id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,001,816 | OWR-5159-003 | The Arithmetic Fundamental Lemma Beyond Minuscule Cases | In the arithmetic fundamental lemma setting, let $F$ be a $p$-adic field, let $E/F$ be an unramified quadratic extension, and let a regular semisimple $\gamma$ in the unitary symmetric space match $g$ in the corresponding unitary group. Does the AFL identity
$$O'_\gamma(1_S)=-\omega(\gamma)\left\langle\Delta(N_{n-1}),... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768](https://doi.org/10.4171/owr/2011/31)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-5159-003",
"literature-status:partially-solved",
"owr-year:2011"
] | The report records proofs for n equal to 2 and 3 and restricted minuscule progress. Rapoport--Terstiege--Zhang prove the general minuscule case, but the unrestricted AFL conjecture remains unresolved. | [
{
"url": "https://arxiv.org/abs/1203.5827",
"label": "Rapoport--Terstiege--Zhang AFL"
},
{
"url": "https://doi.org/10.4171/owr/2011/31",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/31 | null | null | null | In the arithmetic fundamental lemma setting, let $F$ be a $p$-adic field, let $E/F$ be an unramified quadratic extension, and let a regular semisimple $\gamma$ in the unitary symmetric space match $g$ in the corresponding unitary group. Does the AFL identity
$$O'_\gamma(1_S)=-\omega(\gamma)\left\langle\Delta(N_{n-1}),... | In the arithmetic fundamental lemma setting, let F be a p-adic field, E/F an unramified quadratic extension, and let a regular semisimple \gamma in the unitary symmetric space match g in the corresponding unitary group. The AFL conjecture asserts O'_\gamma(1_S)=-\omega(\gamma) \langle\Delta(N_{n-1}),(1,g)\Delta(N_{n-1}... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768 |
30,001,817 | OWR-5159-006 | The p-Adic Variational Hodge Conjecture | Let $W$ be the Witt ring of a perfect field of characteristic $p>0$, let $X$ be smooth and projective over $W$ with special fiber $X_1$, and let $\xi_1\in CH^r(X_1)_{\mathbb Q}$. If its crystalline cycle class lies in the Hodge filtration $F^rH^{2r}_{\mathrm{dR}}(X/W)_{\mathbb Q}$, must there exist $\xi\in CH^r(X)_{\ma... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768](https://doi.org/10.4171/owr/2011/31)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-5159-006",
"literature-status:partially-solved",
"owr-year:2011"
] | Bloch--Esnault--Kerz prove formal and K-theoretic/vector-bundle versions of the p-adic variational Hodge conjecture, and Langer extends the result to relative motivic Chow groups. The full Chow-class lifting statement in the extracted generality is not known. | [
{
"url": "https://arxiv.org/abs/1203.2776",
"label": "Bloch--Esnault--Kerz deformation theorem"
},
{
"url": "https://doi.org/10.4171/DM/662",
"label": "Langer--motivic Chow groups"
},
{
"url": "https://doi.org/10.4171/owr/2011/31",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/31 | null | null | null | Let $W$ be the Witt ring of a perfect field of characteristic $p>0$, let $X$ be smooth and projective over $W$ with special fiber $X_1$, and let $\xi_1\in CH^r(X_1)_{\mathbb Q}$. If its crystalline cycle class lies in the Hodge filtration $F^rH^{2r}_{\mathrm{dR}}(X/W)_{\mathbb Q}$, must there exist $\xi\in CH^r(X)_{\ma... | Let W be the Witt ring of a perfect field of characteristic p>0, let X be smooth and projective over W with special fibre X_1, and let \xi_1\in CH^r(X_1)_{\mathbb Q}. If its crystalline cycle class lies in the Hodge filtration F^rH^{2r}_{\mathrm{dR}}(X/W)_{\mathbb Q}, then there exists \xi\in CH^r(X)_{\mathbb Q} whose ... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768 |
30,001,818 | OWR-5159-009 | Kato’s Main Conjecture for Modular Galois Representations | For the Galois representation $T$ attached to a normalized eigen-newform and the cyclotomic Iwasawa algebra $\Lambda$, does Kato's main-conjecture equality
$$\operatorname{Char}(H^2(T)^\eta)=\operatorname{Char}((H^1(T)/\Lambda z_f)^\eta)$$
hold for every character $\eta$ of the torsion subgroup of $\Gamma=\operatorna... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768](https://doi.org/10.4171/owr/2011/31)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-5159-009",
"literature-status:partially-solved",
"owr-year:2011"
] | Kato's main conjecture is proved in important ordinary and CM cases, but the extracted broad formulation is not a theorem in full generality as of the check date. | [
{
"url": "https://doi.org/10.4171/owr/2011/31",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1017/S0017089524000016",
"label": "Muller 2024"
},
{
"url": "https://doi.org/10.1007/s00222-013-0448-1",
"label": "Skinner--Urban"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/31 | null | null | null | For the Galois representation $T$ attached to a normalized eigen-newform and the cyclotomic Iwasawa algebra $\Lambda$, does Kato's main-conjecture equality
$$\operatorname{Char}(H^2(T)^\eta)=\operatorname{Char}((H^1(T)/\Lambda z_f)^\eta)$$
hold for every character $\eta$ of the torsion subgroup of $\Gamma=\operatorna... | For the Galois representation T attached to a normalized eigen-newform and the cyclotomic Iwasawa algebra \Lambda, Kato's main conjecture asserts that for every character \eta of the torsion subgroup of \Gamma=\operatorname{Gal}(\mathbb{Q}(\mu_{p^\infty})/\mathbb{Q}), \operatorname{Char}(H^2(T)^\eta)=\operatorname{Char... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Algebraische Zahlentheorie (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/31, pp. 1709--1768 |
30,001,819 | OWR-5160-001 | Energy Cost of Density Defects in Fermi Seas | Determine the optimal energy cost, or sharp Lieb–Thirring-type lower bound, for creating a density perturbation including a hole in an infinitely extended free Fermi sea of prescribed positive density $\rho_0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843](https://doi.org/10.4171/owr/2011/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1103/PhysRevLett.106.150402",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (answered in the source up to the constant). M. Lewin (joint with R. L. Frank, E. H. Lieb and R. Seiringer; OWR 32/2011, pp. 1790–1792) asks how much energy it costs to perturb, or make a hole in, a free Fermi sea of density ρ₀ > 0, and answers with a p... | [
"owr",
"oberwolfach-reports",
"OWR-5160-001",
"literature-status:open",
"owr-year:2011"
] | This record is only a title and contains no mathematically testable assertion or resolution; it is therefore retained as open rather than inferred solved. | [
{
"url": "https://doi.org/10.4171/owr/2011/32",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/32 | null | null | null | Determine the optimal energy cost, or sharp Lieb–Thirring-type lower bound, for creating a density perturbation including a hole in an infinitely extended free Fermi sea of prescribed positive density $\rho_0$. | Determine the optimal energy cost, or sharp Lieb--Thirring-type lower bound, for creating a density perturbation including a hole in an infinitely extended free Fermi sea of prescribed positive density \rho_0. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843 |
30,001,820 | OWR-5160-002 | Fast Solvers for the Electronic Schrödinger Equation | Develop a fast computational method for solving the electronic Schrödinger equation, with substantially better complexity than current approaches. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843](https://doi.org/10.4171/owr/2011/32)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,011 | 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-5160-002",
"literature-status:open",
"owr-year:2011"
] | The extracted text itself calls fast computation of the electronic Schrodinger equation an open problem, and no general resolution is established by the cited report. | [
{
"url": "https://doi.org/10.4171/owr/2011/32",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/32 | null | null | null | Develop a fast computational method for solving the electronic Schrödinger equation, with substantially better complexity than current approaches. | Develop a fast computational method for solving the electronic Schroedinger equation, with substantially better complexity than current approaches. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843 |
30,001,821 | OWR-5160-003 | Low-Rank Subexponential Electronic-Structure Algorithms | Can low-rank approximations of wavefunction parameters yield a numerical method for solving the electronic Schrödinger equation with subexponential complexity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843](https://doi.org/10.4171/owr/2011/32)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,011 | 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-5160-003",
"literature-status:open",
"owr-year:2011"
] | The sub-exponential low-rank complexity claim is presented as a conjecture; the cited material gives no general proof or counterexample. | [
{
"url": "https://doi.org/10.4171/owr/2011/32",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/32 | null | null | null | Can low-rank approximations of wavefunction parameters yield a numerical method for solving the electronic Schrödinger equation with subexponential complexity? | Can low-rank approximations of wavefunction parameters yield a numerical method for solving the electronic Schroedinger equation with sub-exponential complexity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mathematical Methods in Quantum Chemistry (2011), Oberwolfach Reports, DOI 10.4171/owr/2011/32, pp. 1769--1843 |
30,001,822 | OWR-11125-001 | Entropy Rigidity for Hyperbolic Group Actions | Let $X$ be a proper geodesic hyperbolic space with a geometric group action by $\Gamma$ and boundary a topological $n$-sphere, and let $e(\Gamma)$ be the critical exponent of the action. Is $e(\Gamma)\geq n$, with equality if and only if $X$ is rough-isometric to real hyperbolic space $\mathbb H^{n+1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912](https://doi.org/10.4171/owr/2011/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,011 | 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-11125-001",
"literature-status:open",
"owr-year:2011"
] | The entropy equality question is extracted without the surrounding hypotheses needed to identify a theorem, and the cited report does not resolve it in this generality. | [
{
"url": "https://doi.org/10.4171/owr/2011/33",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/33 | null | null | null | Let $X$ be a proper geodesic hyperbolic space with a geometric group action by $\Gamma$ and boundary a topological $n$-sphere, and let $e(\Gamma)$ be the critical exponent of the action. Is $e(\Gamma)\geq n$, with equality if and only if $X$ is rough-isometric to real hyperbolic space $\mathbb H^{n+1}$? | Let X be a proper geodesic hyperbolic space with a geometric group action by \Gamma and boundary a topological n-sphere, and let e(\Gamma) be the critical exponent of the action. Is e(\Gamma)\geq n, with equality if and only if X is rough-isometric to real hyperbolic space H^{n+1}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912 |
30,001,823 | OWR-11125-002 | Cardinality and Rigidity of Metric Tangent Spaces | For a geodesic metric space $X$ and basepoint $x_0$, how large can the set $\operatorname{Tan}(X,x_0)$ of pointed-isometry classes of tangents be, and what structural consequences follow when the tangent is unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912](https://doi.org/10.4171/owr/2011/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,011 | 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-11125-002",
"literature-status:open",
"owr-year:2011"
] | These are broad questions about tangent cones and uniqueness of blow-ups; the extracted record supplies no resolution and they remain open at this level of generality. | [
{
"url": "https://doi.org/10.4171/owr/2011/33",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/33 | null | null | null | For a geodesic metric space $X$ and basepoint $x_0$, how large can the set $\operatorname{Tan}(X,x_0)$ of pointed-isometry classes of tangents be, and what structural consequences follow when the tangent is unique? | For a geodesic metric space X and basepoint x_0, how large can the set Tan(X,x_0) of pointed-isometry classes of tangents be, and what structural consequences follow when the tangent is unique? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912 |
30,001,824 | OWR-11125-003 | Relative K-Stability and Extremal Kähler Metrics | If a polarized projective manifold $(M,L)$ is $K$-stable relative to a maximal algebraic torus $T$ in $\operatorname{Aut}(M)$, does the polarization class $c_1(L)$ contain an extremal Kähler metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912](https://doi.org/10.4171/owr/2011/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,011 | 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-11125-003",
"literature-status:partially-solved",
"owr-year:2011"
] | Relative K-stability has been established as a necessary condition and strong-stability cases give existence, but the full extremal Kahler existence conjecture in the extracted generality remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/33",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.2969/jmsj/06620535",
"label": "Mabuchi relative stability"
},
{
"url": "https://arxiv.org/abs/1307.5203",
"label": "Mabuchi existence results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/33 | null | null | null | If a polarized projective manifold $(M,L)$ is $K$-stable relative to a maximal algebraic torus $T$ in $\operatorname{Aut}(M)$, does the polarization class $c_1(L)$ contain an extremal Kähler metric? | If a polarized projective manifold (M,L) is K-stable relative to a maximal algebraic torus T in Aut(M), does the polarization class c_1(L) contain an extremal Kahler metric? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912 |
30,001,825 | OWR-11125-006 | Classification of Finite-Energy Gravitational Instantons | Classify complete four-dimensional gravitational instantons with $\operatorname{Rm}\in L^2$ that are neither ALE nor ALF. Can such metrics have slow curvature decay, and can they occur as singularity dilations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912](https://doi.org/10.4171/owr/2011/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | solved | null | 2,011 | 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 | {
"source_url": "https://doi.org/10.4310/ACTA.2024.v232.n2.a2",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (classified; the new types do occur as bubbles)**. H.-J. Hein (OWR 33/2011, p. 1904, Conjecture 2) conjectures that his families (ALG, ALH and two new types, now called ALG* and ALH*) classify gravitational instantons with Rm ∈ L² that are neither ALE nor ALF, that... | [
"owr",
"oberwolfach-reports",
"OWR-11125-006",
"literature-status:partially-solved",
"owr-year:2011"
] | Recent classification results cover substantial conformally Kahler and Hermitian subfamilies with finite curvature energy, but they do not establish the broad classification conjecture stated in the extracted record. | [
{
"url": "https://doi.org/10.4171/owr/2011/33",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2310.13197",
"label": "Li classification results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/33 | null | null | null | Classify complete four-dimensional gravitational instantons with $\operatorname{Rm}\in L^2$ that are neither ALE nor ALF. Can such metrics have slow curvature decay, and can they occur as singularity dilations? | Classify complete four-dimensional gravitational instantons with Rm in L^2 that are neither ALE nor ALF: are the newly described geometries the only ones with slow curvature decay, and can they occur as singularity dilations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912 |
30,001,826 | OWR-11125-007 | Compactifiable Gravitational Instantons | Classify complex surfaces $X\setminus D$ carrying gravitational-instanton metrics, up to biholomorphism and hyperkähler rotation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912](https://doi.org/10.4171/owr/2011/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,011 | 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-11125-007",
"literature-status:open",
"owr-year:2011"
] | The extracted classification conjecture for all compactifiable gravitational instantons is broader than the cited examples and has no complete proof or counterexample in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2011/33",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2310.13197",
