , . . . , Tk Ď S pairwise disjoint and an ordering of each Ti so that each product is the same? 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 | Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/1, pp. 5--89 |
30,005,356 | OWR-12697685-001 | Definable Endomorphisms of Generic Multiplicative Fields | Is every definable endomorphism of a generic multiplicative field $(K,\sigma)$ contained in $\mathbb{Z}[\sigma]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-001",
"literature-status:open",
"owr-year:2023"
] | Mutchnik disproves universal forking existence in NSOP1 theories, so the first sentence is outdated; the bundled question about all definable endomorphisms of the generic multiplicative field lying in Z of the endomorphism remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "Oberwolfach Reports 2023/2"
},
{
"url": "https://arxiv.org/abs/2407.13082",
"label": "Mutchnik, An NSOP1 Theory without the Existence Axiom"
},
{
"url": "https://doi.org/10.1016/j.apal.2025.103554",
"label": "d'Elbee, Generic M... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | Is every definable endomorphism of a generic multiplicative field $(K,\sigma)$ contained in $\mathbb{Z}[\sigma]$? | an open problem whether the existence axiom always holds for forking in NSOP1 theories. The question of whether every deûnable endomorphism of (K, ») is in Z[»] was raised by the author. 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 | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,357 | OWR-12697685-005 | Very Ample Internal Strongly Minimal Sets | Is there a very ample strongly minimal set internal to $M$; more specifically, is there a definable equivalence relation $E$ on $M$ such that $M/E$ is very ample? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-005",
"literature-status:open",
"owr-year:2023"
] | The report explicitly leaves the internal very-ampleness question open and proves only special cases; no later primary source located by the check date resolves the general question. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "Oberwolfach report, stated open question"
},
{
"url": "https://doi.org/10.2140/mt.2024.3.213",
"label": "Castle--Hasson--Ye, related classification results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | Is there a very ample strongly minimal set internal to $M$; more specifically, is there a definable equivalence relation $E$ on $M$ such that $M/E$ is very ample? | Is there a very ample strongly minimal set internal to M ? More speciûcally: is there a deûnable equivalence relation E on M such that M/E is very ample. With all of the above we can answer Martin9s question: Theorem. Let K be an algebraically closed ûeld, (G, \cdot) a divisible 1-dimensional algebraic group over K. Le... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,358 | OWR-12697685-006 | Elementary Extensions of Definable Group Dynamics | How does the definable topological dynamics of a group $G$ change under elementary extension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-006",
"literature-status:open",
"owr-year:2023"
] | The question is broad; later work gives model-independence or homomorphism results only under extra hypotheses and also gives counterexamples to the general Ellis-group conjecture, so no general resolution is established. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.apal.2021.103010",
"label": "Topological dynamics and NIP fields"
},
{
"url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D86369293DF8... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | How does the definable topological dynamics of a group $G$ change under elementary extension? | How does the (deûnable) topological dynamics of a group G change when we extend the group elementarily? Ellis groups Ludomir Newelski (joint work with Adam Malinowski) When A is d-closed, then (S(A), 7) is a left-continuous semigroup isomorphic to the Ellis semigroup E(S(A)). We work in the following combinatorial set-... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,359 | OWR-12697685-007 | Elementary Equivalence of Hyperbolic Groups with Torsion | Are two hyperbolic groups $\forall\exists$-equivalent if and only if they are elementarily equivalent, including in the presence of torsion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-007",
"literature-status:open",
"owr-year:2023"
] | Sela classifies torsion-free hyperbolic groups, while the all-hyperbolic-group conjecture including torsion remains unsettled; later work preserves hyperbolicity under elementary equivalence but does not give the claimed full classification. | [
{
"url": "https://doi.org/10.1112/plms/pdn052",
"label": "Sela, torsion-free hyperbolic groups"
},
{
"url": "https://doi.org/10.2140/gt.2020.24.1075",
"label": "André, elementary equivalence and hyperbolicity"
},
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "original Oberw... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | Are two hyperbolic groups $\forall\exists$-equivalent if and only if they are elementarily equivalent, including in the presence of torsion? | free product G = H 7 Fn (for some n g 0) or a hyperbolic tower over H, Ë is true in G if and only if \times is true in G. Since H and G are "\#-equivalent (see [9]), they are elementarily equivalent. In particular, it follows that two torsion-free hy- perbolic groups are "\#-equivalent if and only if they are elementar... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,360 | OWR-12697685-008 | Stratification by Canonical Definable Partitions | Do the canonical definable pieces $S_d$ form a stratification of $X$ in a classical sense? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-008",
"literature-status:open",
"owr-year:2023"
] | The record asks a general stratification question without specifying the required classical sense; no theorem resolving that exact formulation was identified, so the unclear claim is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | Do the canonical definable pieces $S_d$ form a stratification of $X$ in a classical sense? | Now that we have our canonical partition of X into deûnable sets Sd , a natural question is: do these sets form a stratiûcation of X, in some of the classical senses? Model Theory: Combinatorics, Groups, Valued Fields and Neostability 117 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,361 | OWR-12697685-010 | NIP Conjecture for k-Dependent Fields | Is every $k$-dependent field, whether pure or equipped with valuation, derivation, or similar structure, NIP? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-010",
"literature-status:open",
"owr-year:2023"
] | The conjecture that every k-dependent field is NIP remains open; current work supplies structural consequences and partial results, but no proof or counterexample to the general statement. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "original Oberwolfach report"
},
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/on-ndependent-groups-and-fields-ii/0C88DB70DC29AAD54EFE858F1679D011",
"label": "Chernikov--Hempel, n-dependent fields II"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | Is every $k$-dependent field, whether pure or equipped with valuation, derivation, or similar structure, NIP? | Conjecture 1. If K is an k-dependent field (pure, or with valuation, derivation, etc.), then K is NIP. There is some mounting evidence for this conjecture: k-dependent ûelds are Artin-Schreier closed ([7], generalizing Kaplan-Scanlon-Wagner for k = 1), valued ûelds of positive characteristic are Henselian ([2], general... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,362 | OWR-12697685-011 | Structure of k-Dependent Fields | What structural restrictions follow for a $k$-dependent field, and in particular must every such field be NIP? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149](https://doi.org/10.4171/owr/2023/2)
## Literature revi... | 3 | open | null | 2,023 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697685-011",
"literature-status:open",
"owr-year:2023"
] | The extraction repeats a fragment of the k-dependent-field discussion and omits a complete claim; the report contains only related theorems, so the exact problem is unresolved and unclear. | [
{
"url": "https://doi.org/10.4171/owr/2023/2",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/2 | null | null | null | What structural restrictions follow for a $k$-dependent field, and in particular must every such field be NIP? | There is some mounting evidence for this conjecture: k-dependent ûelds are Artin-Schreier closed ([7], generalizing Kaplan-Scanlon-Wagner for k = 1), valued ûelds of positive characteristic are Henselian ([2], generalizing Johnson for k = 1), the question for valued ûelds reduces to pure ûelds (Boissonneau). A key gene... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Model Theory: Combinatorics, Groups, Valued Fields and Neostability (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/2, pp. 91--149 |
30,005,363 | OWR-12697686-001 | Workshop Contents Listing for Low-Dimensional Topology | conjecture . . . . . . . . . . . . . . 160 Sarah Blackwell (joint with Robion Kirby, Michael Klug, Vincent Longo, Benjamin Ruppik) How not to study low-dimensional topology . . . . . . . . . . . . . . . . . . . . . . . . . 163 Nir Lazarovich (joint with Yoav Moriah, Tali Pinsky) Highly twisted diagrams . . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-001",
"literature-status:open",
"owr-year:2023"
] | The extracted value is only a fragment ending in the word conjecture and contains no identifiable mathematical assertion; it cannot be verified as solved or false. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | null | conjecture . . . . . . . . . . . . . . 160 Sarah Blackwell (joint with Robion Kirby, Michael Klug, Vincent Longo, Benjamin Ruppik) How not to study low-dimensional topology . . . . . . . . . . . . . . . . . . . . . . . . . 163 Nir Lazarovich (joint with Yoav Moriah, Tali Pinsky) Highly twisted diagrams . . . . . . . . ... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,364 | OWR-12697686-002 | Trisection Distance Bounds from Nonseparating Hypersurfaces | Suppose a smooth $4$-manifold $X$ contains a nonseparating $3$-manifold $Y$, and $\Sigma$ is the central surface of a trisection of $X$. Can the topology of $Y$ and the induced loop in the three disk sets be used to bound the trisection distance $d(\Sigma)$ from above? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-002",
