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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,016 | OWR-13952-007 | Adelic Harmonic Metrics on Line Bundles | Does every line bundle $M$ on $X$ have an admissible adelic metrization $\overline{M}$ whose metric at each place has harmonic curvature and satisfies $\overline{M}\cdot\omega^n=\lambda(M)\omega^{n+1}$, unique up to multiplication by a degree-zero element of $\operatorname{Div}(K)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,015 | 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-13952-007",
"literature-status:partially-solved",
"owr-year:2015"
] | The adelic harmonic metrization conjecture has the stated uniqueness and existence in important special cases, but the global-field assertion for arbitrary varieties and line bundles remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/57",
"label": "Non-Archimedean Geometry and Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | Does every line bundle $M$ on $X$ have an admissible adelic metrization $\overline{M}$ whose metric at each place has harmonic curvature and satisfies $\overline{M}\cdot\omega^n=\lambda(M)\omega^{n+1}$, unique up to multiplication by a degree-zero element of $\operatorname{Div}(K)$? | Does every line bundle M on X have an admissible adelic metrization \overline{M} whose metric at each place has harmonic curvature and satisfies \overline{M}\cdot\omega^n=\lambda(M) \omega^{n+1}, unique up to multiplication by a degree-zero element of Div(K)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,017 | OWR-13952-008 | Equality of Refined Tropical and Algebraic Curve Counts | For each tropical curve $\Gamma$, is its Block–Göttsche refined tropical curve-counting multiplicity equal to the refined curve-counting polynomial $N_{g-\delta}(y)$, with the equality specializing correctly at $y=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,015 | 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-13952-008",
"literature-status:partially-solved",
"owr-year:2015"
] | The Block--Göttsche geometric interpretation is proved for genus one, for the first low-codimension cases, and after specialization to ordinary Euler characteristic; higher-genus geometric equalities remain only partly established. | [
{
"url": "https://msp.org/gt/2018/22-6/gt-v22-n6-p02-s.pdf",
"label": "Nicaise, Payne, and Schroeter"
},
{
"url": "https://doi.org/10.1007/s00222-018-0823-z",
"label": "Bousseau, higher-genus refined curve counting"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | For each tropical curve $\Gamma$, is its Block–Göttsche refined tropical curve-counting multiplicity equal to the refined curve-counting polynomial $N_{g-\delta}(y)$, with the equality specializing correctly at $y=1$? | For each tropical curve \Gamma, is its Block--Goettsche refined tropical curve-counting multiplicity equal to the refined curve-counting polynomial N_{g-\delta}(y), with the equality specializing correctly at y=1? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,018 | OWR-13952-009 | Geometric Langlands Sheaves for Discrete Parameters | For a discrete Langlands parameter $\varphi:W_E\to{}^LG$, does there exist a perverse Weil sheaf $F_\varphi$ on $\operatorname{Bun}_G\otimes\mathbb F_q$ with an $S_\varphi$-action satisfying the prescribed central-character, L-packet, Hecke-eigenvalue, and local-global compatibility properties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,015 | 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-13952-009",
"literature-status:open",
"owr-year:2015"
] | The existence of the perverse Weil sheaf with all stated Hecke and component-group properties is Fargues' conjecture; constructions for selected parameters do not establish the full conjecture. | [
{
"url": "https://webusers.imj-prg.fr/~laurent.fargues/Geometrization_review.pdf",
"label": "Fargues, geometrization review"
},
{
"url": "https://doi.org/10.4171/owr/2015/57",
"label": "Non-Archimedean Geometry and Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | For a discrete Langlands parameter $\varphi:W_E\to{}^LG$, does there exist a perverse Weil sheaf $F_\varphi$ on $\operatorname{Bun}_G\otimes\mathbb F_q$ with an $S_\varphi$-action satisfying the prescribed central-character, L-packet, Hecke-eigenvalue, and local-global compatibility properties? | For a discrete Langlands parameter \varphi:W_E\to{}^LG, does there exist a perverse Weil sheaf F_\varphi on Bun_G\otimes F_q with an S_\varphi-action satisfying the prescribed central-character, L-packet, Hecke-eigenvalue, and local-global compatibility properties? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,019 | OWR-13952-010 | Uniform Mordell Conjecture | For every integer $g\geq2$, does there exist $N(g)$ such that every smooth, proper, geometrically connected curve $C/\mathbb Q$ of genus $g$ satisfies $\lvert C(\mathbb Q)\rvert\leq N(g)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,015 | 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-13952-010",
"literature-status:partially-solved",
"owr-year:2015"
] | Faltings proved finiteness, and Vojta, Dimitrov--Gao--Habegger, and Kühne proved strong uniform bounds depending on genus, field degree, and Mordell--Weil rank, with explicit 2026 constants; the exact genus-only bound stated here remains unresolved. | [
{
"url": "https://annals.math.princeton.edu/2021/194-1/p04",
"label": "Dimitrov, Gao, and Habegger, uniform Mordell--Lang"
},
{
"url": "https://arxiv.org/abs/2101.10272",
"label": "Kühne, equidistribution and uniformity"
},
{
"url": "https://arxiv.org/abs/2602.01820",
"label": "Yu, Y... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | For every integer $g\geq2$, does there exist $N(g)$ such that every smooth, proper, geometrically connected curve $C/\mathbb Q$ of genus $g$ satisfies $\lvert C(\mathbb Q)\rvert\leq N(g)$? | Uniform Mordell conjecture: for every integer g\geq2, does there exist a number N(g) such that every smooth proper geometrically connected curve C over Q of genus g satisfies |C(Q)|\leq N(g)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,020 | OWR-14209-001 | Generic Closedness of the Canonical $\Gamma$-Field | Let $G$ be either $\mathbb G_m$ or an abelian variety over $k_0$, set $O=\operatorname{End}(G)$, and let $C$ be the canonical $\Gamma$-field with $\Gamma(C)=\{(x,\exp_G(x)):x\in LG(C)\}$, $\Gamma(k_0)=\{0\}$, and $C_0=\Gamma\operatorname{cl}_C(k_0)$. Is $C$ generically $\Gamma$-closed? Explicitly, whenever $k\supseteq ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50](https://doi.org/10.4171/owr/2016/1)
## Literature review (checked 2026-08-... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14209-001",
"literature-status:open",
"owr-year:2016"
] | The generic Gamma-closedness of the complex Gamma-field is stated as a conjecture; later quasiminimality results are conditional on generic or almost generic closedness and do not prove this assertion. | [
{
"url": "https://doi.org/10.4171/owr/2016/1",
"label": "Model Theory report"
},
{
"url": "https://pure.mpg.de/rest/items/item_3057824_3/component/file_3057825/content",
"label": "Pseudo-exponential maps and variants"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/1 | null | null | null | Let $G$ be either $\mathbb G_m$ or an abelian variety over $k_0$, set $O=\operatorname{End}(G)$, and let $C$ be the canonical $\Gamma$-field with $\Gamma(C)=\{(x,\exp_G(x)):x\in LG(C)\}$, $\Gamma(k_0)=\{0\}$, and $C_0=\Gamma\operatorname{cl}_C(k_0)$. Is $C$ generically $\Gamma$-closed? Explicitly, whenever $k\supseteq ... | Is the canonical \Gamma-field C generically \Gamma-closed, meaning that for every finitely generated \Gamma-field extension k over the prescribed closure, every irreducible n-dimensional variety V\subseteq L G^n\times G^n satisfying the stated non-translate, quotient-dimension, and positive-projection conditions contai... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50 |
30,003,021 | OWR-14209-003 | Full-Dimension Intersections in Definable Families | Let $(X_a)_{a\in A}$ be a definable family of subsets of a pseudofinite set $Y$, with $\delta(X_a)=\delta(Y)$ for every $a\in A$. Under what hypotheses does generic $a$ make $X_a$ intersect every definable $B\subseteq Y$ of full $\delta$-dimension properly, in the sense that $\delta(X_a\cap B)=\delta(X_a)+\delta(B)-\de... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50](https://doi.org/10.4171/owr/2016/1)
## Literature review (checked 2026-08-... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14209-003",
"literature-status:open",
"owr-year:2016"
] | The extracted question gives no definitions beyond an equality of delta-dimensions and no precise conclusion to test; the underlying fragment is therefore unresolved and is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2016/1",
"label": "Model Theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/1 | null | null | null | Let $(X_a)_{a\in A}$ be a definable family of subsets of a pseudofinite set $Y$, with $\delta(X_a)=\delta(Y)$ for every $a\in A$. Under what hypotheses does generic $a$ make $X_a$ intersect every definable $B\subseteq Y$ of full $\delta$-dimension properly, in the sense that $\delta(X_a\cap B)=\delta(X_a)+\delta(B)-\de... | For a definable family X_a\subseteq Y with \delta(X)=\delta(X_a), what can be said about proper intersections of X_a with definable subsets B\subseteq Y of full \delta-dimension? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50 |
30,003,022 | OWR-14209-004 | Henselian Valuations on NIP Fields | Is every valued NIP field $(K,v)$ henselian? If an NIP field $K$ is neither separably closed nor real closed, does it admit a definable nontrivial henselian valuation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50](https://doi.org/10.4171/owr/2016/1)
## Literature review (checked 2026-08-... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14209-004",
"literature-status:open",
"owr-year:2016"
] | The henselianity and definability questions for arbitrary NIP fields remain open; current work classifies many NIP henselian fields and proves substantial transfer results but leaves the general conjectures unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/32802",
"label": "Jahnke and Simon, NIP henselian fields"
},
{
"url": "https://doi.org/10.4171/owr/2016/1",
"label": "Model Theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/1 | null | null | null | Is every valued NIP field $(K,v)$ henselian? If an NIP field $K$ is neither separably closed nor real closed, does it admit a definable nontrivial henselian valuation? | (1) Is every valued NIP field (K,v) henselian? (2) If K is an NIP field that is neither separably closed nor real closed, does K admit a definable non-trivial henselian valuation, and is the resulting valued field NIP? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50 |
