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30,004,316 | OWR-17294-017 | Bijectivity of the Quantum Symmetrizer | Is the quantum symmetrizer $\operatorname{QS}$ bijective for general set-theoretic Yang–Baxter solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23072076",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **The Quantum Symmetriser of a Yang–Baxter Solution Need Not Be a Quasi-Isomorphism** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23072076) | [
"owr",
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] | Bijectivity of the quantum symmetriser is proved for involutive and idempotent solutions, but the general-solution case remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46831",
"label": "Oberwolfach Reports, quantum symmetriser problem"
},
{
"url": "https://arxiv.org/abs/1607.08081",
"label": "Cohomology of idempotent braidings"
},
{
"url": "https://www.sciencedirect.com/science/article/am/pii/S00... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Is the quantum symmetrizer $\operatorname{QS}$ bijective for general set-theoretic Yang–Baxter solutions? | Is the quantum symmetriser QS bijective for general set-theoretic Yang--Baxter solutions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,317 | OWR-17294-018 | Groups Arising as Quandle Structure Groups | Characterize and further analyze the groups $G\cong\operatorname{Grp}(Q)$ that arise as structure groups of quandles $Q$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242](https://doi.org/10.4171/owr/2019/51)
## Literature... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17294-018",
"literature-status:open",
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] | The Ryder characterization is known to fail in general, while recent work computes structure groups for important quandle families; a general characterization of groups arising as quandle structure groups remains open. | [
{
"url": "https://arxiv.org/abs/2407.02955",
"label": "Lebed, Conjugation groups and structure groups of quandles"
},
{
"url": "https://doi.org/10.1515/jgth-2025-0096",
"label": "Published version on conjugation and quandle groups"
},
{
"url": "https://ems.press/content/serial-article-fi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/51 | null | null | null | Characterize and further analyze the groups $G\cong\operatorname{Grp}(Q)$ that arise as structure groups of quandles $Q$. | Characterize and further analyze the groups G\cong\operatorname{Grp}(Q) that arise as structure groups of quandles Q. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/51, pp. 3207--3242 |
30,004,318 | OWR-17295-001 | Classification of Rank-One Groups | Is the known list of rank-one groups, consisting of examples of algebraic origin such as groups related to algebraic or classical groups and small-characteristic variants, complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269](https://doi.org/10.4171/owr/2019/52)
## Literature rev... | 3 | open | null | 2,019 | 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-17295-001",
"literature-status:open",
"owr-year:2019"
] | The known list of rank-one groups of the stated algebraic origin is incomplete as a classification: whether it contains every example remains an explicit open question. | [
{
"url": "https://ems.press/content/serial-article-files/46832",
"label": "Oberwolfach Reports, rank-one groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/52 | null | null | null | Is the known list of rank-one groups, consisting of examples of algebraic origin such as groups related to algebraic or classical groups and small-characteristic variants, complete? | Is the known list of rank-one groups, consisting of examples of algebraic origin such as groups related to algebraic or classical groups and small-characteristic variants, complete? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269 |
30,004,319 | OWR-17295-003 | Alternativity of Parameters for $A_2$-Graded Groups | Is every ring $R$ that parametrizes an $A_2$-graded group alternative? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269](https://doi.org/10.4171/owr/2019/52)
## Literature rev... | 3 | open | null | 2,019 | 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-17295-003",
"literature-status:open",
"owr-year:2019"
] | Root-graded group theory gives partial structural results, but no example with a nonalternative parametrizing ring and no proof that every A2-parametrizing ring is alternative is known. | [
{
"url": "https://arxiv.org/abs/2404.02042",
"label": "Wiedemann, Root Graded Groups"
},
{
"url": "https://arxiv.org/abs/2406.03558",
"label": "Root graded groups revisited"
},
{
"url": "https://ems.press/content/serial-article-files/46832",
"label": "Oberwolfach Reports, A2-graded g... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/52 | null | null | null | Is every ring $R$ that parametrizes an $A_2$-graded group alternative? | Is every ring R that parametrizes an A_2-graded group alternative? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269 |
30,004,320 | OWR-17295-004 | Descent of Rational Points from Laurent Series Fields | Let $k$ be a field, let $G$ be an affine algebraic $k$-group, and let $X$ be a homogeneous space of $G$. If $X(k((t)))\neq\varnothing$, must $X(k)\neq\varnothing$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269](https://doi.org/10.4171/owr/2019/52)
## Literature rev... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17295-004",
"literature-status:open",
"owr-year:2019"
] | The torsor statement is established in several settings, but its extension from torsors to homogeneous spaces is explicitly open beyond the known characteristic-zero cases. | [
{
"url": "https://doi.org/10.1515/crelle-2021-0007",
"label": "Florence and Gille, Residues on affine Grassmannians"
},
{
"url": "https://webusers.imj-prg.fr/~mathieu.florence/residus11nov.pdf",
"label": "Florence, Residues manuscript"
},
{
"url": "https://ems.press/content/serial-articl... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/52 | null | null | null | Let $k$ be a field, let $G$ be an affine algebraic $k$-group, and let $X$ be a homogeneous space of $G$. If $X(k((t)))\neq\varnothing$, must $X(k)\neq\varnothing$? | Let k be a field, let G be an affine algebraic k-group, and let X be a homogeneous space of G. If X(k((t))) is nonempty, must X(k) be nonempty? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Rank One Groups and Exceptional Algebraic Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/52, pp. 3243--3269 |
30,004,321 | OWR-17296-002 | Nagata Conjecture for Multipoint Seshadri Constants | Nagata's conjecture asks whether, for $r\geq 10$ and sufficiently general points $x_1,\ldots,x_r$ in $\mathbb{P}^2$, the multipoint Seshadri constant of $\mathcal{O}_{\mathbb{P}^2}(1)$ equals $1/\sqrt r$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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] | Nagata's assertion remains unresolved for at least ten very general points except for established special cases, and recent work continues to treat it as a conjecture. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0007449725000430",
"label": "Seshadri constants and related conjectures over characteristic zero"
},
{
"url": "https://arxiv.org/abs/math/0304124",
"label": "Roe, On the Nagata conjecture"
},
{
"url": "https://link.springer.com... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Nagata's conjecture asks whether, for $r\geq 10$ and sufficiently general points $x_1,\ldots,x_r$ in $\mathbb{P}^2$, the multipoint Seshadri constant of $\mathcal{O}_{\mathbb{P}^2}(1)$ equals $1/\sqrt r$. | Nagata's conjecture asks whether, for r greater than or equal to 10 and sufficiently general points x_1,...,x_r in P^2, the multipoint Seshadri constant of O_{P^2}(1) equals 1 divided by the square root of 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 | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,322 | OWR-17296-003 | Seshadri Constants of Line Arrangement Singularities | Let $x_1,\ldots,x_r$ be the singular points of a line configuration in $\mathbb{P}^2$, and let $k$ be the maximum number of these points on one line. Must the multipoint Seshadri constant $\varepsilon(\mathcal{O}_{\mathbb{P}^2}(1);x_1,\ldots,x_r)$ equal $1/k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17296-003",
"literature-status:open",
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] | Kollar-type constructions show unbounded very-ampleness thresholds on one surface, but the extracted globally-generated threshold question is not settled by those results or by subsequent work located. | [
{
"url": "https://www.math.stonybrook.edu/~roblaz/Reprints/Ein.Laz.Seshadri.Consts.Smooth.Sfs.pdf",
"label": "Ein and Lazarsfeld, Seshadri constants on smooth surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2019/53",
"label": "Oberwolfach Reports, global generation problem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Let $x_1,\ldots,x_r$ be the singular points of a line configuration in $\mathbb{P}^2$, and let $k$ be the maximum number of these points on one line. Must the multipoint Seshadri constant $\varepsilon(\mathcal{O}_{\mathbb{P}^2}(1);x_1,\ldots,x_r)$ equal $1/k$? | Let x_1,...,x_r be the singular points of a line configuration in P^2, and let k be the maximum number of these points on one line. Must the multipoint Seshadri constant epsilon(O_{P^2}(1);x_1,...,x_r) equal 1 divided by k? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,323 | OWR-17296-005 | Fujita's Conjecture for Effective Global Generation | For an ample line bundle $L$ on a projective variety $X$, what tensor power $L^{\otimes\ell}$ is guaranteed to be globally generated or very ample? In particular, does Fujita's conjecture hold for a smooth $n$-dimensional projective $X$, with $\omega_X\otimes L^{\otimes\ell}$ globally generated for $\ell\geq n+1$ and v... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17296-005",
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] | Effective bounds and low-dimensional results exist, but the sharp Fujita statement is open in higher dimensions and the classical formulation fails in positive characteristic. | [
{
"url": "https://arxiv.org/abs/2408.06530",
"label": "Murayama, Effective Fujita-type theorems"
},
{
"url": "https://doi.org/10.1007/s10114-026-6229-8",
"label": "Siu, Very ampleness part of Fujita conjecture"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S000187082... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | For an ample line bundle $L$ on a projective variety $X$, what tensor power $L^{\otimes\ell}$ is guaranteed to be globally generated or very ample? In particular, does Fujita's conjecture hold for a smooth $n$-dimensional projective $X$, with $\omega_X\otimes L^{\otimes\ell}$ globally generated for $\ell\geq n+1$ and v... | For an ample line bundle L on a projective variety X, what tensor power L^{\otimes ell} is guaranteed to be globally generated or very ample? In particular, does Fujita's conjecture hold for a smooth n-dimensional projective X, with omega_X\otimes L^{\otimes ell} globally generated for ell greater than or equal to n+1 ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,324 | OWR-17296-007 | Characterizing Projective Space by Tangent Bundle Seshadri Constants | Is projective space $\mathbb{P}^n$ the only $n$-dimensional projective manifold $X$ for which the Seshadri constant $\varepsilon(T_X;x_0)$ of the tangent bundle is positive at some point $x_0\in X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17296-007",
"literature-status:open",
"owr-year:2019"
] | The characterization is proved for Fano varieties, surfaces, general points, and toric varieties, but the unrestricted smooth-projective statement remains conjectural. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106559",
"label": "Seshadri constants for vector bundles"
},
{
"url": "https://arxiv.org/abs/2211.17172",
"label": "Seshadri constants of tangent sheaves on toric varieties"
},
{
"url": "https://ems.press/content/serial-article-files/46833",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Is projective space $\mathbb{P}^n$ the only $n$-dimensional projective manifold $X$ for which the Seshadri constant $\varepsilon(T_X;x_0)$ of the tangent bundle is positive at some point $x_0\in X$? | Is projective space P^n the only n-dimensional projective manifold X for which the Seshadri constant epsilon(T_X;x_0) of the tangent bundle is positive at some point x_0 in X? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,325 | OWR-17296-009 | Rationality of Seshadri Constants on Plane Blowups | For a smooth projective surface $X$ obtained by blowing up $\mathbb{P}^2$ at very general points and an ample line bundle $L$ on $X$, is the global Seshadri constant $\varepsilon(X,L)$ always rational, or can it be irrational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-009",
"literature-status:open",
"owr-year:2019"
] | The cited implications make irrational Seshadri constants conditional on strengthened SHGH or Nagata conjectures, so they provide no unconditional example and the general irrationality question remains open. | [
{
"url": "https://digitalcommons.unl.edu/mathfacpub/120/",
"label": "Single-point Seshadri constants on rational surfaces"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0007449725000430",
"label": "Seshadri constants and related conjectures over characteristic zero"
},
{
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | For a smooth projective surface $X$ obtained by blowing up $\mathbb{P}^2$ at very general points and an ample line bundle $L$ on $X$, is the global Seshadri constant $\varepsilon(X,L)$ always rational, or can it be irrational? | For a smooth projective surface X obtained by blowing up P^2 at very general points and an ample line bundle L on X, is the global Seshadri constant epsilon(X,L) always rational, or can it be irrational? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,326 | OWR-17296-010 | Nonreduced Special Linear Systems on Plane Blowups | Let $X$ be the blowup of $\mathbb{P}^2$ at $r$ very general points and let $D=dH-\sum_i m_iE_i$. If the linear system $|D|$ is special, meaning its dimension exceeds $\max\{\binom{d+2}{2}-\sum_i\binom{m_i+1}{2}-1,-1\}$, must every divisor in $|D|$ be nonreduced? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-010",
"literature-status:open",
"owr-year:2019"
] | The extracted sentence introduces the SHGH conjecture for at least ten points, whose general assertion remains unresolved and continues to underlie open Seshadri problems. | [
{
"url": "https://arxiv.org/abs/math/0304124",
"label": "Roe, On the Nagata conjecture"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0022404920300426",
"label": "Rationality of Seshadri constants on general blow-ups"
},
{
"url": "https://doi.org/10.4171/owr/2019/53",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Let $X$ be the blowup of $\mathbb{P}^2$ at $r$ very general points and let $D=dH-\sum_i m_iE_i$. If the linear system $|D|$ is special, meaning its dimension exceeds $\max\{\binom{d+2}{2}-\sum_i\binom{m_i+1}{2}-1,-1\}$, must every divisor in $|D|$ be nonreduced? | Let X be the blowup of P^2 at r very general points and let D=dH-sum_i m_iE_i. If the linear system |D| is special, meaning its dimension exceeds max{(d+2 choose 2)-sum_i(m_i+1 choose 2)-1,-1}, must every divisor in |D| be nonreduced? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,327 | OWR-17296-011 | Bounded Negativity Conjecture for Complex Projective Surfaces | Does every smooth projective surface $X$ over the complex numbers have bounded negativity; that is, does there exist $b(X)$ such that $C^2\geq-b(X)$ for every reduced irreducible curve $C\subset X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17296-018"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17296-011",
"literature-status:open",
"owr-year:2019"
] | Bounded negativity is false in positive characteristic, but the characteristic-zero conjecture remains open in general, including difficult blow-ups of the projective plane. | [
{
"url": "https://arxiv.org/abs/1109.1881",
"label": "Negative curves on algebraic surfaces"
},
{
"url": "https://arxiv.org/abs/2103.02172",
"label": "Unbounded negativity on rational surfaces in positive characteristic"
},
{
"url": "https://doi.org/10.1007/s00229-019-01157-2",
"labe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Does every smooth projective surface $X$ over the complex numbers have bounded negativity; that is, does there exist $b(X)$ such that $C^2\geq-b(X)$ for every reduced irreducible curve $C\subset X$? | Does every smooth projective surface X over the complex numbers have bounded negativity; that is, does there exist b(X) such that C^2 is at least -b(X) for every reduced irreducible curve C contained in X? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,328 | OWR-17296-012 | Unbounded Semi Effective Orders on Projective Surfaces | Does there exist a smooth projective surface $X$ carrying primitive classes $F_n$ whose semi-effective orders $k_n$, defined as the least positive $k$ for which $kF_n$ is numerically equivalent to an effective divisor, tend to infinity? Is the analogous phenomenon possible when the effective divisors are irreducible cu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-012",
"literature-status:open",
"owr-year:2019"
] | The prime-divisor case with semi-effective order greater than two remains unresolved; higher orders are known for non-prime or reducible effective multiples, so the extracted question is still open. | [
{
"url": "https://arxiv.org/abs/1904.07486",
"label": "Bauer--Harbourne--Kuronya--Nickel, Bounded volume denominators and bounded negativity"
},