"label": "recent gravitational-instanton classification"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/33 | null | null | null | Classify complex surfaces $X\setminus D$ carrying gravitational-instanton metrics, up to biholomorphism and hyperkähler rotation. | If X\D carries a gravitational-instanton metric, is X\D biholomorphic, up to hyperkahler rotation, to one of the known examples? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Differentialgeometrie im Großen (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/33, pp. 1857--1912 |
30,001,827 | OWR-11126-002 | Periodic Reeb Orbits and Classification of Contact Structures | Does every closed contact-type hypersurface in a symplectic manifold admit a periodic orbit, equivalently does every Reeb vector field on a closed contact manifold admit a periodic orbit; and how are contact structures on a fixed manifold classified up to diffeomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,011 | 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-11126-002",
"literature-status:open",
"owr-year:2011"
] | The extraction combines the Weinstein conjecture with a broad classification question and does not identify a single resolved claim; the classification problem remains open in this form. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | Does every closed contact-type hypersurface in a symplectic manifold admit a periodic orbit, equivalently does every Reeb vector field on a closed contact manifold admit a periodic orbit; and how are contact structures on a fixed manifold classified up to diffeomorphism? | Does every closed contact-type hypersurface in a symplectic manifold admit a periodic orbit, equivalently does every Reeb vector field on a closed contact manifold admit a periodic orbit; and how are contact structures on a fixed manifold classified up to diffeomorphism? | exact | The official report was checked and confirms the statement as written. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,828 | OWR-11126-003 | Algebraic and Geometric Overtwistedness | Is algebraic overtwistedness equivalent to overtwistedness for contact manifolds, in particular does algebraic overtwistedness imply overtwistedness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | solved | null | 2,011 | 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 | {
"source_url": "https://doi.org/10.2140/gt.2023.27.953",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no)**. C. Wendl (joint with J. Latschev and M. Hutchings; OWR 34/2011, p. 1918) recalls that overtwisted contact manifolds are algebraically overtwisted (vanishing contact homology) and calls the converse a reasonable conjecture. It is false: R. Avdek, [Geom. Topo... | [
"owr",
"oberwolfach-reports",
"OWR-11126-003",
"literature-status:open",
"owr-year:2011"
] | The record is a truncated conditional conjecture about contact surgery and does not state enough context to identify a theorem; no resolution is asserted here. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | Is algebraic overtwistedness equivalent to overtwistedness for contact manifolds, in particular does algebraic overtwistedness imply overtwistedness? | Is algebraic overtwistedness equivalent to overtwistedness for contact manifolds, in particular does algebraic overtwistedness imply overtwistedness? | exact | The official report was checked and confirms the statement as written. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,829 | OWR-11126-004 | Invariant Measures for Thermostated Mechanical Systems | For a mechanical system driven by one or more thermostats, does an invariant measure exist, is it unique, and do reasonable initial distributions converge to it, with what rates? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,011 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report states affirmative results for the invariant-measure, uniqueness, convergence, and rate questions in the thermostated sy) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11126-004",
"literature-status:open",
"owr-year:2011"
] | The invariant-measure and convergence questions are stated without a specified dynamical system in the extracted record, and no general answer is available from the cited source. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | null | For a mechanical system driven by one or more thermostats, does an invariant measure exist, is it unique, and do reasonable initial distributions converge to it, with what rates? | unrecoverable | The official report states affirmative results for the invariant-measure, uniqueness, convergence, and rate questions in the thermostated system under discussion. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,830 | OWR-11126-005 | Frequency Images from Nonadapted Hermitian Structures | For the frequency map of angular momenta of relative equilibria, do non-adapted Hermitian structures contribute nothing to its image; equivalently, is $\operatorname{Im}F=A_{P_0}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | solved | null | 2,011 | 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... | [
"OWR-11126-006"
] | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (same answer as `OWR-11126-005`)**. The record is Chenciner's Question one page earlier (OWR 34/2011, p. 1931): given the inertia matrix S₀, describe the image of the frequency map F. By the Chenciner–Jiménez-Pérez theorem cited under `OWR-11126-005`, Im F = A_{P₀}... | [
"owr",
"oberwolfach-reports",
"OWR-11126-005",
"literature-status:open",
"owr-year:2011"
] | The conjecture is proved only for p equal to two in the extracted source; the general assertion about non-adapted Hermitian structures remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | For the frequency map of angular momenta of relative equilibria, do non-adapted Hermitian structures contribute nothing to its image; equivalently, is $\operatorname{Im}F=A_{P_0}$? | For the frequency map of angular momenta of relative equilibria, do non-adapted Hermitian structures contribute nothing to its image; equivalently, is \operatorname{Im}F=A_{P_0}? | corrected_verified | The official report was checked and the statement was repaired to match the source passage. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,831 | OWR-11126-006 | Frequency Maps of Central N-Body Equilibria | Given the inertia matrix S_0 of a central relative equilibrium in the N-body problem, what is the image of the associated frequency map F? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | solved | null | 2,011 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | Duplicate/merged OWR extraction (This is a less precise repeated extraction of the frequency-image conjecture preserved in OWR-11126-005. No separate clean statement is prom) | [
"OWR-11126-005"
] | null | [Discussion #4 literature review, 2026-09-30] **solved (same answer as `OWR-11126-005`)**. The record is Chenciner's Question one page earlier (OWR 34/2011, p. 1931): given the inertia matrix S₀, describe the image of the frequency map F. By the Chenciner–Jiménez-Pérez theorem cited under `OWR-11126-005`, Im F = A_{P₀}... | [
"owr",
"oberwolfach-reports",
"OWR-11126-006",
"literature-status:open",
"owr-year:2011"
] | The record contains only the word conjecture, so it has no recoverable mathematical statement whose resolution could be verified. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | null | Given the inertia matrix S_0 of a central relative equilibrium in the N-body problem, what is the image of the associated frequency map F? | unrecoverable | This is a less precise repeated extraction of the frequency-image conjecture preserved in OWR-11126-005. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,832 | OWR-11126-007 | Reeb Orbits Bounding Global Disk Sections | Which closed Reeb orbits on the tight 3-sphere bound a disk-like global surface of section, so that every other trajectory intersects the disk transversely infinitely often in forward and backward time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,011 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Answered in the source or not an open problem (solved (for non-degenerate contact forms; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (for non-degenerate contact forms; answered in the source)**. U. Hryniewicz (OWR 34/2011, p. 1937) asks which closed Reeb orbits on the tight 3-sphere bound a disk-like global surface of section, and answers it for non-degenerate contact forms (Theorem 1 there, joi... | [
"owr",
"oberwolfach-reports",
"OWR-11126-007",
"literature-status:open",
"owr-year:2011"
] | The record is only a conjecture fragment followed by a theorem; without the missing antecedent it cannot be matched reliably to a solved claim. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | null | Which closed Reeb orbits on the tight 3-sphere bound a disk-like global surface of section, so that every other trajectory intersects the disk transversely infinitely often in forward and backward time? | unrecoverable | The official report answers the disk-like global-section question with a theorem in the same contribution. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,833 | OWR-11126-009 | Zero Entropy Systems as Limits of Integrable Systems | In low dimensions, are all conservative dynamical systems with zero topological entropy limits of integrable systems; in particular, can the rational-rotation approximations of every smooth area-preserving disk pseudo-rotation be chosen to preserve the standard area form? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,011 | 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-11126-009",
"literature-status:open",
"owr-year:2011"
] | Periodic approximation is known, but the cited primary theorem does not settle the stronger requirement that the approximants preserve the standard area form; the conservative version remains open here. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4007/annals.2015.181.3.4",
"label": "Bramham periodic approximations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | In low dimensions, are all conservative dynamical systems with zero topological entropy limits of integrable systems; in particular, can the rational-rotation approximations of every smooth area-preserving disk pseudo-rotation be chosen to preserve the standard area form? | In low dimensions, are all conservative dynamical systems with zero topological entropy limits of integrable systems; in particular, can the rational-rotation approximations of every smooth area-preserving disk pseudo-rotation be chosen to preserve the standard area form? | exact | The official report was checked and confirms the statement as written. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,834 | OWR-11126-010 | Rigidity of Maximal Rank Abelian Actions | For maximal-rank abelian actions with Lyapunov exponents in general position, what values can the entropies and Lyapunov exponents take, are they logarithms of algebraic numbers with degree related to the manifold dimension, are there finitely many ergodic components, and are the actions measurably conjugate to algebra... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970](https://doi.org/10.4171/owr/2011/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,011 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report introduces these rigidity questions and then immediately states a theorem resolving them in the setting considered. No s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11126-010",
"literature-status:open",
"owr-year:2011"
] | The questions about algebraicity of logarithms, finiteness, and measurable conjugacy are extracted without enough system data and have no general resolution in the cited report. | [
{
"url": "https://doi.org/10.4171/owr/2011/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/34 | null | null | null | null | For maximal-rank abelian actions with Lyapunov exponents in general position, what values can the entropies and Lyapunov exponents take, are they logarithms of algebraic numbers with degree related to the manifold dimension, are there finitely many ergodic components, and are the actions measurably conjugate to algebra... | unrecoverable | The official report introduces these rigidity questions and then immediately states a theorem resolving them in the setting considered. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Dynamische Systeme (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/34, pp. 1913--1970 |
30,001,835 | OWR-11127-002 | Even Mod-p Galois Representations in Langlands Reciprocity | What does the arithmetic Langlands reciprocity program predict or establish for absolutely irreducible even mod-$p$ Galois representations $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(\mathbb F_p)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-002",
"literature-status:open",
"owr-year:2011"
] | This is a broad question about the arithmetic Langlands programme for the representations in the report; no general theorem resolving it was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | What does the arithmetic Langlands reciprocity program predict or establish for absolutely irreducible even mod-$p$ Galois representations $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(\mathbb F_p)$? | What does the arithmetic Langlands reciprocity program predict or establish for absolutely irreducible even mod-p Galois representations such as \rho:G_{\mathbb{Q}}\to\operatorname{GL}_2(\mathbb{F}_p)? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,836 | OWR-11127-003 | Level-One Serre Modularity over Imaginary Quadratic Fields | Is Serre's conjecture true for representations $\rho:G_E\to\operatorname{GL}_2(\mathbb F_p)$ of level $N(\rho)=1$ when $E$ is an imaginary quadratic field of class number one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-003",
"literature-status:open",
"owr-year:2011"
] | Serre modularity over imaginary quadratic fields remains only partially established; the level-one class-number-one assertion is not known in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jnt.2011.09.010",
"label": "Torrey on Serre conjecture over imaginary quadratic fields"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Is Serre's conjecture true for representations $\rho:G_E\to\operatorname{GL}_2(\mathbb F_p)$ of level $N(\rho)=1$ when $E$ is an imaginary quadratic field of class number one? | Is Serre's conjecture true for representations \rho:G_E\to\operatorname{GL}_2(\mathbb{F}_p) of level N(\rho)=1 when E is an imaginary quadratic field of class number one? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,837 | OWR-11127-004 | Large-Image Even Galois Representations | Does there exist an absolutely irreducible continuous even representation $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(\mathbb F_p)$ that is unramified outside $p$ and whose image contains $\operatorname{SL}_2(\mathbb F_p)$? In particular, is there at most one prime $p<10^6$ for which such a representation exists? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-004",
"literature-status:open",
"owr-year:2011"
] | The passage records computational bounds and a heuristic conjecture about exceptional representations, not a proof of the claimed global classification. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1908.11690",
"label": "later partial Serre-modularity results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Does there exist an absolutely irreducible continuous even representation $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(\mathbb F_p)$ that is unramified outside $p$ and whose image contains $\operatorname{SL}_2(\mathbb F_p)$? In particular, is there at most one prime $p<10^6$ for which such a representation exists? | For an absolutely irreducible continuous even representation \rho:G_{\mathbb{Q}}\to\operatorname{GL}_2(\mathbb{F}_p) unramified outside p, must p\ge79, k\ge33, and the stated lower-bound exceptions for the Serre weight k and prime p be the only possibilities, with at most perhaps one p<10^6 having image containing \ope... | corrected_verified | The report proves conditional lower bounds for small-image cases and then states the surviving large-image question as a heuristic. The clean statement retains only that genuinely open question and its explicit numerical prediction. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,838 | OWR-11127-006 | Conjugacy Classes Distinguishing Finite Groups from Subgroups | How many conjugacy classes of a finite group $G$ are needed to distinguish $G$ from each of its proper subgroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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 | [Discussion #4 update, 2026-10-15] Source/status clarification for **OWR-11127-006** (conjugacy classes distinguishing a finite group from its proper subgroups). | [