30,003,023 | OWR-14209-005 | NIP Preservation under Henselian Valuations | If $K$ is an NIP field and $v$ is a henselian valuation on $K$, must the valued field $(K,v)$ be NIP? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50](https://doi.org/10.4171/owr/2016/1)
## Literature review (checked 2026-08-... | 3 | solved | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes)**. F. Jahnke (OWR 1/2016, p. 29, Question 2) asks whether (K,v) is NIP when K is an NIP field and v is a henselian valuation. The report itself answers the case where the residue field Kv is not separably closed (Cor. 12, p. 31). | [
"owr",
"oberwolfach-reports",
"OWR-14209-005",
"literature-status:open",
"owr-year:2016"
] | The question whether every henselian expansion with NIP residue field in the remaining imperfect or separably closed cases is NIP is not settled; the literature proves broad special cases and structural classifications only. | [
{
"url": "https://doi.org/10.1112/jlms.12868",
"label": "Anscombe, characterizing NIP henselian fields"
},
{
"url": "https://doi.org/10.4171/owr/2016/1",
"label": "Model Theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/1 | null | null | null | If $K$ is an NIP field and $v$ is a henselian valuation on $K$, must the valued field $(K,v)$ be NIP? | If K is an NIP field with a henselian valuation v, must the valued field (K,v) be NIP? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50 |
30,003,024 | OWR-14209-007 | Generic Transitivity and Projective Linear Actions | Let $(X,G)$ be a transitive, generically $(n+2)$-transitive permutation group of finite Morley rank, with $G$ connected and $\operatorname{rk}(X)=n$. Is $(X,G)$ equivalent to $(\mathbb P^n(K),\operatorname{PGL}_{n+1}(K))$ for some algebraically closed field $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50](https://doi.org/10.4171/owr/2016/1)
## Literature review (checked 2026-08-... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14209-007",
"literature-status:open",
"owr-year:2016"
] | The exact record contains no mathematical proposition beyond saying that a conjecture is clear, so its resolution cannot be established from the identified claim; under the triage rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/1",
"label": "Oberwolfach Report 1/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/1 | null | null | null | Let $(X,G)$ be a transitive, generically $(n+2)$-transitive permutation group of finite Morley rank, with $G$ connected and $\operatorname{rk}(X)=n$. Is $(X,G)$ equivalent to $(\mathbb P^n(K),\operatorname{PGL}_{n+1}(K))$ for some algebraically closed field $K$? | If (X,G) is a transitive and generically (n+2)-transitive permutation group of finite Morley rank, with G connected and rk(X)=n, is (X,G) equivalent to (P^n(K),PGL_{n+1}(K)) for some algebraically closed field K? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Model Theory: groups, geometry, and combinatorics (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/1, pp. 5--50 |
30,003,025 | OWR-14210-001 | Color Savings and Strong Chromatic Index Bounds | For a graph with maximum degree $\Delta$ and clique number $\omega$, how many colors can be saved in ordinary, list, or correspondence coloring relative to bounds from $\Delta$, $\omega$, and maximum average degree; in particular, is the strong chromatic index at most $1.25\Delta^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86](https://doi.org/10.4171/owr/2016/2)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment.... | 3 | open | null | 2,016 | 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-14210-001",
"literature-status:open",
"owr-year:2016"
] | This is an underspecified broad question rather than a single falsifiable theorem; the report discusses several coloring bounds and improvements but does not state a general answer to the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2016/2",
"label": "Oberwolfach Report 2/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/2 | null | null | null | For a graph with maximum degree $\Delta$ and clique number $\omega$, how many colors can be saved in ordinary, list, or correspondence coloring relative to bounds from $\Delta$, $\omega$, and maximum average degree; in particular, is the strong chromatic index at most $1.25\Delta^2$? | For a graph with maximum degree \Delta and clique number \omega, how many colors can be saved in ordinary, list, or correspondence coloring relative to bounds from \Delta, \omega, and maximum average degree; in particular, is the strong chromatic index at most 1.25\Delta^2? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86 |
30,003,026 | OWR-14210-002 | Complete Graph Immersions from Minimum Degree | For every integer $n\geq 1$, does every graph of minimum degree at least n contain an immersion of the complete graph $K_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86](https://doi.org/10.4171/owr/2016/2)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment.... | 3 | open | null | 2,016 | 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-14210-002",
"literature-status:open",
"owr-year:2016"
] | The exact minimum-degree-at-least-t immersion question is still posed as an open problem; known results give strong K_t immersions from minimum degree 11t+7, while constructions at degree t-1 do not refute the degree-t statement. | [
{
"url": "https://arxiv.org/abs/1512.00513",
"label": "Dvorak and Yepremyan, Complete graph immersions and minimum degree"
},
{
"url": "https://arxiv.org/abs/1206.1545",
"label": "Collins and Heenehan, Constructing graphs with no immersion of large complete graphs"
},
{
"url": "https://d... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/2 | null | null | null | For every integer $n\geq 1$, does every graph of minimum degree at least n contain an immersion of the complete graph $K_n$? | For every integer n\geq 1, does every graph of minimum degree at least n contain an immersion of the complete graph K_n? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86 |
30,003,027 | OWR-14210-005 | Packing and Covering for Infinite Matroids | Let $M$ and $N$ be matroids on a common ground set $E$. Does there exist a partition $E=P\mathbin{\dot\cup}C$ such that the restrictions $M|P$ and $N|P$ have disjoint spanning sets, while the contractions $M.C$ and $N.C$ have independent sets whose union is $C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86](https://doi.org/10.4171/owr/2016/2)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessment.... | 3 | open | null | 2,016 | 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-14210-005",
"literature-status:open",
"owr-year:2016"
] | The packing--covering conjecture for arbitrary infinite matroids remains unresolved; recent work proves important subclasses, including finitary matroids, but not the unrestricted conjecture. | [
{
"url": "https://doi.org/10.1007/s11856-023-2595-4",
"label": "Joo, On the packing and covering conjecture of infinite matroids"
},
{
"url": "https://arxiv.org/abs/2501.04321",
"label": "Matroid intersection and packing and covering conjectures for finitary matroids"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/2 | null | null | null | Let $M$ and $N$ be matroids on a common ground set $E$. Does there exist a partition $E=P\mathbin{\dot\cup}C$ such that the restrictions $M|P$ and $N|P$ have disjoint spanning sets, while the contractions $M.C$ and $N.C$ have independent sets whose union is $C$? | Packing/Covering conjecture for infinite matroids: for any two matroids M and N on a common ground set E, does there exist a partition E=P\mathbin{\dot\cup}C such that M|P and N|P have disjoint spanning sets, while M.C and N.C have independent sets whose union is C? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Graph Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/2, pp. 51--86 |
30,003,028 | OWR-14211-001 | Kummer–Vandiver Conjecture | Kummer–Vandiver conjecture: for every odd prime $p$, if $C$ is the $p$-Sylow subgroup of the ideal class group of $\mathbb{Q}(\zeta_p)$, then the plus part $C^+$, equivalently each even character component $C^{(i)}$ for $0\leq i\leq p-3$, is zero. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,016 | 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-14211-001",
"literature-status:open",
"owr-year:2016"
] | The exact record is only a table-of-contents fragment saying conjecture, with no identifiable mathematical assertion; no resolution can be assigned to the extracted claim. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | Kummer–Vandiver conjecture: for every odd prime $p$, if $C$ is the $p$-Sylow subgroup of the ideal class group of $\mathbb{Q}(\zeta_p)$, then the plus part $C^+$, equivalently each even character component $C^{(i)}$ for $0\leq i\leq p-3$, is zero. | Kummer--Vandiver conjecture: for every odd prime p, if C is the p-Sylow subgroup of the class group of Q(\zeta_p), then the plus part C^+ (equivalently, each even character component C^{(i)} for 0\leq i\leq p-3) is zero. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,029 | OWR-14211-004 | Ground States of the Gaussian Core Model | For the Gaussian core model in Euclidean space with pair potential $r\mapsto e^{-\alpha r^2}$ and fixed particle density 1, what are the ground-state point configurations minimizing the average energy, particularly for values of $\alpha\geq 4\pi/e$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,016 | 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-14211-004",
"literature-status:open",
"owr-year:2016"
] | The record asks for the ground states of an unspecified system and gives no model, Hamiltonian, or admissible class; the exact claim is therefore unresolved and cannot be classified more strongly. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | For the Gaussian core model in Euclidean space with pair potential $r\mapsto e^{-\alpha r^2}$ and fixed particle density 1, what are the ground-state point configurations minimizing the average energy, particularly for values of $\alpha\geq 4\pi/e$? | For the Gaussian core model in Euclidean space with pair potential r\mapsto e^{-\alpha r^2} and fixed particle density 1, what are the ground-state point configurations minimizing the average energy, particularly for values of \alpha\geq 4\pi/e? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,030 | OWR-14211-005 | Geometry of Lattices from Finite Abelian Groups | Given a finite Abelian group G and $S=\{0=g_0,g_1,\ldots,g_{n-1}\}\subseteq G$, determine the geometric properties of $L_G(S)=\{x\in A_{n-1}:\sum_{j=1}^{n-1}x_jg_j=0\}$, including its minimum norm and determinant, number of minimal vectors, well-roundedness, minimal-vector bases, and automorphism group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,016 | 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-14211-005",