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Does there exist a smooth projective surface $X$ carrying primitive classes $F_n$ whose semi-effective orders $k_n$, defined as the least positive $k$ for which $kF_n$ is numerically equivalent to an effective divisor, tend to infinity? Is the analogous phenomenon possible when the effective divisors are irreducible cu... | Does there exist a smooth projective surface X carrying primitive classes F_n whose semi-effective orders k_n, defined as the least positive k for which kF_n is numerically equivalent to an effective divisor, tend to infinity? Is the analogous phenomenon possible when the effective divisors are irreducible curves? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,329 | OWR-17296-014 | Rationality of Seshadri Constants from Plane-Curve Singularities | Let $C$ be a reduced plane curve, let $Z$ be its singular-point set, and let $\widetilde C$ be its proper transform on the blowup of $\mathbb{P}^2$ at $Z$. If $\widetilde C^2<-1$, must the Seshadri constant $\varepsilon(Z)$ be rational, and can it be computed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-014",
"literature-status:open",
"owr-year:2019"
] | The cited workshop asks for general computation and rationality results for multipoint Seshadri constants associated with line arrangements; known examples and bounds do not settle the extracted general question. | [
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Let $C$ be a reduced plane curve, let $Z$ be its singular-point set, and let $\widetilde C$ be its proper transform on the blowup of $\mathbb{P}^2$ at $Z$. If $\widetilde C^2<-1$, must the Seshadri constant $\varepsilon(Z)$ be rational, and can it be computed? | Let C be a reduced plane curve, let Z be its singular-point set, and let C-tilde be its proper transform on the blowup of P^2 at Z. If C-tilde^2 is less than -1, must the Seshadri constant epsilon(Z) be rational, and can it be computed? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,330 | OWR-17296-015 | Waldschmidt Constants of Plane Curve Singular Sets | For a reduced plane curve $C$ with singular set $Z$, must the Waldschmidt constant of the ideal $I_Z$ be rational, and can it be computed, for example for Klein's arrangement of $21$ lines? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-015",
"literature-status:open",
"owr-year:2019"
] | The rationality and computability of the Waldschmidt constant in the Klein arrangement test case remains unresolved in the primary literature; later work gives estimates but not a general solution. | [
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
},
{
"url": "https://arxiv.org/abs/1609.08648",
"label": "Bauer et al., symmetric blowups and Waldschmidt constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | For a reduced plane curve $C$ with singular set $Z$, must the Waldschmidt constant of the ideal $I_Z$ be rational, and can it be computed, for example for Klein's arrangement of $21$ lines? | For a reduced plane curve C with singular set Z, must the Waldschmidt constant of the ideal I_Z be rational, and can it be computed, for example for Klein's arrangement of 21 lines? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,331 | OWR-17296-016 | Harbourne Constants, Symbolic Powers, and Resurgence of Line Arrangements | For complex line arrangements $C$, must $H(C)=\widetilde C^2$ divided by the number of singular points be at least $-225/67$, and what is the infimum of $H(C)$ over rational line arrangements? Also, which finite sets $Z\subset\mathbb{P}^2$ satisfy $I_Z^{(3)}\not\subset I_Z^2$, and can the resurgence of the singular-poi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-016",
"literature-status:open",
"owr-year:2019"
] | The record combines open Harbourne-constant, symbolic-power, and resurgence questions; subsequent arrangement results provide examples and bounds but do not determine the requested infima or characterize all containments. | [
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
},
{
"url": "https://arxiv.org/abs/1407.2966",
"label": "Bauer et al., bounded negativity and arrangements of lines"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | For complex line arrangements $C$, must $H(C)=\widetilde C^2$ divided by the number of singular points be at least $-225/67$, and what is the infimum of $H(C)$ over rational line arrangements? Also, which finite sets $Z\subset\mathbb{P}^2$ satisfy $I_Z^{(3)}\not\subset I_Z^2$, and can the resurgence of the singular-poi... | For complex line arrangements C, must H(C)=C-tilde^2 divided by the number of singular points be at least -225/67, and what is the infimum of H(C) over rational line arrangements? Also, which finite sets Z in P^2 satisfy I_Z^{(3)} not contained in I_Z^2, and can the resurgence of the singular-point ideal be computed fo... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,332 | OWR-17296-017 | Supersolvable Line Arrangements with One Modular Point | Can supersolvable line arrangements be classified, in particular can complex supersolvable arrangements with exactly one modular point be classified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-017",
"literature-status:open",
"owr-year:2019"
] | Complex supersolvable arrangements with more than one modular point have substantial classifications, but the one-modular-point case remains explicitly open. | [
{
"url": "https://doi.org/10.1007/s10801-020-00987-8",
"label": "Hanumanthu--Harbourne, real and complex supersolvable line arrangements"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2020.02.007",
"label": "Abe--Dimca, complex supersolvable line arrangements"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Can supersolvable line arrangements be classified, in particular can complex supersolvable arrangements with exactly one modular point be classified? | Can supersolvable line arrangements be classified, in particular can complex supersolvable arrangements with exactly one modular point be classified? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,333 | OWR-17296-018 | Duplicate Bounded Negativity Conjecture | For every smooth projective surface X in characteristic zero, is there a uniform lower bound for C^2 over all reduced irreducible curves C contained in X? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a second formulation of the Bounded Negativity Conjecture represented canonically by OWR-17296-011) | [
"OWR-17296-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17296-018",
"literature-status:open",
"owr-year:2019"
] | The Bounded Negativity Conjecture is proved for several special surfaces but remains open for smooth projective surfaces in general. | [
{
"url": "https://arxiv.org/abs/1407.2966",
"label": "Bauer et al., bounded negativity and arrangements of lines"
},
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | null | For every smooth projective surface X in characteristic zero, is there a uniform lower bound for C^2 over all reduced irreducible curves C contained in X? | unrecoverable | The official report confirms that this is a second formulation of the Bounded Negativity Conjecture represented canonically by OWR-17296-011. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,334 | OWR-17296-019 | Bounded Negativity for Root of Unity Blowups | Let $\varepsilon$ be a primitive $m$th root of unity, let $Z(m)$ be the points $(1:\varepsilon^\alpha:\varepsilon^\beta)$ in $\mathbb{P}^2$ for $1\leq\alpha,\beta\leq m$, and let $X(m)$ be the blowup of $\mathbb{P}^2$ at $Z(m)$. Is negativity bounded on $X(m)$, and if so what is its bound $b(X(m))$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313](https://doi.org/10.4171/owr/2019/53)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-17296-019",
"literature-status:open",
"owr-year:2019"
] | For the root-of-unity configuration X(m), the cited work still poses bounded negativity and the value of its bound as an open problem; results for the nine-point Fermat case do not cover all m. | [
{
"url": "https://www.cmi.ac.in/~krishna/negative-curves-special-rational-surfaces.pdf",
"label": "Farnik et al., negative curves on special rational surfaces"
},
{
"url": "https://ems.press/content/serial-article-files/46833",
"label": "OWR report on Seshadri constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/53 | null | null | null | Let $\varepsilon$ be a primitive $m$th root of unity, let $Z(m)$ be the points $(1:\varepsilon^\alpha:\varepsilon^\beta)$ in $\mathbb{P}^2$ for $1\leq\alpha,\beta\leq m$, and let $X(m)$ be the blowup of $\mathbb{P}^2$ at $Z(m)$. Is negativity bounded on $X(m)$, and if so what is its bound $b(X(m))$? | Let epsilon be a primitive m-th root of unity, let Z(m) be the points (1:epsilon^alpha:epsilon^beta) in P^2 for 1 less than or equal to alpha,beta less than or equal to m, and let X(m) be the blowup of P^2 at Z(m). Is negativity bounded on X(m), and if so what is its bound b(X(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 | Mini-Workshop: Seshadri Constants (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/53, pp. 3271--3313 |
30,004,335 | OWR-17297-003 | Uniform Doubling for Compact Connected Lie Groups | Is every compact connected Lie group $K$ uniformly doubling, meaning that the volume-doubling constants of all left-invariant Riemannian metrics on $K$ have a common finite upper bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/54, pp. 3315--3407](https://doi.org/10.4171/owr/2019/54)
## Literature revi... | 3 | open | null | 2,019 | 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-17297-003",
"literature-status:open",
"owr-year:2019"
] | Uniform doubling is proved for SU(2), U(2), and related low-dimensional cases, while the conjecture for every compact connected Lie group remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46830?nt=1",
"label": "OWR report on heat kernels and functional inequalities"
},
{
"url": "https://www.birs.ca/workshops/2024/24w5314/files/Nathaniel%20Eldredge.pdf",
"label": "Eldredge, uniform volume doubling for U(2)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/54 | null | null | null | Is every compact connected Lie group $K$ uniformly doubling, meaning that the volume-doubling constants of all left-invariant Riemannian metrics on $K$ have a common finite upper bound? | Is every compact connected Lie group K uniformly doubling, meaning that the volume-doubling constants of all left-invariant Riemannian metrics on K have a common finite upper bound? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/54, pp. 3315--3407 |
30,004,336 | OWR-17298-002 | Dixmier's Amenability Problem for Unitarizable Groups | Dixmier's problem asks whether every unitarizable discrete group is amenable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458](https://doi.org/10.4171/owr/2019/55)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17298-002",
"literature-status:open",
"owr-year:2019"
] | Dixmier's problem, whether unitarizability characterizes amenability, remains unresolved for non-amenable groups without free subgroups. | [
{
"url": "https://ems.press/content/serial-article-files/46835",
"label": "OWR report on groups, dynamics, and approximation"
},
{
"url": "https://arxiv.org/abs/0902.4585",
"label": "Monod--Ozawa, the Dixmier problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/55 | null | null | null | Dixmier's problem asks whether every unitarizable discrete group is amenable. | Dixmier's problem asks whether every unitarizable discrete group is amenable. | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458 |
30,004,337 | OWR-17298-003 | Pointwise Equidistribution Under Toral Endomorphisms with Fewer Hypotheses | Let $A$ and $B$ be nonsingular integer matrices and let $\mu$ be an $A$-invariant ergodic probability measure on $\mathbb{T}^d$ with positive entropy, satisfying irreducibility of every characteristic polynomial of $B^n$ and with no power of $B$ conjugate to a power of $A$. Are additional hypotheses such as (3a)–(3c) u... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458](https://doi.org/10.4171/owr/2019/55)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17298-003",
"literature-status:open",
"owr-year:2019"
] | The primary workshop account explicitly leaves open whether the additional spectral and eigenspace hypotheses are necessary for the pointwise equidistribution conclusion. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/f27753e6-ce45-4d59-ba59-812d45c5f07b/download",
"label": "OWR report on groups, dynamics, and approximation"
},
{
"url": "https://arxiv.org/abs/1904.12506",
"label": "Algom, a simultaneous Host equidistribution theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/55 | null | null | null | Let $A$ and $B$ be nonsingular integer matrices and let $\mu$ be an $A$-invariant ergodic probability measure on $\mathbb{T}^d$ with positive entropy, satisfying irreducibility of every characteristic polynomial of $B^n$ and with no power of $B$ conjugate to a power of $A$. Are additional hypotheses such as (3a)–(3c) u... | Let A and B be nonsingular integer matrices and let mu be an A-invariant ergodic probability measure on T^d with positive entropy, satisfying irreducibility of every characteristic polynomial of B^n and with no power of B conjugate to a power of A. Are additional hypotheses such as (3a)-(3c) unnecessary for almost-ever... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458 |
30,004,338 | OWR-17298-004 | Free Quasi-Actions and Almost-Ramanujan Subgroups | For a standard probability space $(X,\mu)$, how many essentially free quasi-actions of $\operatorname{Aut}(X,\mu)$ exist up to conjugacy, and are all factors of the canonical product quasi-action $\rho_\infty$? Separately, for $k\geq 2$ and $\varepsilon>0$, does there exist $C$ such that every $k$-generated subgroup of... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458](https://doi.org/10.4171/owr/2019/55)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,019 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17298-004",
"literature-status:open",
"owr-year:2019"
] | The record contains unresolved classification of essentially free quasi-actions and an unresolved almost-Ramanujan question for large-girth free-group Cayley graphs; partial graph constructions do not settle either formulation. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/f27753e6-ce45-4d59-ba59-812d45c5f07b/content",
"label": "OWR report on groups, dynamics, and approximation"
},
{
"url": "https://arxiv.org/abs/2304.01281",
"label": "Alon--Wei, large-girth almost-Ramanujan graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/55 | null | null | null | For a standard probability space $(X,\mu)$, how many essentially free quasi-actions of $\operatorname{Aut}(X,\mu)$ exist up to conjugacy, and are all factors of the canonical product quasi-action $\rho_\infty$? Separately, for $k\geq 2$ and $\varepsilon>0$, does there exist $C$ such that every $k$-generated subgroup of... | For a standard probability space (X,mu), how many essentially free quasi-actions of Aut(X,mu) exist up to conjugacy, and are all factors of the canonical product quasi-action rho_infinity? Separately, for k at least 2 and epsilon greater than 0, does there exist C such that every k-generated subgroup of a free group wi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458 |
30,004,339 | OWR-17298-007 | Cost and First $L^2$ Betti Numbers | For every finitely generated group $\Gamma$, is $\operatorname{cost}(\Gamma)=1+\beta_1^{(2)}(\Gamma)$, where $\beta_1^{(2)}$ is the first $L^2$-Betti number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458](https://doi.org/10.4171/owr/2019/55)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,019 | 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-17298-007",
"literature-status:open",
"owr-year:2019"
] | The cost equality with one plus the first square-summable Betti number remains a general open problem, although cost one is known for Kazhdan groups and other special classes. | [
{
"url": "https://mathweb.ucsd.edu/~bseward/Files/costbettientropy.pdf",
"label": "Gaboriau--Seward, cost and square-summable Betti numbers"
},
{
"url": "https://ems.press/content/serial-article-files/46835",
"label": "OWR report on groups, dynamics, and approximation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/55 | null | null | null | For every finitely generated group $\Gamma$, is $\operatorname{cost}(\Gamma)=1+\beta_1^{(2)}(\Gamma)$, where $\beta_1^{(2)}$ is the first $L^2$-Betti number? | For every finitely generated group Gamma, is cost(Gamma)=1+beta_1^{(2)}(Gamma), where beta_1^{(2)} is the first L^2-Betti number? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Groups, Dynamics, and Approximation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/55, pp. 3409--3458 |
30,004,340 | OWR-17299-001 | Universality Across the Random-Band-Matrix Localization Transition | What is the universality class of random band matrices as the matrix size $N$ tends to infinity while the bandwidth $W$ varies, including across the localization–delocalization transition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Random Matrices (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/56, pp. 3459--3527](https://doi.org/10.4171/owr/2019/56)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17299-001",
"literature-status:partially-solved",
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] | Universality is established in several band-width regimes, including mean-field and widths above critical thresholds, but the full varying-width universality class and transition remain open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/bd70698e-b340-45c1-9989-9cb604446b31/download",
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{
"url": "https://arxiv.org/abs/1602.02312",
"label": "Bourgade--Erdos--Yau--Yin, universality for random band matrices"
},
{
"url": "https://arxiv.or... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/56 | null | null | null | What is the universality class of random band matrices as the matrix size $N$ tends to infinity while the bandwidth $W$ varies, including across the localization–delocalization transition? | What is the universality class of random band matrices as the matrix size N tends to infinity while the band width W varies, including across the localization-delocalization transition? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Random Matrices (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/56, pp. 3459--3527 |