"literature-status:open",
"owr-year:2023"
] | The report presents this as Problem 4 after defining trisection distance; no later primary result located supplies the requested general upper bound in the stated setting. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1806.04870",
"label": "Koenig, 3-manifolds lying in trisected 4-manifolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | Suppose a smooth $4$-manifold $X$ contains a nonseparating $3$-manifold $Y$, and $\Sigma$ is the central surface of a trisection of $X$. Can the topology of $Y$ and the induced loop in the three disk sets be used to bound the trisection distance $d(\Sigma)$ from above? | Problem 4. Suppose that X is a smooth 4-manifold containing a non-separating 3-manifold Y , and let Σ be the central surface of a trisection of X. Use the topology of Y and the induced loop in D0 Y D1 Y D2 to give an upper bound on dpΣq. The proof uses many ingredients of the 3-dimensional argument, with the ad- dition... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,365 | OWR-12697686-003 | Reducibility of Trisections with Nonseparating Three Spheres | If a smooth $4$-manifold $X$ contains a nonseparating $3$-sphere, is every trisection of $X$ reducible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-003",
"literature-status:open",
"owr-year:2023"
] | The report states this as Conjecture 5; related reducibility results are known, but no proof or counterexample for the general non-separating 3-sphere claim was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2503.04607",
"label": "weakly reducible genus-three trisections"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | If a smooth $4$-manifold $X$ contains a nonseparating $3$-sphere, is every trisection of $X$ reducible? | Conjecture 5. If X is a smooth 4-manifold containing a non-separating 3-sphere, then every trisection of X is reducible. Problem 4. Suppose that X is a smooth 4-manifold containing a non-separating 3-manifold Y , and let Σ be the central surface of a trisection of X. Use the topology of Y and the induced loop in D0 Y D... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,366 | OWR-12697686-004 | Background on Circle Actions and the L-Space Conjecture | Throughout we take M to be a closed, connected, oriented, irreducible rational homology 3-sphere. In this talk we discussed how Homeo` pS 1 q-representations of \pi1 pM q arising from foliations and flows on M can be used to verify the left-orderability of \pi1 pM q in a number of interesting situations. We also discus... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is introductory exposition rather than a standalone problem; the adjacent records represent) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-004",
"literature-status:open",
"owr-year:2023"
] | The record is background on circle-homeomorphism representations and the L-space conjecture, not a complete question; no exact mathematical claim can be assessed, so it remains open under the unclear-claim rule. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | null | Throughout we take M to be a closed, connected, oriented, irreducible rational homology 3-sphere. In this talk we discussed how Homeo` pS 1 q-representations of \pi1 pM q arising from foliations and flows on M can be used to verify the left-orderability of \pi1 pM q in a number of interesting situations. We also discus... | unrecoverable | The official report confirms that the extraction is introductory exposition rather than a standalone problem; the adjacent records represent the specific conjectures. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,367 | OWR-12697686-005 | Ozsváth–Szabó Conjecture for Integer Homology Spheres | If $M$ is an integer homology $3$-sphere, is $M$ a non-L-space if and only if it is neither $S^3$ nor the Poincaré homology sphere $\Sigma(2,3,5)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-005",
"literature-status:open",
"owr-year:2023"
] | The Ozsvath--Szabo claim remains a conjecture for irreducible integer homology spheres; substantial families, including graph and toroidal cases, are proved, but the general statement is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1112/topo.12275",
"label": "Lidman--Pinzon-Caicedo--Zentner, toroidal homology spheres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | If $M$ is an integer homology $3$-sphere, is $M$ a non-L-space if and only if it is neither $S^3$ nor the Poincaré homology sphere $\Sigma(2,3,5)$? | Conjecture (Ozsváth-Szabó). If M is an integer homology 3-sphere then M is N LS if and only if M is neither S 3 nor the Poincaré homology sphere Σp2, 3, 5q. This is known to hold in many cases, for instance Eftekhary showed that M is N LS if it is toroidal ([Eft]). Our first result uses Thurston’s universal circle r... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,368 | OWR-12697686-006 | Coincidence of Detected Slopes for Knot Manifolds | For every knot manifold, do the sets of left-orderability-detected, cooriented-taut-foliation-detected, and non-L-space-detected boundary slopes coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-006",
"literature-status:open",
"owr-year:2023"
] | The extracted record says only that a following conjecture is related to the L-space conjecture and omits the conjecture itself; the exact claim is therefore unclear and classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | For every knot manifold, do the sets of left-orderability-detected, cooriented-taut-foliation-detected, and non-L-space-detected boundary slopes coincide? | The following conjecture is closely related to the L-space conjecture for toroidal manifolds. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,369 | OWR-12697686-007 | Concordance Versus Isotopy for Positive Knots | For positive knots, does concordance imply isotopy? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-007",
"literature-status:open",
"owr-year:2023"
] | Primary discussions still describe concordance-implies-isotopy for positive knots as open; existing results give finiteness or special-family theorems rather than a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1503.01946",
"label": "Baader--Dehornoy--Liechti, positive knots"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | For positive knots, does concordance imply isotopy? | It is an open question whether concordance implies isotopy for the set of positive knots. 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 | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,370 | OWR-12697686-008 | Weeks Manifold Realization of the Margulis Constant | Is the three-dimensional Margulis constant $\varepsilon_3$ uniquely realized by the Weeks manifold $M_W$, with $\varepsilon_3=\mu(M_W)\approx 0.774$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-008",
"literature-status:open",
"owr-year:2023"
] | The general three-dimensional Margulis constant and unique Weeks realization remain open; the 2023 project proves only the symmetric analogue. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://bpb-us-e2.wpmucdn.com/websites.umass.edu/dist/b/22144/files/2026/04/K3-problem-list-watermarked.pdf",
"label": "K3 problem list, current status"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | Is the three-dimensional Margulis constant $\varepsilon_3$ uniquely realized by the Weeks manifold $M_W$, with $\varepsilon_3=\mu(M_W)\approx 0.774$? | Conjecture 1. The 3–dimensional Margulis constant ǫ3 is uniquely realized by the Weeks manifold MW . In particular, ǫ3 “ µpMW q “ 0.774 . . .. The method of attack is to first bound the possibilities to a compact domain, and then rigorously analyze that domain by computer. Parameter methods. Over the past 25 years, mat... | 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 | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,371 | OWR-12697686-011 | Genus-Free Intersection Bounds for Embedded Graphs | Can two graphs $G_1$ and $G_2$ embedded on a common surface be redrawn with at most $O(|E(G_1)||E(G_2)|)$ intersections, with a constant independent of the genus? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-011",
"literature-status:open",
"owr-year:2023"
] | The extracted statement is an incomplete tail of a conjectural asymptotic bound; the surrounding report gives a theorem for a special canonical-loop algorithm, not the omitted conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | Can two graphs $G_1$ and $G_2$ embedded on a common surface be redrawn with at most $O(|E(G_1)||E(G_2)|)$ intersections, with a constant independent of the genus? | by Op|EpG1 q||EpG2 q|q, where the constant in the Op¨q is independent of the genus. The best known bound on this general problem is Opg|EpG1 q||EpG2 q|q, also due to Negami [12]. See also [1] and [14] for more results around this conjecture. In this talk, I first presented a recent result obtained with Niloufar Fuladi ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,372 | OWR-12697686-012 | Smooth Isotopy of Boundary Twists on Spin Four Manifolds | For which closed spin simply connected smooth $4$-manifolds $X$ is the boundary twist $t_X$ smoothly isotopic to the identity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-012",
"literature-status:open",
"owr-year:2023"
] | The question remains open in general for closed spin simply connected smooth 4-manifolds; known results include smooth triviality in the non-spin case and nontriviality for K3 and related connected sums. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://www.maths.gla.ac.uk/~mpowell/pseudoisotopy.pdf",
"label": "Powell, mapping class groups of simply connected 4-manifolds"
},
{
"url": "https://doi.org/10.2140/gt.2023.27.1987",