"literature-status:partially-solved",
"owr-year:2016"
] | For the full-group lattices L_G, determinant, minimal-vector counts, well-roundedness, minimal bases, and a permutation-part of the automorphism group are known; for general L_G(S), only special families and subgroup results are established. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | Given a finite Abelian group G and $S=\{0=g_0,g_1,\ldots,g_{n-1}\}\subseteq G$, determine the geometric properties of $L_G(S)=\{x\in A_{n-1}:\sum_{j=1}^{n-1}x_jg_j=0\}$, including its minimum norm and determinant, number of minimal vectors, well-roundedness, minimal-vector bases, and automorphism group. | Given a finite Abelian group G and S=\{0=g_0,g_1,\ldots,g_{n-1}\}\subseteq G, determine the geometric properties of L_G(S)=\{x\in A_{n-1}:\sum_{j=1}^{n-1}x_jg_j=0\}, including its minimum norm and determinant, number of minimal vectors, well-roundedness, minimal-vector bases, and automorphism group. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,031 | OWR-14211-006 | Representation of Quadratic Forms by Lattices and Genera | For a lattice $\Lambda$ and $T_d=\{T:\det(T)=d\}$, study which forms in subsets $S_d\subseteq T_d$ are represented by $\Lambda$ or by every $\Lambda'\in\operatorname{gen}(\Lambda)$, determine how many $T\in T_d$ a given $\Lambda$ represents, and determine the average and asymptotics of $r(\Lambda,T)$ over $T\in T_d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,016 | 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-14211-006",
"literature-status:partially-solved",
"owr-year:2016"
] | Representation and averaging questions have substantial partial results, including asymptotics in restricted dimensions and quaternionic-genus settings, but the broad four-part program in the record remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | For a lattice $\Lambda$ and $T_d=\{T:\det(T)=d\}$, study which forms in subsets $S_d\subseteq T_d$ are represented by $\Lambda$ or by every $\Lambda'\in\operatorname{gen}(\Lambda)$, determine how many $T\in T_d$ a given $\Lambda$ represents, and determine the average and asymptotics of $r(\Lambda,T)$ over $T\in T_d$. | For a lattice \Lambda and T_d=\{T:\det(T)=d\}, study which forms in subsets S_d\subseteq T_d are represented by \Lambda or by every \Lambda'\in\operatorname{gen}(\Lambda), determine how many T\in T_d a given \Lambda represents, and determine the average and asymptotics of r(\Lambda,T) over T\in T_d. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,032 | OWR-14211-007 | Bounds for Quaternary Local–Global Representation Exceptions | If Q is a positive-definite quaternary quadratic form with discriminant $D(Q)$, is the largest positive integer n that is locally represented by Q but not represented by Q always $O_\varepsilon(D(Q)^{1+\varepsilon})$ for every $\varepsilon>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,016 | 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-14211-007",
"literature-status:open",
"owr-year:2016"
] | The record explicitly labels this as an open problem; later work improves bounds for exceptional locally represented integers but does not establish the proposed D(Q) to the power 1 plus epsilon bound in general. | [
{
"url": "https://arxiv.org/abs/1802.03437",
"label": "Rouse, Integers represented by positive-definite quadratic forms"
},
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | If Q is a positive-definite quaternary quadratic form with discriminant $D(Q)$, is the largest positive integer n that is locally represented by Q but not represented by Q always $O_\varepsilon(D(Q)^{1+\varepsilon})$ for every $\varepsilon>0$? | If Q is a positive-definite quaternary quadratic form with discriminant D(Q), is the largest positive integer n that is locally represented by Q but not represented by Q always O_\varepsilon(D(Q)^{1+\varepsilon}) for every \varepsilon>0? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,033 | OWR-14211-008 | Indefinite Theta Series and Real Jacobi Representations | Can indefinite theta series formed from lattice sums over cones, together with modular completions annihilated by the real-Jacobi Casimir operator, be realized through principal-series representations of the real Jacobi group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,016 | 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-14211-008",
"literature-status:open",
"owr-year:2016"
] | Indefinite theta series have been connected to modular, mock, and Jacobi-form structures in important cases, but the exact connection to principal series of the real Jacobi group asked in the record is not established generally. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
},
{
"url": "https://doi.org/10.1007/s40687-021-00252-9",
"label": "Indefinite zeta functions and indefinite theta methods"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | Can indefinite theta series formed from lattice sums over cones, together with modular completions annihilated by the real-Jacobi Casimir operator, be realized through principal-series representations of the real Jacobi group? | Can indefinite theta series of the described type be connected to principal series representations of the real Jacobi group? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,034 | OWR-14211-009 | Chern Class Comparison for Arithmetic General Linear Groups | For which integers n is the natural morphism $\gamma_{n,\mathbb{Z}[1/2]}$ from Grothendieck's mod-2 Chern-class algebra to $H^*(GL_n(\mathbb{Z}[1/2]);\mathbb{F}_2)$ an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,016 | 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-14211-009",
"literature-status:partially-solved",
"owr-year:2016"
] | The comparison map is known to be an isomorphism through n equal to 3 and to fail for n at least 14; the intermediate range is not settled by the cited results, so the classification is partial. | [
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
},
{
"url": "https://doi.org/10.1112/blms/25.2.145",
"label": "Dwyer, Homology isomorphisms between algebraic groups made discrete"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | For which integers n is the natural morphism $\gamma_{n,\mathbb{Z}[1/2]}$ from Grothendieck's mod-2 Chern-class algebra to $H^*(GL_n(\mathbb{Z}[1/2]);\mathbb{F}_2)$ an isomorphism? | For which integers n is the natural morphism \gamma_{n,\mathbb Z[1/2]} from Grothendieck's mod-2 Chern-class algebra to H^*(GL_n(\mathbb Z[1/2]);\mathbb F_2) an isomorphism? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,035 | OWR-14211-010 | Formal Duality of Energy Minimizing Periodic Point Sets | Why do energy-minimizing periodic point sets appear to have the rare formal-duality property, namely equality of their averaged pair sums with the density-scaled Fourier-dual sums for every Schwartz function? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,016 | 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,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14211-010",
"literature-status:open",
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] | Formal duality has been formalized and partially classified in finite abelian groups, but no general theorem explains why the numerically observed energy minimizers should possess it; the explanatory question remains open. | [
{
"url": "https://doi.org/10.1016/j.jcta.2018.11.005",
"label": "Formal duality in finite abelian groups"
},
{
"url": "https://doi.org/10.4171/owr/2016/3",
"label": "Oberwolfach Report 3/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | Why do energy-minimizing periodic point sets appear to have the rare formal-duality property, namely equality of their averaged pair sums with the density-scaled Fourier-dual sums for every Schwartz function? | Why do energy-minimizing periodic point sets appear to have the rare formal-duality property, namely equality of their averaged pair sums with the density-scaled Fourier-dual sums for every Schwartz function? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,036 | OWR-14211-011 | Grothendieck–Serre Conjecture in Mixed Characteristic | Grothendieck–Serre conjecture: if $R$ is a regular local integral domain with fraction field $F$, then for every smooth reductive group scheme $G$ over $R$, the map $H^1_{\mathrm{et}}(R,G)\to H^1_{\mathrm{et}}(F,G)$ is injective. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154](https://doi.org/10.4171/owr/2016/3)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,016 | 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-14211-011",
"literature-status:partially-solved",
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] | The Grothendieck--Serre injectivity conjecture is proved for regular local rings containing a field and for several mixed-characteristic cases, including quasi-split unramified and constant reductive groups, but the unrestricted mixed-characteristic statement remains open. | [
{
"url": "https://doi.org/10.1090/tran/8490",
"label": "Fedorov, Grothendieck--Serre in mixed characteristic"
},
{
"url": "https://www.imo.universite-paris-saclay.fr/~kestutis.cesnavicius/split-unramified.pdf",
"label": "Cesnavicius, Grothendieck--Serre in the quasi-split unramified case"
},
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/3 | null | null | null | Grothendieck–Serre conjecture: if $R$ is a regular local integral domain with fraction field $F$, then for every smooth reductive group scheme $G$ over $R$, the map $H^1_{\mathrm{et}}(R,G)\to H^1_{\mathrm{et}}(F,G)$ is injective. | Grothendieck--Serre conjecture: if R is a regular local integral domain with fraction field F, then for every smooth reductive group scheme G over R, the map H^1_{\mathrm{et}}(R,G)\to H^1_{\mathrm{et}}(F,G) is injective. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Lattices and Applications in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/3, pp. 87--154 |
30,003,037 | OWR-14212-001 | Higher-Order Principal Components on Riemannian Manifolds | Can higher-order derivative constructions of barycentric or affine subspaces, and the associated principal-component analysis, be generalized from spheres to arbitrary Riemannian manifolds using sub-Riemannian geometry? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214](https://doi.org/10.4171/owr/2016/4)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,016 | 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-14212-001",