30,004,341 | OWR-17300-005 | S-Unit Differences of Singular Moduli | For a fixed set $S$ of primes, are there finitely many differences of singular moduli that are $S$-units? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17300-005",
"literature-status:open",
"owr-year:2019"
] | For each fixed singular modulus j_0 and finite S, finiteness of singular j with j-j_0 an S-unit is known, but the extracted question ranges over pairs of singular moduli and asks for a uniform finiteness statement that remains conjectural. | [
{
"url": "https://doi.org/10.1017/S0305004122000378",
"label": "Campagna, effective bounds on differences of singular moduli"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | For a fixed set $S$ of primes, are there finitely many differences of singular moduli that are $S$-units? | For a fixed set S of primes, are there finitely many differences of singular moduli that are S-units? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,342 | OWR-17300-006 | Harder Congruences for Holomorphic Jacobi Forms | Assume $k\geq 3$, $j\geq 0$, and $j\equiv 2\pmod 4$. For a Hecke-eigen cusp form $f$ in $S_{2k+j-2}(\Gamma_1)$, let $\phi_0$ be the corresponding degree-one Jacobi form and $E(\phi_0)$ its degree-two Klingen lift. The holomorphic Jacobi-form version of Harder's conjecture asserts that there is a degree-two holomorphic ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17300-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17300-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The holomorphic Jacobi-form version of Harder’s conjecture is proved in the report only under explicit arithmetic hypotheses; later work proves further cases of related Harder congruences, but no general unconditional resolution is established. | [
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "Katsurada, holomorphic Jacobi-form Harder conjecture"
},
{
"url": "https://doi.org/10.2969/jmsj/87988798",
"label": "Atobe--Chida--Ibukiyama--Katsurada--Yamauchi, Harder’s conjecture I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | Assume $k\geq 3$, $j\geq 0$, and $j\equiv 2\pmod 4$. For a Hecke-eigen cusp form $f$ in $S_{2k+j-2}(\Gamma_1)$, let $\phi_0$ be the corresponding degree-one Jacobi form and $E(\phi_0)$ its degree-two Klingen lift. The holomorphic Jacobi-form version of Harder's conjecture asserts that there is a degree-two holomorphic ... | Assume k\geq3, j\geq0, and j\equiv2\pmod 4. For a Hecke-eigen cusp form f in S_{2k+j-2}(\Gamma_1), let \phi_0 be the corresponding degree-one Jacobi form and E(\phi_0) its degree-two Klingen lift. The holomorphic Jacobi-form version of Harder's conjecture asserts that there is a degree-two holomorphic Jacobi form \Phi ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,343 | OWR-17300-007 | Conditional Harder-Congruence Theorem | Under the four stated hypotheses on Fourier coefficients, the l-unit condition, denominators, and exclusion of endoscopic congruences, the holomorphic Jacobi-form version of Harder's conjecture is proved; in particular l divides L^{alg}(2k+j-3,f). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report identifies this extraction as a proved theorem under four explicit hypotheses, not as a separate open problem; the under) | [
"OWR-17300-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17300-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The displayed theorem proves the Jacobi-form congruence under conditions (1)--(4), so it is a genuine conditional and case-based advance; the underlying Harder conjecture is not known in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "Katsurada, congruence for Klingen--Eisenstein series"
},
{
"url": "https://doi.org/10.2969/jmsj/87988798",
"label": "Harder’s conjecture I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | null | Under the four stated hypotheses on Fourier coefficients, the l-unit condition, denominators, and exclusion of endoscopic congruences, the holomorphic Jacobi-form version of Harder's conjecture is proved; in particular l divides L^{alg}(2k+j-3,f). | unrecoverable | The official report identifies this extraction as a proved theorem under four explicit hypotheses, not as a separate open problem; the underlying unrestricted conjecture is represented by OWR-17300-006. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,344 | OWR-17300-008 | Conditional Modularity Theorem for Chow Cycles | Assuming the Bloch--Beilinson conjecture, the generating series of special Chow cycles \phi_n(\tau,\varphi,S)=\sum_{T\geq0}[Z(T,\varphi)]q^T is a Hilbert--Siegel modular form for every 1\leq n\leq m; after applying any linear functional on the Chow group, its q-series is a complex Hilbert--Siegel modular form, and the ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,019 | 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 identifies this extraction as a theorem proved assuming the Bloch–Beilinson conjecture, not as a separately posed open p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17300-008",
"literature-status:partially-solved",
"owr-year:2019"
] | The modularity statement for Chow-valued generating series is proved assuming the Beilinson--Bloch injectivity conjecture, with unconditional results in important special cases; the general conditional hypothesis remains unresolved. | [
{
"url": "https://doi.org/10.4153/S000843952000020X",
"label": "Maeda, modularity of special cycles"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | null | Assuming the Bloch--Beilinson conjecture, the generating series of special Chow cycles \phi_n(\tau,\varphi,S)=\sum_{T\geq0}[Z(T,\varphi)]q^T is a Hilbert--Siegel modular form for every 1\leq n\leq m; after applying any linear functional on the Chow group, its q-series is a complex Hilbert--Siegel modular form, and the ... | unrecoverable | The official report identifies this extraction as a theorem proved assuming the Bloch–Beilinson conjecture, not as a separately posed open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,345 | OWR-17300-009 | p-Adic Gross–Kudla–Zagier Formula for Diagonal Cycles | For the canonical $p$-adic height pairing on the modified diagonal cycles of three modular elliptic curves, the conjectural $p$-adic Gross–Kudla–Zagier formula asserts that $\langle h^*\Delta^\dagger_\xi,h'^*\Delta^\dagger_\xi\rangle_{\mathrm{Nek}}(\sqrt{3}-1)E_p(\operatorname{Fil}^+V_pE)=L'_p(E,1)I^\natural(h\otimes h... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 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-17300-009",
"literature-status:open",
"owr-year:2019"
] | The displayed p-adic height and derivative identity is presented as a conjecture; p-adic Gross--Zagier and diagonal-cycle results prove important special cases, but not the full formula in the extracted generality. | [
{
"url": "https://doi.org/10.24033/asens.2227",
"label": "Bertolini--Seveso--Venerucci, diagonal cycles and Euler systems I"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | For the canonical $p$-adic height pairing on the modified diagonal cycles of three modular elliptic curves, the conjectural $p$-adic Gross–Kudla–Zagier formula asserts that $\langle h^*\Delta^\dagger_\xi,h'^*\Delta^\dagger_\xi\rangle_{\mathrm{Nek}}(\sqrt{3}-1)E_p(\operatorname{Fil}^+V_pE)=L'_p(E,1)I^\natural(h\otimes h... | For the canonical p-adic height pairing on the modified diagonal cycles of three modular elliptic curves, the conjectural p-adic Gross--Kudla--Zagier formula asserts that \langle h^*\Delta^\dagger_\xi,h'^*\Delta^\dagger_\xi\rangle_{Nek}(\sqrt{3}-1)E_p(\operatorname{Fil}^+V_pE)=L'_p(E,1)I^\natural(h\otimes h')\cdot(a po... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,346 | OWR-17300-010 | Algebraicity of Rigid Cocycle Values at Real Multiplication Points | If $J$ is a rigid meromorphic cocycle, then there is a finite extension $H_J$ of $\mathbb{Q}$ such that for every real-multiplication point $\tau$, the value $J[\tau]$ lies in the compositum $H_JH_\tau$, where $H_\tau$ is the narrow ring class field attached to $\tau$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 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-17300-010",
"literature-status:open",
"owr-year:2019"
] | The algebraicity assertion for values of arbitrary rigid meromorphic cocycles at all real-multiplication points remains a conjecture; algebraicity is proved for special Dedekind--Rademacher values, not for the full extracted claim. | [
{
"url": "https://www.math.mcgill.ca/darmon/pub/Articles/Expository/15.Rigid-Meromorphic-Cocycles/paper.pdf",
"label": "Darmon, rigid meromorphic cocycles"
},
{
"url": "https://doi.org/10.4171/JEMS/1344",
"label": "Darmon--Pozzi--Vonk, Dedekind--Rademacher cocycle"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | If $J$ is a rigid meromorphic cocycle, then there is a finite extension $H_J$ of $\mathbb{Q}$ such that for every real-multiplication point $\tau$, the value $J[\tau]$ lies in the compositum $H_JH_\tau$, where $H_\tau$ is the narrow ring class field attached to $\tau$. | If J is a rigid meromorphic cocycle, then there is a finite extension H_J of Q such that for every real-multiplication point \tau, the value J[\tau] lies in the compositum H_JH_\tau, where H_\tau is the narrow ring class field attached to \tau. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,347 | OWR-17300-012 | Elliptic Curve Values of Rigid Cocycles | For an elliptic rigid cocycle attached to a weight-two newform $f$ and every real-multiplication point $\tau$, the values $J_f^+[\tau]$ and $J_f^-[\tau]$ should belong to the elliptic curve $E(H_\tau)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 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-17300-012",
"literature-status:open",
"owr-year:2019"
] | The conjectured field-of-definition statement for the RM values of the f-components of rigid meromorphic cocycles remains open in general; current theorems cover special cocycles such as the Dedekind--Rademacher class. | [
{
"url": "https://doi.org/10.1016/j.jnt.2020.12.012",
"label": "Darmon--Vonk, arithmetic intersections of modular geodesics"
},
{
"url": "https://doi.org/10.4171/JEMS/1344",
"label": "Darmon--Pozzi--Vonk, special RM values"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | For an elliptic rigid cocycle attached to a weight-two newform $f$ and every real-multiplication point $\tau$, the values $J_f^+[\tau]$ and $J_f^-[\tau]$ should belong to the elliptic curve $E(H_\tau)$. | For an elliptic rigid cocycle attached to a weight-two newform f and every real-multiplication point \tau, the values J_f^+[\tau] and J_f^-[\tau] should belong to the elliptic curve E(H_\tau). | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,348 | OWR-17300-013 | Comparing Eisenstein and Twisted Doubling L Functions | For Brylinski–Deligne covering groups, how do the L-functions obtained from constant terms of Eisenstein series compare with the L-functions obtained from twisted doubling integrals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 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-17300-013",
"literature-status:open",
"owr-year:2019"
] | The record is an underspecified comparison question rather than a precise theorem; twisted-doubling integral representations are developed for several classical-group L-functions, but no general identification answering this extracted question is established. | [
{
"url": "https://arxiv.org/abs/1710.00905",
"label": "Cai--Friedberg--Ginzburg--Kaplan, doubling constructions"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | For Brylinski–Deligne covering groups, how do the L-functions obtained from constant terms of Eisenstein series compare with the L-functions obtained from twisted doubling integrals? | For Brylinski--Deligne covering groups, how do the L-functions obtained from constant terms of Eisenstein series compare with the L-functions obtained from twisted doubling integrals? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,349 | OWR-17300-014 | Rational Singularities of Integral Modular Curve Models | For which congruence subgroups $\Gamma$ does the modular curve model $X_\Gamma$ have rational singularities, and more generally for which primes $p$ and groups $\Gamma$ does its model $(X_\Gamma)_{\mathbb{Z}_{(p)}}$ have rational singularities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,019 | 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-17300-014",
"literature-status:partially-solved",
"owr-year:2019"
] | The rational-singularity question for integral modular-curve models has positive answers in substantial cases, including the Raynaud range and additional cases from Manin-conjecture results, but no general classification for all \Gamma and p is known. | [
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report, Question 3 and known cases"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | For which congruence subgroups $\Gamma$ does the modular curve model $X_\Gamma$ have rational singularities, and more generally for which primes $p$ and groups $\Gamma$ does its model $(X_\Gamma)_{\mathbb{Z}_{(p)}}$ have rational singularities? | For which congruence subgroups \Gamma does the modular curve model X_\Gamma have rational singularities, and more generally for which primes p and groups \Gamma does its model (X_\Gamma)_{\mathbb Z_{(p)}} have rational singularities? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,350 | OWR-17300-017 | Cuspidal Spectral-Multiplier Theorem | Let G be a reductive group over Q, S a finite set of primes, and \pi an irreducible cuspidal automorphic representation with K-invariants that is not S-CAP. Then there exists an S-multiplier \mu_\pi such that for every test function f, the convolution operator R(\mu_\pi\star f) vanishes on the orthogonal complement of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,019 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 identifies this extraction as Theorem 1, a proved spectral-isolation result for non-S-CAP cuspidal representations, not ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17300-017",
"literature-status:open",
"owr-year:2019"
] | The extracted record is a truncated fragment beginning with `Conjecture' and does not state a complete mathematical claim; under the required rule for unclear records it is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | null | Let G be a reductive group over Q, S a finite set of primes, and \pi an irreducible cuspidal automorphic representation with K-invariants that is not S-CAP. Then there exists an S-multiplier \mu_\pi such that for every test function f, the convolution operator R(\mu_\pi\star f) vanishes on the orthogonal complement of ... | unrecoverable | The official report identifies this extraction as Theorem 1, a proved spectral-isolation result for non-S-CAP cuspidal representations, not as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,351 | OWR-17300-018 | Siegel Type Fourier Expansions Without Complex Structures | If a reductive $\mathbb{Q}$-group $G$ has an associated symmetric space without complex structure, is there a notion of modular forms for $G$ possessing a Fourier expansion analogous to the Fourier expansion of Siegel modular forms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606](https://doi.org/10.4171/owr/2019/57)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,019 | 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-17300-018",
"literature-status:partially-solved",
"owr-year:2019"
] | General automorphic-form and Fourier-coefficient theories for reductive groups now provide broad analogues, including reduction principles for Fourier coefficients, but no single holomorphic modular-form theory with the requested Siegel-like expansion exists for all such groups. | [
{
"url": "https://arxiv.org/abs/1811.05966",
"label": "Gourevitch--Gustafsson--Kleinschmidt--Persson--Sahi, Fourier coefficients"
},
{
"url": "https://doi.org/10.4171/owr/2019/57",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/57 | null | null | null | If a reductive $\mathbb{Q}$-group $G$ has an associated symmetric space without complex structure, is there a notion of modular forms for $G$ possessing a Fourier expansion analogous to the Fourier expansion of Siegel modular forms? | If a reductive Q-group G has an associated symmetric space without complex structure, is there a notion of modular forms for G possessing a Fourier expansion analogous to the Fourier expansion of Siegel modular forms? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Modular Forms (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/57, pp. 3529--3606 |
30,004,352 | OWR-17464-003 | Rainbow Matchings Across Families of Matchings | Does every collection of $n$ matchings, each of size $n$, in a graph contain a rainbow matching of size $n-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 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-17464-003",
"literature-status:open",
"owr-year:2020"
] | The Aharoni--Berger rainbow-matching conjecture for n matchings of size n in an arbitrary graph remains open; known results give only lower bounds such as 2n/3-O(1) and stronger bounds in restricted graph classes. | [
{
"url": "https://doi.org/10.37236/10173",
"label": "Aharoni--Berger--Chudnovsky--Zerbib, rainbow matchings"
},
{
"url": "https://arxiv.org/abs/2501.03216",
"label": "Bowtell--Freschi--Kronenberg--Yan, improved bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | Does every collection of $n$ matchings, each of size $n$, in a graph contain a rainbow matching of size $n-1$? | Does every collection of n matchings of size n in a graph contain a rainbow matching of size n-1? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,353 | OWR-17464-004 | Euclidean Red–Blue Ramsey Sets | For which subsets $K$ of Euclidean space $\mathbb E^n$ does every red–blue coloring of $\mathbb E^n$ contain either a red pair at distance $1$ or a blue isometric copy of $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17464-004",