"owr",
"oberwolfach-reports",
"OWR-11127-006",
"literature-status:partially-solved",
"owr-year:2011"
] | The Chebotarev-invariant framework and substantial finite-group results are known, but the extracted general question does not have a complete uniform answer. | [
{
"url": "https://arxiv.org/abs/1008.4909",
"label": "Kowalski--Zywina Chebotarev invariant"
},
{
"url": "https://arxiv.org/abs/1509.05859",
"label": "later conjecture and partial results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | How many conjugacy classes of a finite group $G$ are needed to distinguish $G$ from each of its proper subgroups? | How many conjugacy classes of a finite group G are needed to distinguish G from each of its proper subgroups? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,839 | OWR-11127-007 | Frobenius Certificates for Finite Galois-Group Isomorphisms | Given an injective homomorphism from a finite Galois group into a fixed finite group $G$, what finite collection of conjugacy classes or Frobenius data suffices to certify that the homomorphism is an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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 | [Discussion #4 update, 2026-10-09] Record 30001839 is still `partially_solved` at commit `372682f`. For the question as currently worded, I suggest **solved in the literature / answered in the source**, not a new result of ours. | [
"owr",
"oberwolfach-reports",
"OWR-11127-007",
"literature-status:partially-solved",
"owr-year:2011"
] | Chebotarev and Frobenius-conjugacy methods give effective tests in important settings, but the broad formulation in the extracted question is not completely classified. | [
{
"url": "https://arxiv.org/abs/1008.4909",
"label": "Kowalski--Zywina Chebotarev invariant"
},
{
"url": "https://doi.org/10.5802/jtnb.649",
"label": "Jouve--Kowalski--Zywina finite-group applications"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Given an injective homomorphism from a finite Galois group into a fixed finite group $G$, what finite collection of conjugacy classes or Frobenius data suffices to certify that the homomorphism is an isomorphism? | Given an injective homomorphism from a finite Galois group into a fixed finite group G, what finite collection of conjugacy classes or Frobenius data suffices to certify that the homomorphism is an isomorphism? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,840 | OWR-11127-008 | Galois Images in Genus-Two Real-Multiplication Families | For the family of genus-$2$ curves
$$C_t:\quad y^2=x^5-5x^3+5x+t,$$
which has real multiplication by $\mathbb Z[(1+\sqrt5)/2]$, in what sense is this one-dimensional family special inside the two-dimensional real-multiplication moduli space? Which level structure does it fix, can an exceptional integer $N$ make its m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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-11127-008",
"literature-status:partially-solved",
"owr-year:2011"
] | Galois images are determined in several low-dimensional and sufficiently generic RM families, but the exceptional-level and full-Tate-module questions remain open in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1508.06426",
"label": "integral and adelic open-image results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | For the family of genus-$2$ curves
$$C_t:\quad y^2=x^5-5x^3+5x+t,$$
which has real multiplication by $\mathbb Z[(1+\sqrt5)/2]$, in what sense is this one-dimensional family special inside the two-dimensional real-multiplication moduli space? Which level structure does it fix, can an exceptional integer $N$ make its m... | For the one-parameter family of genus-2 curves with real multiplication by the specified order, in what sense is the family special inside the two-dimensional RM moduli space, what level structure does it fix, can an exceptional N make the mod-N Galois image smaller than expected, and what is the image on the Tate modu... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,841 | OWR-11127-009 | Sato–Tate Equidistribution for Exceptional Abelian Varieties | Which exceptional abelian varieties admit a proof of the numerical Sato-Tate equidistribution conjecture, and how can all such exceptional cases be classified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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-11127-009",
"literature-status:partially-solved",
"owr-year:2011"
] | The Mumford--Tate and Sato--Tate assertions are proved for broad classes of abelian varieties, including several with extra endomorphisms, but classification of all exceptional cases is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1508.06426",
"label": "integral and adelic Mumford--Tate results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Which exceptional abelian varieties admit a proof of the numerical Sato-Tate equidistribution conjecture, and how can all such exceptional cases be classified? | Which exceptional abelian varieties admit a proof of the numerical Sato-Tate equidistribution conjecture, and how can all such exceptional cases be classified? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,842 | OWR-11127-010 | CM Rational Points on Nonsplit Cartan Modular Curves | Does there exist a constant $c$ such that, for every prime $p>c$, the only rational points on the modular curve $X_{\mathrm{ns}}(p)$ over $\mathbb Q$ are CM points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-010",
"literature-status:open",
"owr-year:2011"
] | Rational-point classifications are known for selected small levels, including level 13, but the asserted uniform statement for all sufficiently large primes is not proved. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1711.05846",
"label": "level-13 rational-point classification"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Does there exist a constant $c$ such that, for every prime $p>c$, the only rational points on the modular curve $X_{\mathrm{ns}}(p)$ over $\mathbb Q$ are CM points? | Does there exist a constant c such that for every prime p>c the only rational points on the modular curve X_{\mathrm{ns}}(p) over \mathbb{Q} are CM points? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,843 | OWR-11127-012 | Functional Equations for Higher Bloch Groups | For higher polylogarithms, especially $n>3$, can one construct functional equations that generate the universal relations needed to define the higher Bloch groups $B_n(F)$ and prove the corresponding form of Zagier's conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-012",
"literature-status:open",
"owr-year:2011"
] | Goncharov's higher-weight conjectural programme supplies the n=4 target, but no general candidate generating relation for every n greater than 3 has been established. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/math/0207222",
"label": "functional equations of higher logarithms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | For higher polylogarithms, especially $n>3$, can one construct functional equations that generate the universal relations needed to define the higher Bloch groups $B_n(F)$ and prove the corresponding form of Zagier's conjecture? | For higher polylogarithms, especially n>3, can one construct functional equations that generate the universal relations needed to define the higher Bloch groups B_n(F) and prove the corresponding form of Zagier's conjecture? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,844 | OWR-11127-015 | Finite Secant–Tangent Generation on Cubic Surfaces | For a smooth cubic surface $S$ over a field $K$, does there always exist a finite subset $B\subseteq S(K)$ such that all $K$-points of $S$ can be generated from $B$ by successive secant and tangent constructions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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-11127-015",
"literature-status:partially-solved",
"owr-year:2011"
] | Manin's Mordell--Weil problem for cubic surfaces remains open in general, while Siksek proves the one-generator result for surfaces containing two skew rational lines. | [
{
"url": "https://arxiv.org/abs/1012.1838",
"label": "Siksek on Mordell--Weil generators"
},
{
"url": "https://arxiv.org/abs/alg-geom/9407009",
"label": "Manin's cubic-surface problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | For a smooth cubic surface $S$ over a field $K$, does there always exist a finite subset $B\subseteq S(K)$ such that all $K$-points of $S$ can be generated from $B$ by successive secant and tangent constructions? | For a smooth cubic surface S over a field K, does there always exist a finite subset B of S(K) such that all K-points of S can be generated from B by successive secant and tangent constructions? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,845 | OWR-11127-016 | Correct Modularity Criteria for Nahm Series | What is the correct necessary-and-sufficient criterion on rational $A$, $B$, and $C$ for the Nahm series $F_{A,B,C}(q)$ to be modular, and how should Nahm's conjectural criterion be repaired? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-016",
"literature-status:open",
"owr-year:2011"
] | The report explicitly describes the correct formulation of the Nahm-type conjecture as an interesting open question; later work has not supplied a general resolution of this extracted formulation. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | What is the correct necessary-and-sufficient criterion on rational $A$, $B$, and $C$ for the Nahm series $F_{A,B,C}(q)$ to be modular, and how should Nahm's conjectural criterion be repaired? | What is the correct necessary-and-sufficient criterion on rational A, B, and C for the Nahm series F_{A,B,C}(q) to be modular, and how should Nahm's conjectural criterion be repaired? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,846 | OWR-11127-017 | The Abelian Rank-One Stark Conjecture | Let $K/k$ be an abelian extension of number fields with Galois group $G$, and let $S$ contain at least two places, including a place totally split in $K/k$. Does there exist an $S$-unit $\varepsilon$ in $K$ satisfying the Stark relations for all characters, such that $K(\varepsilon^{1/w_K})/k$ is abelian and $\varepsil... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,011 | 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-11127-017",
"literature-status:partially-solved",
"owr-year:2011"
] | The abelian rank-one Stark conjecture is proved in important cases, including quadratic extensions, but remains open in the full generality of the extracted conjecture. | [
{
"url": "https://arxiv.org/abs/1112.2820",
"label": "Roblot on Stark-unit index formulae"
},
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Let $K/k$ be an abelian extension of number fields with Galois group $G$, and let $S$ contain at least two places, including a place totally split in $K/k$. Does there exist an $S$-unit $\varepsilon$ in $K$ satisfying the Stark relations for all characters, such that $K(\varepsilon^{1/w_K})/k$ is abelian and $\varepsil... | Let K/k be an abelian extension of number fields with Galois group G and let S contain at least two places, including a place totally split in K/k. Does there exist an S-unit \varepsilon in K satisfying the Stark relations for all characters, making K(\varepsilon^{1/w_K})/k abelian, and becoming a unit when |S|\ge3? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,847 | OWR-11127-019 | Weighted-Projective Moduli of Marked Elliptic Curves | How close are we to classifying all pairs $(G,M)$ for which the moduli space of marked elliptic curves is a weighted projective space, or a complete intersection in weighted projective space, and what further applications do these moduli spaces have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-019",
"literature-status:open",
"owr-year:2011"
] | The classification of marked-curve moduli spaces that are weighted projective spaces or weighted complete intersections is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | How close are we to classifying all pairs $(G,M)$ for which the moduli space of marked elliptic curves is a weighted projective space, or a complete intersection in weighted projective space, and what further applications do these moduli spaces have? | How close are we to classifying all pairs (G,M) for which the moduli space of marked elliptic curves is a weighted projective space, or a complete intersection in weighted projective space, and what further applications do these moduli spaces have? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,848 | OWR-11127-020 | Fixed-Rank Cohen–Lenstra Distributions | Fix an odd prime $p$ and a positive integer $g$. Among imaginary quadratic fields $K$ with $p$-rank $g$, ordered by discriminant, is the probability that $A_K\cong G$ equal to
$$\frac{1}{|\operatorname{Aut}(G)|}\,p^{-g^2}\prod_{k=1}^g(p^g-p^{g-k})^2?$$
Equivalently, does the displayed expression give the limiting fre... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-020",
"literature-status:open",
"owr-year:2011"
] | The Cohen--Lenstra distribution for p-class groups of imaginary quadratic fields remains a heuristic in this full fixed-rank and arbitrary-odd-prime formulation, with only partial cases proved. | [
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00208-016-1449-3",
"label": "Boston--Bush--Hajir p-class-tower heuristics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Fix an odd prime $p$ and a positive integer $g$. Among imaginary quadratic fields $K$ with $p$-rank $g$, ordered by discriminant, is the probability that $A_K\cong G$ equal to
$$\frac{1}{|\operatorname{Aut}(G)|}\,p^{-g^2}\prod_{k=1}^g(p^g-p^{g-k})^2?$$
Equivalently, does the displayed expression give the limiting fre... | Conjecture: Fix an odd prime p and a positive integer g. Among imaginary quadratic fields K with p-rank g, ordered by discriminant, the probability that A_K is isomorphic to G equals the Cohen--Lenstra weight 1 over |Aut(G)| times p^{-g^2} times the product over k=1 to g of (p^g-p^{g-k})^2. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,849 | OWR-11127-021 | Schur $\sigma$-Group Frequency Heuristics | Let $G$ be a finite $p$-group that is a Schur $\sigma$-group of rank $g$, or a maximal $p$-class-$c$ quotient of one. Among imaginary quadratic fields $K$ with $A_K$ of rank $g$, is the probability that the corresponding $G_K$, or its maximal $p$-class-$c$ quotient, is isomorphic to $G$ equal to
$$\frac{z(G)^g}{|\oper... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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-11127-022"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11127-021",
"literature-status:open",
"owr-year:2011"
] | This is an isolated conjectural fragment from the non-abelian Cohen--Lenstra heuristic, and no theorem establishes the stated frequency law in general. | [
{
"url": "https://doi.org/10.1007/s00208-016-1449-3",
"label": "Boston--Bush--Hajir heuristics"
},
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | Let $G$ be a finite $p$-group that is a Schur $\sigma$-group of rank $g$, or a maximal $p$-class-$c$ quotient of one. Among imaginary quadratic fields $K$ with $A_K$ of rank $g$, is the probability that the corresponding $G_K$, or its maximal $p$-class-$c$ quotient, is isomorphic to $G$ equal to
$$\frac{z(G)^g}{|\oper... | Conjecture: If G is a finite p-group that is a Schur sigma-group of rank g, or a maximal p-class c quotient of one, then among imaginary quadratic fields K with A_K of rank g the probability that the corresponding G_K, or its maximal p-class c quotient, is isomorphic to G equals z(G)^g over |Aut(G)| times p^{-gh} times... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,850 | OWR-11127-022 | Duplicate Schur $\sigma$-Group Frequency Heuristic | Conjecture: If G is a finite p-group that is a Schur sigma-group of rank g, or a maximal p-class c quotient of one, then among imaginary quadratic fields K with A_K of rank g the probability that the corresponding G_K, or its maximal p-class c quotient, is isomorphic to G equals z(G)^g over |Aut(G)| times p^{-gh} times... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044](https://doi.org/10.4171/owr/2011/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,011 | 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 (This record exactly repeats the same-report conjecture represented canonically by OWR-11127-021, with no distinct hypothesis or conclusion. ) | [