"literature-status:open",
"owr-year:2016"
] | The record states a conjectural extension of the PCA and unexplained-variance framework to higher derivatives on general manifolds; no general theorem validating that conjecture was identified. | [
{
"url": "https://doi.org/10.4171/owr/2016/4",
"label": "Oberwolfach Report 4/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/4 | null | null | null | Can higher-order derivative constructions of barycentric or affine subspaces, and the associated principal-component analysis, be generalized from spheres to arbitrary Riemannian manifolds using sub-Riemannian geometry? | Conjecture: higher-order derivative constructions of barycentric or affine subspaces, and the associated principal-component analysis, can be generalized from spheres to general Riemannian manifolds using sub-Riemannian geometry. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214 |
30,003,038 | OWR-14212-002 | Scale-Invariant Distances between Curves in Shape Space | How should shapes such as cardiac configurations at different times or different hand postures be compared, and what scale-invariant distance measure should be used along the resulting curves in shape space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214](https://doi.org/10.4171/owr/2016/4)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,016 | 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"
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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-14212-002",
"literature-status:partially-solved",
"owr-year:2016"
] | Elastic shape analysis supplies practical Riemannian distances for curves, with invariance under reparameterization and standard shape transformations, but no unique universal scale-invariant distance answers the broad natural-shape question. | [
{
"url": "https://pubmed.ncbi.nlm.nih.gov/20921581/",
"label": "Srivastava, Klassen, Joshi, and Jermyn, Shape analysis of elastic curves"
},
{
"url": "https://doi.org/10.4171/owr/2016/4",
"label": "Oberwolfach Report 4/2016"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/4 | null | null | null | How should shapes such as cardiac configurations at different times or different hand postures be compared, and what scale-invariant distance measure should be used along the resulting curves in shape space? | How should shapes such as cardiac configurations at different times or different hand postures be compared, and what scale-invariant distance measure should be used along the resulting curves in shape space? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214 |
30,003,039 | OWR-14212-003 | Discretization of Elastic Curves in Shape Spaces | How can elastic curves be discretized in infinite-dimensional shape spaces in a way compatible with the continuous elastic-bending variational problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214](https://doi.org/10.4171/owr/2016/4)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,016 | 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"
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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-14212-003",
"literature-status:partially-solved",
"owr-year:2016"
] | Variational time discretization, discrete curve models, and convergence results provide principled discretizations for important infinite-dimensional shape spaces, but not a single general discretization for every elastic shape space. | [
{
"url": "https://arxiv.org/abs/1210.2097",
"label": "Rumpf and Wirth, Variational time discretization of geodesic calculus"
},
{
"url": "https://arxiv.org/abs/1703.05107",
"label": "A discrete framework for matching manifold-valued curves"
},
{
"url": "https://doi.org/10.4171/owr/2016/4... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/4 | null | null | null | How can elastic curves be discretized in infinite-dimensional shape spaces in a way compatible with the continuous elastic-bending variational problem? | How can elastic curves be discretized in infinite-dimensional shape spaces in a way compatible with the continuous elastic-bending variational problem? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/4, pp. 155--214 |
30,003,040 | OWR-14213-003 | Serre Conjecture II for Type $E_7$ Groups | Serre's conjecture II in type $E_7$: for a perfect field $k$ of cohomological dimension at most 2 and a semisimple simply connected group $G$ of type $E_7$ over $k$, is $H^1(k,G)$ trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | open | null | 2,016 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14213-003",
"literature-status:open",
"owr-year:2016"
] | Serre Conjecture II is proved in several classical and exceptional cases, but the survey still identifies unresolved exceptional cases including E8 and related remaining cases; the extracted general claim is therefore open. | [
{
"url": "https://math.univ-lyon1.fr/homes-www/gille/publis/hyderabad.pdf",
"label": "Gille survey on Serre Conjecture II"
},
{
"url": "https://doi.org/10.4171/owr/2016/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | Serre's conjecture II in type $E_7$: for a perfect field $k$ of cohomological dimension at most 2 and a semisimple simply connected group $G$ of type $E_7$ over $k$, is $H^1(k,G)$ trivial? | Serre's conjecture II in the type-E_7 case: for a perfect field k of cohomological dimension at most 2 and a semisimple simply connected group G of type E_7 over k, is H^1(k,G) trivial? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,041 | OWR-14213-006 | Stanley–Stembridge Chromatic Symmetric Function Conjecture | Stanley–Stembridge conjecture: if $G=G(m)$ is the incomparability graph associated with a Hessenberg function $m$, then its chromatic symmetric function $X_G(x)$ is a nonnegative sum of elementary symmetric functions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | solved | null | 2,016 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "resolution",
"evidence": "published"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14213-006",
"literature-status:open",
"owr-year:2016"
] | Hikita proves the Stanley–Stembridge conjecture by giving nonnegative elementary-symmetric-function coefficients for the chromatic quasisymmetric function of every unit interval graph. This covers the Hessenberg formulation in the record.
**What remains.** The stated e-positivity question is resolved. | [
{
"url": "https://arxiv.org/abs/2410.12758",
"label": "T. Hikita, A proof of the Stanley–Stembridge conjecture"
},
{
"url": "https://doi.org/10.1090/jams/1090",
"label": "Hikita — Journal of the American Mathematical Society version"
},
{
"url": "https://doi.org/10.4171/owr/2016/5",
... | 2026-09-28T00:00:00 | T. Hikita, A proof of the Stanley–Stembridge conjecture: https://arxiv.org/abs/2410.12758
Hikita — Journal of the American Mathematical Society version: https://doi.org/10.1090/jams/1090
Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265: https://d... | https://doi.org/10.4171/owr/2016/5 | null | null | null | Stanley–Stembridge conjecture: if $G=G(m)$ is the incomparability graph associated with a Hessenberg function $m$, then its chromatic symmetric function $X_G(x)$ is a nonnegative sum of elementary symmetric functions. | Stanley--Stembridge conjecture: if G=G(m) is the incomparability graph associated with a Hessenberg function m, then its chromatic symmetric function X_G(x) is a nonnegative sum of elementary symmetric functions. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,042 | OWR-14213-008 | Schubert Classes in the Gamma Filtration | For $n\geq 8$, the special Schubert class $e_n\in K(X_{F(S)})$ does not belong to term $n+1-\lfloor(n+1)/2\rfloor$ of the gamma filtration. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14213-008",
"literature-status:open",
"owr-year:2016"
] | The special Schubert-class gamma-filtration assertion remains stated as a conjecture in Karpenko's primary treatment; no verified later proof of this exact claim was found. | [
{
"url": "https://sites.ualberta.ca/~karpenko/publ/a16i3.pdf",
"label": "Karpenko on 16-dimensional forms"
},
{
"url": "https://doi.org/10.4171/owr/2016/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | For $n\geq 8$, the special Schubert class $e_n\in K(X_{F(S)})$ does not belong to term $n+1-\lfloor(n+1)/2\rfloor$ of the gamma filtration. | For n\geq 8, the special Schubert class e_n\in K(X_{F(S)}) does not belong to term n+1-\lfloor(n+1)/2\rfloor of the gamma filtration. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,043 | OWR-14213-009 | Exact Indices of Orthogonal Grassmannians | For every even $m\geq 18$, the index of the $\lfloor m/4\rfloor$-th orthogonal Grassmannian of any generic m-dimensional quadratic form $\varphi/F$ in $I^3_q$ is $2^{\lfloor m/4\rfloor}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14213-009",
"literature-status:open",
"owr-year:2016"
] | The stated exact index formula for the orthogonal Grassmannian is explicitly left as a conjecture in the primary source; related work on I- and quadratic-form invariants does not verify this formula. | [
{
"url": "https://sites.ualberta.ca/~karpenko/publ/a16i3.pdf",
"label": "Karpenko on 16-dimensional forms"
},
{
"url": "https://doi.org/10.4171/owr/2016/5",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | For every even $m\geq 18$, the index of the $\lfloor m/4\rfloor$-th orthogonal Grassmannian of any generic m-dimensional quadratic form $\varphi/F$ in $I^3_q$ is $2^{\lfloor m/4\rfloor}$. | For every even m\geq 18, the index of the floor(m/4)-th orthogonal Grassmannian of any generic m-dimensional quadratic form \varphi/F in I^3_q is 2^{\lfloor m/4\rfloor}. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,044 | OWR-14213-011 | Kato Cohomology Kernels of Quadratic Pfister Forms | Let $Q=\langle 1,a_1\rangle\otimes\cdots\otimes\langle 1,a_m\rangle\otimes[1,b]$ be an anisotropic quadratic Pfister form over $F$. Is the Kato-cohomology kernel $H_2^{n+1}(F(Q)/F)$ equal to $b\,\frac{d a_1}{a_1}\wedge\cdots\wedge\frac{d a_m}{a_m}\wedge\nu_F(n-m)$ when $n\geq m$, and zero when $n<m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14213-011",
"literature-status:open",
"owr-year:2016"
] | The report records positive special cases and a conditional theorem, while the displayed Kato-cohomology equality for general Pfister data remains a question; the related kernel computations do not prove the full statement. | [
{
"url": "https://doi.org/10.4171/owr/2016/5",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2015.11.022",