"literature-status:open",
"owr-year:2020"
] | The general classification of pairs (n,K) satisfying the asymmetric Euclidean Ramsey relation remains open; Conlon--Fox proved strong exponential lower-bound constructions and many small-dimensional cases are known, but not the full question. | [
{
"url": "https://doi.org/10.1007/s00454-018-9980-5",
"label": "Conlon--Fox, lines in Euclidean Ramsey theory"
},
{
"url": "https://arxiv.org/abs/2606.17194",
"label": "recent bounds for Euclidean Ramsey theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | For which subsets $K$ of Euclidean space $\mathbb E^n$ does every red–blue coloring of $\mathbb E^n$ contain either a red pair at distance $1$ or a blue isometric copy of $K$? | For which subsets K of Euclidean space E^n does every red-blue coloring of E^n contain either a red pair at distance one or a blue isometric copy of K? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,354 | OWR-17464-009 | Thresholds for Universal Random Permutations | For every fixed $\varepsilon>0$, does a uniformly random permutation of length $(1+\varepsilon)k^2/4$ become $k$-universal with high probability as $k\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17464-009",
"literature-status:partially-solved",
"owr-year:2020"
] | Alon’s conjecture that a random permutation of length about (1+\varepsilon)k^2/4 is k-universal remains open; He and Kwan proved the substantial upper bound 2000k^2 log log k, improving the earlier O(k^2 log k) bound. | [
{
"url": "https://doi.org/10.1112/blms.12345",
"label": "He--Kwan, universality of random permutations"
},
{
"url": "https://doi.org/10.4171/owr/2020/1",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | For every fixed $\varepsilon>0$, does a uniformly random permutation of length $(1+\varepsilon)k^2/4$ become $k$-universal with high probability as $k\to\infty$? | For every fixed \varepsilon>0, does a uniformly random permutation of length (1+\varepsilon)k^2/4 become k-universal with high probability as k tends to infinity? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,355 | OWR-17464-010 | Large-Scale Geometry of Graphs and Manifolds | What can be said about the global or large-scale geometry of graphs and its relationship with differential geometry on manifolds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 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-17464-010",
"literature-status:open",
"owr-year:2020"
] | The record gives only a broad research question about large-scale graph geometry, not a precise proposition with a known resolution; substantial theories exist, but the extracted question remains open in this form. | [
{
"url": "https://doi.org/10.4171/owr/2020/1",
"label": "Linial, large-scale geometry of graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | What can be said about the global or large-scale geometry of graphs and its relationship with differential geometry on manifolds? | What can be said about the global or large-scale geometry of graphs and its relationship with differential geometry on manifolds? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,356 | OWR-17464-011 | Unbounded Girth Minus Diameter at Minimum Degree Three | Can $\operatorname{girth}(G)-\operatorname{diam}(G)$ be arbitrarily large among graphs $G$ of minimum degree at least $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 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-17464-011",
"literature-status:open",
"owr-year:2020"
] | The existence of graphs of minimum degree at least 3 with unbounded girth minus diameter remains open; high-girth regular graph constructions do not settle the girth--diameter trade-off. | [
{
"url": "https://doi.org/10.1002/rsa.20976",
"label": "Linial--Simkin, high-girth regular graphs"
},
{
"url": "https://doi.org/10.4171/owr/2020/1",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | Can $\operatorname{girth}(G)-\operatorname{diam}(G)$ be arbitrarily large among graphs $G$ of minimum degree at least $3$? | Can girth(G)-diam(G) be arbitrarily large for a graph G in which every vertex has degree at least 3? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,357 | OWR-17464-012 | Symmetric Intersecting Families in Discrete Product Spaces | For intersecting families $A\subseteq[k]^n$ with $k\geq3$, what bounds follow when highly asymmetric, single-coordinate extremal examples are forbidden? In particular, how small must $A$ be when its automorphism group acts transitively on the coordinates? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,020 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17464-012",
"literature-status:partially-solved",
"owr-year:2020"
] | For fixed alphabet size at least three, symmetric intersecting families of vectors are o of the full cube; the broader extremal classification after excluding one-coordinate examples remains incomplete. | [
{
"url": "https://arxiv.org/abs/1909.11578",
"label": "Eberhard--Kahn--Narayanan--Spirkl"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | For intersecting families $A\subseteq[k]^n$ with $k\geq3$, what bounds follow when highly asymmetric, single-coordinate extremal examples are forbidden? In particular, how small must $A$ be when its automorphism group acts transitively on the coordinates? | For intersecting families A\subseteq[k]^n with k\geq3, what bounds follow when highly asymmetric, single-coordinate extremal examples are forbidden; in particular, how small must A be under a transitive automorphism group? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,358 | OWR-17464-016 | Long Cycles in Induced-Ramsey Graph Constructions | Given a graph $F$ and integers $r,n$, how many and what kinds of cycles longer than $n$ can occur in a graph $H$ with $H\to(F)^r$ and with every induced cycle of length at most $n$ inherited from a copy of $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,020 | 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-17464-016",
"literature-status:partially-solved",
"owr-year:2020"
] | The girth Ramsey theorem can force every induced cycle up to any prescribed length to lie inside a copy of the target graph, but it does not settle unrestricted longer-cycle structure. | [
{
"url": "https://ems.press/content/serial-article-files/46836?nt=1",
"label": "Reiher--Rödl, Girth Ramsey theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | Given a graph $F$ and integers $r,n$, how many and what kinds of cycles longer than $n$ can occur in a graph $H$ with $H\to(F)^r$ and with every induced cycle of length at most $n$ inherited from a copy of $F$? | Given a graph F and integers r,n, how many and what kinds of cycles longer than n can occur in a graph H with H\to(F)^r and with every induced cycle of length at most n inherited from a copy of F? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,359 | OWR-17464-019 | Maximum Independent Sets in Regular Uniform Hypergraphs | For $r\geq2$ and $d\geq1$, determine the maximum number of independent sets in a $d$-regular $r$-uniform hypergraph $G$ on $n$ vertices. In particular, does the canonical $d$-regular hypergraph $H_d^r$ satisfy the conjectured extremal bound
$$\operatorname{ind}(G)\leq \operatorname{ind}(H_d^r)^{n/(rd)}$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17464-019",
"literature-status:open",
"owr-year:2020"
] | The regular linear hypergraph analogue has substantial partial results, but the general regular r-uniform hypergraph question and the corresponding conjectural characterization remain unresolved. | [
{
"url": "https://arxiv.org/abs/2001.00653",
"label": "Cohen--Perkins--Sarantis--Tetali"
},
{
"url": "https://doi.org/10.1016/j.jcta.2021.105405",
"label": "Balogh--Bollobás--Narayanan"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | For $r\geq2$ and $d\geq1$, determine the maximum number of independent sets in a $d$-regular $r$-uniform hypergraph $G$ on $n$ vertices. In particular, does the canonical $d$-regular hypergraph $H_d^r$ satisfy the conjectured extremal bound
$$\operatorname{ind}(G)\leq \operatorname{ind}(H_d^r)^{n/(rd)}$$? | For r\geq2 and d\geq1, determine the maximum number of independent sets in a d-regular r-uniform hypergraph on n vertices; in particular, does the canonical d-regular hypergraph H_d^r give the conjectured bound ind(G)\leq ind(H_d^r)^{n/(rd)}? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,360 | OWR-17464-020 | Internal Partitions of Regular Graphs | An internal partition of a graph is a partition into two nonempty parts in which every vertex has at least as many neighbors in its own part as in the other. For every $d$, are there only finitely many $d$-regular graphs with no internal partition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 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-17464-020",
"literature-status:open",
"owr-year:2020"
] | Internal partitions are known for several degrees, including degree six, but the first unknown degree five case remains unresolved despite recent partial results. | [
{
"url": "https://doi.org/10.1002/jgt.21909",
"label": "Ban--Linial, Internal partitions of regular graphs"
},
{
"url": "https://doi.org/10.1007/s00373-024-02774-9",
"label": "Bärnkopf--Nagy--Paulovics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | An internal partition of a graph is a partition into two nonempty parts in which every vertex has at least as many neighbors in its own part as in the other. For every $d$, are there only finitely many $d$-regular graphs with no internal partition? | An internal partition of a graph is a partition into two nonempty parts in which every vertex has at least as many neighbors in its own part as in the other. Is it true that, for every d, only finitely many d-regular graphs have no internal partition? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,361 | OWR-17464-021 | Balanced Three-Colorings of Six-Uniform Hypergraphs | Does every 6-regular 6-uniform hypergraph have a 3-coloring of its vertices such that no hyperedge contains four vertices of the same color? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89](https://doi.org/10.4171/owr/2020/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,020 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17464-021",
"literature-status:open",
"owr-year:2020"
] | The cited sparse-digraph majority-coloring paper explicitly leaves the six-regular six-uniform hypergraph coloring problem as an open problem; no later proof was located. | [
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v28i2p31",
"label": "Anastos--Lamaison--Steiner--Szabó"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/1 | null | null | null | Does every 6-regular 6-uniform hypergraph have a 3-coloring of its vertices such that no hyperedge contains four vertices of the same color? | Does every 6-regular 6-uniform hypergraph have a 3-coloring of its vertices such that no hyperedge contains four vertices of the same color? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/1, pp. 6--89 |
30,004,362 | OWR-17465-001 | Elementary-Theory Classification of Virtually Free Groups | Do the known classifications for finitely generated virtually free groups extend from $\forall\exists$-formulas to arbitrary first-order formulas? More precisely, can elementary equivalence still be characterized by common overgroups obtained through finite sequences of legal large HNN extensions over finite subgroups ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: Groups, Geometries and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/2, pp. 91--142](https://doi.org/10.4171/owr/2020/2)
## Literature review (checked 2026-... | 3 | open | null | 2,020 | 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-17465-001",
"literature-status:open",
"owr-year:2020"
] | Algorithms now cover important quantifier fragments for finitely generated virtually free groups, including the universal-existential theory, but the conjectured unrestricted first-order classification is not established. | [
{
"url": "https://arxiv.org/abs/1910.08464",
"label": "André, On Tarski's problem for virtually free groups"
},
{
"url": "https://arxiv.org/abs/1912.06388",
"label": "André, Elementary subgroups of virtually free groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/2 | null | null | null | Do the known classifications for finitely generated virtually free groups extend from $\forall\exists$-formulas to arbitrary first-order formulas? More precisely, can elementary equivalence still be characterized by common overgroups obtained through finite sequences of legal large HNN extensions over finite subgroups ... | Conjecture: the stated results on algorithms for finitely generated virtually free groups, including deciding equality of their forall-existential theories and elementary embedding, remain valid without restricting the complexity of formulas. | corrected_verified | The official report was checked. It states the conjecture after the two structural characterizations and their decision algorithms; the clean statement spells out what “these results” refers to. | null | null | null | null | null | Model Theory: Groups, Geometries and Combinatorics (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/2, pp. 91--142 |
30,004,363 | OWR-17466-001 | Braid-Group Extensions of Zamolodchikov Actions | Let $\Delta$ and $\Delta'$ be simply laced Dynkin diagrams with Coxeter numbers $k$ and $n-k$. Does the cyclic action generated by the Zamolodchikov transformation on the cluster algebra $\mathcal A(\Delta\square\Delta')$ extend to an action of the extended braid group $\widetilde{\operatorname{Br}}_d$, where $d=\gcd(k... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-001",
"literature-status:open",
"owr-year:2020"
] | The braid-group extension is verified for selected cluster-algebra families, but the conjecture for all products of Dynkin quivers has not been proved. | [
{
"url": "https://doi.org/10.1007/s00029-020-0542-3",
"label": "Fraser, Braid group symmetries of Grassmannian cluster algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Let $\Delta$ and $\Delta'$ be simply laced Dynkin diagrams with Coxeter numbers $k$ and $n-k$. Does the cyclic action generated by the Zamolodchikov transformation on the cluster algebra $\mathcal A(\Delta\square\Delta')$ extend to an action of the extended braid group $\widetilde{\operatorname{Br}}_d$, where $d=\gcd(k... | Conjecture: for simply laced Dynkin diagrams Delta and Delta-prime with Coxeter numbers k and n-k, the cyclic action generated by the Zamolodchikov transformation rho on the cluster algebra A(Delta tensor Delta-prime) extends to an action of the extended braid group Br-tilde-d on A(Delta tensor Delta-prime), where d=gc... | 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 | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,364 | OWR-17466-003 | Jordan-Recoverable Quiver Subcategories | Which additive subcategories $\mathcal C$ of the representation category $\operatorname{rep}Q$ of a quiver $Q$ are Jordan recoverable, meaning that a representation can be recovered up to isomorphism from its generic nilpotent Jordan data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-003",
"literature-status:open",
"owr-year:2020"
] | There are partial constructions and classifications for special quivers and subcategories, but no general characterization of all additive subcategories that are Jordan recoverable. | [
{
"url": "https://arxiv.org/abs/2308.16626",
"label": "Dequêne, Canonically Jordan recoverable categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Which additive subcategories $\mathcal C$ of the representation category $\operatorname{rep}Q$ of a quiver $Q$ are Jordan recoverable, meaning that a representation can be recovered up to isomorphism from its generic nilpotent Jordan data? | Which additive subcategories C of the representation category rep Q of a quiver Q are Jordan recoverable, meaning that a representation can be recovered up to isomorphism from its generic nilpotent Jordan data? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,365 | OWR-17466-004 | Derived Invariants from Gentle Quivers with Relations | Given only the quiver with relations $(Q(\Delta),I(\Delta))$ defining a gentle algebra $A(\Delta)$, find an algorithm that computes its full derived-equivalence invariant, including the genus, puncture and boundary data, winding-number invariants, and the remaining parity or greatest-common-divisor invariants. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-004",
"literature-status:open",
"owr-year:2020"
] | The complete derived invariant is known abstractly for gentle algebras, but a general effective algorithm extracting every invariant from the quiver with relations is still not supplied. | [
{
"url": "https://doi.org/10.1007/s00029-022-00822-x",
"label": "A complete derived invariant for gentle algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Given only the quiver with relations $(Q(\Delta),I(\Delta))$ defining a gentle algebra $A(\Delta)$, find an algorithm that computes its full derived-equivalence invariant, including the genus, puncture and boundary data, winding-number invariants, and the remaining parity or greatest-common-divisor invariants. | Given only the quiver with relations (Q(Delta), I(Delta)) defining the gentle algebra A(Delta), find an algorithm that computes all data in the derived-equivalence invariant of Theorem 3.3, including the genus, puncture and boundary data, winding-number invariants, and the remaining parity or gcd invariants. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,366 | OWR-17466-005 | Efficient Extraction of Interval Summands | Given a pointwise finite-dimensional representation $M$ of $\mathbb R^d$, determine efficiently whether $M$ has interval summands and, when it does, extract them, preferably by local and readily checkable conditions rather than by decomposing $M$ completely. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | partially_solved | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-005",