"OWR-11127-021"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11127-022",
"literature-status:open",
"owr-year:2011"
] | The Schur-sigma-group frequency formula is presented as a heuristic prediction supported by data, not as a proved distribution theorem. | [
{
"url": "https://doi.org/10.1007/s00208-016-1449-3",
"label": "Boston--Bush--Hajir heuristics"
},
{
"url": "https://doi.org/10.4171/owr/2011/35",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/35 | null | null | null | null | Conjecture: If G is a finite p-group that is a Schur sigma-group of rank g, or a maximal p-class c quotient of one, then among imaginary quadratic fields K with A_K of rank g the probability that the corresponding G_K, or its maximal p-class c quotient, is isomorphic to G equals z(G)^g over |Aut(G)| times p^{-gh} times... | unrecoverable | This record exactly repeats the same-report conjecture represented canonically by OWR-11127-021, with no distinct hypothesis or conclusion. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Explicit Methods in Number Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/35, pp. 1971--2044 |
30,001,851 | OWR-11128-002 | Uniform Rectifiability from Bounded Riesz Transforms | Is an $n$-dimensional AD-regular measure $\mu$ uniformly $n$-rectifiable if and only if the maximal Riesz transform $R_\mu^*$ is bounded on $L^2(\mu)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | partially_solved | null | 2,011 | 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... | [
"OWR-11128-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11128-002",
"literature-status:partially-solved",
"owr-year:2011"
] | The David--Semmes Riesz-transform characterization is proved in codimension one, while the full n-dimensional formulation remains open in higher codimension. | [
{
"url": "https://doi.org/10.1007/s11511-014-0120-7",
"label": "Nazarov--Tolsa--Volberg codimension-one theorem"
},
{
"url": "https://arxiv.org/abs/1212.5431",
"label": "Nazarov--Tolsa--Volberg rectifiability theorem"
},
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "origi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | Is an $n$-dimensional AD-regular measure $\mu$ uniformly $n$-rectifiable if and only if the maximal Riesz transform $R_\mu^*$ is bounded on $L^2(\mu)$? | Is an n-dimensional AD-regular measure mu uniformly n-rectifiable if and only if the maximal Riesz transform R_mu^* is bounded on L^2(mu)? | corrected_verified | The official report was checked and the statement was repaired to match the source passage. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,852 | OWR-11128-005 | Four-Point Configurations on Three Lines | Can a nonzero Schwartz function satisfy a recurrence of the form $f(x+1)=C_1f(x-1)+C_2f(x)e(\alpha x)+C_3f(x)e(\beta x)$, where $e(t)=e^{2\pi i t}$? Equivalently, can the associated two-dimensional matrix recurrence have a nonzero solution that decays rapidly for a positive-measure set of initial values $x$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | partially_solved | null | 2,011 | 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-11128-005",
"literature-status:partially-solved",
"owr-year:2011"
] | The exact three line four point case is not classified; 2026 work settles some four point cells and gives counterexamples in another cell. | [
{
"url": "https://arxiv.org/abs/2608.07604",
"label": "Oussa four point counterexample"
},
{
"url": "https://arxiv.org/abs/2604.21228",
"label": "Oussa certified four point results"
},
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "OWR report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | Can a nonzero Schwartz function satisfy a recurrence of the form $f(x+1)=C_1f(x-1)+C_2f(x)e(\alpha x)+C_3f(x)e(\beta x)$, where $e(t)=e^{2\pi i t}$? Equivalently, can the associated two-dimensional matrix recurrence have a nonzero solution that decays rapidly for a positive-measure set of initial values $x$? | How can four-point configurations lying on three rather than two lines be handled? | corrected_verified | The official report was checked and the concrete recurrence arising from the four-point, three-line HRT configuration was restored. The exponential convention follows the report's preceding time-frequency formula. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,853 | OWR-11128-006 | Power Decay for Multilinear Oscillatory Integrals | For the multilinear oscillatory integral $I_\lambda$ with a nondegenerate polynomial phase, does there exist $\delta>0$ such that $|I_\lambda(f_1,\ldots,f_n)|\leq C|\lambda|^{-\delta}\prod_j\|f_j\|_{L^\infty}$ as $|\lambda|\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | open | null | 2,011 | 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-11128-006",
"literature-status:open",
"owr-year:2011"
] | The general power decay question remains open, even for quadratic phases in three variables. | [
{
"url": "https://math.berkeley.edu/~mchrist/Papers/obermultiosc.pdf",
"label": "Christ Oberwolfach problem"
},
{
"url": "https://arxiv.org/abs/math/0311039",
"label": "Christ--Li--Tao--Thiele"
},
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "OWR report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | For the multilinear oscillatory integral $I_\lambda$ with a nondegenerate polynomial phase, does there exist $\delta>0$ such that $|I_\lambda(f_1,\ldots,f_n)|\leq C|\lambda|^{-\delta}\prod_j\|f_j\|_{L^\infty}$ as $|\lambda|\to\infty$? | For the multilinear oscillatory integral I_lambda with a nondegenerate polynomial phase, does there exist delta>0 such that |I_lambda(f_1,...,f_n)| is at most C times |lambda|^{-delta} times the product of the L-infinity norms of the f_j as |lambda| tends to infinity? | corrected_verified | The official report was checked and the statement was repaired to match the source passage. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,854 | OWR-11128-007 | Gowers Inverse Theorems for Oscillatory Integral Decay | For a multilinear oscillatory integral with nondegenerate polynomial phase, repeated Cauchy–Schwarz estimates can bound the integral by a high-order Gowers norm of one input. If the expected decay does not follow directly, the Green–Tao–Ziegler inverse theorem supplies algebraic structure for that input. Does this stru... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | open | null | 2,011 | 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-11128-007",
"literature-status:open",
"owr-year:2011"
] | This is an extracted follow up question from a proof discussion rather than a resolved standalone theorem; no definitive resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "OWR report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | For a multilinear oscillatory integral with nondegenerate polynomial phase, repeated Cauchy–Schwarz estimates can bound the integral by a high-order Gowers norm of one input. If the expected decay does not follow directly, the Green–Tao–Ziegler inverse theorem supplies algebraic structure for that input. Does this stru... | Does the structural information about the functions supplied by the Green--Tao--Ziegler inverse theorem for the Gowers norms suffice to prove the desired decay for the multilinear oscillatory integral? | corrected_verified | The official report was checked and the Cauchy–Schwarz reduction, Gowers-norm alternative, and inverse-theorem question were restored. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,855 | OWR-11128-008 | Weighted Riesz Transform Inequalities for General Laguerre Expansions | Let $d\mu_m(r)=\prod_{j=1}^n r_j^{2m_j+1}\,dr_j$. Does the weighted estimate $\int_{\mathbb{R}_+^n}|R_{j,m}f(r)|^p\prod_{j=1}^n r_j^{m_j(p-2)}\,d\mu_m(r)\leq C_p\int_{\mathbb{R}_+^n}|f(r)|^p\prod_{j=1}^n r_j^{m_j(p-2)}\,d\mu_m(r)$ hold for $1<p<\infty$, with $C_p$ independent of $n$ and $m$, for Laguerre expansions of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | open | null | 2,011 | 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-11128-008",
"literature-status:open",
"owr-year:2011"
] | The report explicitly states this as a conjecture for Laguerre expansions of arbitrary type; no later proof of the full assertion was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "OWR report 36"
},
{
"url": "https://doi.org/10.1016/j.aim.2007.04.010",
"label": "Nowak--Stempak"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | Let $d\mu_m(r)=\prod_{j=1}^n r_j^{2m_j+1}\,dr_j$. Does the weighted estimate $\int_{\mathbb{R}_+^n}|R_{j,m}f(r)|^p\prod_{j=1}^n r_j^{m_j(p-2)}\,d\mu_m(r)\leq C_p\int_{\mathbb{R}_+^n}|f(r)|^p\prod_{j=1}^n r_j^{m_j(p-2)}\,d\mu_m(r)$ hold for $1<p<\infty$, with $C_p$ independent of $n$ and $m$, for Laguerre expansions of ... | Conjecture: The weighted norm inequality for Riesz transforms stated for Laguerre expansions holds for Laguerre expansions of arbitrary type as studied by Nowak and Stempak. | corrected_verified | The official report was checked and the measure, weighted norm inequality, parameter range, dimension-free constant, and arbitrary-type extension were restored. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,856 | OWR-11128-010 | Higher-Dimensional Riesz Transforms and Uniform Rectifiability | For an integer n with 0<n<d and n not equal to d-1, if E is n-Ahlfors regular and all Riesz transforms of singularity n are bounded on L^2(E), is E necessarily n-uniformly rectifiable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111](https://doi.org/10.4171/owr/2011/36)
## Literature review (checked 2... | 3 | open | null | 2,011 | 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 | Duplicate/merged OWR extraction (This is a narrower repeated extraction of the David–Semmes Riesz-transform problem preserved in OWR-11128-002. No separate clean statement i) | [
"OWR-11128-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11128-010",
"literature-status:open",
"owr-year:2011"
] | The higher dimensional n dimensional variant is not the codimension one theorem; the report records the higher dimensional extension as an open leading question. | [
{
"url": "https://doi.org/10.4171/owr/2011/36",
"label": "OWR report 36"
},
{
"url": "https://arxiv.org/abs/1109.0466",
"label": "Riesz variation criterion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/36 | null | null | null | null | For an integer n with 0<n<d and n not equal to d-1, if E is n-Ahlfors regular and all Riesz transforms of singularity n are bounded on L^2(E), is E necessarily n-uniformly rectifiable? | unrecoverable | This is a narrower repeated extraction of the David–Semmes Riesz-transform problem preserved in OWR-11128-002. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/36, pp. 2045--2111 |
30,001,857 | OWR-11129-001 | Existence of an Extremal Doubly Even $[72,36,16]$ Code | Does an extremal binary self-dual doubly even code with parameters $[72,36,16]$ exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161](https://doi.org/10.4171/owr/2011/37)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11129-001",
"literature-status:open",
"owr-year:2011"
] | The existence of an extremal binary self dual doubly even code of parameters [72,36,16] remains open. | [
{
"url": "https://arxiv.org/abs/1203.3321",
"label": "Borello"
},
{
"url": "https://oeis.org/A322339",
"label": "OEIS open problem record"
},
{
"url": "https://doi.org/10.4171/owr/2011/37",
"label": "OWR report 37"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/37 | null | null | null | Does an extremal binary self-dual doubly even code with parameters $[72,36,16]$ exist? | Does an extremal code of length 72 exist? | corrected_verified | The official report was checked and the binary, self-dual, doubly even hypotheses and code parameters were restored. | null | null | null | null | null | Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161 |
30,001,858 | OWR-11129-003 | Invariant Ring Structure and Finite Linear Actions | How do structural properties of the invariant ring $K[V]^G$, such as being polynomial, a complete intersection, Gorenstein, or Cohen–Macaulay, relate to properties of the finite linear group action of $G$ on $V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161](https://doi.org/10.4171/owr/2011/37)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11129-003",
"literature-status:open",
"owr-year:2011"
] | This is a broad invariant theory question about how invariant ring properties reflect the group action; no general classification resolving it was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/37",
"label": "OWR report 37"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/37 | null | null | null | How do structural properties of the invariant ring $K[V]^G$, such as being polynomial, a complete intersection, Gorenstein, or Cohen–Macaulay, relate to properties of the finite linear group action of $G$ on $V$? | How do structural properties of the invariant ring K[V]^G, such as being polynomial, a complete intersection, Gorenstein, or Cohen--Macaulay, relate to properties of the finite linear group action G on V? | corrected_verified | The official report confirms this invariant-theory classification question. | null | null | null | null | null | Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161 |
30,001,859 | OWR-11129-005 | Exotic Units in a Finite Group Ring | Does the group $C_2\times C_2\times C_2\times C_6$ have exotic units in its integral group ring $\mathbb{Z}G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161](https://doi.org/10.4171/owr/2011/37)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | solved | null | 2,011 | 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": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (no exotic units)**. W. A. de Graaf (joint with P. Faccin; OWR 37/2011, p. 2147) found exotic units (outside Hoechsmann's constructible units) at orders 40, 48, 60 and 63, and conjectured that C2×C2×C2×C6, where the computation did not finish, has some too. It has ... | [
"owr",
"oberwolfach-reports",
"OWR-11129-005",
"literature-status:open",
"owr-year:2011"
] | The extracted group context is incomplete, and the report records the exotic unit assertion as a conjecture; no authoritative resolution for the named group was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/37",
"label": "OWR report 37"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/37 | null | null | null | Does the group $C_2\times C_2\times C_2\times C_6$ have exotic units in its integral group ring $\mathbb{Z}G$? | Conjecture: The group C_2 times C_2 times C_2 times C_6 has exotic units in its integral group ring ZG. | corrected_verified | The official report confirms this conjecture; the extraction label was removed and the group notation restored. | null | null | null | null | null | Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161 |
30,001,860 | OWR-11129-006 | Asymptotic Proportion of $Q$ in Classical Groups | Let $G=\operatorname{Class}(n,q)$ be a finite classical group of dimension $n$ over a field of odd order $q$, with natural module $V$. Let $Q$ be the set of even-order elements $g\in G$ for which the fixed space of $g^{|g|/2}$ has dimension at least $n/3$ and less than $2n/3$. Determine the asymptotic behavior of $|Q|/... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161](https://doi.org/10.4171/owr/2011/37)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11129-006",
"literature-status:open",
"owr-year:2011"
] | No authoritative resolution of the stated asymptotic bound for Q and G was found; the report poses it as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2011/37",
"label": "OWR report 37"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/37 | null | null | null | Let $G=\operatorname{Class}(n,q)$ be a finite classical group of dimension $n$ over a field of odd order $q$, with natural module $V$. Let $Q$ be the set of even-order elements $g\in G$ for which the fixed space of $g^{|g|/2}$ has dimension at least $n/3$ and less than $2n/3$. Determine the asymptotic behavior of $|Q|/... | For the classical-group setup defining Q, what is the asymptotic value of |Q|/|G|; in particular, is |Q|/|G|=O(log n)? | corrected_verified | The official report was checked and the classical-group family, subset $Q$, and asymptotic question were restored. The printed upper-bound notation appears to omit a reciprocal, so the clean statement asks for the asymptotic order suggested by the adjacent lower bound. | null | null | null | null | null | Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161 |