"label": "Aravire--Laghribi--O'Ryan kernel computations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | Let $Q=\langle 1,a_1\rangle\otimes\cdots\otimes\langle 1,a_m\rangle\otimes[1,b]$ be an anisotropic quadratic Pfister form over $F$. Is the Kato-cohomology kernel $H_2^{n+1}(F(Q)/F)$ equal to $b\,\frac{d a_1}{a_1}\wedge\cdots\wedge\frac{d a_m}{a_m}\wedge\nu_F(n-m)$ when $n\geq m$, and zero when $n<m$? | Let Q=\langle1,a_1\rangle\otimes\cdots\otimes\langle1,a_m\rangle\otimes[1,b] be an anisotropic quadratic Pfister form over F. Is H^{2n+1}(F(Q)/F) equal to the stated symbol involving b, a_1,\ldots,a_m and \nu_F(n-m) when n\geq m, and equal to 0 when n<m? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,045 | OWR-14213-012 | Cohomology Kernels for Inseparable Pfister Composita | Let $L/F$ be a finite purely inseparable extension, let $B$ be an anisotropic bilinear Pfister form over $F$, and let $K/F$ be a separable quadratic extension, with $B$ remaining anisotropic over $L$. Is $H_2^{n+1}(L\mathbin{\cdot}K(B)/F)=H_2^{n+1}(L/F)+H_2^{n+1}(K/F)+H_2^{n+1}(F(B)/F)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14213-012",
"literature-status:open",
"owr-year:2016"
] | The compositum-of-kernels equality in characteristic 2 is still posed in the report; published bilinear-Pfister kernel results cover important cases but do not establish the full asserted equality. | [
{
"url": "https://doi.org/10.4171/owr/2016/5",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2015.11.022",
"label": "Aravire--Laghribi--O'Ryan kernel computations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | Let $L/F$ be a finite purely inseparable extension, let $B$ be an anisotropic bilinear Pfister form over $F$, and let $K/F$ be a separable quadratic extension, with $B$ remaining anisotropic over $L$. Is $H_2^{n+1}(L\mathbin{\cdot}K(B)/F)=H_2^{n+1}(L/F)+H_2^{n+1}(K/F)+H_2^{n+1}(F(B)/F)$? | Let L/F be finite purely inseparable, B an anisotropic bilinear Pfister form over F, and K/F separable quadratic, with B anisotropic over L. Is H^{2n+1}(L\mathbin{\cdot}K(B)/F)=H^{2n+1}(L/F)+H^{2n+1}(K/F)+H^{2n+1}(F(B)/F)? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,046 | OWR-14213-013 | Orientable Cohomology Theories with Universal Chern Operations | For a generalized cohomology theory $K$, is there a notion of $K$-orientable theories equipped with $K$-analogue Chern-class operations that freely generate all operations into an oriented theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265](https://doi.org/10.4171/owr/2016/5)
## Literature review (checke... | 3 | partially_solved | null | 2,016 | 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-14213-013",
"literature-status:partially-solved",
"owr-year:2016"
] | A general formulation of K-orientability is not supplied, but Sechin constructs the predicted Chern operations from Morava K-theory to Chow groups and to p^n-typical oriented theories, including free-generation results under stated hypotheses. | [
{
"url": "https://arxiv.org/abs/1605.04444",
"label": "Sechin on Morava K-theory Chern classes"
},
{
"url": "https://arxiv.org/abs/1805.09050",
"label": "Sechin on p^n-typical theories"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/5 | null | null | null | For a generalized cohomology theory $K$, is there a notion of $K$-orientable theories equipped with $K$-analogue Chern-class operations that freely generate all operations into an oriented theory? | For a generalized cohomology theory K, is there a notion of K-orientable theories equipped with K-analogue Chern-class operations that freely generate all operations into an oriented theory? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Algebraic Cobordism and Projective Homogeneous Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/5, pp. 215--265 |
30,003,047 | OWR-14214-001 | Dynamical Reconstruction from Bare Crossed Product Banach Algebras | Can the dynamics $I_K$ acting on $X_K$ be reconstructed from the non-involutive Banach algebra obtained as the closure of $C(X_K)\rtimes_{\mathrm{alg}} I_K$ in its natural bounded-operator representation; can this be done without preserving the MASA $C(X_K)$; and can K be reconstructed from $A_K$ without using $\sigma_... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Spaces and Noncommutative Geometry in Interaction (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/6, pp. 267--295](https://doi.org/10.4171/owr/2016/6)
## Literatu... | 3 | partially_solved | null | 2,016 | 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-14214-001",
"literature-status:partially-solved",
"owr-year:2016"
] | Field and dynamical reconstruction is proved when the relevant diagonal algebra or time evolution is respected, but reconstruction from the bare Banach algebra, without the MASA, and from A_K without sigma_K remains open in the extracted formulation. | [
{
"url": "https://doi.org/10.4171/owr/2016/6",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1009.0736",
"label": "Cornelissen--Marcolli QSM and anabelian geometry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/6 | null | null | null | Can the dynamics $I_K$ acting on $X_K$ be reconstructed from the non-involutive Banach algebra obtained as the closure of $C(X_K)\rtimes_{\mathrm{alg}} I_K$ in its natural bounded-operator representation; can this be done without preserving the MASA $C(X_K)$; and can K be reconstructed from $A_K$ without using $\sigma_... | Can the dynamics I_K acting on X_K be reconstructed from the non-involutive Banach algebra obtained as the closure of C(X_K)\rtimes_{\mathrm{alg}} I_K in its natural bounded-operator representation; can this be done without preserving the MASA C(X_K); and can K be reconstructed from A_K without using \sigma_K? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Mini-Workshop: Operator Spaces and Noncommutative Geometry in Interaction (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/6, pp. 267--295 |
30,003,048 | OWR-14214-002 | Factorization of Equivariant Dirac Operators and Spectral Triples | What should it mean for an equivariant Dirac operator on a principal G-bundle $M\to M/G$ to factor into Dirac operators on G and M/G, and how can this factorization be generalized to noncommutative equivariant spectral triples? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Operator Spaces and Noncommutative Geometry in Interaction (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/6, pp. 267--295](https://doi.org/10.4171/owr/2016/6)
## Literatu... | 3 | open | null | 2,016 | 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-14214-002",
"literature-status:open",
"owr-year:2016"
] | The extracted question asks for a general meaning and framework for factorisation of Dirac operators; the cited discussion formulates this as a research direction and does not provide a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2016/6",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/6 | null | null | null | What should it mean for an equivariant Dirac operator on a principal G-bundle $M\to M/G$ to factor into Dirac operators on G and M/G, and how can this factorization be generalized to noncommutative equivariant spectral triples? | What should it mean for an equivariant Dirac operator on a principal G-bundle M\to M/G to factor into Dirac operators on G and M/G, and how can this factorization be generalized to noncommutative equivariant spectral triples? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Mini-Workshop: Operator Spaces and Noncommutative Geometry in Interaction (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/6, pp. 267--295 |
30,003,049 | OWR-14215-001 | Polynomial Algorithms for Mean-Payoff Games and Linear Programming | Does there exist a polynomial-time algorithm for solving mean-payoff games? Does there exist a strongly polynomial algorithm for linear programming? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14215-001",
"literature-status:open",
"owr-year:2016"
] | Mean-payoff games remain in NP intersection coNP without a known polynomial-time algorithm, and the corresponding strongly polynomial linear-programming question also remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.ic.2015.03.010",
"label": "mean-payoff games survey paper"
},
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol334-icalp2025/html/LIPIcs.ICALP.2025.145/LIPIcs.ICALP.2025.145.html",
"label": "ICALP 2025 paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | Does there exist a polynomial-time algorithm for solving mean-payoff games? Does there exist a strongly polynomial algorithm for linear programming? | Does there exist a polynomial-time algorithm for solving mean-payoff games, and does there exist a strongly polynomial algorithm for linear programming (Smale Problem 9)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,050 | OWR-14215-002 | Koopman Operators for Switched Infinite-Dimensional Systems | Can the joint spectral quantities and stabilizability radius of switched linear systems be generalized to infinite-dimensional linear operators such as Koopman operators, and can a canonical Koopman operator be defined for a given switching system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14215-002",
"literature-status:open",
"owr-year:2016"
] | The report's proposed infinite-dimensional and unique Koopman construction for switching systems is not canonical in general; later switched-system work gives applications but does not settle the extracted existence and uniqueness questions. | [
{
"url": "https://doi.org/10.4171/owr/2016/7",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.sysconle.2025.106340",
"label": "2025 switched-systems Koopman paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | Can the joint spectral quantities and stabilizability radius of switched linear systems be generalized to infinite-dimensional linear operators such as Koopman operators, and can a canonical Koopman operator be defined for a given switching system? | Can the joint spectral quantities and stabilizability radius of switched linear systems be generalized to infinite-dimensional linear operators such as Koopman operators, and can a canonical Koopman operator be defined for a given switching system? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,051 | OWR-14215-003 | State-Dependent Koopman Operators for Switching Systems | Let $\mathcal M=\{A_0,A_1\}$, let $\widehat{\mathcal M}=\mathcal M/\rho(\mathcal M)$, and suppose $\widehat{\mathcal M}^{*}$ is bounded. Define
$$
f(x)=\begin{cases}
A_0x,&\sup_{A\in\widehat{\mathcal M}^{*}}\lVert Ax\rVert_2=\sup_{A\in\widehat{\mathcal M}^{*}}\lVert AA_0x\rVert_2,\\
A_1x,&\text{otherwise}.