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | For which closed spin simply connected smooth $4$-manifolds $X$ is the boundary twist $t_X$ smoothly isotopic to the identity? | Question 3. For which closed, spin, simply connected, smooth manifolds X is tX smoothly isotopic to the identity? Homeomorphisms not restricting to the identity on the boundary. We consider the implications of our results when we relax the assumption that home- omorphisms must fix the boundary pointwise. Let X be a com... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,373 | OWR-12697686-013 | Slice–Ribbon Conjecture | Is every smoothly slice knot a ribbon knot? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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 of canonical problem TOP-004 | [
"TOP-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-013",
"literature-status:open",
"owr-year:2023"
] | The Slice--Ribbon Conjecture remains open as of the check date; recent work proves many special cases and records evidence in both directions but no general counterexample or proof. | [
{
"url": "https://doi.org/10.1017/S030500412400029X",
"label": "Boden--et al., ribbon knotted surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | Is every smoothly slice knot a ribbon knot? | I believe the common consensus in the 4-dimensional topology community is that the Slice–Ribbon Conjecture is likely false. Slice obstructions from genus bounds in definite 4-manifolds Maggie Miller (joint work with Paolo Aceto, Nickolas A. Castro, JungHwan Park, András Stipsicz) | 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 | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,374 | OWR-12697686-014 | Background on Cable Sliceness and Genus Bounds | Conjecture. Instead of summarizing the Floer-theoretic techniques of Dai–Kang–Mallick– Park–Stoffregen, I give an alternate argument making use of minimum-genus bounds for integral second homology classes in definite 4-manifolds coming from gauge theory. The key fact in this particular proof is due to Bryan [3]. Theore... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is explanatory prose surrounding a proved argument, not a separately stated open problem. N) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-014",
"literature-status:open",
"owr-year:2023"
] | The record contains only the word conjecture followed by a proof of a neighboring cable non-sliceness theorem, so the extracted claim is not identifiable and is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | null | Conjecture. Instead of summarizing the Floer-theoretic techniques of Dai–Kang–Mallick– Park–Stoffregen, I give an alternate argument making use of minimum-genus bounds for integral second homology classes in definite 4-manifolds coming from gauge theory. The key fact in this particular proof is due to Bryan [3]. Theore... | unrecoverable | The official report confirms that the extraction is explanatory prose surrounding a proved argument, not a separately stated open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,375 | OWR-12697686-015 | Topological Sliceness of the Figure-Eight Cable | Is the $(2,1)$-cable of the figure-eight knot topologically slice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 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-12697686-015",
"literature-status:open",
"owr-year:2023"
] | The cable is proved not smoothly slice, but the report explicitly says its topological sliceness is not obstructed by available methods and leaves the question open. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1908.03760",
"label": "Ray, topological slice genus of satellite knots"
},
{
"url": "https://doi.org/10.1007/s00222-024-01286-w",
"label": "Dai--Kang--Mallick--Par... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | Is the $(2,1)$-cable of the figure-eight knot topologically slice? | We end with some remaining open questions. Is the (2,1)-cable of the figure eight knot topologically slice? introduce negative twists to the cross-sections of A. We perform further isotopy to see that the other boundary C1 of A is the (mirror image of, if we are careful with orientations) torus knot T p2, ´19q. Note th... | 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 | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,376 | OWR-12697686-016 | Minimum Genus Connected Sums of Complex Plane Curves | For positive integers $n,m$, is the connected sum of smooth complex plane curves of degrees $n$ and $m$, embedded in the two summands of $\mathbb{CP}^2\#\mathbb{CP}^2$, a smoothly minimum-genus representative of its homology class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,023 | 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-12697686-016",
"literature-status:partially-solved",
"owr-year:2023"
] | Ait Nouh disproved Lawson's general minimum-genus formula with infinite counterexample families, while the report's narrower degree-2n and degree-6n subfamily and related positive cases are not completely resolved. | [
{
"url": "https://doi.org/10.2140/agt.2014.14.671",
"label": "Ait Nouh, minimal genus in CP2 connected sum CP2"
},
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | For positive integers $n,m$, is the connected sum of smooth complex plane curves of degrees $n$ and $m$, embedded in the two summands of $\mathbb{CP}^2\#\mathbb{CP}^2$, a smoothly minimum-genus representative of its homology class? | surfaces of degrees 2n, 6n in either summand, has genus p2n ´ 1qp2n ´ 2q p6n ´ 1qp6n ´ 2q ` “ 2n2 ´3n`1`18n2 ´9n`1 “ 20n2 ´12n`2. 2 2 This prompts the following question. Question 8. For n ą 1, is the connected sum of complex surfaces of degrees 2n and 6n in two copies of CP2 a smoothly minimum-genus surface in CP2 \#C... | 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 | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,377 | OWR-12697686-017 | Incomplete Slice-Missing-Slice-Disc Lead-In | Problem 3. (Slice missing slice disc problem). The knot K Ă S 1 ˆS 2 “ BS 1 ˆB 3 shown in Figure 1 bounds two obvious ribbon discs D1 and D2 such that the simple 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:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is the first half of a figure-dependent problem and is not independently self-contained. N) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-017",
"literature-status:open",
"owr-year:2023"
] | The extracted problem is truncated before its actual condition or question; current literature on slice and ribbon discs in S1 times S2 does not identify a resolution of this exact fragment, so it is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1112/jlms.12125",
"label": "Davis--Nagel--Park--Ray, concordance in S1 times S2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | null | Problem 3. (Slice missing slice disc problem). The knot K Ă S 1 ˆS 2 “ BS 1 ˆB 3 shown in Figure 1 bounds two obvious ribbon discs D1 and D2 such that the simple The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is the first half of a figure-dependent problem and is not independently self-contained. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,378 | OWR-12697686-018 | Figure-Dependent Slice Curves in Disc Complements | Is it true that for any smooth disc D bounded by K, one of \alpha or \beta slices in the complement of D? 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:** [Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213](https://doi.org/10.4171/owr/2023/3)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the knot and the curves in this question are defined only by a figure absent from the dataset, so a self-c) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697686-018",
"literature-status:open",
"owr-year:2023"
] | The slice missing slice disc question is still posed as an open problem; Gabai's related constructions and the Oberwolfach report provide context but no proof or counterexample. | [
{
"url": "https://doi.org/10.4171/owr/2023/3",
"label": "Oberwolfach Report 3\\slash 2023"
},
{
"url": "https://arxiv.org/abs/1912.09029",
"label": "Gabai, Knotted 3-balls in S4"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/3 | null | null | null | null | Is it true that for any smooth disc D bounded by K, one of \alpha or \beta slices in the complement of D? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that the knot and the curves in this question are defined only by a figure absent from the dataset, so a self-contained text-only formulation cannot be certified. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/3, pp. 151--213 |
30,005,379 | OWR-12697687-001 | Slice-Genus Bounds for Homogeneous Braid Quasimorphisms | For every homogeneous quasimorphism $f:B_n\to\mathbb R$, do constants $A,C\in\mathbb R$ exist such that $|f(\beta)|\leq A\chi_4(\widehat\beta)+C$ for every braid $\beta\in B_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,023 | 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-12697687-001",
"literature-status:partially-solved",
"owr-year:2023"
] | The universal quasimorphism conjecture remains unresolved, but Feller proves the required affine slice-genus bound for the fractional Dehn twist coefficient. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://doi.org/10.1017/S1474748024000276",
"label": "Feller, Slice-Bennequin inequality for FDTC"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | For every homogeneous quasimorphism $f:B_n\to\mathbb R$, do constants $A,C\in\mathbb R$ exist such that $|f(\beta)|\leq A\chi_4(\widehat\beta)+C$ for every braid $\beta\in B_n$? | hqm f : Bn \to R, there exist constants A, C \in R such Conjecture. For every b that |f (\beta)| \leq Aχ4 \beta + C for all \beta \in Bn . We answer the conjecture for the fractional Dehn twist coeeficient \omega : Bn \to R, which is a hqm with many interesting relations to low-dimensional topology (knots, 3-manifolds,... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,380 | OWR-12697687-003 | Lipschitz Concordance Homomorphisms for Braid Quasimorphisms | Does there exist a one-Lipschitz concordance homomorphism $I$ such that the braid quasimorphism $f$ is a real scalar multiple of $I$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,023 | 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-12697687-003",
"literature-status:open",
"owr-year:2023"
] | The existence of a single 1-Lipschitz concordance homomorphism whose homogenization generates every such braid quasimorphism is stated as a question and no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://doi.org/10.1017/S1474748024000276",