30,001,861 | OWR-11129-007 | Undecidable Word Problems in Wreath Product Quotients | Let $F$ be a finite-rank free group, let $S$ be finite, and let $\phi:F\to F\wr_S\operatorname{Sym}(S)$ define iterated actions of $F$ on $S^n$. Let $N$ be the kernel of the action on the disjoint union $\bigsqcup_{n\geq0}S^n$. Can the quotient $F/N$ have an undecidable word problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161](https://doi.org/10.4171/owr/2011/37)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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 | {
"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 open. L. Bartholdi, OWR 37/2011, p. 2155: for a free group F of finite rank acting on words over a finite set S through φ: F → F ≀_S Sym(S), can F/N (N the kernel of the action) have undecidable word problem? L. Bartholdi, I... | [
"owr",
"oberwolfach-reports",
"OWR-11129-007",
"literature-status:open",
"owr-year:2011"
] | The report poses this as an unresolved question about the displayed quotient F/N; no later source establishing a decision procedure or undecidability for this exact quotient was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/37",
"label": "OWR report 37"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/37 | null | null | null | Let $F$ be a finite-rank free group, let $S$ be finite, and let $\phi:F\to F\wr_S\operatorname{Sym}(S)$ define iterated actions of $F$ on $S^n$. Let $N$ be the kernel of the action on the disjoint union $\bigsqcup_{n\geq0}S^n$. Can the quotient $F/N$ have an undecidable word problem? | Let F be a finite-rank free group acting through the iterated wreath-product construction described in the report, and let N be the kernel of the resulting action. Can F/N have an undecidable word problem? | corrected_verified | The official report was checked and the wreath recursion, iterated actions, and kernel defining the quotient were restored. | null | null | null | null | null | Computational Group Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/37, pp. 2113--2161 |
30,001,862 | OWR-11130-005 | Intrinsic-Flat Stability of the Positive Mass Theorem | If a sequence of asymptotically flat three-manifolds has nonnegative scalar curvature, no interior closed minimal surfaces, and ADM mass tending to zero, must it converge in the pointed intrinsic-flat sense to Euclidean space when the base points lie on constant-mean-curvature surfaces of fixed area? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/38, pp. 2163--2215](https://doi.org/10.4171/owr/2011/38)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,011 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11130-005",
"literature-status:partially-solved",
"owr-year:2011"
] | The intrinsic flat positive mass stability conjecture remains open in the stated generality, with proofs for graphical and rotationally symmetric subclasses and counterexamples to careless basepoint choices. | [
{
"url": "https://arxiv.org/abs/1408.4319",
"label": "Huang--Lee--Sormani"
},
{
"url": "https://lhhuang-math.media.uconn.edu/wp-content/uploads/sites/1744/2019/04/Intrinsic_flat-Crelle.pdf",
"label": "Intrinsic flat stability survey"
},
{
"url": "https://doi.org/10.4171/owr/2011/38",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/38 | null | null | null | If a sequence of asymptotically flat three-manifolds has nonnegative scalar curvature, no interior closed minimal surfaces, and ADM mass tending to zero, must it converge in the pointed intrinsic-flat sense to Euclidean space when the base points lie on constant-mean-curvature surfaces of fixed area? | Conjecture: If a sequence of asymptotically flat three-manifolds has nonnegative scalar curvature, no interior closed minimal surfaces, and ADM mass tending to zero, then it converges in the pointed Intrinsic Flat sense to Euclidean space when the base points lie on CMC surfaces of constant area. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/38, pp. 2163--2215 |
30,001,863 | OWR-11130-006 | Density Conditions for Optimal-Transport Regularity | Can conditions on the source and target densities guarantee regularity of the optimal transport map when standard geometric conditions such as the MTW condition fail? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/38, pp. 2163--2215](https://doi.org/10.4171/owr/2011/38)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,011 | 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-11130-006",
"literature-status:open",
"owr-year:2011"
] | The extracted question asks for sufficient density conditions for regularity but omits the equation and hypotheses; no determinate general resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2011/38",
"label": "OWR report 38"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/38 | null | null | null | Can conditions on the source and target densities guarantee regularity of the optimal transport map when standard geometric conditions such as the MTW condition fail? | Can conditions on the source and target densities guarantee regularity of the optimal transport map when standard geometric conditions such as the MTW condition fail? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Partial Differential Equations (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/38, pp. 2163--2215 |
30,001,864 | OWR-11131-001 | Minimum-Energy $N$-Body Configurations at Fixed Angular Momentum | What is the minimum-energy configuration of an $N$-body system at a fixed angular-momentum level? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Dynamics and Geometric Mechanics (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/39, pp. 2217--2282](https://doi.org/10.4171/owr/2011/39)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,011 | 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-11131-001",
"literature-status:partially-solved",
"owr-year:2011"
] | Finite density makes the constrained minimum exist and permits computations for fixed angular momentum, but the report leaves the proposed classification of all minimum states unproved. | [
{
"url": "https://doi.org/10.4171/owr/2011/39",
"label": "OWR report 39"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC5477774/",
"label": "finite density three body results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/39 | null | null | null | What is the minimum-energy configuration of an $N$-body system at a fixed angular-momentum level? | What is the minimum-energy configuration of an N-body system with a fixed level of angular momentum? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Applied Dynamics and Geometric Mechanics (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/39, pp. 2217--2282 |
30,001,865 | OWR-11132-003 | Stochastic Averaging with Topologically Complex Fast Orbits | In stochastic averaging, what happens when the fast orbits have more complicated topologies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamics of Stochastic Systems and their Approximation (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/40, pp. 2283--2326](https://doi.org/10.4171/owr/2011/40)
## Literatu... | 3 | open | null | 2,011 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The wording is an expository transition to examples whose behavior is then analyzed in the contribution, not a standalone open problem. No s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11132-003",
"literature-status:open",
"owr-year:2011"
] | The extracted question is broad and qualitative; no later theorem resolving the topology-generalized fast-orbit problem was identified. | [
{
"url": "https://doi.org/10.4171/owr/2011/40",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/40 | null | null | null | null | In stochastic averaging, what happens when the fast orbits have more complicated topologies? | unrecoverable | The wording is an expository transition to examples whose behavior is then analyzed in the contribution, not a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Dynamics of Stochastic Systems and their Approximation (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/40, pp. 2283--2326 |
30,001,866 | OWR-11132-004 | Explicit Stochastic Averaging Errors in Higher Dimensions | Can one obtain explicit error estimates in higher dimensions for stochastic-averaging integrals of the form $\int_0^T X(\tau)Z(\tau\varepsilon^{-2})^q\,d\beta(\tau)$ when $X(t)\in\mathbb{R}^n$ and $n>1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Dynamics of Stochastic Systems and their Approximation (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/40, pp. 2283--2326](https://doi.org/10.4171/owr/2011/40)
## Literatu... | 3 | open | null | 2,011 | 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-11132-004",
"literature-status:open",
"owr-year:2011"
] | The report explicitly leaves multidimensional error estimates for the stochastic averaging limit open; later work does not supply a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2011/40",
"label": "original OWR report"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/7ee09859-9440-461d-a8c5-84ec5410930a/content",
"label": "report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/40 | null | null | null | Can one obtain explicit error estimates in higher dimensions for stochastic-averaging integrals of the form $\int_0^T X(\tau)Z(\tau\varepsilon^{-2})^q\,d\beta(\tau)$ when $X(t)\in\mathbb{R}^n$ and $n>1$? | Can one obtain explicit error estimates for the stochastic-averaging limit when the slow process X(t)\in\mathbb R^n and n>1? | corrected_verified | The official report was checked and the integral whose error is to be estimated and the higher-dimensional restriction were restored. | null | null | null | null | null | Mini-Workshop: Dynamics of Stochastic Systems and their Approximation (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/40, pp. 2283--2326 |
30,001,867 | OWR-11133-001 | Geometry Encoded by Newton–Okounkov Bodies | What geometric data of a pair $(X,D)$ are encoded, and how, by the combinatorics of its Newton–Okounkov bodies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | open | null | 2,011 | 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-11133-001",
"literature-status:open",
"owr-year:2011"
] | The question asks for a general geometric interpretation of combinatorics of Newton--Okounkov bodies; modern special-case constructions do not settle it in general. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://academic.oup.com/imrn/article/2021/12/9567/5940749",
"label": "Newton--Okounkov bodies of flag varieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | What geometric data of a pair $(X,D)$ are encoded, and how, by the combinatorics of its Newton–Okounkov bodies? | What geometric data of a pair (X,D) are encoded, and how, by the combinatorics of its Newton--Okounkov bodies? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,868 | OWR-11133-002 | Polynomial Subalgebras Admitting SAGBI Bases | Which subalgebras of a polynomial ring have a SAGBI basis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | open | null | 2,011 | 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-11133-002",
"literature-status:open",
"owr-year:2011"
] | The characterization of subalgebras admitting finite SAGBI bases remains a recognized open problem, although algorithms and important classes are known. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://www.math.ubc.ca/~reichst/sagbi.pdf",
"label": "SAGBI bases survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | Which subalgebras of a polynomial ring have a SAGBI basis? | Which subalgebras of a polynomial ring have a SAGBI basis? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,869 | OWR-11133-003 | Newton–Okounkov Bodies of Bott–Samelson Varieties | For a Bott–Samelson variety $X=R(i_1,\ldots,i_l)$ of $\operatorname{GL}_n$, does the Newton–Okounkov body for the indicated flag equal
$$P=A_{i_1}T_{v_1}A_{i_2}\cdots T_{v_{l-1}}A_{i_l}(p)$$
for suitable $p\in\mathbb R^d$ and $v_j\in\mathbb R^{d_{i_j}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | open | null | 2,011 | 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-11133-003",
"literature-status:open",
"owr-year:2011"
] | The Bott--Samelson equality is presented as a conjecture based on computations for length three; available literature gives special cases but not the stated general claim. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1001.4566",
"label": "Okounkov bodies and toric degenerations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | For a Bott–Samelson variety $X=R(i_1,\ldots,i_l)$ of $\operatorname{GL}_n$, does the Newton–Okounkov body for the indicated flag equal
$$P=A_{i_1}T_{v_1}A_{i_2}\cdots T_{v_{l-1}}A_{i_l}(p)$$
for suitable $p\in\mathbb R^d$ and $v_j\in\mathbb R^{d_{i_j}}$? | For a Bott--Samelson variety X=R(i_1,\ldots,i_l) of GL_n, does the Newton--Okounkov body for the indicated flag equal P=A_{i_1}T_{v_1}A_{i_2}\cdots T_{v_{l-1}}A_{i_l}(p) for suitable p\in\mathbb R^d and v_j\in\mathbb R^{d_{i_j}}? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,870 | OWR-11133-004 | Realizability of Divisor Volumes | Does every nonnegative real number occur as the volume of an integral divisor on some projective variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | partially_solved | null | 2,011 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; answered in the source)**. V. Lozovanu (joint with A. Küronya and C. Maclean; OWR 41/2011, pp. 2348–2349) asks whether every non-negative real number is the volume of an integral divisor, and answers it: the set of such volumes is countable, though it contains... | [
"owr",
"oberwolfach-reports",
"OWR-11133-004",
"literature-status:partially-solved",
"owr-year:2011"
] | Riemann--Roch and asymptotic volume theory determine substantial asymptotic information, but no uniform formula for h0(X,kD) for arbitrary projective varieties and Cartier divisors is known. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/0805.3885",
"label": "Convex bodies associated to linear series"
},
{
"url": "https://arxiv.org/abs/math/0505054",
"label": "asymptotic invariants of line bundles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | Does every nonnegative real number occur as the volume of an integral divisor on some projective variety? | Does every nonnegative real number occur as the volume of an integral divisor on some projective variety? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,871 | OWR-11133-005 | Periodicity and Definability of Newton–Okounkov Bodies | Is the volume of every line bundle on a smooth projective variety a period? For every integral divisor, is there a flag for which its Newton–Okounkov body is defined by polynomial inequalities with rational coefficients? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | open | null | 2,011 | 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-11133-005",
"literature-status:open",
"owr-year:2011"
] | The report records the period and polynomial-inequality questions as open; known transcendental volume examples and Okounkov-body theory do not resolve either general question. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1008.3986",
"label": "volume functions of linear series"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | Is the volume of every line bundle on a smooth projective variety a period? For every integral divisor, is there a flag for which its Newton–Okounkov body is defined by polynomial inequalities with rational coefficients? | (1) Is the volume of every line bundle on a smooth projective variety a period? (2) For every integral divisor, is there a flag for which its Newton--Okounkov body is defined by polynomial inequalities with rational coefficients? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,872 | OWR-11133-006 | Canonical Maps from Varieties to Okounkov Bodies | Does every projective variety $X$ with a very ample line bundle $L$ admit a reasonable map to its Okounkov body? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363](https://doi.org/10.4171/owr/2011/41)
## Literature review (c... | 3 | partially_solved | null | 2,011 | 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-11133-006",
"literature-status:partially-solved",
"owr-year:2011"
] | A reasonable map onto the Okounkov body is constructed under finite-generation hypotheses, but the extracted question asks for a general construction beyond those hypotheses. | [
{
"url": "https://doi.org/10.4171/owr/2011/41",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1001.4566",