\end{cases}
... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14215-003",
"literature-status:open",
"owr-year:2016"
] | Whether the proposed Koopman operator is the right information-preserving definition for a switching system remains a modeling question; current applications do not establish a general affirmative theorem. | [
{
"url": "https://doi.org/10.4171/owr/2016/7",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.sysconle.2025.106340",
"label": "2025 switched-systems Koopman paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | Let $\mathcal M=\{A_0,A_1\}$, let $\widehat{\mathcal M}=\mathcal M/\rho(\mathcal M)$, and suppose $\widehat{\mathcal M}^{*}$ is bounded. Define
$$
f(x)=\begin{cases}
A_0x,&\sup_{A\in\widehat{\mathcal M}^{*}}\lVert Ax\rVert_2=\sup_{A\in\widehat{\mathcal M}^{*}}\lVert AA_0x\rVert_2,\\
A_1x,&\text{otherwise}.
\end{cases}
... | For a switching system, is the Koopman operator induced by the proposed state-dependent map that selects between the matrices A_0 and A_1 the right definition, and does it provide useful information about the system? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,052 | OWR-14215-004 | Spectra of Koopman Operators for Linear Maps | For a matrix $A$ acting on the unit ball $U\subseteq\mathbb C^k$, how is the spectrum, and especially the point spectrum, of the Koopman operator $T_A$ on $C(U)$ determined by the spectrum of $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,016 | 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-14215-004",
"literature-status:partially-solved",
"owr-year:2016"
] | The report proves point-spectrum formulas for Koopman operators in several linear systems on a unit ball, but no general relation between the Koopman spectrum and the dynamics spectrum is established. | [
{
"url": "https://doi.org/10.4171/owr/2016/7",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | For a matrix $A$ acting on the unit ball $U\subseteq\mathbb C^k$, how is the spectrum, and especially the point spectrum, of the Koopman operator $T_A$ on $C(U)$ determined by the spectrum of $A$? | For a matrix A acting on the unit ball U of C^k, how is the spectrum, in particular the point spectrum, of the Koopman operator T_A on C(U) determined by the spectrum of A? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,053 | OWR-14215-005 | Observable Spaces Capturing Koopman Dynamics | What space of observables $F$ should be chosen for a Koopman operator so that its spectral properties meaningfully encode the dynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14215-005",
"literature-status:open",
"owr-year:2016"
] | The appropriate observable space is unresolved in general: the report identifies information loss in L2 and an oversized spectrum in C of K, while constructing a natural space only for a hyperbolic-attractor setting. | [
{
"url": "https://doi.org/10.4171/owr/2016/7",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | What space of observables $F$ should be chosen for a Koopman operator so that its spectral properties meaningfully encode the dynamics? | What space of observables F should be chosen for a Koopman operator so that its spectral properties meaningfully encode the dynamics? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,054 | OWR-14215-006 | Pointwise Convergence of Koopman Laplace Averages | For generalized Laplace averages used to construct Koopman eigenfunctions, does the known norm convergence also hold pointwise? For which other observable spaces, especially spaces with readily computable norms, does the same eigenfunction construction remain valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340](https://doi.org/10.4171/owr/2016/7)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14215-006",
"literature-status:open",
"owr-year:2016"
] | The source explicitly states that pointwise convergence of the generalized Laplace averages remains open and asks whether other observable spaces yield a usable norm-convergence result. | [
{
"url": "https://doi.org/10.4171/owr/2016/7",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/7 | null | null | null | For generalized Laplace averages used to construct Koopman eigenfunctions, does the known norm convergence also hold pointwise? For which other observable spaces, especially spaces with readily computable norms, does the same eigenfunction construction remain valid? | For the generalized Laplace-average construction of Koopman eigenfunctions, does the convergence hold pointwise, and are there other spaces of observables with easier-to-compute norms for which the construction remains valid? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Applied Koopmanism (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/7, pp. 297--340 |
30,003,055 | OWR-14216-001 | Comparative Accuracy of Spline and Finite-Element Bases | For numerical approximation, how accurate and robust are maximally continuous splines, minimally continuous splines, divergence-conforming splines, and curl-conforming splines; how do splines compare with classical finite elements; how do the answers depend on dimension; which polynomial and Fourier bases are best for ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Isogeometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/8, pp. 341--385](https://doi.org/10.4171/owr/2016/8)
## Literature review... | 3 | open | null | 2,016 | 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-14216-001",
"literature-status:open",
"owr-year:2016"
] | The extracted item is a broad collection of unresolved numerical-analysis comparisons across spline, finite-element, divergence, curl, tensor-product, and Fourier settings; no single theorem answers the full list. | [
{
"url": "https://doi.org/10.4171/owr/2016/8",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.cma.2023.116659",
"label": "recent spline-basis comparison"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/8 | null | null | null | For numerical approximation, how accurate and robust are maximally continuous splines, minimally continuous splines, divergence-conforming splines, and curl-conforming splines; how do splines compare with classical finite elements; how do the answers depend on dimension; which polynomial and Fourier bases are best for ... | For numerical approximation, how accurate and robust are maximally continuous splines, minimally continuous splines, divergence-conforming splines, and curl-conforming splines; how do splines compare with classical finite elements; how do the answers depend on dimension; which polynomial and Fourier bases are best for ... | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Foundations of Isogeometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/8, pp. 341--385 |
30,003,056 | OWR-14216-002 | General Quadrature for Isogeometric Galerkin Methods | Can a general and effective quadrature solution be developed for Galerkin-based isogeometric analysis methods? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Isogeometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/8, pp. 341--385](https://doi.org/10.4171/owr/2016/8)
## Literature review... | 3 | open | null | 2,016 | 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-14216-002",
"literature-status:open",
"owr-year:2016"
] | Special and optimized quadrature rules now exist, including consistency conditions, but the general effective quadrature solution for Galerkin-based IGA requested in the record remains unresolved. | [
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0045782514003235",
"label": "Galerkin IGA quadrature paper"
},
{
"url": "https://doi.org/10.1016/j.cma.2024.117395",
"label": "2024 consistent-integration paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/8 | null | null | null | Can a general and effective quadrature solution be developed for Galerkin-based isogeometric analysis methods? | Can a general and effective quadrature solution be developed for Galerkin-based isogeometric analysis methods? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Mathematical Foundations of Isogeometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/8, pp. 341--385 |
30,003,057 | OWR-14217-003 | Hemisphere Partition Functions and Stability Across GLSM Phases | In the GLSM setting, is the hemisphere partition function $Z_{D^2}:K_0(D)\to\mathbb C$ a central-charge function for a Bridgeland stability condition on $D$, and for the grade-restriction subcategory $W_n$ are the phase quotient categories $D_{\zeta\gg0}$ and $D_{\zeta\ll0}$ related to $W_n$ by the conjectured commutin... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topological Recursion and TQFTs (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/9, pp. 387--448](https://doi.org/10.4171/owr/2016/9)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,016 | 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-14217-003",
"literature-status:open",
"owr-year:2016"
] | The report presents the hemisphere partition function as conjectural central charge data for a Bridgeland stability condition; window and grade-restriction results now cover important examples, but the general stability assertion remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2016/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2402.07109",
"label": "GLSM brane transport"
},
{
"url": "https://arxiv.org/abs/math/0212237",
"label": "Bridgeland stability conditions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/9 | null | null | null | In the GLSM setting, is the hemisphere partition function $Z_{D^2}:K_0(D)\to\mathbb C$ a central-charge function for a Bridgeland stability condition on $D$, and for the grade-restriction subcategory $W_n$ are the phase quotient categories $D_{\zeta\gg0}$ and $D_{\zeta\ll0}$ related to $W_n$ by the conjectured commutin... | In the GLSM setting, is the hemisphere partition function Z_{D^2}:K_0(D)\to C a central-charge function for a Bridgeland stability condition on D, and for the grade-restriction subcategory W_n are the phase quotient categories D_{\zeta\gg0} and D_{\zeta\ll0} related to W_n by the conjectured commuting equivalences? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topological Recursion and TQFTs (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/9, pp. 387--448 |
30,003,058 | OWR-14218-001 | Donovan’s Finiteness Conjecture for Fixed Defect Groups | For a fixed finite $p$-group $P$, are there only finitely many Morita-equivalence classes of block algebras of finite groups whose defect groups are isomorphic to $P$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | open | null | 2,016 | 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-14218-001",
"literature-status:open",
"owr-year:2016"
] | Donovan's conjecture is verified for several defect-group families, including abelian and Suzuki 2-groups, but no general proof is known for all finite p-groups. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1803.03539",
"label": "abelian defect groups"
},
{
"url": "https://arxiv.org/abs/2401.04028",