"label": "Feller, Slice-Bennequin inequality for FDTC"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | Does there exist a one-Lipschitz concordance homomorphism $I$ such that the braid quasimorphism $f$ is a real scalar multiple of $I$? | Does there exist a 1-Lipschitz concordance e homomorphism I and r \in R such that f = rI? This theorem in particular answers [HKK+ 20, Question 1.6]. It turns out that both the slice-Bennequin inequality and the theorem can be proven by realizing the involved hqms (wr and \omega, respectively) as the homogenization of ... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,381 | OWR-12697687-004 | Collapse and Involutions in the Khovanov-Floer Spectral Sequence | For which knots does the involutive Khovanov–Floer spectral sequence collapse immediately, and what does its collapse page signify? When can it determine the involutive Heegaard Floer homology of the branched double cover? Does $\widetilde{BN}$ arise from a nontrivial homotopy involution of the Khovanov complex, and wh... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,023 | 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-12697687-004",
"literature-status:open",
"owr-year:2023"
] | The involutive Khovanov-Heegaard Floer spectral sequence is constructed and collapses for quasi-alternating knots, but the listed general collapse, page, functoriality, and chain-involution questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2305.07172",
"label": "Alishahi, Truong, and Zhang, Involutive branched-cover spectral sequence"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | For which knots does the involutive Khovanov–Floer spectral sequence collapse immediately, and what does its collapse page signify? When can it determine the involutive Heegaard Floer homology of the branched double cover? Does $\widetilde{BN}$ arise from a nontrivial homotopy involution of the Khovanov complex, and wh... | We also have the following questions: • Is there a (describable) larger class of knots for which the spectral sequence collapses immediately? • What is the significance of the page of the spectral sequence on which it collapses? • In what situations can this spectral sequence be used to deduce information about the inv... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,382 | OWR-12697687-005 | Concordance Homomorphisms from Knot Floer Modules | How can one extract a concordance homomorphism directly from the knot Floer module $J\cdot K$ without first tensoring with a simpler module? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,023 | 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-12697687-005",
"literature-status:open",
"owr-year:2023"
] | The report describes substantial obstacles from non-PID indecomposable complexes and presents extraction of a direct concordance homomorphism as an unresolved research question. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2202.00445",
"label": "Schuetz, Integral Rasmussen invariant"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | How can one extract a concordance homomorphism directly from the knot Floer module $J\cdot K$ without first tensoring with a simpler module? | How can one extract a concordance homomorphism from J \cdot K without tensoring with a simpler module first? 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,383 | OWR-12697687-006 | Isomorphism Type of the Khovanov-Complex Concordance Group | Determine the isomorphism type of the abelian group $G$ formed by equivalence classes of the graded Khovanov chain complexes $\llbracket K\rrbracket$ under tensor product. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,023 | 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-12697687-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The group G is established and its structure is constrained by a surjection onto an infinite-rank free abelian group with infinitely generated kernel, but its full isomorphism type is not determined. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2202.00445",
"label": "Schuetz, Integral Rasmussen invariant"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | Determine the isomorphism type of the abelian group $G$ formed by equivalence classes of the graded Khovanov chain complexes $\llbracket K\rrbracket$ under tensor product. | What can one say about the isomorphism type of G? 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,384 | OWR-12697687-007 | Homeomorphism Classification of Compact Oriented Four-Manifolds | How can one try to decide if two 4-manifolds M and N are home- omorphic? In what follows, manifolds are assumed to be compact, connected and oriented. We work in the topological category unless stated otherwise. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,023 | 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 extracted sentence is an expository heading that is immediately followed by the modified-surgery strategy; it is not posed as a standalo) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697687-007",
"literature-status:open",
"owr-year:2023"
] | Stable surgery and homotopy equivalence give useful decision procedures in restricted settings, but no general classification or homeomorphism test for arbitrary compact oriented 4-manifolds is known. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2109.00654",
"label": "Conway, Crowley, Powell, and Sixt, Large homotopy stable classes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | null | How can one try to decide if two 4-manifolds M and N are home- omorphic? In what follows, manifolds are assumed to be compact, connected and oriented. We work in the topological category unless stated otherwise. | unrecoverable | The extracted sentence is an expository heading that is immediately followed by the modified-surgery strategy; it is not posed as a standalone open classification problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,385 | OWR-12697687-008 | Cancellation and Fixed-Form Stable Classes of Manifolds | Can boundaries of thickened even-dimensional complexes be used systematically to produce manifolds with arbitrarily large fixed-form homotopy stable class $\mathcal S_{\lambda}^{\mathrm{st},h}(M)$? For which fundamental groups is $\mathcal S_{\lambda}^{\mathrm{st},h}(M)$ trivial, finite, or infinite, particularly for c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,023 | 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-12697687-008",
"literature-status:partially-solved",
"owr-year:2023"
] | Cancellation with fixed equivariant form is proved for several fundamental groups and large stable classes are constructed in higher dimensions and for 4-manifolds with boundary, while the closed 4-dimensional case and the general fundamental-group questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2210.00927",
"label": "Conway, Crowley, and Powell, Infinite homotopy stable class"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | Can boundaries of thickened even-dimensional complexes be used systematically to produce manifolds with arbitrarily large fixed-form homotopy stable class $\mathcal S_{\lambda}^{\mathrm{st},h}(M)$? For which fundamental groups is $\mathcal S_{\lambda}^{\mathrm{st},h}(M)$ trivial, finite, or infinite, particularly for c... | What about the cancellation aspect of the modified surgery approach? Some questions now arise: can one systematise the Kreck-Schafer construction to produce man- ifolds with larger S\lambdast,h (M )? Can one get a sense of the fundamental groups for which S\lambdast,h (M ) is trivial? finite? infinite? Statement of res... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,386 | OWR-12697687-009 | Characterising and Non-Characterising Slopes of Knots | Given a knot $K\subset S^3$, classify all of its characterizing and noncharacterizing Dehn-surgery slopes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,023 | 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-12697687-009",
"literature-status:partially-solved",
"owr-year:2023"
] | Characterising and non-characterising slopes are known in many families, and Sorya proves sufficiently large-denominator slopes characterising for every knot, but a complete classification for each knot is not known. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.109746",
"label": "Sorya, Characterizing slopes for satellite knots"
},
{
"url": "https://arxiv.org/abs/2307.00739",
"label": "Sorya, Characterizing slopes for satellite knots preprint"
},
{
"url": "https://doi.org/10.4171/owr/2023/4",
"la... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | Given a knot $K\subset S^3$, classify all of its characterizing and noncharacterizing Dehn-surgery slopes. | Question 3. Given a knot K \subset S3 , can we classify all of its characterising and non-characterising slopes? Non-characterising slopes. There are many knots with non-characterising slopes. Brakes suggested a method of constructing these using the idea of gluing together a pair of knot complements [3]; this is reali... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,387 | OWR-12697687-012 | Cable Torsion and Sliceness of Knots | Is the $(p,q)$-cable of a knot $K$ torsion in the knot concordance group if and only if $K$ is slice and $|q|=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,023 | 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-12697687-012",
"literature-status:partially-solved",
"owr-year:2023"
] | The cable-torsion conjecture is not settled; Kang and Park prove that a nontrivial homomorphism detects half of the torsion knots and forces infinite order for broad families of odd,1 cables. | [
{
"url": "https://arxiv.org/abs/2207.11870",
"label": "Kang and Park, Torsion in the knot concordance group and cabling"
},