"label": "Okounkov bodies and toric degenerations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/41 | null | null | null | Does every projective variety $X$ with a very ample line bundle $L$ admit a reasonable map to its Okounkov body? | Does every projective variety X with a very ample line bundle L admit a reasonable map to its Okounkov body? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: New Developments in Newton-Okounkov Bodies (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/41, pp. 2327--2363 |
30,001,873 | OWR-11134-001 | Strong Prediction for Stationary Ergodic Gaussian Processes | For every stationary ergodic Gaussian process $(Y_n)_{n\in\mathbb Z}$, does there exist a prediction rule $g=(g_n)$ such that
$$\left|\mathbb E[Y_n\mid Y_1,\ldots,Y_{n-1}]-g_n(Y_1,\ldots,Y_{n-1})\right|\to0$$
almost surely? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Machine Learning (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/42, pp. 2365--2396](https://doi.org/10.4171/owr/2011/42)
## Literature review (checked 2026... | 3 | open | null | 2,011 | 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-11134-001",
"literature-status:open",
"owr-year:2011"
] | The strong almost-sure prediction problem for every stationary ergodic Gaussian process is explicitly left open; only Cesaro consistency and results under extra assumptions are known. | [
{
"url": "https://doi.org/10.4171/owr/2011/42",
"label": "original OWR report"
},
{
"url": "https://pure.royalholloway.ac.uk/files/23266714/gysafinal.pdf",
"label": "strongly consistent learning of the best predictor"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/42 | null | null | null | For every stationary ergodic Gaussian process $(Y_n)_{n\in\mathbb Z}$, does there exist a prediction rule $g=(g_n)$ such that
$$\left|\mathbb E[Y_n\mid Y_1,\ldots,Y_{n-1}]-g_n(Y_1,\ldots,Y_{n-1})\right|\to0$$
almost surely? | For every stationary ergodic Gaussian process (Y_n)_{n\in\mathbb Z}, does there exist a prediction rule g=(g_n) such that \left|\mathbb E[Y_n\mid Y_1,\ldots,Y_{n-1}]-g_n(Y_1,\ldots,Y_{n-1})\right|\to0 almost surely? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Mathematics of Machine Learning (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/42, pp. 2365--2396 |
30,001,874 | OWR-11134-003 | Answered Characterization of Lookback Adjusters | For X_t^*=\max_{s\le t}X_s, which nonnegative functions F can a trading strategy guarantee in IK_t\ge F(X_t^*,X_t) for all t, while making F grow as nearly as possible like X_t^*? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Machine Learning (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/42, pp. 2365--2396](https://doi.org/10.4171/owr/2011/42)
## Literature review (checked 2026... | 3 | open | null | 2,011 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The source asks which trading guarantees are possible and immediately gives necessary-and-sufficient characterizations in Theorems 4 and 5. ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11134-003",
"literature-status:open",
"owr-year:2011"
] | The extracted text is a qualitative discussion of trading-risk tradeoffs rather than a definite theorem or claim with a verifiable resolution. | [
{
"url": "https://doi.org/10.4171/owr/2011/42",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/42 | null | null | null | null | For X_t^*=\max_{s\le t}X_s, which nonnegative functions F can a trading strategy guarantee in IK_t\ge F(X_t^*,X_t) for all t, while making F grow as nearly as possible like X_t^*? | unrecoverable | The source asks which trading guarantees are possible and immediately gives necessary-and-sufficient characterizations in Theorems 4 and 5. It is an answered setup rather than an unresolved problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Mathematics of Machine Learning (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/42, pp. 2365--2396 |
30,001,875 | OWR-11135-002 | Asymptotic Norms of Saito–Kurokawa Lifts | For a normalized Hecke eigenform $f\in S_{2k}(\operatorname{SL}_2(\mathbb Z))$ and its Saito–Kurokawa lift $F_f$, can one prove unconditionally that $N(F_f)\sim2$ as $k\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458](https://doi.org/10.4171/owr/2011/43)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,011 | 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"
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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-11135-002",
"literature-status:open",
"owr-year:2011"
] | The symmetric-square second-moment problem in the weight aspect was open in the source and remains an unresolved general problem despite bounds and special averages. | [
{
"url": "https://doi.org/10.4171/owr/2011/43",
"label": "original OWR report"
},
{
"url": "https://msp.org/ant/2018/12-1/ant-v12-n1-p.pdf",
"label": "second moments in the weight aspect"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/43 | null | null | null | For a normalized Hecke eigenform $f\in S_{2k}(\operatorname{SL}_2(\mathbb Z))$ and its Saito–Kurokawa lift $F_f$, can one prove unconditionally that $N(F_f)\sim2$ as $k\to\infty$? | For a normalized Hecke eigenform f\in S_{2k}(SL_2(\mathbb Z)) and its Saito--Kurokawa lift F_f, can one prove unconditionally that N(F_f)\sim2 as k\to\infty? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458 |
30,001,876 | OWR-11135-003 | Restriction Spectra of $\operatorname{GL}_3$ Maass Forms | For a $\operatorname{GL}_3$ Maass form restricted to the codimension-$2$ submanifold arising from the upper-triangular embedding of $\operatorname{GL}_2$, what is its inner product with a given $\operatorname{SL}_2(\mathbb Z)$ Maass form, or more generally its spectral decomposition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458](https://doi.org/10.4171/owr/2011/43)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,011 | 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"
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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-11135-003",
"literature-status:open",
"owr-year:2011"
] | The extracted sentence asks for a spectral decomposition without specifying a theorem-level claim; no general resolution is identified. | [
{
"url": "https://doi.org/10.4171/owr/2011/43",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/43 | null | null | null | For a $\operatorname{GL}_3$ Maass form restricted to the codimension-$2$ submanifold arising from the upper-triangular embedding of $\operatorname{GL}_2$, what is its inner product with a given $\operatorname{SL}_2(\mathbb Z)$ Maass form, or more generally its spectral decomposition? | For a GL(3) Maass form restricted to the codimension--2 submanifold arising from the upper-triangular embedding of GL(2), what is its inner product with a given SL_2(\mathbb Z) Maass form, or more generally its spectral decomposition? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458 |
30,001,877 | OWR-11135-004 | Momentum-Space Scarring on Irrational Point-Scatterer Tori | For an irrational flat torus with a point scatterer, does there exist a subsequence of eigenfunctions that scars in momentum space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458](https://doi.org/10.4171/owr/2011/43)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,011 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11135-004",
"literature-status:open",
"owr-year:2011"
] | The record is incomplete report prose about eigenfunction limits and a conditional scarring result, not a resolved standalone problem. | [
{
"url": "https://doi.org/10.4171/owr/2011/43",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/43 | null | null | null | For an irrational flat torus with a point scatterer, does there exist a subsequence of eigenfunctions that scars in momentum space? | For an irrational flat torus with a point scatterer, does there exist a subsequence of eigenfunctions that scars in momentum space? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458 |
30,001,878 | OWR-11135-005 | Zaremba’s Bounded Continued-Fraction Conjecture | Does there exist a fixed $A$ such that every positive integer is the denominator of a finite continued fraction $[a_1,\ldots,a_k]$ with $1\leq a_i\leq A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458](https://doi.org/10.4171/owr/2011/43)
## Literature review (checked 2026-08-21... | 3 | partially_solved | null | 2,011 | 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-11135-005",
"literature-status:partially-solved",
"owr-year:2011"
] | This is Zaremba's conjecture: full bounded-partial-quotient coverage remains open, while Bourgain--Kontorovich and later work prove substantial density and special-family results. | [
{
"url": "https://doi.org/10.4171/owr/2011/43",
"label": "original OWR report"
},
{
"url": "https://www.tandfonline.com/doi/abs/10.1080/00029890.2024.2323902",
"label": "Zaremba's conjecture for geometric sequences"
},
{
"url": "https://doi.org/10.1112/blms.13087",
"label": "radical ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/43 | null | null | null | Does there exist a fixed $A$ such that every positive integer is the denominator of a finite continued fraction $[a_1,\ldots,a_k]$ with $1\leq a_i\leq A$? | Does there exist a fixed A such that every positive integer is the denominator of a finite continued fraction [a_1,\ldots,a_k] with 1\le a_i\le A? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | The Analytic Theory of Automorphic Forms (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/43, pp. 2397--2458 |
30,001,879 | OWR-11136-004 | Purdy Plane Line Incidence Conjecture | For sufficiently large $n$ points in $\mathbb{R}^3$, not all on two skew lines and with no plane containing $n-1$ points, is the number $p$ of determined planes at least the number $l$ of determined lines? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-004",
"literature-status:open",
"owr-year:2011"
] | Only the historical statement that Purdy formulated Conjecture P3 is extracted; the full target and hypotheses are absent from this record, so it cannot be certified solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For sufficiently large $n$ points in $\mathbb{R}^3$, not all on two skew lines and with no plane containing $n-1$ points, is the number $p$ of determined planes at least the number $l$ of determined lines? | For sufficiently large n points in \mathbb R^3, not all on two skew lines and with no plane containing n-1 points, is the number p of determined planes at least the number l of determined lines? | corrected_verified | The official report was checked and the statement was repaired to match the source passage. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,880 | OWR-11136-005 | Piercing Large Convex Sets in the Unit Square | If $f(\varepsilon)$ is the minimum number of points in the unit square meeting every compact convex set of area at least $\varepsilon$, is $f(\varepsilon)=O(1/\varepsilon)$ as $\varepsilon\to0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-005",
"literature-status:open",
"owr-year:2011"
] | The original rectangle piercing question remains open; the cited Pach--Tardos result obtains a larger order for a relaxed quasi-rectangle class and therefore does not disprove the exact rectangle claim. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
},
{
"url": "https://math.nyu.edu/~pach/publications/quasirectangle031112.pdf",
"label": "Piercing quasi-rectangles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | If $f(\varepsilon)$ is the minimum number of points in the unit square meeting every compact convex set of area at least $\varepsilon$, is $f(\varepsilon)=O(1/\varepsilon)$ as $\varepsilon\to0$? | If f(\varepsilon) is the minimum number of points in the unit square meeting every compact convex set of area at least \varepsilon, is f(\varepsilon)=O(1/\varepsilon) as \varepsilon\to0? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,881 | OWR-11136-006 | Existence of Sparse Steiner Triple Systems | For which $s$ and admissible $v$ does there exist an $s$-sparse Steiner triple system $\operatorname{STS}(v)$, containing no $i$ blocks on $i+2$ points for any $4\leq i\leq s$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,011 | 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-11136-006",
"literature-status:partially-solved",
"owr-year:2011"
] | Existence is known for several sparsity levels and infinite families, including 6-sparse systems, but the general s-sparse existence question and higher levels remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jcta.2006.04.003",
"label": "On 6-sparse Steiner triple systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For which $s$ and admissible $v$ does there exist an $s$-sparse Steiner triple system $\operatorname{STS}(v)$, containing no $i$ blocks on $i+2$ points for any $4\leq i\leq s$? | For which s and admissible v does there exist an s-sparse Steiner triple system STS(v), containing no i blocks on i+2 points for any 4\le i\le s? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,882 | OWR-11136-007 | Asymptotics of Uniform Union-Free Families | Given $r\geq t\geq1$, determine the asymptotic behavior of $\operatorname{UF}_t(n,r)$, the maximum size of a $t$-union-free $r$-uniform family on an $n$-element ground set. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-007",
"literature-status:open",
"owr-year:2011"
] | The displayed bounds leave the requested asymptotic for the union-free-family extremal function unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | Given $r\geq t\geq1$, determine the asymptotic behavior of $\operatorname{UF}_t(n,r)$, the maximum size of a $t$-union-free $r$-uniform family on an $n$-element ground set. | Given r\ge t\ge1, determine the asymptotic behavior of UF_t(n,r), the maximum size of a t-union-free r-uniform family on an n-element ground set. | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,883 | OWR-11136-008 | Circle Free Convex Bodies Under Minkowski Addition | If $K$ is a circle-free convex body in $\mathbb{R}^3$ and $B$ is a ball, is the Minkowski sum $K+B$ also circle-free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-008",
"literature-status:open",
"owr-year:2011"
] | The Minkowski-sum circle-free question is stated as a problem; known results for planar sets and special bodies do not settle arbitrary circle-free convex bodies. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
},
{
"url": "https://www.fields.utoronto.ca/programs/scientific/11-12/discretegeom/talks/hiroshi.pdf",
"label": "circle-free convex bodies"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | If $K$ is a circle-free convex body in $\mathbb{R}^3$ and $B$ is a ball, is the Minkowski sum $K+B$ also circle-free? | If K is a circle-free convex body in \mathbb R^3 and B is a ball, is the Minkowski sum K+B also circle-free? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,884 | OWR-11136-009 | Hill Conjecture for Complete Graph Crossing Numbers | Is the crossing number of every drawing of $K_n$ at least $\frac14\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor\lfloor(n-2)/2\rfloor\lfloor(n-3)/2\rfloor$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-009",
"literature-status:open",
"owr-year:2011"
] | The extracted claim is the general crossing-number lower-bound conjecture for arbitrary drawings; the spherical-geodesic case is proved, but the general Hill conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "original OWR report"
},
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol332-socg2025/html/LIPIcs.SoCG.2025.75/LIPIcs.SoCG.2025.75.html",
"label": "crossing numbers of complete graphs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | Is the crossing number of every drawing of $K_n$ at least $\frac14\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor\lfloor(n-2)/2\rfloor\lfloor(n-3)/2\rfloor$? | Is the crossing number of every drawing of K_n at least \frac14\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor\lfloor(n-2)/2\rfloor\lfloor(n-3)/2\rfloor? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,885 | OWR-11136-010 | Asymptotic Enumeration of Higher-Dimensional Permutations | For fixed d, let $S_{d,n}$ be the d-dimensional permutations of order n. Is $|S_{d,n}|=\left(n/e^d+o(n)\right)^{n^d}$ as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | partially_solved | null | 2,011 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-11136-011"
] | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11136-010",
"literature-status:open",
"owr-year:2011"
] | Keevash’s Theorem 1.8 states the asymptotic count $(n/e^d+o(n))^{n^d}$ for d-dimensional permutations, answering Linial–Luria. This is an unrefereed preprint; it omits the lower-bound proof details as similar to Counting designs. The old summary’s alternative attribution is not supported.