"label": "Suzuki 2-groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | For a fixed finite $p$-group $P$, are there only finitely many Morita-equivalence classes of block algebras of finite groups whose defect groups are isomorphic to $P$? | For a fixed finite p-group P, are there only finitely many Morita-equivalence classes of block algebras of finite groups whose defect groups are isomorphic to P? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,059 | OWR-14218-002 | Hochschild Regularity Under Separable Equivalence | Do separable equivalences between symmetric $k$-algebras preserve the Castelnuovo–Mumford regularity of Hochschild cohomology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | open | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-14218-002",
"literature-status:open",
"owr-year:2016"
] | The general invariance of Castelnuovo--Mumford regularity of Hochschild cohomology under separable equivalence remains an explicitly recorded open question; known zero-regularity theorems concern group and block cases, not arbitrary symmetric algebras. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://openaccess.city.ac.uk/id/eprint/1949/1/1211.5999v1.pdf",
"label": "Tate--Hochschild regularity"
},
{
"url": "https://doi.org/10.1017/CBO9781316227343.020",
"label": "regularity for block algebr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | Do separable equivalences between symmetric $k$-algebras preserve the Castelnuovo–Mumford regularity of Hochschild cohomology? | Do separable equivalences between symmetric k-algebras preserve, in general, the Castelnuovo--Mumford regularity of Hochschild cohomology? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,060 | OWR-14218-004 | Koszulness from Vanishing Higher Koszul Homology | For a quadratic algebra $A$, is $A$ Koszul if and only if its higher Koszul homology vanishes in positive degrees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | open | null | 2,016 | 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-14218-004",
"literature-status:open",
"owr-year:2016"
] | The Koszul-calculus paper proves the vanishing implication for Koszul quadratic algebras and records the converse as a conjecture; examples support it, but no general proof was located. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1512.00183",
"label": "Koszul calculus"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869318306239",
"label": "higher Koszul calculus"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | For a quadratic algebra $A$, is $A$ Koszul if and only if its higher Koszul homology vanishes in positive degrees? | For a quadratic algebra A, is A Koszul if and only if its higher Koszul homology vanishes in positive degrees? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,061 | OWR-14218-005 | Invariant and Smash-Product Hochschild Cohomology | When $\operatorname{char}(k)$ divides $|G|$, how are the graded algebras $\operatorname{HH}^*(A,M)^G$ and $\operatorname{HH}^*(A\# kG,M)$ related? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | partially_solved | null | 2,016 | 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-14218-005",
"literature-status:partially-solved",
"owr-year:2016"
] | The modular spectral sequence gives inequalities and collapse criteria for cyclic p-groups and certain extensions, while the general relation between invariant Hochschild cohomology and smash-product Hochschild cohomology remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1511.05388",
"label": "smash products in the nonsemisimple case"
},
{
"url": "https://arxiv.org/abs/1401.3551",
"label": "smash-product spectral sequences"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | When $\operatorname{char}(k)$ divides $|G|$, how are the graded algebras $\operatorname{HH}^*(A,M)^G$ and $\operatorname{HH}^*(A\# kG,M)$ related? | When char(k) divides |G|, how are the graded algebras HH^*(A,M)^G and HH^*(A\# kG,M) related? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,062 | OWR-14218-006 | Cartan Determinant Conjecture | If $A$ is an Artin algebra of finite global dimension, must its Cartan determinant satisfy $\det C(A)=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | open | null | 2,016 | 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-14218-006",
"literature-status:open",
"owr-year:2016"
] | The Cartan determinant conjecture still asks whether a finite-global-dimension Artin algebra must have Cartan determinant one; it is proved for many classes but remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1410.3223",
"label": "reduction by n-recollements"
},
{
"url": "https://arxiv.org/abs/2501.09447",
"label": "recent homological-conjectures paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | If $A$ is an Artin algebra of finite global dimension, must its Cartan determinant satisfy $\det C(A)=1$? | If A is an artin algebra of finite global dimension, must its Cartan determinant satisfy det C(A)=1? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,063 | OWR-14218-007 | Intrinsic Gerstenhaber Brackets from Projective Resolutions | Given a projective resolution $P\to A\to0$ of $A$ over $A^e$, how can the Gerstenhaber Lie bracket on $\operatorname{HH}^*(A)$ be expressed in terms of $P$, and how can one intrinsically define a bimap on $D(A^e)(A,\Sigma^*A)$ that corresponds to this bracket under $\operatorname{HH}^*(A)\cong D(A^e)(A,\Sigma^*A)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506](https://doi.org/10.4171/owr/2016/10)
## Literature review (chec... | 3 | partially_solved | null | 2,016 | 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-14218-007",
"literature-status:partially-solved",
"owr-year:2016"
] | The Gerstenhaber bracket can now be computed from an arbitrary projective bimodule resolution for the action of HH^1, and extension-theoretic descriptions exist, but the full intrinsic bimap requested in the record is not established in complete generality. | [
{
"url": "https://doi.org/10.4171/owr/2016/10",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2016.10.015",
"label": "bracket from projective resolutions"
},
{
"url": "https://doi.org/10.1090/S0002-9949-03-03373-7",
"label": "extension interpretation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/10 | null | null | null | Given a projective resolution $P\to A\to0$ of $A$ over $A^e$, how can the Gerstenhaber Lie bracket on $\operatorname{HH}^*(A)$ be expressed in terms of $P$, and how can one intrinsically define a bimap on $D(A^e)(A,\Sigma^*A)$ that corresponds to this bracket under $\operatorname{HH}^*(A)\cong D(A^e)(A,\Sigma^*A)$? | Given a projective resolution P\to A\to0 of A over A^e, how can the Gerstenhaber Lie bracket on HH^*(A) be expressed in terms of P, and how can one intrinsically define a bimap on D(A^e)(A,\Sigma^*A) that corresponds to this bracket under HH^*(A)\cong D(A^e)(A,\Sigma^*A)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Hochschild Cohomology in Algebra, Geometry, and Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/10, pp. 449--506 |
30,003,064 | OWR-14219-005 | Classification of Elliptic Affine Spheres and Hemispheres | Why are complete elliptic affine spheres much rarer than hyperbolic affine spheres, and can replacing completeness by the affine-hemisphere condition provide a meaningful classification? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565](https://doi.org/10.4171/owr/2016/11)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,016 | 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-14219-005",
"literature-status:open",
"owr-year:2016"
] | The record proposes affine hemispheres as a way to study the scarcity of complete elliptic affine spheres, but it contains no classification theorem resolving the broader existence and classification question. | [
{
"url": "https://doi.org/10.4171/owr/2016/11",
"label": "OWR report"
},
{
"url": "https://www.weizmann.ac.il/math/klartag/sites/math.klartag/files/uploads/hemi_paper.pdf",
"label": "affine hemispheres"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/11 | null | null | null | Why are complete elliptic affine spheres much rarer than hyperbolic affine spheres, and can replacing completeness by the affine-hemisphere condition provide a meaningful classification? | Why are complete elliptic affine spheres much rarer than hyperbolic affine spheres, and can replacing completeness by the affine-hemisphere condition provide a meaningful classification? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565 |
30,003,065 | OWR-14219-006 | Polytope Approximation in Surface-Area Deviation | How well can a convex body be approximated by a polytope, particularly in symmetric surface-area deviation as a function of the number of vertices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565](https://doi.org/10.4171/owr/2016/11)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,016 | 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-14219-006",
"literature-status:partially-solved",
"owr-year:2016"
] | Sharp asymptotic rates are known for many volume, Hausdorff, surface-area, and random-approximation models, but the broad approximation question across arbitrary bodies, metrics, and positioning remains model-dependent and incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2016/11",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1007/s10959-016-0701-9",
"label": "surface-area deviation"
},
{
"url": "https://doi.org/10.1017/9781009701761.022",
"label": "polytopal approximation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/11 | null | null | null | How well can a convex body be approximated by a polytope, particularly in symmetric surface-area deviation as a function of the number of vertices? | How well can a convex body be approximated by a polytope, particularly in symmetric surface-area deviation as a function of the number of vertices? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565 |
30,003,066 | OWR-14219-009 | Intrinsic-Volume Deficits of Random Spherical Polytopes | Let $K$ be a spherically convex body in an open hemisphere and $P_n$ the spherical convex hull of $n$ independent uniform random points of $K$. Is $\mathbb E[U_j(K)-U_j(P_n)]$ of order $n^{-(d+1-j)}$ as $n\to\infty$ for every $j=1,\ldots,d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565](https://doi.org/10.4171/owr/2016/11)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,016 | 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-14219-009",
"literature-status:partially-solved",
"owr-year:2016"
] | The conjectured n^{-(d+1-j)} expectation scale is established in important smooth or rolling-ball settings and for several intrinsic volumes, while the report notes that precise asymptotic relations for the remaining j are not known in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2016/11",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1007/s10998-008-8143-4",
"label": "expected intrinsic volumes"
},
{
"url": "https://arxiv.org/abs/1103.4978",
"label": "boundary random polytopes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/11 | null | null | null | Let $K$ be a spherically convex body in an open hemisphere and $P_n$ the spherical convex hull of $n$ independent uniform random points of $K$. Is $\mathbb E[U_j(K)-U_j(P_n)]$ of order $n^{-(d+1-j)}$ as $n\to\infty$ for every $j=1,\ldots,d$? | Let K be a spherically convex body in an open hemisphere and P_n the spherical convex hull of n independent uniform random points of K. Is E[U_j(K)-U_j(P_n)] of order n^{-(d+1-j)} as n\to\infty for every j=1,\ldots,d? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565 |