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | Is the $(p,q)$-cable of a knot $K$ torsion in the knot concordance group if and only if $K$ is slice and $|q|=1$? | Given a knot K and relatively prime integers p, q, one can consider the cabled knot Kp,q . When K is slice and q = 1, then it is clear that Kp,q is also slice. Miyazaki asked if the converse of this fact also holds. In fact, we go one step further and focus on the following stronger conjecture. Involutive knot Floer ho... | 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,388 | OWR-12697687-013 | Equality of Involutive and Arf Knot Invariants | For every torsion knot $K$ in the smooth concordance group, is $A(K)=\operatorname{Arf}(K)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259](https://doi.org/10.4171/owr/2023/4)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,023 | 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-12697687-013",
"literature-status:open",
"owr-year:2023"
] | For torsion knots, equality of the involutive invariant A and the Arf invariant is explicitly left as Conjecture 4; no proof or counterexample was located. | [
{
"url": "https://arxiv.org/abs/2207.11870",
"label": "Kang and Park, Torsion in the knot concordance group and cabling"
},
{
"url": "https://doi.org/10.4171/owr/2023/4",
"label": "Oberwolfach Report 4\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/4 | null | null | null | For every torsion knot $K$ in the smooth concordance group, is $A(K)=\operatorname{Arf}(K)$? | It is a very interesting question whether the invariant A takes the same value as the Arf invariant, so we leave this as a 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 | Morphisms in Low Dimensions (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/4, pp. 215--259 |
30,005,389 | OWR-12697688-002 | Middle-Degree Concentration of Non-Eisenstein Cohomology | If $\mathfrak m$ is non-Eisenstein, meaning $\overline\rho_{\mathfrak m}$ is absolutely irreducible, prove that $H^*(X_K(\mathbb C),\mathbb F_\ell)_{\mathfrak m}$ is concentrated in the middle degree $d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Middle-degree concentration is proved in important generic Hilbert-modular and related cases, including non-solvable residual image hypotheses, but the general conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2107.10081",
"label": "Caraiani and Tamiozzo, Hilbert modular varieties with torsion coefficients"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | If $\mathfrak m$ is non-Eisenstein, meaning $\overline\rho_{\mathfrak m}$ is absolutely irreducible, prove that $H^*(X_K(\mathbb C),\mathbb F_\ell)_{\mathfrak m}$ is concentrated in the middle degree $d$. | Conjecture 1. If m is non-Eisenstein, i.e. ρ̄m is (absolutely) irreducible, then the localisation H ∗ (XK (C), Fℓ )m is concentrated in the middle degree d. This is a special case of a general folkore conjecture on the cohomology of locally symmetric spaces, with many potential applications to the Langlands program. Ho... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,390 | OWR-12697688-003 | Generalized Ihara Lemma for Locally Symmetric Spaces | If $\mathfrak m$ is non-Eisenstein, prove that $\pi_{1*}+\pi_{2*}:H^d(X_K,\mathbb F_\ell)_{\mathfrak m}^{\oplus 2}\to H^d(X_{K_0(\mathfrak p)},\mathbb F_\ell)_{\mathfrak m}$ is injective. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-003",
"literature-status:partially-solved",
"owr-year:2023"
] | The generalized Ihara lemma is proved in dimension zero, dimension one under hypotheses, and several higher-dimensional Fontaine-Laffaille or large-image cases, but not in the full stated generality. | [
{
"url": "https://arxiv.org/abs/math/0503134",
"label": "Manning and Shotton, Ihara lemma for Hilbert modular varieties"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | If $\mathfrak m$ is non-Eisenstein, prove that $\pi_{1*}+\pi_{2*}:H^d(X_K,\mathbb F_\ell)_{\mathfrak m}^{\oplus 2}\to H^d(X_{K_0(\mathfrak p)},\mathbb F_\ell)_{\mathfrak m}$ is injective. | Conjecture 2. If m is non-Eisenstein, then the map \pi1∗ + \pi2∗ : H d (XK , Fℓ )m ⊕2 \to H d (XK0 (p) , Fℓ )m is injective. This is (a generalisation of) Ihara’s lemma. When d = 0, it can be proved using strong approximation. When d = 1 it was recently proved by Manning and Shot- ton [6] under a mild technical assumpt... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,391 | OWR-12697688-004 | Generic Vanishing of Localized Shimura-Variety Cohomology | Let $\mathfrak m_p$ be a generic maximal ideal of the local Hecke algebra. Prove that $H^i(X_K,R)_{\mathfrak m_p}\neq 0$ implies $i\geq q_0$, and that $H_c^i(X_K,R)_{\mathfrak m_p}\neq 0$ implies $i\leq q_0+l_0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-004",
"literature-status:partially-solved",
"owr-year:2023"
] | The generic-cohomology vanishing conjecture has proofs for some unitary Shimura varieties and related settings, but the report and current literature still describe the general conjecture as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
},
{
"url": "https://arxiv.org/abs/2107.10081",
"label": "Caraiani and Tamiozzo, Hilbert modular varieties with torsion coefficients"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Let $\mathfrak m_p$ be a generic maximal ideal of the local Hecke algebra. Prove that $H^i(X_K,R)_{\mathfrak m_p}\neq 0$ implies $i\geq q_0$, and that $H_c^i(X_K,R)_{\mathfrak m_p}\neq 0$ implies $i\leq q_0+l_0$. | Our main conjecture is the following. For R = Fℓ , Qℓ , C, where ℓ is a prime, we consider cohomology groups H i (XK , R) and Hci (XK , R), and they are equipped with the Hecke action. More specifically, Q a set of bad primes so that Gp is unramified if p 6\in S and K has the let S denote form KS p6\inS Kp , where Kp i... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,392 | OWR-12697688-005 | Oort’s Hecke-Orbit Conjecture | Let $x=(A_x,\lambda)$ be an $\mathbb F_p$-point of $\mathcal A_g$. Prove that the Hecke orbit of $x$ under symplectic isogenies is Zariski dense in the Newton stratum containing $x$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-005",
"literature-status:partially-solved",
"owr-year:2023"
] | Oort's Hecke orbit conjecture is proved for Siegel varieties and for Hodge-type Shimura data under a lower bound on p, but the unrestricted conjecture in the extracted statement is not settled. | [
{
"url": "https://arxiv.org/abs/2205.10344",
"label": "DAddezio and van Hoften, Hecke orbits on Hodge-type Shimura varieties"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Let $x=(A_x,\lambda)$ be an $\mathbb F_p$-point of $\mathcal A_g$. Prove that the Hecke orbit of $x$ under symplectic isogenies is Zariski dense in the Newton stratum containing $x$. | Problem 15 on Oort’s 1995 list of open problems in algebraic geometry, [14], is the following conjecture. Hecke orbits on Shimura varieties of Hodge type Pol van Hoften (joint work with Marco D’Addezio) Conjecture 1. Let x = (Ax , \lambda) be an Fp -point of the moduli space Ag of prin- cipally polarised abelian variet... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,393 | OWR-12697688-006 | Hecke-Orbit Density in Hodge-Type Newton Strata | For a Hodge-type Shimura variety with good reduction at $p$, prove that every isogeny class is Zariski dense in its Newton stratum, without restrictions relating $p$ to the Shimura datum. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The explicit Hecke-orbit conjecture for Ag is proved for p\geq g, while the report records unconditional Siegel results and many special cases; the all-prime general formulation remains incomplete. | [
{
"url": "https://arxiv.org/abs/2205.10344",
"label": "DAddezio and van Hoften, Hecke orbits on Hodge-type Shimura varieties"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | For a Hodge-type Shimura variety with good reduction at $p$, prove that every isogeny class is Zariski dense in its Newton stratum, without restrictions relating $p$ to the Shimura datum. | Conjecture 1. Let x = (Ax , \lambda) be an Fp -point of the moduli space Ag of prin- cipally polarised abelian varieties of dimension g over Fp . The Hecke orbit of x, consisting of all points y \in Ag (Fp ) corresponding to principally polarised abelian varieties related to (Ax , \lambda) by symplectic isogenies, is Z... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,394 | OWR-12697688-007 | Central Leaves Under Prime-to-p Hecke Correspondences | This conjecture is known as the Hecke orbit conjecture (for Ag ). The discrete part of the conjecture is Theorem C of [10] (see [7] for related results). 1.2. Main result. Let (G, X) be a Shimura datum of Hodge type with reflex field E, and assume for simplicity that Gad is Q-simple throughout this introduction. Let p ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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 passage states a proved theorem on the stability of central leaves under Hecke correspondences, not an open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-007",
"literature-status:partially-solved",
"owr-year:2023"
] | The discrete part and the continuous part under a Coxeter-number bound are established, with further ordinary and Siegel cases known, but the general Hodge-type conjecture without the size restriction remains open. | [
{
"url": "https://arxiv.org/abs/2205.10344",
"label": "DAddezio and van Hoften, Hecke orbits on Hodge-type Shimura varieties"
},
{
"url": "https://arxiv.org/abs/2112.12422",
"label": "van Hoften, Ordinary Hecke orbit conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"labe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | This conjecture is known as the Hecke orbit conjecture (for Ag ). The discrete part of the conjecture is Theorem C of [10] (see [7] for related results). 1.2. Main result. Let (G, X) be a Shimura datum of Hodge type with reflex field E, and assume for simplicity that Gad is Q-simple throughout this introduction. Let p ... | unrecoverable | The official report passage states a proved theorem on the stability of central leaves under Hecke correspondences, not an open problem. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,395 | OWR-12697688-008 | p-Adic Arithmetic Gan–Gross–Prasad Formula | Assume $\pi$ is tempered and ordinary at every $p$-adic place. For $\phi\in\pi_f$ and $\phi^\vee\in\pi_f^\vee$, prove, up to a nonzero explicit factor, $(\int_{\operatorname{Sh}(H)}\phi,\int_{\operatorname{Sh}(H)}\phi^\vee)_p=e_p(\pi)^{-1}L_p'(\tfrac12,\pi,R)\prod_v\alpha_v(\phi_v,\phi_v^\vee)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-008",