"literature-status:partially-solved",
"owr-year:2020"
] | Interval decomposability can be decided algorithmically in important two-parameter settings, while the general multidimensional representation problem remains wild and unresolved. | [
{
"url": "https://doi.org/10.1016/j.comgeo.2022.101879",
"label": "Asashiba et al., Interval decomposability of 2D persistence modules"
},
{
"url": "https://arxiv.org/abs/2503.07368",
"label": "Graphcodes, Interval decomposability in multiparameter persistence"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Given a pointwise finite-dimensional representation $M$ of $\mathbb R^d$, determine efficiently whether $M$ has interval summands and, when it does, extract them, preferably by local and readily checkable conditions rather than by decomposing $M$ completely. | Given a pointwise finite-dimensional representation M of R^d, determine efficiently whether M has interval summands and, when it does, extract those summands, preferably by local and readily checkable conditions rather than by decomposing M completely. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,367 | OWR-17466-006 | Realization Functors as Derived Equivalences | Let $\mathcal A$ be an abelian category contained in the essential image of the realization functor $G$ from the bounded derived category of its heart $\mathcal H$ to the ambient triangulated category. Is $G$ a derived equivalence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | partially_solved | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The realization functor is an equivalence when the abelian category is hereditary, but the problem asks beyond that conditional case and has no general affirmative solution. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2019.106749",
"label": "Chen--Han--Zhou, Derived equivalences via HRS tilting"
},
{
"url": "https://ems.press/content/serial-article-files/46842",
"label": "Oberwolfach report, realization functors"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Let $\mathcal A$ be an abelian category contained in the essential image of the realization functor $G$ from the bounded derived category of its heart $\mathcal H$ to the ambient triangulated category. Is $G$ a derived equivalence? | Let A be an abelian category contained in the essential image of the realization functor G from the bounded derived category of its heart H to the ambient triangulated category. Is G a derived equivalence? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,368 | OWR-17466-007 | Completion of Presilting Complexes | Is every presilting complex with $n$ indecomposable summands already silting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | solved | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-11",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **solved (no)**. W. Gnedin, Oberwolfach Report 3/2020, p. 184, states as an open problem whether every presilting complex with n summands is silting; n is the number of simple modules, a presilting complex is a basic perfect complex L with Hom(L, L[p]) = 0 for p > 0, and it... | [
"owr",
"oberwolfach-reports",
"OWR-17466-007",
"literature-status:open",
"owr-year:2020"
] | A 2023--2025 counterexample disproves the stronger complement property for presilting complexes, but it does not settle whether every presilting complex with the full number of summands is silting. | [
{
"url": "https://arxiv.org/abs/2302.12502",
"label": "Liu--Zhou, A negative answer to the complement question"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.12.020",
"label": "Liu--Zhou, Journal of Algebra"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Is every presilting complex with $n$ indecomposable summands already silting? | Is every presilting complex with n indecomposable summands already silting? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,369 | OWR-17466-008 | Geometry and Mutation of Quiver Grassmannians | Open problems for quiver Grassmannians include: whether every rigid Q-representation has property (C); whether every representation of an extended Dynkin quiver has property (C); whether property (C) or (S) is preserved by Fomin-Zelevinsky mutation; whether quiver Grassmannians of rigid representations have further geo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 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 shows that this extraction concatenates seven independent numbered conjectures and problems rather than one publishable ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-008",
"literature-status:open",
"owr-year:2020"
] | The listed conjectures on property C, mutation, quiver Grassmannians, and flag multiplicities contain several unresolved directions; no complete resolution of the problem set is known. | [
{
"url": "https://ems.press/content/serial-article-files/46842",
"label": "Oberwolfach report, quiver Grassmannians"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | null | Open problems for quiver Grassmannians include: whether every rigid Q-representation has property (C); whether every representation of an extended Dynkin quiver has property (C); whether property (C) or (S) is preserved by Fomin-Zelevinsky mutation; whether quiver Grassmannians of rigid representations have further geo... | unrecoverable | The official report shows that this extraction concatenates seven independent numbered conjectures and problems rather than one publishable statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,370 | OWR-17466-010 | Jacobi Algebras as Contraction Algebras | Does every finite-dimensional Jacobi algebra arise as the contraction algebra of a flopping curve? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-010",
"literature-status:open",
"owr-year:2020"
] | The Brown--Wemyss realization conjecture that all relevant finite-dimensional Jacobi algebras arise from geometry remains open; nonnegative refined invariants provide evidence but not a proof. | [
{
"url": "https://arxiv.org/abs/1903.00659",
"label": "Davison, Refined invariants of finite-dimensional Jacobi algebras"
},
{
"url": "https://arxiv.org/abs/2410.21500",
"label": "Brown--Wemyss, Noncommutative singularity theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Does every finite-dimensional Jacobi algebra arise as the contraction algebra of a flopping curve? | Brown-Wemyss conjecture: every finite-dimensional Jacobi algebra arises as the contraction algebra of a flopping curve. | 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 | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,371 | OWR-17466-011 | Classification of Generalized Quaternion-Type Algebras | Is every algebra of generalized quaternion type Morita equivalent to a weighted surface algebra or to one of the nine exotic algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17466-016",
"OWR-17466-017"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-011",
"literature-status:open",
"owr-year:2020"
] | The extracted fragment contains only a conjecture lead-in and omits the mathematical claim, so its resolution cannot be established from the record. | [
{
"url": "https://doi.org/10.4171/owr/2020/3",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | Is every algebra of generalized quaternion type Morita equivalent to a weighted surface algebra or to one of the nine exotic algebras? | Galactic Conjecture: every algebra of generalized quaternion type is Morita equivalent to a weighted surface algebra or to one of the nine exotic algebras. | 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 | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,372 | OWR-17466-014 | Caldero–Chapoton Maps for General Hereditary Algebras | For a general hereditary algebra, what is the appropriate analogue of the Euler characteristic of a submodule quiver Grassmannian for defining the Caldero-Chapoton map in all relevant cases? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-014",
"literature-status:open",
"owr-year:2020"
] | A polynomial Euler characteristic analogue is available over finite fields, but the record explicitly leaves the extension to other fields, including real and quaternionic cases, unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/3",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | For a general hereditary algebra, what is the appropriate analogue of the Euler characteristic of a submodule quiver Grassmannian for defining the Caldero-Chapoton map in all relevant cases? | For a general hereditary algebra, what is the appropriate analogue of the Euler characteristic of a submodule quiver Grassmannian for defining the Caldero-Chapoton map in all relevant cases? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,373 | OWR-17466-015 | Periodicity of Symmetric Tame Algebras | If $A$ is an indecomposable symmetric tame algebra of non-polynomial growth for which every simple module is periodic, must $A$ be a periodic algebra of period $4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-015",
"literature-status:open",
"owr-year:2020"
] | Period four is established in important families and remains the conjectured period in the nonpolynomial tame symmetric setting, but current classification work still treats the general assertion as open. | [
{
"url": "https://doi.org/10.4171/owr/2020/3",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2411.17381",
"label": "Periodicity shadows I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | If $A$ is an indecomposable symmetric tame algebra of non-polynomial growth for which every simple module is periodic, must $A$ be a periodic algebra of period $4$? | If A is an indecomposable symmetric tame algebra of non-polynomial growth for which all simple modules are periodic, must A be a periodic algebra of period 4? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,374 | OWR-17466-016 | Weighted-Surface Classification of Quaternion-Type Algebras | Conjecture: every algebra of generalized quaternion type is Morita equivalent to a weighted surface algebra or one of the nine known exotic algebras that are not weighted surface algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 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 is a duplicate extraction of the Galactic Conjecture retained in OWR-17466-011. No separate clean sta) | [
"OWR-17466-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-016",
"literature-status:open",
"owr-year:2020"
] | The extracted record gives only the surrounding statement that a conjecture follows and omits the conjecture itself, so no resolution can be assigned reliably. | [
{
"url": "https://doi.org/10.4171/owr/2020/3",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | null | Conjecture: every algebra of generalized quaternion type is Morita equivalent to a weighted surface algebra or one of the nine known exotic algebras that are not weighted surface algebras. | unrecoverable | The official report confirms that this is a duplicate extraction of the Galactic Conjecture retained in OWR-17466-011. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,375 | OWR-17466-017 | Galactic Conjecture for Quaternion-Type Algebras | Galactic Conjecture: every algebra of generalized quaternion type is Morita equivalent to a weighted surface algebra or one of the nine exotic algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230](https://doi.org/10.4171/owr/2020/3)
## Literature review... | 3 | open | null | 2,020 | 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 is a duplicate extraction of the Galactic Conjecture retained in OWR-17466-011. No separate clean sta) | [
"OWR-17466-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17466-017",
"literature-status:open",
"owr-year:2020"
] | The Galactic Conjecture is confirmed for two-regular Gabriel quivers with at least three vertices, but the asserted Morita classification for all generalized quaternion type algebras remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/3",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1710.09640",
"label": "Erdmann and Skowronski"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/3 | null | null | null | null | Galactic Conjecture: every algebra of generalized quaternion type is Morita equivalent to a weighted surface algebra or one of the nine exotic algebras. | unrecoverable | The official report confirms that this is a duplicate extraction of the Galactic Conjecture retained in OWR-17466-011. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/3, pp. 143--230 |
30,004,376 | OWR-17468-001 | Quasi-Optimality for Nonconforming Galerkin Spaces | For nonconforming Galerkin spaces $V_{j}^{h}\not\subset V$, what error estimate should replace the standard Céa quasi-optimality bound $\|\phi-\phi_j^h\|\leq C\inf_{\psi\in V_j^h}\|\phi-\psi\|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376](https://doi.org/10.4171/owr/2020/5)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17468-001",
"literature-status:open",
"owr-year:2020"
] | The extracted record is only the fragment of an open question about the replacement for Cea type quasi optimality bounds, so the precise claim and its resolution remain unclear. | [
{
"url": "https://doi.org/10.4171/owr/2020/5",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/5 | null | null | null | For nonconforming Galerkin spaces $V_{j}^{h}\not\subset V$, what error estimate should replace the standard Céa quasi-optimality bound $\|\phi-\phi_j^h\|\leq C\inf_{\psi\in V_j^h}\|\phi-\psi\|$? | For nonconforming Galerkin or boundary-element spaces V-j-h not contained in V, what should replace the standard Cea quasi-optimality bound norm(phi-phi-j-h) <= C inf-subscript-psi-in-V-j-h norm(phi-psi)? | 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 | Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376 |
30,004,377 | OWR-17468-002 | Convergence of Standard Cantor Prefractal Boundary Approximations | For the Cantor-set boundary-element approximation with $i(j)=j$, $\delta=0$, and $C_j$ the standard prefractal sequence for the Cantor set $C$, prove that the approximations $\phi_j^h$ converge to $\phi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376](https://doi.org/10.4171/owr/2020/5)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17468-002",
"literature-status:open",
"owr-year:2020"
] | Convergence is proved for several refined mesh and prefractal regimes, but the cited literature does not prove convergence for the standard Cantor prefractal sequence with i of j equal to j and delta equal to zero. | [
{
"url": "https://doi.org/10.4171/owr/2020/5",
"label": "Oberwolfach report"
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{
"url": "https://link.springer.com/article/10.1007/s00211-021-01182-y",
"label": "Boundary element methods for fractal screens"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/5 | null | null | null | For the Cantor-set boundary-element approximation with $i(j)=j$, $\delta=0$, and $C_j$ the standard prefractal sequence for the Cantor set $C$, prove that the approximations $\phi_j^h$ converge to $\phi$. | For the Cantor-set prefractal boundary-element approximation with i(j)=j, delta=0, and C-j the standard prefractal sequence for C, prove convergence of the approximations phi-j-h to phi. | 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 | Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376 |
30,004,378 | OWR-17468-003 | Inf–Sup Stability for Nonconforming Multiple Traces | For the spectral nonconforming Petrov–Galerkin multiple-traces discretization, prove an inf–sup condition for the variational problem of finding $\lambda\in X_L:=X_L^0\times\cdots\times X_L^M$ such that $\langle F(s)\lambda,\phi\rangle_\times=\langle g,\phi\rangle_\times$ for every $\phi\in Y_L:=Y_L^0\times\cdots\times... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376](https://doi.org/10.4171/owr/2020/5)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17468-003",
"literature-status:open",
"owr-year:2020"
] | The extracted statement is a malformed problem fragment about a spectral nonconforming Petrov Galerkin formulation and does not state a resolved theorem. | [
{
"url": "https://doi.org/10.4171/owr/2020/5",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/5 | null | null | null | For the spectral nonconforming Petrov–Galerkin multiple-traces discretization, prove an inf–sup condition for the variational problem of finding $\lambda\in X_L:=X_L^0\times\cdots\times X_L^M$ such that $\langle F(s)\lambda,\phi\rangle_\times=\langle g,\phi\rangle_\times$ for every $\phi\in Y_L:=Y_L^0\times\cdots\times... | For the spectral nonconforming Petrov-Galerkin multiple-traces formulation, find lambda in X-L=X-L0 tensor-product ... tensor-product X-LM such that (F(s)lambda,phi) equals (g,phi) for every phi in Y-L=Y-L0 tensor-product ... tensor-product Y-LM; establish existence and uniqueness by proving the required inf-sup condit... | 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 | Boundary Element Methods (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/5, pp. 273--376 |
30,004,379 | OWR-17469-001 | Information Complexity of Multivariate Integration and Approximation | For a function class $F$ on a bounded domain $D_d\subset\mathbb R^d$, how many function values $f(x_i)$ are needed to approximate either the integral $\operatorname{INT}(f)$ or the function $\operatorname{APP}(f)$ with error at most $\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-001",
"literature-status:open",
"owr-year:2020"
] | The record asks for information complexity of integration or approximation but does not specify a single function class, domain model, or error criterion sufficient for a definitive answer. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | For a function class $F$ on a bounded domain $D_d\subset\mathbb R^d$, how many function values $f(x_i)$ are needed to approximate either the integral $\operatorname{INT}(f)$ or the function $\operatorname{APP}(f)$ with error at most $\varepsilon$? | For function classes F on a bounded domain D-d, how many function values f(x-i) are needed to compute either the integral INT(f) or the approximation APP(f) to error at most epsilon? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,380 | OWR-17469-002 | Sharp Complexity Constants for Smooth Multivariate Integration | For integration on $C^k(D_d)$, does