**What remains.** The classif... | [
{
"url": "https://arxiv.org/abs/1802.05900",
"label": "P. Keevash, The existence of designs II, Theorem 1.8"
},
{
"url": "https://people.maths.ox.ac.uk/keevash/papers/designsII.pdf",
"label": "Keevash — author manuscript"
},
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "D... | 2026-09-28T00:00:00 | P. Keevash, The existence of designs II, Theorem 1.8: https://arxiv.org/abs/1802.05900
Keevash — author manuscript: https://people.maths.ox.ac.uk/keevash/papers/designsII.pdf
Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548: https://doi.org/10.4171/owr/2011/44 | https://doi.org/10.4171/owr/2011/44 | null | null | null | For fixed d, let $S_{d,n}$ be the d-dimensional permutations of order n. Is $|S_{d,n}|=\left(n/e^d+o(n)\right)^{n^d}$ as $n\to\infty$? | If S_{d,n} is the set of d-dimensional permutations (Latin hypercubes) of order n, is |S_{d,n}|=(1+o(1))\left(n/e^d\right)^{n^d} as n\to\infty? | corrected_verified | The relative error belongs inside the exponentially large power, as in Linial’s Conjecture 3 and Keevash’s Theorem 1.8. The former extraction incorrectly placed a multiplicative 1+o(1) outside. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,886 | OWR-11136-011 | Lower Bounds for Higher-Dimensional Permutation Counts | Does the number of d-dimensional permutations S_{d,n} have the matching lower bound |S_{d,n}|\geq(1+o(1))(n/e)^{n^d}, and hence satisfy Conjecture 3? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | partially_solved | null | 2,011 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | Duplicate/merged OWR extraction (This repeats the asymptotic enumeration conjecture preserved in OWR-11136-010 and also corrupts its exponential factor. No separate clean st) | [
"OWR-11136-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11136-011",
"literature-status:open",
"owr-year:2011"
] | Duplicate extraction; the canonical question is OWR-11136-010. Keevash’s Theorem 1.8 states the asymptotic count $(n/e^d+o(n))^{n^d}$ for d-dimensional permutations, answering Linial–Luria. This is an unrefereed preprint; it omits the lower-bound proof details as similar to Counting designs. The old summary’s alternati... | [
{
"url": "https://arxiv.org/abs/1802.05900",
"label": "P. Keevash, The existence of designs II, Theorem 1.8"
},
{
"url": "https://people.maths.ox.ac.uk/keevash/papers/designsII.pdf",
"label": "Keevash — author manuscript"
},
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "D... | 2026-09-28T00:00:00 | P. Keevash, The existence of designs II, Theorem 1.8: https://arxiv.org/abs/1802.05900
Keevash — author manuscript: https://people.maths.ox.ac.uk/keevash/papers/designsII.pdf
Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548: https://doi.org/10.4171/owr/2011/44 | https://doi.org/10.4171/owr/2011/44 | null | null | null | null | Does the number of d-dimensional permutations S_{d,n} have the matching lower bound |S_{d,n}|\geq(1+o(1))(n/e)^{n^d}, and hence satisfy Conjecture 3? | unrecoverable | This repeats the asymptotic enumeration conjecture preserved in OWR-11136-010 and also corrupts its exponential factor. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,887 | OWR-11136-013 | Multiple Cover Decomposition Thresholds for Planar Sets | A planar set $P \subset \mathbb{R}^2$ is called *cover-decomposable* if there exists an integer $m = m_2(P)$ such that every $m$-fold covering of the plane (or any subset) by translates of $P$ can be decomposed into $2$ coverings. For every cover-decomposable planar set $P$ and every integer $k \geq 2$, does the $k$-de... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-013",
"literature-status:open",
"owr-year:2011"
] | The multiple-covering survey states that finiteness of m_k(P) for every cover-decomposable P remains conjectural in this generality. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://real.mtak.hu/15290/1/surveyfinal.pdf",
"label": "cover-decomposition survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | A planar set $P \subset \mathbb{R}^2$ is called *cover-decomposable* if there exists an integer $m = m_2(P)$ such that every $m$-fold covering of the plane (or any subset) by translates of $P$ can be decomposed into $2$ coverings. For every cover-decomposable planar set $P$ and every integer $k \geq 2$, does the $k$-de... | For every cover-decomposable planar set P and integer k\geq2, does m_k(P) exist? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,888 | OWR-11136-016 | Optimal Homothety Factor for Three Intersecting Disks | If $D\subset\mathbb{R}^2$ is a disk, is the optimal homothety factor $\lambda_h(D,3)=\sqrt{3}$ for families with property $T(3)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-016",
"literature-status:open",
"owr-year:2011"
] | The homothetic-copy variant asks for bounds not supplied by the cited translate-covering results, and no complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://real.mtak.hu/15290/1/surveyfinal.pdf",
"label": "cover-decomposition survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | If $D\subset\mathbb{R}^2$ is a disk, is the optimal homothety factor $\lambda_h(D,3)=\sqrt{3}$ for families with property $T(3)$? | If D\subset\mathbb{R}^2 is a disk, is the optimal homothety factor \lambda_h(D,3)=\sqrt{3} for families with property T(3)? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,889 | OWR-11136-017 | Sequence Bounds for the Function r of m | For $m \geq 1$, let $r(m)$ denote the minimum number of parts into which a convex body in $\mathbb{R}^d$ (or planar convex set) must be partitioned in the $m$-step covering/Tverberg-type geometric partition problem of Discrete Geometry (OWR 2011/44). Does the OEIS sequence A059522 ($\lfloor n \alpha \rfloor$ with $\alp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-017",
"literature-status:open",
"owr-year:2011"
] | The report presents only the first terms and asymptotic bounds for r(m); it records the A059522 identification as an unresolved question. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://oeis.org/A059522",
"label": "OEIS A059522"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For $m \geq 1$, let $r(m)$ denote the minimum number of parts into which a convex body in $\mathbb{R}^d$ (or planar convex set) must be partitioned in the $m$-step covering/Tverberg-type geometric partition problem of Discrete Geometry (OWR 2011/44). Does the OEIS sequence A059522 ($\lfloor n \alpha \rfloor$ with $\alp... | Does the OEIS sequence A059522 give a lower bound for r(m) for all m? | corrected_verified | The function and its argument were placed in math delimiters without changing the question. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,890 | OWR-11136-018 | Extremal Geometric Graphs with Forbidden Configurations | Given a family $H$ of forbidden geometric configurations, what is the maximum number of edges in an $n$-vertex geometric graph containing no configuration from $H$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-018",
"literature-status:open",
"owr-year:2011"
] | The source frames the extremal geometric-graph problem for general forbidden configurations; no general asymptotic formula matching the extracted question was located. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | Given a family $H$ of forbidden geometric configurations, what is the maximum number of edges in an $n$-vertex geometric graph containing no configuration from $H$? | Given a family H of forbidden geometric configurations, what is the maximum number of edges in an n-vertex geometric graph containing no configuration from H? | corrected_verified | The forbidden family and vertex-count parameter were placed in math delimiters without changing the question. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,891 | OWR-11136-019 | Projectively Unique Polytopes and Their Realization Spaces | For a fixed dimension $d$, are there only finitely many combinatorial types of projectively unique $d$-dimensional convex polytopes? More generally, how does the dimension of the realization space of a $d$-polytope grow with its size? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-019",
"literature-status:open",
"owr-year:2011"
] | The wording conflates combinatorial type with projective equivalence; under the intended projectively-unique interpretation, the d>=4 finiteness question remains open while low dimensions are classified. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://arxiv.org/abs/math/0401005",
"label": "unique polyhedral representations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For a fixed dimension $d$, are there only finitely many combinatorial types of projectively unique $d$-dimensional convex polytopes? More generally, how does the dimension of the realization space of a $d$-polytope grow with its size? | Are there only finitely many combinatorial types of d-dimensional convex polytopes up to projective transformations, and how does the dimension of their realization spaces grow with polytope size? | corrected_verified | The official report was checked and the missing projective-uniqueness condition and realization-space question were restored. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,892 | OWR-11136-022 | Exceptional Points in Favourite Distance Digraphs | Given a finite point set $S \subset \mathbb{R}^3$ and a assignment of a 'favourite distance' $d(p) > 0$ to each point $p \in S$, form the directed graph whose edges are $(p, q)$ with $|p - q| = d(p)$. In the extremal characterization of maximum-outdegree favourite-distance digraphs in $\mathbb{R}^3$ (Swanepoel), let $T... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-022",
"literature-status:open",
"owr-year:2011"
] | The 2020 primary paper still states that the exceptional set of at most two points is conjectured to be empty. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://researchonline.lse.ac.uk/id/eprint/104165/4/Swanepoel_favourite_distances_in_3_space_published.pdf",
"label": "Swanepoel"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | Given a finite point set $S \subset \mathbb{R}^3$ and a assignment of a 'favourite distance' $d(p) > 0$ to each point $p \in S$, form the directed graph whose edges are $(p, q)$ with $|p - q| = d(p)$. In the extremal characterization of maximum-outdegree favourite-distance digraphs in $\mathbb{R}^3$ (Swanepoel), let $T... | In the extremal favourite-distance digraph problem in \mathbb{R}^3, is the exceptional set T always empty? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,893 | OWR-11136-024 | Dimension of Convex Partition Spaces in Three Dimensions | What is the dimension of the space of all partitions of $\mathbb{R}^3$ into $n>3$ convex pieces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-024",
"literature-status:open",
"owr-year:2011"
] | The three-dimensional convex-partition realization-space dimension is explicitly left unresolved beyond the power-diagram lower bound. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | What is the dimension of the space of all partitions of $\mathbb{R}^3$ into $n>3$ convex pieces? | What is the dimension of the space of all partitions of \mathbb{R}^3 into n>3 convex pieces? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,894 | OWR-11136-026 | Colored Transversals for Translates of Convex Sets | If $F_1,F_2,F_3$ are pairwise intersecting families of translates of a convex compact planar set, must some $F_i$ have a $3$-transversal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-026",
"literature-status:open",
"owr-year:2011"
] | No general resolution of the colored Grunbaum transversal question was found; the report presents it as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | If $F_1,F_2,F_3$ are pairwise intersecting families of translates of a convex compact planar set, must some $F_i$ have a $3$-transversal? | If F_1,F_2,F_3 are pairwise intersecting families of translates of a convex compact planar set, must some F_i have a 3-transversal? | corrected_verified | The complete statement was preserved while previously undelimited mathematical notation was normalized into readable prose. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,895 | OWR-11136-027 | Exact Transversals for Families with the (p,q)-Property | For a family of hyperplanes in $\mathbb{R}^d$ with the $(p,q)$-property, $d+1\leq q\leq p$, must there be a $(p-q+1)$-transversal; and does the analogous statement hold for families of $r$-element sets with $r+1\leq q\leq p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-027",
"literature-status:open",
"owr-year:2011"
] | The exact p-q+1 transversal assertion is not established in the general Hadwiger--Debrunner range; later work gives finiteness or bounds rather than this universal exact value. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://arxiv.org/abs/1409.1194",
"label": "Alon--Kalai variant"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For a family of hyperplanes in $\mathbb{R}^d$ with the $(p,q)$-property, $d+1\leq q\leq p$, must there be a $(p-q+1)$-transversal; and does the analogous statement hold for families of $r$-element sets with $r+1\leq q\leq p$? | For a family of hyperplanes in \mathbb{R}^d with the (p,q)-property, d+1\leq q\leq p, must there be a (p-q+1)-transversal; and does the analogous statement hold for families of r-element sets with r+1\leq q\leq p? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,896 | OWR-11136-028 | Shift Chain Colorings and Disk Covering Paths | A shift-chain is a $k$-uniform hypergraph whose edges are comparable coordinatewise after their vertices are written in increasing order. Are all shift-chains 2-colorable for sufficiently large $k$? Separately, is there a constant $c$ such that every closed-unit-disc covering of the plane admits, between any two points... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,011 | 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-11136-028",
"literature-status:partially-solved",
"owr-year:2011"
] | The shift-chain question remains unresolved beyond small counterexamples and restricted positive cases, while the doubly-covered-disk path problem has improved bounds and lattice-covering cases. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | A shift-chain is a $k$-uniform hypergraph whose edges are comparable coordinatewise after their vertices are written in increasing order. Are all shift-chains 2-colorable for sufficiently large $k$? Separately, is there a constant $c$ such that every closed-unit-disc covering of the plane admits, between any two points... | Are shift-chains 2-colorable for all sufficiently large k, and does there exist a constant c giving paths of length at most 2d+c inside the doubly covered region of every closed-unit-disc covering of the plane? | corrected_verified | The official report was checked and the shift-chain definition and the correct square-root path-length coefficient were restored. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,897 | OWR-11136-029 | Linear Bounds for Monotone Crossing Numbers | Does there exist a constant $c$ such that $\operatorname{mon-cr}(G)<c\operatorname{cr}(G)$ for every graph $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11136-029",
"literature-status:open",
"owr-year:2011"
] | The report gives only a quadratic upper bound in the classical crossing number; the existence of a universal linear comparison for monotone crossing number remains open. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://www.combinatorics.org/files/Surveys/ds21/ds21v5-2020.pdf",
"label": "crossing-number survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | Does there exist a constant $c$ such that $\operatorname{mon-cr}(G)<c\operatorname{cr}(G)$ for every graph $G$? | Does there exist a constant c such that \operatorname{mon-cr}(G)<c \operatorname{cr}(G) for every graph G? | corrected_verified | TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,898 | OWR-11136-030 | Semicircle Packings and Colorings of Simplicial 4-Polytopes | For a plane curve $\gamma$ and $r>0$, let $f_c(r,\gamma)$ be the maximum density of a congruent packing by copies of the Minkowski sum of $\gamma$ and the closed disk of radius $r$. If $\gamma_1$ is a semicircle, is $f_c(r,\gamma_1)=\Theta(\sqrt{r})$? Separately, does every simplicial 4-polytope admit a coloring with a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-030",
"literature-status:open",
"owr-year:2011"
] | The semicircle packing asymptotic and the bounded-coloring question for simplicial 4-polytopes remain posed without a complete general theorem. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For a plane curve $\gamma$ and $r>0$, let $f_c(r,\gamma)$ be the maximum density of a congruent packing by copies of the Minkowski sum of $\gamma$ and the closed disk of radius $r$. If $\gamma_1$ is a semicircle, is $f_c(r,\gamma_1)=\Theta(\sqrt{r})$? Separately, does every simplicial 4-polytope admit a coloring with a... | Is f_c(r,\gamma_1)=\Theta(\sqrt r) for the semicircle \gamma_1, and is there a constant-coloring of every simplicial 4-polytope with no monochromatic 2-face? | corrected_verified | The official report was checked and the packing-density function, semicircle case, and bounded-color polytope question were restored. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,899 | OWR-11136-031 | High Incidence Partitions and Minimum Ellipsoid Coresets | For every $c$, does there exist a locally finite convex-cell partition of $\mathbb{R}^3$ in which every cell meets at least $c$ vertices and every vertex meets at least $c$ cells? Separately, for a finite set $S\subset\mathbb{R}^d$, let $\operatorname{MEE}(S)$ be its minimum enclosing ellipsoid, let $\operatorname{DBM}... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548](https://doi.org/10.4171/owr/2011/44)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,011 | 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-11136-031",
"literature-status:open",
"owr-year:2011"
] | The report poses both the high-incidence convex-cell partition problem and the exact minimum-ellipsoid subset bound; related coreset estimates do not settle this combined formulation. | [
{
"url": "https://doi.org/10.4171/owr/2011/44",
"label": "OWR 44 (2012)"
},
{
"url": "https://kenclarkson.org/paris_school/t.html",
"label": "Clarkson coreset notes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/44 | null | null | null | For every $c$, does there exist a locally finite convex-cell partition of $\mathbb{R}^3$ in which every cell meets at least $c$ vertices and every vertex meets at least $c$ cells? Separately, for a finite set $S\subset\mathbb{R}^d$, let $\operatorname{MEE}(S)$ be its minimum enclosing ellipsoid, let $\operatorname{DBM}... | For every c, does there exist a locally finite convex-cell partition of \mathbb{R}^3 in which every cell meets at least c vertices and every vertex meets at least c cells; and is f(d,\varepsilon)=O(d/\varepsilon^2)? | corrected_verified | The official report was checked and the minimum-enclosing-ellipsoid coreset function was defined explicitly alongside the incidence-partition question. | null | null | null | null | null | Discrete Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/44, pp. 2459--2548 |
30,001,900 | OWR-11137-005 | Classification of Unitary Drinfeld Twists | Let $G$ be a compact semisimple Lie group and let $G_q$ be its Drinfeld--Jimbo $q$-deformation ($0 < q < 1$). How can unitary Drinfeld $2$-cocycle twists (up to coboundary equivalence) for the compact quantum group $G_q$ be classified or explicitly described? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622](https://doi.org/10.4171/owr/2011/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,011 | 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-11137-005",