"literature-status:partially-solved",
"owr-year:2023"
] | The p-adic arithmetic GGP height formula is proved under substantial local, ordinarity, and ramification hypotheses, but the conjecture as stated for all tempered ordinary representations remains open. | [
{
"url": "https://arxiv.org/abs/2410.08401",
"label": "Disegni and Zhang, GGP cycles and p-adic L-functions"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Assume $\pi$ is tempered and ordinary at every $p$-adic place. For $\phi\in\pi_f$ and $\phi^\vee\in\pi_f^\vee$, prove, up to a nonzero explicit factor, $(\int_{\operatorname{Sh}(H)}\phi,\int_{\operatorname{Sh}(H)}\phi^\vee)_p=e_p(\pi)^{-1}L_p'(\tfrac12,\pi,R)\prod_v\alpha_v(\phi_v,\phi_v^\vee)$. | Conjecture 1. Assume that \pi is tempered, and ordinary at all p-adic places. Let \phi \in \pif , \phi∨ \in \pif∨ . Then, up to a certain non-zero explicit factor, Z Z ! 1 Y \phi, \phi∨ = ep (\pi)−1 L′p ( , \pi, R) \alphav (\phiv , \phi∨ v ), Sh(H) Sh(H) 2 v p depending on some auxiliary choice (a certain splitting of ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,396 | OWR-12697688-009 | Local Nonvanishing in Arithmetic Gan–Gross–Prasad Theory | Note that \alphav is non-zero if and only if HomH(F0,v ) (\piv , C) 6= 0. In [1] we prove some cases of the conjecture. Here the local factor \alphav \in HomH(F0,v )\timesH(F0,v ) (\piv ⊠ \piv∨ , C) is the Ichino–Ikeda canonical invariant linear functional: Z ∨ \alphav (\phiv , \phiv ) = h\piv (h)\phiv , \phi∨ v iv dh.... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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 gives a local nonvanishing fact and then states proved cases; the passage does not formulate an unresolved problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-009",
"literature-status:partially-solved",
"owr-year:2023"
] | The recorded theorem supplies a proved family of cases of the p-adic height conjecture, including split ordinary and specified stable cuspidal situations, not a general proof. | [
{
"url": "https://arxiv.org/abs/2410.08401",
"label": "Disegni and Zhang, GGP cycles and p-adic L-functions"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | Note that \alphav is non-zero if and only if HomH(F0,v ) (\piv , C) 6= 0. In [1] we prove some cases of the conjecture. Here the local factor \alphav \in HomH(F0,v )\timesH(F0,v ) (\piv ⊠ \piv∨ , C) is the Ichino–Ikeda canonical invariant linear functional: Z ∨ \alphav (\phiv , \phiv ) = h\piv (h)\phiv , \phi∨ v iv dh.... | unrecoverable | The official report gives a local nonvanishing fact and then states proved cases; the passage does not formulate an unresolved problem. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,397 | OWR-12697688-011 | Langlands–Rapoport Conjecture for Parahoric Level | Therefore the proof of the LR-\tau conjecture should suffice for most applications although the LR-\tau conjecture is not as strong as the original LR conjecture. Cohomology of Shimura varieties Sug Woo Shin (joint work with Mark Kisin, Yihang Zhu) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,023 | 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 explicitly says that the conjecture discussed in this extraction has been proved, so it is not an open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-011",
"literature-status:open",
"owr-year:2023"
] | The LR-tau conjecture has been proved and yields important trace-formula consequences, but the report explicitly states that the original Langlands-Rapoport conjecture remains wide open. | [
{
"url": "https://arxiv.org/abs/2110.05381",
"label": "Kisin, Shin, and Zhu, Stable trace formula for Shimura varieties"
},
{
"url": "https://doi.org/10.4171/owr/2023/5",
"label": "Oberwolfach Report 5\\slash 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | Therefore the proof of the LR-\tau conjecture should suffice for most applications although the LR-\tau conjecture is not as strong as the original LR conjecture. Cohomology of Shimura varieties Sug Woo Shin (joint work with Mark Kisin, Yihang Zhu) | unrecoverable | The official report explicitly says that the conjecture discussed in this extraction has been proved, so it is not an open problem. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,398 | OWR-12697688-016 | Fargues’ Cohomological Conjectures for the Curve | For an étale abelian torsion sheaf $\mathcal F$ on $X_{E,F}^{\mathrm{alg}}$, prove that $H^i(X_{E,F}^{\mathrm{alg}},\mathcal F)=0$ for $i\geq 3$; that adification gives $H^i(X_{E,F}^{\mathrm{alg}},\mathcal F)\cong H^i(X_{E,F}^{\mathrm{ad}},\mathcal F^{\mathrm{ad}})$ for $i\geq 0$; and that the function field $E(X_{E,F}... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-016",
"literature-status:partially-solved",
"owr-year:2023"
] | Bartling proves the prime-to-p vanishing and algebraic--adic comparison conjectures, while the p-torsion statement remains conditional and the C1 function-field assertion remains unresolved. | [
{
"url": "https://arxiv.org/abs/2206.14253",
"label": "Bartling, etale cohomology of the Fargues--Fontaine curve"
},
{
"url": "https://ems.press/content/serial-article-files/46998?nt=1",
"label": "original Fargues conjectures in OWR"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | For an étale abelian torsion sheaf $\mathcal F$ on $X_{E,F}^{\mathrm{alg}}$, prove that $H^i(X_{E,F}^{\mathrm{alg}},\mathcal F)=0$ for $i\geq 3$; that adification gives $H^i(X_{E,F}^{\mathrm{alg}},\mathcal F)\cong H^i(X_{E,F}^{\mathrm{ad}},\mathcal F^{\mathrm{ad}})$ for $i\geq 0$; and that the function field $E(X_{E,F}... | conjecture (also in [3]). Conjecture 1. (Fargues) alg (1): Let F be an étale abelian torsion sheaf on XE,F . Then alg H i (XE,F , F) = 0 for i \geq 3. ad alg (2): The morphism of locally ringed spaces u : XE,F \to XE,F induces a mor- ad alg phism of étale sites u : (XE,F )et \to (XE,F )et and for F as in (1), let F a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,399 | OWR-12697688-017 | Dualizing Complexes and p-Torsion on the Fargues–Fontaine Curve | Describe the dualizing complex of the Fargues–Fontaine curve and determine the corresponding cohomological behavior for $p$-torsion coefficients. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,023 | 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-12697688-017",
"literature-status:open",
"owr-year:2023"
] | The dualizing-complex and p-torsion questions are still presented as speculative problems; existing Banach--Colmez and etale-cohomology results do not supply a general answer. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/ae468b44-47d2-4568-9d88-ffcb4023f8d4/download",
"label": "OWR-2023-5, open questions"
},
{
"url": "https://arxiv.org/abs/2206.14253",
"label": "Bartling, partial cohomology results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Describe the dualizing complex of the Fargues–Fontaine curve and determine the corresponding cohomological behavior for $p$-torsion coefficients. | Can one describe the dualizing complex? What happens in the p-torsion case? The main result ([1]) presented in the talk was the following: alg Theorem 1. Let F be an étale abelian torsion sheaf on XE,F . (a): If F is of torsion prime to p, then Conjectures (1) and (2) are true. Fur- alg thermore, cdℓ (E(XE,F )) \leq 1... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,400 | OWR-12697688-018 | Banach–Colmez Proofs of the Fargues–Fontaine C-One Property | Can Tsen's dimension-count proof of the $C_1$ property for function fields of algebraic curves be adapted to the Fargues–Fontaine curve using Banach–Colmez spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-018",
"literature-status:partially-solved",
"owr-year:2023"
] | Banach--Colmez spaces are related rigorously to coherent sheaves on the Fargues--Fontaine curve and used to compute selected pro-etale cohomology, but no general adaptation of the proposed proof is established. | [
{
"url": "https://arxiv.org/abs/1801.00422",
"label": "Le Bras, Banach--Colmez spaces and coherent sheaves"
},
{
"url": "https://arxiv.org/abs/2108.12785",
"label": "Colmez--Nizioł, p-adic analytic cohomology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Can Tsen's dimension-count proof of the $C_1$ property for function fields of algebraic curves be adapted to the Fargues–Fontaine curve using Banach–Colmez spaces? | In view of the analogy of affine spaces and Banach-Colmez spaces in perfectoid geometry one could be tempted to ask the following question: Can one adapt this proof using Banach-Colmez spaces? 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 | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,401 | OWR-12697688-019 | Fargues Eigensheaf Construction Context | cocharacters µ \in X∗ (TQp )+ , this category comes equipped with an action by Hecke operators Tµ : D(BunG ) \to D(BunG )BWQp taking a sheaf on BunG to a sheaf with continuous WQp -action. For b \in B(G) varying in the Kottiwtz set of G, the stack BunG has a locally closed stratification jb : BunbG ֒\to BunG by Harder-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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 contextual setup duplicated by the following complete open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-019",
"literature-status:partially-solved",
"owr-year:2023"
] | Geometric Eisenstein constructions now produce Hecke eigensheaves for sufficiently nice toral parameters and describe their stalks conditionally, but the general extension of Fargues vision is not complete. | [
{
"url": "https://arxiv.org/abs/2209.08175",
"label": "Hamann, geometric Eisenstein series"
},
{
"url": "https://arxiv.org/abs/2102.13459",
"label": "Fargues--Scholze, geometrization of local Langlands"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | cocharacters µ \in X∗ (TQp )+ , this category comes equipped with an action by Hecke operators Tµ : D(BunG ) \to D(BunG )BWQp taking a sheaf on BunG to a sheaf with continuous WQp -action. For b \in B(G) varying in the Kottiwtz set of G, the stack BunG has a locally closed stratification jb : BunbG ֒\to BunG by Harder-... | unrecoverable | The official report confirms that this extraction is contextual setup duplicated by the following complete open problem. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,402 | OWR-12697688-020 | Fargues Eigensheaves for General Langlands Parameters | Extend Fargues's eigensheaf construction from supercuspidal Langlands parameters to general semisimple $L$-parameters, beginning with parameters induced from a torus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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-12697688-020",