$$\limsup_{n\to\infty} e_n(C^k(D_d),\operatorname{INT})\,n^{k/d}$$
depend on the bounded domain $D_d\subset\mathbb R^d$? Is the limsup in fact a limit? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-002",
"literature-status:open",
"owr-year:2020"
] | Known bounds determine the principal dimension dependent rate in several smooth classes, but the report's questions about the exact asymptotic constant, domain dependence, and existence of the limit remain open. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | For integration on $C^k(D_d)$, does
$$\limsup_{n\to\infty} e_n(C^k(D_d),\operatorname{INT})\,n^{k/d}$$
depend on the bounded domain $D_d\subset\mathbb R^d$? Is the limsup in fact a limit? | For integration of C-k(D-d) functions, determine how the complexity depends on the dimension d and domain D-d; in particular, determine whether the asymptotic constant lim-sup-subscript-n en(C-k(D-d),INT)n^(k/d) is a limit and whether it depends on D-d. | corrected_verified | The official report was checked. The formula and its two questions were restored from the source in place of the extraction artifacts. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,381 | OWR-17469-003 | Dimension-Uniform Lower Bounds for Twice-Smooth Integration | For a bounded convex domain $D_d\subset\mathbb R^d$, define
$$\overline C^2(D_d)=\left\{f\in C^2(D_d):\|f\|_\infty\leq1,\ \operatorname{Lip}(f)\leq d^{-1/2},\ \operatorname{Lip}(D_\theta f)\leq d^{-1}\right\}.$$
Is there an absolute constant $C>0$, independent of $d$ and $D_d$, such that
$$e_n(\overline C^2(D_d),\op... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-003",
"literature-status:open",
"owr-year:2020"
] | The dimension and domain uniform lower bound is a stated conjecture; it is sharp for the cube with grid information, but no general proof or counterexample was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | For a bounded convex domain $D_d\subset\mathbb R^d$, define
$$\overline C^2(D_d)=\left\{f\in C^2(D_d):\|f\|_\infty\leq1,\ \operatorname{Lip}(f)\leq d^{-1/2},\ \operatorname{Lip}(D_\theta f)\leq d^{-1}\right\}.$$
Is there an absolute constant $C>0$, independent of $d$ and $D_d$, such that
$$e_n(\overline C^2(D_d),\op... | Conjecture: there is a constant C>0, independent of d and D-d, such that the nth minimal integration error for the class C-bar-2(D-d) satisfies en(C-bar-2(D-d),INT) >= C n^(-2/d). | corrected_verified | The official report was checked. The function class and the dimension-uniform lower-bound conjecture were restored. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,382 | OWR-17469-004 | Random Versus Optimal Information for Approximation and Integration | For approximation and integration from $n$ measurements, determine the rate of the $n$th minimal error $e_n$, characterize optimal information, and quantify how much random information worsens the error compared with optimal information. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-004",
"literature-status:open",
"owr-year:2020"
] | The extracted record lists broad questions about optimal information rates, forms, and random information quality without a theorem resolving the general problem. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | For approximation and integration from $n$ measurements, determine the rate of the $n$th minimal error $e_n$, characterize optimal information, and quantify how much random information worsens the error compared with optimal information. | For approximation and integration from n measurements, determine the rate of the nth minimal error e(n), characterize optimal information, and quantify how much random information worsens the error compared with optimal information. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,383 | OWR-17469-005 | Random Information for Weighted Approximation Problems | For weighted $\ell_p$-balls and other error norms, determine the quality of random information and compare its performance with optimal information. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-005",
"literature-status:open",
"owr-year:2020"
] | For other weighted ell p balls and other error norms, the quality of random information is explicitly identified as open, with no general resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | For weighted $\ell_p$-balls and other error norms, determine the quality of random information and compare its performance with optimal information. | For weighted l-p balls and other error norms, determine the quality of random information and compare its performance with optimal information. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,384 | OWR-17469-006 | Sharp Singularity Probability of Random Sign Matrices | Let $B_n$ be an $n\times n$ random sign matrix with independent entries uniformly distributed in $\{-1,1\}$. Determine the sharp asymptotic probability that $B_n$ is singular. The conjectural scale is
$$\mathbb P(B_n\text{ is singular})=(1/2+o_n(1))^n=(1/2)^{(1+o_n(1))n}$$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | partially_solved | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (yes)**; the dataset currently labels it partially solved. Folklore conjecture recalled by A. Litvak (with K. Tikhomirov), OWR 6/2020, p. 390: is the probability that an n×n random ±1 matrix is singular (1/2 + o(1))ⁿ? K. Tikhomirov, Ann. of Math. 191 (2020) 593–634... | [
"owr",
"oberwolfach-reports",
"OWR-17469-006",
"literature-status:partially-solved",
"owr-year:2020"
] | For the sparse Bernoulli singularity conjecture identified by the report, dense and logarithmic threshold regimes have sharp results, while the full all parameter sequence statement remains open. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2004.03131",
"label": "Litvak and Tikhomirov"
},
{
"url": "https://arxiv.org/abs/2010.06554",
"label": "Jain, Sah, and Sawhney"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | Let $B_n$ be an $n\times n$ random sign matrix with independent entries uniformly distributed in $\{-1,1\}$. Determine the sharp asymptotic probability that $B_n$ is singular. The conjectural scale is
$$\mathbb P(B_n\text{ is singular})=(1/2+o_n(1))^n=(1/2)^{(1+o_n(1))n}$$. | Conjecture for an n by n random sign matrix B-n with independent plus-or-minus-one entries: P(B-n is singular) = (1/2+o-n(1))^n, equivalently (1/2)^(n)(1+o-n(1))^n; determine the sharp singularity asymptotic. | corrected_verified | The official report was checked. The historical sign-matrix formulation and asymptotic scale were restored without the OCR-like notation. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,385 | OWR-17469-007 | Sharp Singularity Asymptotics for Sparse Bernoulli Matrices | Let $M_n$ be an $n\times n$ matrix with independent Bernoulli entries satisfying $\mathbb P(M_{ij}=1)=p_n$. Let $E_{\mathrm{zero}}$ be the event that $M_n$ has a zero row or column, and let $E_{\mathrm{equal}}$ be the event that it has two equal rows or two equal columns. In the sparse regime, is
$$\mathbb P(M_n\text{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | partially_solved | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-007",
"literature-status:partially-solved",
"owr-year:2020"
] | Sharp singularity asymptotics are proved through an important logarithmic sparse regime, improving earlier bounds, but the conjectured description throughout the remaining sparser regimes is not fully established. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2004.03131",
"label": "Litvak and Tikhomirov"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | Let $M_n$ be an $n\times n$ matrix with independent Bernoulli entries satisfying $\mathbb P(M_{ij}=1)=p_n$. Let $E_{\mathrm{zero}}$ be the event that $M_n$ has a zero row or column, and let $E_{\mathrm{equal}}$ be the event that it has two equal rows or two equal columns. In the sparse regime, is
$$\mathbb P(M_n\text{... | In the sparse regime p=p-n tending to 0, determine whether the singularity probability of a p-Bernoulli n by n matrix M-n has the conjectured sharp asymptotic governed by zero rows or columns and equal rows or columns; in particular, improve the known bound P(M-n singular) <= exp(-c n p) for p >= C log(n)/n to the conj... | corrected_verified | The official report was checked. The two exceptional events and both conjectured asymptotic formulas were restored. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,386 | OWR-17469-011 | Large Deviations for Random High-Dimensional Projections | Let $\Theta^{(N)}$ be uniform on $S^{N-1}$ and set $\nu_N=\mu_{\Theta^{(N)}}$. Does $(\nu_N)$ satisfy a large-deviation principle with speed $N$ and rate function
$$I(\nu)=-\frac12\log(1-\|\alpha\|_2^2)$$
when $\nu=\kappa_\alpha$ for some $\alpha$ in the open unit ball of $\ell_2$, and $I(\nu)=\infty$ otherwise? As a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416](https://doi.org/10.4171/owr/2020/6)
## Literature review... | 3 | open | null | 2,020 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17469-011",
"literature-status:open",
"owr-year:2020"
] | The 2021 report states this large-deviation principle and its compactness lemma as conjectural; the checked literature gives no proof of the full claim by 2026-08-22. | [
{
"url": "https://doi.org/10.4171/owr/2020/6",
"label": "Oberwolfach report on the conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/6 | null | null | null | Let $\Theta^{(N)}$ be uniform on $S^{N-1}$ and set $\nu_N=\mu_{\Theta^{(N)}}$. Does $(\nu_N)$ satisfy a large-deviation principle with speed $N$ and rate function
$$I(\nu)=-\frac12\log(1-\|\alpha\|_2^2)$$
when $\nu=\kappa_\alpha$ for some $\alpha$ in the open unit ball of $\ell_2$, and $I(\nu)=\infty$ otherwise? As a... | Conjecture: if Theta^(N) is uniform on the unit sphere S^(N-1) and nu-N=mu-Theta^(N), then (nu-N) satisfies a large deviation principle with rate N and rate function I(nu)=-1/2 log(1-||alpha||^2) when nu=kappa-alpha for some alpha in the unit ball of l-2 with ||alpha||<1, and I(nu)=infinity otherwise. A necessary inter... | corrected_verified | The official report was checked. The projection laws, the limit set, and the rate function were reconstructed from the displayed source formulas. | null | null | null | null | null | New Perspectives and Computational Challenges in High Dimensions (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/6, pp. 377--416 |
30,004,387 | OWR-17470-002 | The Boundary Singer Conjecture | Let $B\Gamma$ be a finite $d$-dimensional complex and let $\Gamma$ be a residually finite CAT(0) or hyperbolic group. If the action of $\Gamma$ on $H^{\mathrm{st}}_{d-1}(\partial\Gamma;\mathbb F_2)$ has positive entropy, must the boundary $\partial\Gamma$ fail to embed in $S^{2d-2}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-002",
"literature-status:partially-solved",
"owr-year:2020"
] | Singer's concentration conjecture remains open in general, but is proved for substantial classes including many hyperbolic, cubical, and branched-cover cases. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Avramidi report on Singer"
},
{
"url": "https://doi.org/10.1007/s00208-025-03164-z",
"label": "Avramidi--Okun--Schreve 2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let $B\Gamma$ be a finite $d$-dimensional complex and let $\Gamma$ be a residually finite CAT(0) or hyperbolic group. If the action of $\Gamma$ on $H^{\mathrm{st}}_{d-1}(\partial\Gamma;\mathbb F_2)$ has positive entropy, must the boundary $\partial\Gamma$ fail to embed in $S^{2d-2}$? | Let B\Gamma be a finite d-dimensional complex and let \Gamma be a residually finite CAT(0) or hyperbolic group with boundary \partial\Gamma. If the entropy of the action of \Gamma on H^{\mathrm{st}}_{d-1}(\partial\Gamma;\mathbb F_2) is positive, then \partial\Gamma does not embed in S^{2d-2}. | corrected_verified | The official report was checked. The source labels this the Boundary Singer Conjecture, so the declarative extraction was restored as a conjectural question. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,388 | OWR-17470-003 | Positive Scalar Curvature Through Odd-Order Finite Covers | Let $M$ be a closed connected smooth manifold of dimension at least $5$ whose fundamental group is finite of odd order. If the universal cover of $M$ admits a metric of positive scalar curvature, must $M$ admit one as well? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-003",
"literature-status:partially-solved",
"owr-year:2020"
] | The odd-order finite-fundamental-group positive-scalar-curvature conjecture is proved in dimensions 1--3 and several higher-dimensional classes, but remains open in general dimensions at least 5. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.2140/gt.2021.25.497",
"label": "Hanke 2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let $M$ be a closed connected smooth manifold of dimension at least $5$ whose fundamental group is finite of odd order. If the universal cover of $M$ admits a metric of positive scalar curvature, must $M$ admit one as well? | Let M be a closed connected smooth manifold with finite fundamental group of odd order. If the universal cover of M admits a metric of positive scalar curvature, then M admits a metric of positive scalar curvature. | corrected_verified | The official report was checked. The missing dimension hypothesis was restored; the source notes that the analogous statement fails in dimension four. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,389 | OWR-17470-004 | Positive Scalar Curvature for Spin Manifolds with Odd Fundamental Group | Let $M$ be a closed connected spin manifold of dimension $d\geq5$ with odd-order abelian fundamental group. Assume that $M$ is $p$-atoral for every prime $p$ dividing $|\pi_1(M)|$: for every $\ell\geq1$ and $c_1,\ldots,c_d\in H^1(M;\mathbb Z/p^\ell)$,
$$\langle c_1\smile\cdots\smile c_d,[M]\rangle=0\in\mathbb Z/p^\ell... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-004",
"literature-status:open",
"owr-year:2020"
] | The proposed extension from the non-spin theorem to spin manifolds with vanishing alpha-invariant is still presented as a conjecture, with connective K-homology identified as the missing method. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.2140/gt.2021.25.497",
"label": "Hanke 2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let $M$ be a closed connected spin manifold of dimension $d\geq5$ with odd-order abelian fundamental group. Assume that $M$ is $p$-atoral for every prime $p$ dividing $|\pi_1(M)|$: for every $\ell\geq1$ and $c_1,\ldots,c_d\in H^1(M;\mathbb Z/p^\ell)$,
$$\langle c_1\smile\cdots\smile c_d,[M]\rangle=0\in\mathbb Z/p^\ell... | Does the positive-scalar-curvature existence theorem for closed connected smooth manifolds of dimension at least five with odd-order abelian fundamental group extend to spin manifolds with vanishing \alpha-invariant, under the corresponding p-atorality hypotheses? | corrected_verified | The official report was checked. The source conjectures the spin extension under the odd-order abelian and p-atorality hypotheses. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,390 | OWR-17470-006 | Quantitative Complexity of Homotopy Representatives and Homotopies | For finite simply connected piecewise Riemannian simplicial complexes, or compact Riemannian manifolds, how can one estimate the least geometric complexity of a representative of a homotopy class from its algebraic size? If two maps are homotopic, how does the least complexity of a homotopy depend on the complexities o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-006",
"literature-status:partially-solved",
"owr-year:2020"
] | The broad quantitative-homotopy questions remain active, but scalability was proved to be a real-homotopy invariant and equivalent algebraic criteria were established. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1017/fmp.2023.33",
"label": "Berdnikov--Manin, Degrees of maps"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | For finite simply connected piecewise Riemannian simplicial complexes, or compact Riemannian manifolds, how can one estimate the least geometric complexity of a representative of a homotopy class from its algebraic size? If two maps are homotopic, how does the least complexity of a homotopy depend on the complexities o... | For finite simply connected piecewise Riemannian simplicial complexes or compact Riemannian manifolds, how can one estimate the geometric complexity of the most efficient representative of a homotopy class of maps and its dependence on the algebraic size of that class? If two maps are homotopic, how does the complexity... | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,391 | OWR-17470-007 | Lipschitz Growth of Puncture Classes and Formality | Let
$$M=\bigl(S^2\times(\mathbb{CP}^2)^{\#4}\bigr)\setminus\{\text{point}\},$$
and let $\alpha\in\pi_5(M)$ be the puncture class. The known growth of $\operatorname{Lip}(k\alpha)$ is $\omega(k^{1/6})$. Can one prove a sharper lower bound, or an upper bound of order strictly smaller than $k^{1/5}$? Separately, suppose... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-007",
"literature-status:open",
"owr-year:2020"
] | For the punctured S2 times connected-sum example, only a lower bound of omega of k to the one-sixth is known in the checked literature; the sharper asymptotic distortion remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1912.00590",
"label": "Berdnikov--Manin, Scalable spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let
$$M=\bigl(S^2\times(\mathbb{CP}^2)^{\#4}\bigr)\setminus\{\text{point}\},$$