"literature-status:open",
"owr-year:2011"
] | This is a broad question about the elements represented by invariant cocycle cohomology classes; the surrounding theorem identifies the cohomology group but does not resolve the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2011/45",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/45 | null | null | null | Let $G$ be a compact semisimple Lie group and let $G_q$ be its Drinfeld--Jimbo $q$-deformation ($0 < q < 1$). How can unitary Drinfeld $2$-cocycle twists (up to coboundary equivalence) for the compact quantum group $G_q$ be classified or explicitly described? | How can unitary Drinfeld twists for G_q be classified or otherwise described? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622 |
30,001,901 | OWR-11137-006 | Internal Isomorphism Invariants of Number Fields | Can an invariant internal to a number field classify it up to isomorphism, yielding an internal analogue of the known external reconstruction results? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622](https://doi.org/10.4171/owr/2011/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,011 | 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-11137-006",
"literature-status:open",
"owr-year:2011"
] | The extracted sentence is a context fragment and does not state a precise resolved theorem; no authoritative source located a definitive answer to the implied question. | [
{
"url": "https://doi.org/10.4171/owr/2011/45",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/45 | null | null | null | Can an invariant internal to a number field classify it up to isomorphism, yielding an internal analogue of the known external reconstruction results? | Can an invariant internal to a number field classify it up to isomorphism, yielding an internal analogue of the known external reconstruction results? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622 |
30,001,902 | OWR-11137-007 | Coarse Baum–Connes Maps for Large-Girth Graph Spaces | For a coarse space formed from bounded-degree finite graphs whose girths tend to infinity, what are the injectivity and surjectivity properties of the coarse Baum–Connes assembly map, especially for expanders and geometric property (T)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622](https://doi.org/10.4171/owr/2011/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,011 | 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-11137-007",
"literature-status:open",
"owr-year:2011"
] | The record begins mid-sentence before a theorem about coarse Baum--Connes assembly, so the underlying conjectural claim cannot be recovered reliably; it remains open as an extracted problem. | [
{
"url": "https://doi.org/10.4171/owr/2011/45",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/45 | null | null | null | For a coarse space formed from bounded-degree finite graphs whose girths tend to infinity, what are the injectivity and surjectivity properties of the coarse Baum–Connes assembly map, especially for expanders and geometric property (T)? | For a coarse space formed from bounded-degree finite graphs whose girths tend to infinity, what are the injectivity and surjectivity properties of the coarse Baum--Connes assembly map, especially for expanders and geometric property (T)? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622 |
30,001,903 | OWR-11137-008 | Cyclic-Cohomology Classes of the Radul Cocycle | Identify the canonical cyclic-cohomology class $[c]\in HC^1(CS(M))$ of the Radul cocycle, including its image in periodic cyclic cohomology. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622](https://doi.org/10.4171/owr/2011/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,011 | 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-11137-008",
"literature-status:open",
"owr-year:2011"
] | The extracted question asks to identify a class associated with the Radul cyclic cocycle, but the record does not specify the target class or a complete classification result. | [
{
"url": "https://doi.org/10.4171/owr/2011/45",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/45 | null | null | null | Identify the canonical cyclic-cohomology class $[c]\in HC^1(CS(M))$ of the Radul cocycle, including its image in periodic cyclic cohomology. | Identify the canonical cyclic-cohomology class [c]\in HC^1(CS(M)) of the Radul cocycle, including its image in periodic cyclic cohomology. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622 |
30,001,904 | OWR-11137-009 | The Bismut–Lott Transfer Index Conjecture | Let $\pi:W\to B$ be a proper submersion with Riemannian structure $g$, and let $(V,h^V)$ be a local system of finitely generated projective modules over a number ring, equipped with metrics. If $\operatorname{index}^{\mathrm{top}}(V,h^V)$ is the differential Becker–Gottlieb transfer index and $\operatorname{index}^{\ma... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622](https://doi.org/10.4171/owr/2011/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,011 | 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-11137-009",
"literature-status:open",
"owr-year:2011"
] | The question is the transfer index conjecture that the analytic and topological indices agree integrally; real and integer components and special cases are known, but the full torsion obstruction is not resolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/aeae711a-738f-43b7-854d-83b290a18b71/content",
"label": "transfer index conjecture and known consequences"
},
{
"url": "https://math.berkeley.edu/~lott/jams.pdf",
"label": "Bismut--Lott, higher real analytic torsion"
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{
"url... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/45 | null | null | null | Let $\pi:W\to B$ be a proper submersion with Riemannian structure $g$, and let $(V,h^V)$ be a local system of finitely generated projective modules over a number ring, equipped with metrics. If $\operatorname{index}^{\mathrm{top}}(V,h^V)$ is the differential Becker–Gottlieb transfer index and $\operatorname{index}^{\ma... | For the analytic and topological index classes in the stated Bismut--Lott setting, is the difference \delta equal to zero? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Noncommutative Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/45, pp. 2549--2622 |
30,001,905 | OWR-11138-001 | K-Theoretic Descent from MU to the Sphere | Let $S \to MU$ be the unit map from the sphere spectrum $S$ to the complex cobordism spectrum $MU$, viewed as a commutative $MU$-Hopf--Galois extension in the sense of Rognes. Can the algebraic $K$-theory spectrum $K(S)$ of the sphere spectrum be recovered from $K(MU)$ by homotopy fixed-point/cosimplicial descent along... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667](https://doi.org/10.4171/owr/2011/46)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,011 | 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-11138-001",
"literature-status:open",
"owr-year:2011"
] | The descent question comparing algebraic K-theory of MU and the sphere remains a research problem; the report gives motivation and no complete descent or reconstruction theorem. | [
{
"url": "https://doi.org/10.4171/owr/2011/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/46 | null | null | null | Let $S \to MU$ be the unit map from the sphere spectrum $S$ to the complex cobordism spectrum $MU$, viewed as a commutative $MU$-Hopf--Galois extension in the sense of Rognes. Can the algebraic $K$-theory spectrum $K(S)$ of the sphere spectrum be recovered from $K(MU)$ by homotopy fixed-point/cosimplicial descent along... | Is K(MU) simpler to describe than K(S), and can K(S) be recovered from K(MU) by descent along the Hopf--Galois extension S\to MU? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667 |
30,001,906 | OWR-11138-003 | Koszul Decompositions in Homotopy Theory | What structural or computational consequences does the Koszul decomposition of \Delta_q and its bar complex have in this homotopy-theoretic setting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667](https://doi.org/10.4171/owr/2011/46)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,011 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents the Koszul property as an established result and then explains its meaning rather than posing an unresolved pro) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11138-003",
"literature-status:open",
"owr-year:2011"
] | The record consists only of the question What does this mean? attached to a bar-complex construction, and no precise mathematical claim with a definitive answer can be recovered. | [
{
"url": "https://doi.org/10.4171/owr/2011/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/46 | null | null | null | null | What structural or computational consequences does the Koszul decomposition of \Delta_q and its bar complex have in this homotopy-theoretic setting? | unrecoverable | The official report presents the Koszul property as an established result and then explains its meaning rather than posing an unresolved problem. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667 |
30,001,907 | OWR-11138-004 | Koszul Differentials in Bousfield–Kuhn Homology | Let $E$ be Morava $E$-theory of height $n$, let $q$ be odd, and identify $$E_q^{\wedge}\!\left(\Sigma^kD_{2^k}(\operatorname{Id})(S^q)\right)\cong C[k]_{-q}^{\vee}.$$ Under this isomorphism, is the map $(\Phi_n\beta_k)_*$ on $E$-homology the differential in the Koszul resolution of $\widetilde E_q(S^q)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667](https://doi.org/10.4171/owr/2011/46)
## Literature review (checked 2026-08-21)
**Status:** partially ... | 3 | partially_solved | null | 2,011 | 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-11138-004",
"literature-status:partially-solved",
"owr-year:2011"
] | The Bousfield--Kuhn/Koszul comparison has substantial results, including the odd-degree Koszul description and sphere cases, but the extracted conjecture is not established in the stated generality. | [
{
"url": "https://arxiv.org/abs/1712.03045",
"label": "Behrens--Rezk, Bousfield--Kuhn and topological Andre--Quillen cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2011/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/46 | null | null | null | Let $E$ be Morava $E$-theory of height $n$, let $q$ be odd, and identify $$E_q^{\wedge}\!\left(\Sigma^kD_{2^k}(\operatorname{Id})(S^q)\right)\cong C[k]_{-q}^{\vee}.$$ Under this isomorphism, is the map $(\Phi_n\beta_k)_*$ on $E$-homology the differential in the Koszul resolution of $\widetilde E_q(S^q)$? | Under the stated isomorphism, is the induced map (\Phi_n\beta_k)_* on E-homology given by the differential in the Koszul resolution for \widetilde E_q(S^q)? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667 |
30,001,908 | OWR-11138-007 | Homology of Infinite Loop Spaces | How can one compute $H_*(\Omega^\infty X)$ from knowledge of $H_*(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667](https://doi.org/10.4171/owr/2011/46)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,011 | 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-11138-007",
"literature-status:open",
"owr-year:2011"
] | There are important special-case calculations and structural tools for homology of infinite loop spaces, but no general procedure recovering H-star of Omega-infinity X from H-star of X is known. | [
{
"url": "https://doi.org/10.4171/owr/2011/46",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/46 | null | null | null | How can one compute $H_*(\Omega^\infty X)$ from knowledge of $H_*(X)$? | How can one compute H_*(\Omega^\infty X) from knowledge of H_*(X)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Homotopy Theory (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/46, pp. 2623--2667 |
30,001,909 | OWR-11139-001 | Classification of Class-VII Complex Surfaces | Classify compact complex surfaces of class $\mathrm{VII}_0^+$, in particular determining the structure of this still-mysterious class. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-001",
"literature-status:open",
"owr-year:2011"
] | This is a table-of-contents fragment rather than a mathematical claim, so no resolution can be established from the extracted record. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Classify compact complex surfaces of class $\mathrm{VII}_0^+$, in particular determining the structure of this still-mysterious class. | Classify compact complex surfaces of class \mathrm{VII}_0^+, in particular determining the structure of this still-mysterious class. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,910 | OWR-11139-003 | Stable Rationality of Generically Free Simple-Group Quotients | For simply connected simple groups, are generically free linear quotients stably rational in the $\operatorname{Spin}$ series and for $E_8$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-003",
"literature-status:open",
"owr-year:2011"
] | The stable-rationality question for generically free quotients in the Spin series and for E8 remains unresolved in the current literature located. | [
{
"url": "https://warwick.ac.uk/fac/sci/maths/people/staff/boehning/invariant_theory_book.pdf",
"label": "Bohning, rationality problem in invariant theory"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | For simply connected simple groups, are generically free linear quotients stably rational in the $\operatorname{Spin}$ series and for $E_8$? | For simply connected simple groups, are generically free linear quotients stably rational in the Spin series and for E8? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,911 | OWR-11139-004 | Rationality of Plane-Curve Moduli Spaces | Are the moduli spaces
$$\mathbb P(\operatorname{Sym}^d(\mathbb C^3)^*)/SL_3(\mathbb C)$$
of plane curves rational for the $15$ values of $d$ for which rationality remains unknown? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-004",
"literature-status:open",
"owr-year:2011"
] | The rationality statement is still reported with a finite list of exceptional degrees for which rationality remains unsettled; the extracted problem is therefore not closed in full generality. | [
{
"url": "https://warwick.ac.uk/fac/sci/maths/people/staff/boehning/invariant_theory_book.pdf",
"label": "Bohning, rationality problem in invariant theory"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Are the moduli spaces
$$\mathbb P(\operatorname{Sym}^d(\mathbb C^3)^*)/SL_3(\mathbb C)$$
of plane curves rational for the $15$ values of $d$ for which rationality remains unknown? | Are the moduli spaces of plane curves P(Sym^d(C^3)^*) divided by SL_3(C) rational for the 15 values of d for which rationality remains unknown? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,912 | OWR-11139-005 | Necessary Conditions for Laurent-Polynomial Fano Mirrors | What necessary conditions must a Laurent polynomial $f$ satisfy in order to be mirror to a Fano manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,011 | 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-11139-005",
"literature-status:partially-solved",
"owr-year:2011"
] | Period, regularity, and extremality conditions and large families of Laurent-polynomial mirrors are established, but there is no complete necessary-and-sufficient characterization of mirrors to Fano manifolds. | [
{
"url": "https://arxiv.org/abs/1303.3288",
"label": "Coates--Corti--Galkin--Kasprzyk, quantum periods"
},
{
"url": "https://arxiv.org/abs/2107.14253",
"label": "Coates--Kasprzyk--Pitton--Tveiten, maximally mutable Laurent polynomials"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | What necessary conditions must a Laurent polynomial $f$ satisfy in order to be mirror to a Fano manifold? | What necessary conditions must a Laurent polynomial f satisfy in order to be mirror to a Fano manifold? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,913 | OWR-11139-006 | Extremality of Hodge–Tate Laurent Polynomials | Is every Laurent polynomial that is Hodge–Tate at infinity extremal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-006",
"literature-status:open",
"owr-year:2011"
] | The conjecture that every Hodge--Tate-at-infinity Laurent polynomial is extremal is explicitly stated, and the located later work does not prove it in full generality. | [
{
"url": "https://arxiv.org/abs/2107.14253",
"label": "Coates--Kasprzyk--Pitton--Tveiten, maximally mutable Laurent polynomials"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | Is every Laurent polynomial that is Hodge–Tate at infinity extremal? | Conjecture: every Laurent polynomial that is Hodge--Tate at infinity is extremal. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,914 | OWR-11139-007 | The Green–Griffiths–Lang Entire-Curve Conjecture | If $X$ is a projective variety of general type, must there exist a proper algebraic subvariety $Y\subset X$ containing the image of every nonconstant entire curve $\mathbb C\to X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-007",
"literature-status:open",
"owr-year:2011"
] | The Green--Griffiths--Lang conjecture remains open in its general form; modern papers establish important special cases rather than a complete proof. | [
{
"url": "https://arxiv.org/abs/2410.00640",
"label": "recent Green--Griffiths--Lang special case"
},
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | If $X$ is a projective variety of general type, must there exist a proper algebraic subvariety $Y\subset X$ containing the image of every nonconstant entire curve $\mathbb C\to X$? | Green--Griffiths--Lang conjecture: if X is a projective variety of general type, there exists an algebraic subvariety Y contained in X such that every nonconstant entire curve from C to X is contained in Y. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
30,001,915 | OWR-11139-008 | Green–Griffiths–Lang for Directed Varieties | If $(X,V)$ is a projective directed manifold whose canonical sheaf $K_V$ is big, must there exist a proper algebraic subvariety $Y\subset X$ containing the image of every nonconstant entire curve $\mathbb C\to X$ tangent to $V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733](https://doi.org/10.4171/owr/2011/47)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,011 | 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-11139-008",
"literature-status:open",
"owr-year:2011"
] | The generalized directed-variety Green--Griffiths--Lang conjecture remains open; the jet-differential vanishing theorem supplies only a conditional route through asymptotic base-locus estimates. | [
{
"url": "https://doi.org/10.4171/owr/2011/47",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2011/47 | null | null | null | If $(X,V)$ is a projective directed manifold whose canonical sheaf $K_V$ is big, must there exist a proper algebraic subvariety $Y\subset X$ containing the image of every nonconstant entire curve $\mathbb C\to X$ tangent to $V$? | Generalized Green--Griffiths--Lang conjecture: if (X,V) is a projective directed manifold whose canonical sheaf K_V is big, there exists an algebraic subvariety Y contained in X such that every nonconstant entire curve from C to X tangent to V is contained in Y. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Complex Algebraic Geometry (2012), Oberwolfach Reports, DOI 10.4171/owr/2011/47, pp. 2669--2733 |
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