"literature-status:partially-solved",
"owr-year:2023"
] | The general-parameter question has partial answers through normalized geometric Eisenstein functors for sufficiently generic toral parameters, with compatibility and full parameter generality still open. | [
{
"url": "https://arxiv.org/abs/2209.08175",
"label": "Hamann, geometric Eisenstein series"
},
{
"url": "https://arxiv.org/abs/2102.13459",
"label": "Fargues--Scholze, geometrization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | Extend Fargues's eigensheaf construction from supercuspidal Langlands parameters to general semisimple $L$-parameters, beginning with parameters induced from a torus. | It is a natural question to wonder if Fargues’ vision can be extended to more general parameters \phi. cocharacters µ \in X∗ (TQp )+ , this category comes equipped with an action by Hecke operators Tµ : D(BunG ) \to D(BunG )BWQp taking a sheaf on BunG to a sheaf with continuous WQp -action. For b \in B(G) varying in th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,403 | OWR-12697688-021 | Naive Local–Global Compatibility Formulation | conjecture. Conjecture 1. (Naive) The sheaf S\phi is an eigensheaf with eigenvalue \phi. Unfortunately, this is too naive; in particular, there can exists representations of non quasi-split groups, whose semi-simplified L-parameter factors through a maximal torus T (e.g the trivial representation of D∗1 , units in the ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,023 | 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 presents this naive formulation only as exposition before a conditional theorem; the extraction does not preserve a stan) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-021",
"literature-status:partially-solved",
"owr-year:2023"
] | The generic-toral eigensheaf claim is proved in restricted settings or under stated Fargues--Scholze compatibility assumptions; the unconditional general assertion remains unproved. | [
{
"url": "https://arxiv.org/abs/2209.08175",
"label": "Hamann, geometric Eisenstein series"
},
{
"url": "https://ems.press/content/serial-article-files/46998?nt=1",
"label": "OWR statement and conditional theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | conjecture. Conjecture 1. (Naive) The sheaf S\phi is an eigensheaf with eigenvalue \phi. Unfortunately, this is too naive; in particular, there can exists representations of non quasi-split groups, whose semi-simplified L-parameter factors through a maximal torus T (e.g the trivial representation of D∗1 , units in the ... | unrecoverable | The official report presents this naive formulation only as exposition before a conditional theorem; the extraction does not preserve a standalone unresolved claim. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,404 | OWR-12697688-022 | Local-Model Description of Shimura Varieties | conjecture. Now focus on n = 3 for simplicity. In particular, for \lambda \in Z3 a dominant weight for gl3 , the BGG resolution gives an exact sequence, M (s1 \cdot \lambda) ⊕ M (s2 \cdot \lambda) −\to M (\lambda) −\to L(\lambda) −\to 0, where M (w \cdot \lambda), w \in W are Verma modules, s1 , s2 are the two simple r... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326](https://doi.org/10.4171/owr/2023/5)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,023 | 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 passage is a proof and local-model exposition, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697688-022",
"literature-status:open",
"owr-year:2023"
] | The record ends mid-argument after describing BGG images and Steinberg-variety supports, so it does not state a complete claim whose truth can be certified; the extracted item is therefore unresolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/ae468b44-47d2-4568-9d88-ffcb4023f8d4/content",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2406.01129",
"label": "related patching results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/5 | null | null | null | null | conjecture. Now focus on n = 3 for simplicity. In particular, for \lambda \in Z3 a dominant weight for gl3 , the BGG resolution gives an exact sequence, M (s1 \cdot \lambda) ⊕ M (s2 \cdot \lambda) −\to M (\lambda) −\to L(\lambda) −\to 0, where M (w \cdot \lambda), w \in W are Verma modules, s1 , s2 are the two simple r... | unrecoverable | The official report passage is a proof and local-model exposition, not an open mathematical problem. | null | null | null | null | null | Arithmetic of Shimura Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/5, pp. 261--326 |
30,005,405 | OWR-12697689-001 | Conjectures on Resolutions and Singular Rings | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Jack Jeffries (joint with Josep Àlvarez Montaner, Daniel Hernández, Luiz Núñez-Betancourt, Pedro Teixeira, Emily Witt, David Lieberman) Bernstein’s inequality for certain singular rings . . . . . . . . . . . . . . . . . . . . . . 365 The report ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this record is a table-of-contents fragment rather than a mathematical question. No separate clean stateme) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-001",
"literature-status:open",
"owr-year:2023"
] | The extracted record is only a truncated table-of-contents fragment ending in `Conjecture`, with no identifiable mathematical assertion to verify. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Jack Jeffries (joint with Josep Àlvarez Montaner, Daniel Hernández, Luiz Núñez-Betancourt, Pedro Teixeira, Emily Witt, David Lieberman) Bernstein’s inequality for certain singular rings . . . . . . . . . . . . . . . . . . . . . . 365 The report ... | unrecoverable | The official report confirms that this record is a table-of-contents fragment rather than a mathematical question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,406 | OWR-12697689-002 | Positive Characteristic Cohomology of Flag Variety Line Bundles | Determine the cohomology groups of line bundles on a flag variety in characteristic $p>0$, including their general vanishing and nonvanishing behavior. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | partially_solved | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-002",
"literature-status:partially-solved",
"owr-year:2023"
] | The broad positive-characteristic flag-variety problem remains open, but substantial cases are solved, including complete vanishing and nonvanishing results for the incidence correspondence and recursive formulas for related flags. | [
{
"url": "https://arxiv.org/abs/2210.03656",
"label": "Gao--Raicu, incidence correspondence"
},
{
"url": "https://arxiv.org/abs/2411.13450",
"label": "cohomology on the incidence correspondence"
},
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Determine the cohomology groups of line bundles on a flag variety in characteristic $p>0$, including their general vanishing and nonvanishing behavior. | question. Problem 3. Determine the cohomology groups of line bundles on a flag variety in characteristic p > 0. In particular, characterize the (non)vanishing behavior of such cohomology groups. A characterization of (non)vanishing of cohomology is given in the case of H 0 by Kempf’s vanishing theorem [9, 8], and for H... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,407 | OWR-12697689-003 | Normalized Ext Limits and Epsilon Multiplicity | Does the limit $\lim_{d\to\infty}\ell(\operatorname{Ext}^3_S(S/I^d,S))/d^6$ exist, as predicted by higher $\varepsilon$-multiplicity theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-003",
"literature-status:open",
"owr-year:2023"
] | The extracted passage explicitly leaves the normalized Ext limit as an open higher epsilon-multiplicity question; no primary source found by the cutoff proves existence in this stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Does the limit $\lim_{d\to\infty}\ell(\operatorname{Ext}^3_S(S/I^d,S))/d^6$ exist, as predicted by higher $\varepsilon$-multiplicity theory? | for intermediate cohomology remain unknown. The explicit description for cohomology of line bundles on X (or for the sheaves Dd R(e) on P) remains an open problem in general, but one which is closely related to the study of determinantal ideals. The explicit calculations in [7, Theorem 1.9] can then be used to conclude... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,408 | OWR-12697689-004 | Gröbner-Cell Parametrization of Punctual Hilbert Schemes | Let $E\subset k[[x,y]]$ be a zero-dimensional monomial ideal, let $T'(E)$ be the parameter space of admissible perturbation matrices of its canonical Hilbert–Burch matrix $H$, and let $V(E)$ be the Gröbner cell of ideals with initial ideal $E$. Is the map $$\Phi_E:T'(E)\longrightarrow V(E),\qquad N\longmapsto I_t(H+N),... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 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-12697689-004",
"literature-status:open",
"owr-year:2023"
] | The conjectural parametrization of Groebner cells for every zero-dimensional monomial ideal is reported with injectivity and surjectivity still unproved; the n<=30 checks are only evidence. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/11773ea5-b1e5-4e9e-b650-808e9d9dc944/content",
"label": "OWR-2023-6, Conjecture 6"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2021.04.021",