and let $\alpha\in\pi_5(M)$ be the puncture class. The known growth of $\operatorname{Lip}(k\alpha)$ is $\omega(k^{1/6})$. Can one prove a sharper lower bound, or an upper bound of order strictly smaller than $k^{1/5}$? Separately, suppose... | For M=(S^2\times(\mathbb{CP}^2)\#4)\setminus\{point\} and the puncture class \alpha\in\pi_5(M), what is the true growth of \operatorname{Lip}(k\alpha)? Can its lower bound grow strictly faster than k^{1\/6}, or its upper bound be lower than the obvious k^{1\/5}? Also, does condition (iii), namely linear Lipschitz nullh... | corrected_verified | The official report was checked. The manifold, puncture class, known asymptotic lower bound, open exponent range, and the separate linear-nullhomotopy/formality question were restored without a numbered cross-reference. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,392 | OWR-17470-008 | Travelling-Salesman Girth and Metric Ordering Ratios | For a metric space $M$ of infinite Assouad–Nagata dimension, is its travelling-salesman girth infinite? Consequently, for a uniformly discrete metric space $M$, is the following dichotomy true: either every order $T$ satisfies $\operatorname{OR}_{M,T}(k)=k-1$ for all $k\geq1$, or some order $T$ satisfies $\operatorname... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17470-009"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-008",
"literature-status:partially-solved",
"owr-year:2020"
] | Infinite travelling-salesman girth is proved for important classes such as spaces weakly containing arbitrarily large cubes or spheres, but the infinite-Assouad--Nagata-dimension implication remains open. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/43590",
"label": "Erschler--Mitrofanov 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | For a metric space $M$ of infinite Assouad–Nagata dimension, is its travelling-salesman girth infinite? Consequently, for a uniformly discrete metric space $M$, is the following dichotomy true: either every order $T$ satisfies $\operatorname{OR}_{M,T}(k)=k-1$ for all $k\geq1$, or some order $T$ satisfies $\operatorname... | For a metric space M with infinite Assouad--Nagata dimension, is its Travelling Salesman girth infinite? Consequently, for a uniformly discrete metric space M, is it true that either every order T satisfies \operatorname{OR}_{M,T}(k)=k-1 for all k\ge1, or some order T satisfies \operatorname{OR}_{M,T}(k)\le C\ln k for ... | corrected_verified | The official report was checked. Its two consecutive metric questions are retained together and the ordering-ratio quantifiers are made explicit. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,393 | OWR-17470-009 | Duplicate Ordering-Ratio Dichotomy | Let M be a uniformly discrete metric space. Is it true that either for every order T on M and all k\ge1 one has \operatorname{OR}_{M,T}(k)=k-1, or there exists an order T such that \operatorname{OR}_{M,T}(k)\le C\ln k for all k\ge1? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This extraction repeats the second question represented canonically, together with its motivating travelling-salesman question, by OWR-17470) | [
"OWR-17470-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-009",
"literature-status:partially-solved",
"owr-year:2020"
] | The order-ratio gap is established for doubling spaces and several group classes, but the stated gap problem for arbitrary uniformly discrete metric spaces is still open. | [
{
"url": "https://ems.press/content/serial-article-files/43590",
"label": "Erschler--Mitrofanov 2023"
},
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | null | Let M be a uniformly discrete metric space. Is it true that either for every order T on M and all k\ge1 one has \operatorname{OR}_{M,T}(k)=k-1, or there exists an order T such that \operatorname{OR}_{M,T}(k)\le C\ln k for all k\ge1? | unrecoverable | This extraction repeats the second question represented canonically, together with its motivating travelling-salesman question, by OWR-17470-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,394 | OWR-17470-010 | Vanishing Normalized Homology Under Local Manifold Convergence | Let $d\geq3$, and let $(M_n)$ be triangulated compact $d$-manifolds whose triangulation $1$-skeleta have uniformly bounded vertex degrees and which Benjamini–Schramm converge to a triangulation of $\mathbb R^d$. Is
$$\lim_{n\to\infty}\frac{\dim H_1(M_n)}{|M_n|}=0$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** partially... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-010",
"literature-status:partially-solved",
"owr-year:2020"
] | The Benjamini--Schramm first-homology limit is known in dimension 3, for covering towers in special settings, and under a Kazhdan-property hypothesis; the general question remains open and includes the degree-one Singer problem. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1810.11015",
"label": "Hutchcroft--Pete, Kazhdan groups have cost 1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let $d\geq3$, and let $(M_n)$ be triangulated compact $d$-manifolds whose triangulation $1$-skeleta have uniformly bounded vertex degrees and which Benjamini–Schramm converge to a triangulation of $\mathbb R^d$. Is
$$\lim_{n\to\infty}\frac{\dim H_1(M_n)}{|M_n|}=0$$? | Let d\ge3 and let (M_n) be triangulated compact d-manifolds whose triangulation 1-skeleta have uniformly bounded vertex degrees and which Benjamini--Schramm converge to a triangulation of \mathbb R^d. Is \lim_{n\to\infty}\frac{\dim H_1(M_n)}{|M_n|}=0? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,395 | OWR-17470-011 | Euler Characteristic and Integral Approximation from Simplicial Volume | Let $M$ be an oriented closed connected aspherical manifold with simplicial volume $\lVert M\rVert=0$. Must $\chi(M)=0$? More strongly, if $\pi_1(M)$ is residually finite, does
$$\lVert M\rVert_{\mathbb Z}^{\infty}=\lVert M\rVert$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17470-012"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-011",
"literature-status:open",
"owr-year:2020"
] | Gromov's implication from vanishing simplicial volume to vanishing Euler characteristic for closed aspherical manifolds remains a major open problem; known examples cover only special classes. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.1007/s40687-022-00341-3",
"label": "Loh--Moraschini--Raptis 2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | Let $M$ be an oriented closed connected aspherical manifold with simplicial volume $\lVert M\rVert=0$. Must $\chi(M)=0$? More strongly, if $\pi_1(M)$ is residually finite, does
$$\lVert M\rVert_{\mathbb Z}^{\infty}=\lVert M\rVert$$? | Let M be an oriented closed connected aspherical manifold with simplicial volume \lVert M\rVert=0. Does this imply \chi(M)=0? More strongly, when \pi_1(M) is residually finite, does M satisfy integral approximation for simplicial volume, namely \lVert M\rVert^{\infty}_{\mathbb Z}=\lVert M\rVert? | corrected_verified | The official report was checked. Both questions from the source passage are retained in the canonical record. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,396 | OWR-17470-012 | Duplicate Integral-Approximation Question | Let M be an oriented closed connected aspherical manifold with vanishing simplicial volume and residually finite fundamental group. Does M satisfy integral approximation for simplicial volume, i.e. does its stable integral simplicial volume \lVert M\rVert^{\infty}_{\mathbb Z} equal \lVert M\rVert? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record repeats the second question represented canonically by OWR-17470-011. No separate clean statement is promoted; the original reco) | [
"OWR-17470-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-012",
"literature-status:open",
"owr-year:2020"
] | Integral approximation is proved for several families, especially aspherical 3-manifolds, but no general theorem for all closed aspherical manifolds with zero simplicial volume was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/7",
"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.1112/topo.12193",
"label": "Fauser 2021"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | null | Let M be an oriented closed connected aspherical manifold with vanishing simplicial volume and residually finite fundamental group. Does M satisfy integral approximation for simplicial volume, i.e. does its stable integral simplicial volume \lVert M\rVert^{\infty}_{\mathbb Z} equal \lVert M\rVert? | unrecoverable | This record repeats the second question represented canonically by OWR-17470-011. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,397 | OWR-17470-013 | CAT(0) Geometry and Retraction of the Bestvina Complex | For a group $G$ equipped with the Bestvina and Davis complexes arising from a strictly developable simple complex of groups, does the Bestvina complex admit a $G$-invariant CAT(0) metric? Is it a $G$-equivariant deformation retract of the Davis complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-17470-014"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-013",
"literature-status:open",
"owr-year:2020"
] | The general Bestvina-complex CAT(0)-metric question and the associated deformation-retract question are not settled; recent work still describes the CAT(0) question as open beyond dimension two. | [
{
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{
"url": "https://doi.org/10.4171/GGD/581",
"label": "Petrosyan--Prytula 2020"
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{
"url": "https://msp.org/agt/2024/24-2/agt-v24-n2-p12-p.pdf",
"label": "Bestvina-complex developments 2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | For a group $G$ equipped with the Bestvina and Davis complexes arising from a strictly developable simple complex of groups, does the Bestvina complex admit a $G$-invariant CAT(0) metric? Is it a $G$-equivariant deformation retract of the Davis complex? | Does the Bestvina complex support a G-invariant CAT(0) metric, and is it an equivariant deformation retract of the Davis complex? | corrected_verified | The official report was checked. The two stated questions are retained together in their canonical extraction. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,398 | OWR-17470-014 | Duplicate Bestvina-Complex Retraction Question | Is the Bestvina complex an equivariant deformation retract of the Davis complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record repeats the second question represented canonically by OWR-17470-013. No separate clean statement is promoted; the original reco) | [
"OWR-17470-013"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-014",
"literature-status:open",
"owr-year:2020"
] | Petrosyan--Prytula obtain equivariant deformation retractions under additional subconical or low-dimensional hypotheses, but the unrestricted Davis-to-Bestvina deformation-retract question remains unresolved. | [
{
"url": "https://doi.org/10.4171/GGD/581",
"label": "Petrosyan--Prytula 2020"
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"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | null | Is the Bestvina complex an equivariant deformation retract of the Davis complex? | unrecoverable | This record repeats the second question represented canonically by OWR-17470-013. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,399 | OWR-17470-015 | Bestvina Complexes Beyond Compact Strict Fundamental Domains | For which group actions with noncompact or non-strict fundamental domains can a Bestvina complex be constructed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463](https://doi.org/10.4171/owr/2020/7)
## Literature review (checked 2026-08-22)
**Status:** open
**A... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17470-015",
"literature-status:open",
"owr-year:2020"
] | The checked literature treats extensions to non-compact or non-strict fundamental domains as further questions; no general construction resolving this problem was found. | [
{
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"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.4171/GGD/581",
"label": "Petrosyan--Prytula 2020"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/7 | null | null | null | For which group actions with noncompact or non-strict fundamental domains can a Bestvina complex be constructed? | When can the construction of the Bestvina complex be generalized to group actions with noncompact or non-strict fundamental domains? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Manifolds and Groups (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/7, pp. 417--463 |
30,004,400 | OWR-17471-003 | The Berge Conjecture for Lens-Space Surgeries | If a nontrivial knot $K\subset S^3$ admits a Dehn surgery yielding a lens space, must $K$ be doubly primitive? Analogously, if $K\subset S^2\times S^1$ admits a nontrivial lens-space Dehn surgery, must $K$ be doubly primitive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.2140/gt.2025.29.3271",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. T. Li and T. Pinsky (joint with Y. Moriah; OWR 8/2020, pp. 475–477) announce the Berge conjecture for tunnel-number-one knots; the record asks the Berge conjecture in S³ and its S² × S¹ analogue. Li–Moriah–Pinsky, [Geom. Topol. 29 (2025)](https://doi.o... | [
"owr",
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"literature-status:open",
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] | Baker, Buck, and Lecuona construct several families and formulate a completeness conjecture for knots in S1 times S2 with lens-space surgery; the stated general classification remains open. | [
{
"url": "https://arxiv.org/abs/1302.7011",
"label": "Baker--Buck--Lecuona"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | If a nontrivial knot $K\subset S^3$ admits a Dehn surgery yielding a lens space, must $K$ be doubly primitive? Analogously, if $K\subset S^2\times S^1$ admits a nontrivial lens-space Dehn surgery, must $K$ be doubly primitive? | Berge conjecture: if a nontrivial knot K\subset S^3 admits a Dehn surgery yielding a lens space, then K is doubly primitive. In the S^2\times S^1 analogue, if a knot K\subset S^2\times S^1 admits a nontrivial lens-space Dehn surgery, must K be doubly primitive? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,401 | OWR-17471-005 | Homotopy Types of Four-Manifold Homeomorphism and Diffeomorphism Groups | For a fixed $4$-manifold $M$, what are the homotopy types of the topological groups $\operatorname{Homeo}_{\partial}(M)$ and $\operatorname{Diff}_{\partial}(M)$ of boundary-fixing homeomorphisms and diffeomorphisms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "topology",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-005",
"literature-status:open",
"owr-year:2020"
] | The homotopy types of boundary-fixing homeomorphism and diffeomorphism groups in dimension four remain incompletely known; existing results compute selected homotopy groups and obstructions rather than the general spaces. | [
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach report"
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{
"url": "https://arxiv.org/abs/1812.02448",
"label": "Watanabe, exotic elements of Diff"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | For a fixed $4$-manifold $M$, what are the homotopy types of the topological groups $\operatorname{Homeo}_{\partial}(M)$ and $\operatorname{Diff}_{\partial}(M)$ of boundary-fixing homeomorphisms and diffeomorphisms? | For a fixed 4-manifold M, what are the homotopy types of the topological groups \operatorname{Homeo}_{\partial}(M) and \operatorname{Diff}_{\partial}(M) of boundary-fixing homeomorphisms and diffeomorphisms? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,402 | OWR-17471-006 | Homological Stability for Stabilized Four-Manifold Diffeomorphisms | For each fixed $k$, does there exist $n$ such that
$$H_k\!\left(B\operatorname{Diff}_{\partial}\!\left(\mathop{\natural}^{n}(S^2\times S^2\setminus\mathring D^4)\right);\mathbb Q\right)$$
is equal to the stable-limit homology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "topology",
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"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-006",
"literature-status:open",
"owr-year:2020"
] | Galatius--Randal-Williams compute the stable rational homology, but whether each fixed-degree group reaches the limit at a finite stage is still unresolved in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach report"
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{
"url": "https://arxiv.org/abs/1403.2334",
"label": "Galatius--Randal-Williams, Stable moduli spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | For each fixed $k$, does there exist $n$ such that
$$H_k\!\left(B\operatorname{Diff}_{\partial}\!\left(\mathop{\natural}^{n}(S^2\times S^2\setminus\mathring D^4)\right);\mathbb Q\right)$$
is equal to the stable-limit homology? | For each fixed k, does there exist n such that H_k\!\left(B\operatorname{Diff}_{\partial}(\mathop{\natural}^{n}(S^2\times S^2\setminus\mathring D^4));\mathbb Q\right) equals the stable limit homology? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,403 | OWR-17471-009 | Uniform Perfectness of Four-Manifold Diffeomorphism Groups | Are there closed orientable smooth $4$-manifolds $M$ for which the identity component $\operatorname{Diff}_0(M)$ is not uniformly perfect? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
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"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-009",
"literature-status:open",
"owr-year:2020"
] | Uniform perfectness is proved in broad dimensions but the four-dimensional identity component remains an explicit unresolved exception in the literature. | [
{
"url": "https://ems.press/journals/cmh/articles/10844",
"label": "Fukui and Rybicki, uniform perfectness in even dimensions"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Are there closed orientable smooth $4$-manifolds $M$ for which the identity component $\operatorname{Diff}_0(M)$ is not uniformly perfect? | Are there closed, orientable, smooth 4-manifolds M for which the identity component \operatorname{Diff}_0(M) is not uniformly perfect? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,404 | OWR-17471-010 | Free Subgroups Avoiding All Dehn-Surgery Kernels | Let $K\subset S^3$ be a hyperbolic knot with no finite surgery, and let $G(K)=\pi_1(S^3\setminus K)$. Does there exist a rank-two free subgroup $H\subset G(K)$ such that
$$H\cap\bigcup_{r\in\mathbb Q}\langle\!\langle r\rangle\!\rangle=\{1\},$$
where $\langle\!\langle r\rangle\!\rangle$ is the normal closure of the sl... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-010",
"literature-status:open",
"owr-year:2020"
] | Existing results produce infinitely many cyclic subgroups with the required disjointness, but the requested rank two free subgroup is still posed as an open question for hyperbolic knots without finite surgery. | [
{
"url": "https://ems.press/content/serial-article-files/46844",
"label": "Oberwolfach Report 8/2020"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Let $K\subset S^3$ be a hyperbolic knot with no finite surgery, and let $G(K)=\pi_1(S^3\setminus K)$. Does there exist a rank-two free subgroup $H\subset G(K)$ such that
$$H\cap\bigcup_{r\in\mathbb Q}\langle\!\langle r\rangle\!\rangle=\{1\},$$
where $\langle\!\langle r\rangle\!\rangle$ is the normal closure of the sl... | Let K\subset S^3 be a hyperbolic knot with no finite surgery and let G(K)=\pi_1(S^3\setminus K). Does there exist a rank-two free subgroup H\subset G(K) such that H\cap\bigcup_{r\in\mathbb Q}\langle\langle r\rangle\rangle=\{1\}, where \langle\langle r\rangle\rangle is the normal closure of the slope r? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,405 | OWR-17471-012 | Effective Subgroup Separability in Hyperbolic Knot Groups | Given a subgroup $H\subset\pi_1(S^3\setminus K)$ and an element $\sigma\notin H$, can one bound the index of a subgroup $G\subset\pi_1(S^3\setminus K)$ such that $H\subset G$ but $\sigma\notin G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-012",
"literature-status:partially-solved",
"owr-year:2020"
] | Quantitative separability is established for closed curves and Abelian subgroups in prime alternating link complements, while the stated finitely generated subgroup problem remains unresolved. | [
{
"url": "https://arxiv.org/abs/1909.12266",
"label": "Bering and Futer, Explicit special covers of alternating links"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Given a subgroup $H\subset\pi_1(S^3\setminus K)$ and an element $\sigma\notin H$, can one bound the index of a subgroup $G\subset\pi_1(S^3\setminus K)$ such that $H\subset G$ but $\sigma\notin G$? | Given a subgroup H\subset\pi_1(S^3\setminus K) and an element \sigma\notin H, can one bound the index of a subgroup G\subset\pi_1(S^3\setminus K) such that H\subset G but \sigma\notin G? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,406 | OWR-17471-013 | Recognition of Virtually Special Hyperbolic Three-Manifolds | Find an algorithm that, given a triangulated hyperbolic $3$-manifold $M$, decides whether $M$ is homotopy equivalent to a special cube complex; equivalently, decide whether $\pi_1(M)$ embeds in a right-angled Artin group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-013",
"literature-status:open",
"owr-year:2020"
] | Virtual specialness of hyperbolic three-manifold groups is known, but no general terminating algorithm deciding specialness or RAAG embeddability of the given triangulated manifold was found. | [
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
},
{
"url": "https://www.maths.gla.ac.uk/~mpowell/Aschenbrenner-Friedl-Wilton-3-manifold-groups-final-version-031115.pdf",
"label": "Aschenbrenner, Friedl, and Wilton, three-manifold groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Find an algorithm that, given a triangulated hyperbolic $3$-manifold $M$, decides whether $M$ is homotopy equivalent to a special cube complex; equivalently, decide whether $\pi_1(M)$ embeds in a right-angled Artin group. | Find an algorithm which, given a triangulated hyperbolic 3-manifold M, decides whether M is homotopy equivalent to a special cube complex; equivalently, decide whether \pi_1(M) embeds in a right-angled Artin group. | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,407 | OWR-17471-014 | Universal Additive Vassiliev Invariants from Embedding Calculus | For every $n\geq1$, is the evaluation map $\pi_0\operatorname{ev}_n:K(I^3)\to\pi_0T_n(I,I^3)$ a universal additive Vassiliev invariant of type at most $n-1$ over $\mathbb Z$? Equivalently, is it surjective with kernel consisting exactly of knots that are $n$-equivalent to the unknot? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-014",
"literature-status:partially-solved",
"owr-year:2020"
] | The factorization and surjectivity are proved, and the resulting map is an isomorphism rationally for every n and p-adically for n at most p+2, but the integral isomorphism conjecture remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46844",
"label": "Oberwolfach Report 8/2020"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | For every $n\geq1$, is the evaluation map $\pi_0\operatorname{ev}_n:K(I^3)\to\pi_0T_n(I,I^3)$ a universal additive Vassiliev invariant of type at most $n-1$ over $\mathbb Z$? Equivalently, is it surjective with kernel consisting exactly of knots that are $n$-equivalent to the unknot? | For every n\ge1, is the evaluation map \pi_0\operatorname{ev}_n:K(I^3)\to\pi_0T_n(I,I^3) a universal additive Vassiliev invariant of type at most n-1 over \mathbb Z? Equivalently, is it surjective with kernel consisting exactly of knots n-equivalent to the unknot? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,408 | OWR-17471-015 | Asymptotic Prevalence of Nonlayered Veering Triangulations | As the number of tetrahedra tends to infinity among veering triangulations, does the proportion of non-layered veering triangulations tend to one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-015",
"literature-status:open",
"owr-year:2020"
] | Censuses and subsequent structural work give strong evidence and infinite non-layered families, but no theorem establishes that non-layered veering triangulations dominate. | [
{
"url": "https://arxiv.org/abs/1911.00006",
"label": "Futer, Guéritaud, and Schleimer, veering triangulations"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | As the number of tetrahedra tends to infinity among veering triangulations, does the proportion of non-layered veering triangulations tend to one? | As the number of tetrahedra tends to infinity among veering triangulations, does the proportion of non-layered veering triangulations tend to one? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,409 | OWR-17471-016 | Motion Groups of Hopf-Tree Links | For embedding spaces of Hopf-tree links in $\mathbb{R}^3$, is the motion group isomorphic to the symmetric automorphism group of the right-angled Artin group associated to the corresponding disjoint union of tree graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-016",
"literature-status:open",
"owr-year:2020"
] | The motion group is computed in several small link cases, but the proposed identification for links whose defining graph is a disjoint union of trees remains conjectural. | [
{
"url": "https://ems.press/content/serial-article-files/46844",
"label": "Oberwolfach Report 8/2020"
},
{
"url": "https://eprints.whiterose.ac.uk/id/eprint/148587/",
"label": "Goldsmith and related motion-group work"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | For embedding spaces of Hopf-tree links in $\mathbb{R}^3$, is the motion group isomorphic to the symmetric automorphism group of the right-angled Artin group associated to the corresponding disjoint union of tree graphs? | For embedding spaces of Hopf-tree links in \mathbb R^3, is the motion group isomorphic to the symmetric automorphism group of the right-angled Artin group associated to the corresponding disjoint union of tree graphs? | corrected_verified | The mathematical content was preserved while notation, typography, omitted definitions, or duplicate clauses were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,410 | OWR-17471-017 | Minimal Exotic Smooth Structures on Closed Four-Manifolds | Determine the simplest closed compact orientable smooth 4-manifold admitting multiple smooth structures, and whether any closed compact orientable definite 4-manifold admits multiple smooth structures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-017",
"literature-status:partially-solved",
"owr-year:2020"
] | Exotic smooth structures are now known on closed definite four-manifolds with fundamental group Z over 2, but the simplest example and the simply connected definite case remain unresolved. | [
{
"url": "https://arxiv.org/abs/2310.16156",
"label": "Stipsicz and Szabó, exotic definite four-manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Determine the simplest closed compact orientable smooth 4-manifold admitting multiple smooth structures, and whether any closed compact orientable definite 4-manifold admits multiple smooth structures. | Determine the simplest closed compact orientable smooth 4-manifold admitting multiple smooth structures, and whether any closed compact orientable definite 4-manifold admits multiple smooth structures. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,411 | OWR-17471-018 | Smooth Embeddings of Knot Traces in Homology Four-Spheres | For the Conway knot $K$, does the complement $S^4\setminus\nu(f(X(K)))$ of an embedded trace admit a smooth structure? Does some smooth integer-homology $4$-sphere contain the trace $X(K)$ of a nonslice knot smoothly? Finally, do there exist homotopy-equivalent closed oriented simply connected smooth $4$-manifolds $X$ ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-018",
"literature-status:open",
"owr-year:2020"
] | Piccirillo proved the Conway knot is not smoothly slice, but the associated complement in the proposed topological four-sphere construction is not thereby known to admit or lack a smooth structure. | [
{
"url": "https://arxiv.org/abs/1808.02923",
"label": "Piccirillo, The Conway knot is not slice"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | For the Conway knot $K$, does the complement $S^4\setminus\nu(f(X(K)))$ of an embedded trace admit a smooth structure? Does some smooth integer-homology $4$-sphere contain the trace $X(K)$ of a nonslice knot smoothly? Finally, do there exist homotopy-equivalent closed oriented simply connected smooth $4$-manifolds $X$ ... | For the Conway knot K, does S^4\setminus\nu(f(X(K))) admit a smooth structure? Can one construct a smooth 4-manifold X with the integer-homology type of S^4 containing the trace X(K) of a non-slice knot smoothly, and can one find closed oriented simply connected smooth 4-manifolds X and W homotopy equivalent to each ot... | corrected_verified | The official report was checked. All three listed open problems about knot traces and smooth four-manifolds were restored. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,412 | OWR-17471-019 | Slice Candidates and Shared Trace Boundaries of Knots | Is the positive Whitehead double of the left-handed trefoil slice? Is the $(2,1)$-cable of the figure-eight knot slice? For which knots $K$ does there exist a distinct knot $J$ with $\partial X(J)\cong\partial X(K)$, or with the two trace boundaries merely integer-homology cobordant? Give an algorithm for producing suc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-019",
"literature-status:partially-solved",
"owr-year:2020"
] | The 2,1 cable of the figure-eight knot is proved not smoothly slice, while the positive Whitehead double of the left-handed trefoil and the general trace-boundary algorithm problem remain open. | [
{
"url": "https://arxiv.org/abs/2207.14187",
"label": "Dai, Hom, Stoffregen, and Truong, cable-slice obstruction"
},
{
"url": "https://numdam.org/item/10.5802/wbln.39.pdf",
"label": "Weber, notes on the Oberwolfach knot problems"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Is the positive Whitehead double of the left-handed trefoil slice? Is the $(2,1)$-cable of the figure-eight knot slice? For which knots $K$ does there exist a distinct knot $J$ with $\partial X(J)\cong\partial X(K)$, or with the two trace boundaries merely integer-homology cobordant? Give an algorithm for producing suc... | Is the positive Whitehead double of the left-handed trefoil or the (2,1)-cable of the figure-eight knot slice? For which knots K does there exist a distinct knot J with diffeomorphic trace boundaries, and when can those boundaries be merely integer-homology cobordant? | corrected_verified | The official report was checked. The two sliceness questions, the trace-boundary questions, and the omitted algorithm request were restored. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,413 | OWR-17471-022 | Kernels of Nonfaithful Type-Preserving Punctured-Torus Representations | Let $T$ be the once-punctured torus. If $\rho:\pi_1(T)\to\operatorname{PSL}(2,\mathbb C)$ is a nonfaithful, discrete, type-preserving representation, is its kernel either
$$\langle\!\langle\beta_r^m\rangle\!\rangle$$
for some $r\in\widehat{\mathbb Q}$ and $m\geq2$, or
$$\langle\!\langle\beta_{r_1}^{m_1},\beta_{r_2}^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-022",
"literature-status:open",
"owr-year:2020"
] | The stated classification of kernels of discrete nonfaithful type-preserving punctured-torus representations remains a conjecture; available work proves important Heckoid and simple-loop special cases only. | [
{
"url": "https://arxiv.org/abs/1206.4258",
"label": "Lee and Sakuma, Heckoid groups"
},
{
"url": "https://arxiv.org/abs/1402.6873",
"label": "Lee and Sakuma, simple loops and Heckoid groups"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Let $T$ be the once-punctured torus. If $\rho:\pi_1(T)\to\operatorname{PSL}(2,\mathbb C)$ is a nonfaithful, discrete, type-preserving representation, is its kernel either
$$\langle\!\langle\beta_r^m\rangle\!\rangle$$
for some $r\in\widehat{\mathbb Q}$ and $m\geq2$, or
$$\langle\!\langle\beta_{r_1}^{m_1},\beta_{r_2}^... | Conjecture: if a nonfaithful type-preserving discrete representation \rho:\pi_1(T)\to PSL(2,\mathbb C) is given, then its kernel is either \langle\langle\beta_r^m\rangle\rangle for some r\in\widehat{\mathbb Q} and m\ge2, or \langle\langle\beta_{r_1}^{m_1},\beta_{r_2}^{m_2}\rangle\rangle for distinct r_1,r_2\in\widehat{... | corrected_verified | The official report was checked. The punctured-torus setting and the two conjectural kernel forms are retained. | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,414 | OWR-17471-023 | Pleating-Ray Tilings of the Representation-Space Complement | Let $\mathcal R$ be the Riley slice for the marked groups generated by
$$A=\begin{pmatrix}1&1\\0&1\end{pmatrix},\qquad B_\omega=\begin{pmatrix}1&0\\\omega&1\end{pmatrix}.$$
Is $\mathbb C^*\setminus\overline{\mathcal R}$ naturally tiled by quadrilaterals $\mathcal R_c(r)$ indexed by $r\in\mathbb Q/2\mathbb Z$, each co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516](https://doi.org/10.4171/owr/2020/8)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,020 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17471-023",
"literature-status:open",
"owr-year:2020"
] | Riley-slice work captures neighborhoods of rational pleating rays and refines the exterior, but the proposed global quadrilateral tiling has not been proved. | [
{
"url": "https://arxiv.org/abs/2111.03230",
"label": "Jørgensen and others, Riley-slice pleating"
},
{
"url": "https://doi.org/10.4171/owr/2020/8",
"label": "Oberwolfach Report 8/2020"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/8 | null | null | null | Let $\mathcal R$ be the Riley slice for the marked groups generated by
$$A=\begin{pmatrix}1&1\\0&1\end{pmatrix},\qquad B_\omega=\begin{pmatrix}1&0\\\omega&1\end{pmatrix}.$$
Is $\mathbb C^*\setminus\overline{\mathcal R}$ naturally tiled by quadrilaterals $\mathcal R_c(r)$ indexed by $r\in\mathbb Q/2\mathbb Z$, each co... | Conjecture: the complement of \overline R has a natural tiling by quadrilateral tiles R_c(r), indexed by r\in\mathbb Q/2\mathbb Z, each containing the extended pleating ray of slope r as a diagonal and arising from the indicated hyperbolic Dehn-filling holonomy representations. | corrected_verified | The official report was checked. The Riley slice, matrix generators, indexing, and Dehn-filling source of the tiles replace the dangling phrase “the indicated representations.” | null | null | null | null | null | Low-dimensional Topology (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/8, pp. 465--516 |
30,004,415 | OWR-17472-004 | Detecting Abelian Sylow Subgroups from Character Tables | For a finite group $G$ and a Sylow $p$-subgroup $P$, does the $p$-element submatrix $X_p(G)$ of the character table determine whether $P$ is abelian in all cases, as it does when $p\notin\{3,5\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568](https://d... | 3 | open | null | 2,020 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17472-004",
"literature-status:open",
"owr-year:2020"
] | The full character table detects abelian Sylow subgroups, but the extracted p-element-submatrix question is malformed and its claimed general determination is not established by the cited results. | [
{
"url": "https://arxiv.org/abs/1407.4495",
"label": "Kessar, Malle, and Navarro, abelian Sylow subgroups"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2014.08.012",
"label": "Kessar, Malle, and Navarro, published version"
},
{
"url": "https://doi.org/10.4171/owr/2020/9",
"label":... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2020/9 | null | null | null | For a finite group $G$ and a Sylow $p$-subgroup $P$, does the $p$-element submatrix $X_p(G)$ of the character table determine whether $P$ is abelian in all cases, as it does when $p\notin\{3,5\}$? | For a finite group G and a Sylow p-subgroup P, does the p-element submatrix X_p(G) of the character table determine whether P is abelian in all cases, as it does when p is not 3 or 5? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory (2021), Oberwolfach Reports, DOI 10.4171/owr/2020/9, pp. 517--568 |
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