"label": "Homs--Winz, canonical Hilbert--Burch matrices"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Let $E\subset k[[x,y]]$ be a zero-dimensional monomial ideal, let $T'(E)$ be the parameter space of admissible perturbation matrices of its canonical Hilbert–Burch matrix $H$, and let $V(E)$ be the Gröbner cell of ideals with initial ideal $E$. Is the map $$\Phi_E:T'(E)\longrightarrow V(E),\qquad N\longmapsto I_t(H+N),... | Our evidence for the conjecture is twofold: • It holds for extremal cases: lex-segment ideals (and a slighlty more general class) and complete intersections. • The dimensions of the cells of the celullar decomposition of Hilbn (k[[x, y]]) resulting from the conjecture are correct for n \leq 30. Resolutions in Local Alg... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,409 | OWR-12697689-005 | Singularity Categories as Invariants of Singularities | What information about a singularity is determined by its singularity category $D_{\mathrm{sg}}(R)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-005",
"literature-status:open",
"owr-year:2023"
] | The question is broad and exploratory; known characterizations detect regularity, hypersurface periodicity, and some Gorenstein cases, but no general reconstruction theorem is established. | [
{
"url": "https://ems.press/content/serial-article-files/47000",
"label": "Kalck, singularity categories"
},
{
"url": "https://arxiv.org/abs/2403.13637",
"label": "DG singular equivalence and singular locus"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | What information about a singularity is determined by its singularity category $D_{\mathrm{sg}}(R)$? | What do singularity categories know about singularities? Hot−,b (proj R) \sim Db (mod R) (2) Dsg (R) := = Hotb (proj R) Perf(R) [1] Resolutions in Local Algebra and Singularity Theory 349 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,410 | OWR-12697689-006 | Classifying Rings Up to Singularity Equivalence | How fine is the invariant $D_{\mathrm{sg}}(R)$; equivalently, when do two rings $R$ and $S$ satisfy $D_{\mathrm{sg}}(R)\simeq D_{\mathrm{sg}}(S)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-006",
"literature-status:open",
"owr-year:2023"
] | The displayed list is a list of examples, not a classification; subsequent singular-equivalence constructions still leave the general commutative classification question unresolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/11773ea5-b1e5-4e9e-b650-808e9d9dc944/content",
"label": "OWR-2023-6, Question 3"
},
{
"url": "https://arxiv.org/abs/2103.06584",
"label": "Kalck, new singular equivalence"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | How fine is the invariant $D_{\mathrm{sg}}(R)$; equivalently, when do two rings $R$ and $S$ satisfy $D_{\mathrm{sg}}(R)\simeq D_{\mathrm{sg}}(S)$? | (2) The 2-periodic ‘stable ranges’ in (P2) are induced by matrix factorizations of f . Question 3. How fine is the invariant Dsg (R), i.e. when are two rings R, S singular equivalent: Dsg (R) \sim = Dsg (S) ? To explain what is known about this question, we introduce some notation. Notation. For a primitive nth root of... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,411 | OWR-12697689-007 | Independent Defects and Rough Deep Ramification | Is every valued field that admits only independent defects roughly deeply ramified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-007",
"literature-status:open",
"owr-year:2023"
] | The converse implication from independent defects to roughly deeply ramified valued fields is explicitly posed as open, and no later primary proof was located. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/11773ea5-b1e5-4e9e-b650-808e9d9dc944/content",
"label": "OWR-2023-6, valued fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Is every valued field that admits only independent defects roughly deeply ramified? | It is an open question whether also the converse of (i) holds, i. e., whether every valued field that admits only independent defects is roughly deeply ramified. Resolutions in Local Algebra and Singularity Theory 353 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,412 | OWR-12697689-008 | Higher Structure Map Criterion for LICCI Ideals | Let $I$ be a perfect codimension-$3$ ideal over a local Gorenstein ring $R$. Is $I$ LICCI if and only if a higher structure map in $W(d_1)$ has a unit entry; and do unit entries in $W(d_2)$ and $W(d_3)$ characterize linkage to ideals with smaller resolution formats? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | partially_solved | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-008",
"literature-status:partially-solved",
"owr-year:2023"
] | The LICCI criterion is proved for the smallest previously unknown ADE format and related linkage reductions, while the stated uniform iff conjecture for all codimension-three perfect ideals remains open. | [
{
"url": "https://arxiv.org/abs/2208.05934",
"label": "Guerrieri--Ni--Weyman, higher structure maps"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/11773ea5-b1e5-4e9e-b650-808e9d9dc944/content",
"label": "OWR-2023-6, Conjecture 2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Let $I$ be a perfect codimension-$3$ ideal over a local Gorenstein ring $R$. Is $I$ LICCI if and only if a higher structure map in $W(d_1)$ has a unit entry; and do unit entries in $W(d_2)$ and $W(d_3)$ characterize linkage to ideals with smaller resolution formats? | Conjecture 2. Let I be a perfect ideal of codimension 3 over a local Gorenstein ring R. Then I is LICCI if and only if there exists a higher structure map in the representation W (d1 ) whose entry is a unit. Similarly, the existence of a unit in W (d2 ) and W (d3 ) should be equivalent to the fact that I can be linked ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,413 | OWR-12697689-009 | Introduction to the Weak-Implies-Strong Conjecture | An introduction to the weak implies strong conjecture. Let (R, m, k) be an excellent Cohen-Macaulay normal domain of prime characteristic p > 0. For each natural number e let F e (−) : Mod(R) \to Mod(R) be the base change functor along the eth iterate of the Frobenius F e : R \to R. If N \subseteq M are R-modules then ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this record is an introductory fragment for the weak-implies-strong conjecture, whose complete statement a) | [
"OWR-12697689-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-009",
"literature-status:open",
"owr-year:2023"
] | The extracted record is an introductory fragment about tight closure and does not state a complete theorem; the general weak-implies-strong problem it introduces remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2022.04.020",
"label": "dimension-four progress"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | null | An introduction to the weak implies strong conjecture. Let (R, m, k) be an excellent Cohen-Macaulay normal domain of prime characteristic p > 0. For each natural number e let F e (−) : Mod(R) \to Mod(R) be the base change functor along the eth iterate of the Frobenius F e : R \to R. If N \subseteq M are R-modules then ... | unrecoverable | The official report confirms that this record is an introductory fragment for the weak-implies-strong conjecture, whose complete statement appears in the adjacent record OWR-12697689-010. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,414 | OWR-12697689-010 | Weak and Strong F-Regularity in Excellent Rings | If $R$ is an excellent weakly $F$-regular ring of prime characteristic $p>0$, is $R$ strongly $F$-regular? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | partially_solved | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12697689-009"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-010",
"literature-status:partially-solved",
"owr-year:2023"
] | Weak F-regularity implies strong F-regularity in several major classes, including dimensions at most four under hypotheses, but the excellent-ring conjecture remains open in full generality. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2022.04.020",
"label": "Aberbach--Polstra, dimension four"
},
{
"url": "https://par.nsf.gov/servlets/purl/10501870",
"label": "arbitrary-dimensional partial progress"
},
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | If $R$ is an excellent weakly $F$-regular ring of prime characteristic $p>0$, is $R$ strongly $F$-regular? | conjecture. There has been incremental progress on the weak implies strong conjecture since the inception of tight closure theory. • Conjecture 1 was settled for the class of Gorenstein rings by Hochster and Huneke, [10]. • Williams settled the weak implies strong conjecture for rings of dimension at most 3, [17]. Will... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
30,005,415 | OWR-12697689-011 | Uniform Local Cohomology Annihilators for Symbolic Powers | Let $(R,\mathfrak m,k)$ be a complete Cohen–Macaulay normal domain of dimension $d$, and let $I$ have pure height $h$. For each $1\leq j\leq d-h-1$, does there exist an ideal $\mathfrak a_j$ of height $d-j+1$ that uniformly annihilates $H^j_{\mathfrak m}(R/I^{(n)})$ for every $n\in\mathbb{N}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395](https://doi.org/10.4171/owr/2023/6)
## Literature review (checked 202... | 3 | open | null | 2,023 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12697689-011",
"literature-status:open",
"owr-year:2023"
] | The stated characteristic-free annihilation problem is presented as an open problem whose solution would imply weak-implies-strong; no general solution is known. | [
{
"url": "https://doi.org/10.4171/owr/2023/6",
"label": "original OWR open problem"
},
{
"url": "https://par.nsf.gov/servlets/purl/10501870",
"label": "partial weak-implies-strong results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/6 | null | null | null | Let $(R,\mathfrak m,k)$ be a complete Cohen–Macaulay normal domain of dimension $d$, and let $I$ have pure height $h$. For each $1\leq j\leq d-h-1$, does there exist an ideal $\mathfrak a_j$ of height $d-j+1$ that uniformly annihilates $H^j_{\mathfrak m}(R/I^{(n)})$ for every $n\in\mathbb{N}$? | We present a characteristic-free problem in commutative algebra that if solved would settle the weak implies strong conjecture: Open Problem: Let (R, m, k) be a complete Cohen-Macaulay normal domain of arbitrary characteristic. For each 1 \leq j \leq d − h − 1 does there exist an ideal aj of height d − j + 1 such that ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Resolutions in Local Algebra and Singularity Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/6, pp. 327--395 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.