30,003,067 | OWR-14219-010 | Thin-Shell Conjecture for Schatten Balls | For the unit balls of the Schatten classes $S_p^n$, does the thin-shell conjecture hold for the remaining values of $p$ not covered by the known large-$p$ results? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565](https://doi.org/10.4171/owr/2016/11)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,016 | 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-14219-010",
"literature-status:open",
"owr-year:2016"
] | For Schatten balls the thin-shell variance is controlled in large-p ranges, but the report leaves the remaining p as an explicit question and no general resolution of those ranges was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/11",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2303.14938",
"label": "thin-shell and slicing progress"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/11 | null | null | null | For the unit balls of the Schatten classes $S_p^n$, does the thin-shell conjecture hold for the remaining values of $p$ not covered by the known large-$p$ results? | For the unit balls of the Schatten classes S_p^n, does the thin-shell conjecture hold for the remaining values of p not covered by the known large-p results? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Asymptotic Geometric Analysis (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/11, pp. 507--565 |
30,003,068 | OWR-14221-001 | Existence of Global Monomial Orders for PBW Bases | For a simple finite-dimensional Lie algebra $\mathfrak g$, is the set $S_{\mathrm{gm}}$ of global monomial degrees nonempty? For every simply laced simple $\mathfrak g$, is $S_{\mathrm{gm}}\cap D^q_{w_0}$ nonempty for some reduced decomposition $w_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | partially_solved | null | 2,016 | 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-14221-001",
"literature-status:partially-solved",
"owr-year:2016"
] | The nonemptiness conjecture for the PBW parameter set is proved for several Lie types listed in the report, but the asserted result for every simple Lie algebra and the stronger simply-laced statement remain unproved in general. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1510.02295",
"label": "essential bases and toric degenerations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | For a simple finite-dimensional Lie algebra $\mathfrak g$, is the set $S_{\mathrm{gm}}$ of global monomial degrees nonempty? For every simply laced simple $\mathfrak g$, is $S_{\mathrm{gm}}\cap D^q_{w_0}$ nonempty for some reduced decomposition $w_0$? | For a simple finite-dimensional Lie algebra g, is the set S_{\mathrm{gm}} of global monomial degrees nonempty; and for every simply-laced simple g, is S_{\mathrm{gm}}\cap D^q_{w_0} nonempty for some reduced decomposition w_0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,069 | OWR-14221-005 | Plabic Newton–Okounkov Bodies and FFLV Polytopes | For the distinguished non-mirror plabic graph $G_0$ associated with $\operatorname{Gr}_{k,n}(\mathbb C)$, is $\operatorname{NO}_{G_0}^r$ unimodularly equivalent to $\operatorname{FFLV}(r\varpi_k)$? This is known for $\operatorname{Gr}_{3,6}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | partially_solved | null | 2,016 | 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-14221-005",
"literature-status:partially-solved",
"owr-year:2016"
] | The Newton--Okounkov/FFLV identification is proved for the mirror or dual rectangle graph and for Gr(3,6), while the stated conjecture for the original graph G0 in all Gr(k,n) remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.crma.2018.05.003",
"label": "plabic graph symmetries"
},
{
"url": "https://arxiv.org/abs/1712.00447",
"label": "Newton--Okounkov bodies and Grassmannians"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | For the distinguished non-mirror plabic graph $G_0$ associated with $\operatorname{Gr}_{k,n}(\mathbb C)$, is $\operatorname{NO}_{G_0}^r$ unimodularly equivalent to $\operatorname{FFLV}(r\varpi_k)$? This is known for $\operatorname{Gr}_{3,6}$. | For the relevant plabic graph G_0 of Gr_{k,n}(C), is the associated Newton--Okounkov body NO_{G_0} unimodularly equivalent to the FFLV polytope FFLV(r\omega_k)? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,070 | OWR-14221-006 | Birational Sequences for Plabic Newton–Okounkov Bodies | Can every Newton–Okounkov body arising from a plabic graph be obtained from a birational sequence of a Grassmannian together with a suitable total order? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14221-006",
"literature-status:open",
"owr-year:2016"
] | Birational sequences recover many Newton--Okounkov bodies from plabic graphs, but no general theorem shows that every such body arises from a birational sequence with a proper total order. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1510.02295",
"label": "birational sequences"
},
{
"url": "https://arxiv.org/abs/2107.04264",
"label": "combinatorial mutations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | Can every Newton–Okounkov body arising from a plabic graph be obtained from a birational sequence of a Grassmannian together with a suitable total order? | Can every Newton--Okounkov body arising from a plabic graph be obtained from a birational sequence of a Grassmannian together with a suitable total order? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,071 | OWR-14221-007 | Kostka–Shoji Formula for Graded Modules | Does the conjectural Kostka–Shoji formula yield the graded $GL_N$-module identity $\Gamma(T_r^*B_N^r,O(\mu))=\Gamma(B_N^r,\operatorname{Sym}^{\bullet}T_rB_N^r\otimes O(\mu))=\bigoplus_{\lambda\geq\mu}K_{\lambda\mu}^{-,\bullet}\otimes V_\lambda$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14221-007",
"literature-status:open",
"owr-year:2016"
] | The extracted passage is a corollary fragment rather than a standalone assertion; its underlying finite-generation claim for the associated birational-sequence monoid is not known in general. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report 13/2016"
},
{
"url": "https://arxiv.org/abs/1510.02295",
"label": "Fang--Fourier--Littelmann"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | Does the conjectural Kostka–Shoji formula yield the graded $GL_N$-module identity $\Gamma(T_r^*B_N^r,O(\mu))=\Gamma(B_N^r,\operatorname{Sym}^{\bullet}T_rB_N^r\otimes O(\mu))=\bigoplus_{\lambda\geq\mu}K_{\lambda\mu}^{-,\bullet}\otimes V_\lambda$? | Does the conjectural Kostka--Shoji formula yield the graded GL_N-module identity \Gamma(T_r^*B_N^r,O(\mu))=\Gamma(B_N^r,\operatorname{Sym}^{\bullet}T_rB_N^r\otimes O(\mu))=\bigoplus_{\lambda\geq\mu}K_{\lambda\mu}^{-,\bullet}\otimes V_\lambda? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,072 | OWR-14221-008 | Finite Generation of Birational-Sequence Monoids | For every birational sequence and proper total order in the PBW/Newton–Okounkov construction, is the associated monoid $\Gamma$ finitely generated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14221-008",
"literature-status:open",
"owr-year:2016"
] | Finite generation is proved for important reduced-decomposition and classical PBW cases, but the report conjectures it for every birational sequence and no general proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report 13/2016"
},
{
"url": "https://arxiv.org/abs/1510.02295",
"label": "Fang--Fourier--Littelmann"
},
{
"url": "https://doi.org/10.4171/ICM2022/81",
"label": "Feigin survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | For every birational sequence and proper total order in the PBW/Newton–Okounkov construction, is the associated monoid $\Gamma$ finitely generated? | For every birational sequence and proper total order in the PBW/Newton--Okounkov construction, is the associated monoid \Gamma always finitely generated? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,073 | OWR-14221-009 | Moment-Map Images as Duistermaat–Heckman Supports | Can one choose a connection $\nabla$ such that the image of the moment map $\Phi$ is the support of the Duistermaat–Heckman measure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651](https://doi.org/10.4171/owr/2016/13)
## Literature review (checke... | 3 | open | null | 2,016 | 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-14221-009",
"literature-status:open",
"owr-year:2016"
] | Paradan and Vergne explicitly leave open whether a connection can make the moment-map image equal to the support of the signed Duistermaat--Heckman measure; their examples show the equality can fail for a chosen connection. | [
{
"url": "https://doi.org/10.4171/owr/2016/13",
"label": "OWR report 13/2016"
},
{
"url": "https://archive.intlpress.com/site/pub/files/_fulltext/journals/acta/2017/0218/0001/ACTA-2017-0218-0001-a003.pdf",
"label": "Paradan--Vergne"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/13 | null | null | null | Can one choose a connection $\nabla$ such that the image of the moment map $\Phi$ is the support of the Duistermaat–Heckman measure? | Can one choose a connection \nabla such that the image of the moment map \Phi is the support of the Duistermaat--Heckman measure? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: PBW Structures in Representation Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/13, pp. 615--651 |
30,003,074 | OWR-14222-002 | Combinatorial Invariance of Strong Lefschetz Properties | Suppose $I=(\ell_1^b,\ldots,\ell_{2b+1}^b)$ is minimally generated and has the Strong Lefschetz Property at range 2 in degree $b-2$. If $J=(h_1^b,\ldots,h_{2b+1}^b)$ is minimally generated and the arrangements defined by the $\ell_i$ and $h_i$ have the same combinatorics, must $J$ also have the Strong Lefschetz Propert... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-002",
"literature-status:open",
"owr-year:2016"
] | The stated conjecture is explicitly equivalent to Terao's conjecture for line arrangements, and current literature still treats that conjecture as open even though many subclasses are settled. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1112/jlms.12829",
"label": "Pagaria"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Suppose $I=(\ell_1^b,\ldots,\ell_{2b+1}^b)$ is minimally generated and has the Strong Lefschetz Property at range 2 in degree $b-2$. If $J=(h_1^b,\ldots,h_{2b+1}^b)$ is minimally generated and the arrangements defined by the $\ell_i$ and $h_i$ have the same combinatorics, must $J$ also have the Strong Lefschetz Propert... | If I=(\ell_1^b,\ldots,\ell_{2b+1}^b) is minimally generated and has the Strong Lefschetz Property at range 2 in degree b-2, and J=(h_1^b,\ldots,h_{2b+1}^b) is minimally generated with the corresponding arrangements having the same combinatorics, then J has the Strong Lefschetz Property at range 2 in degree b-2. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,075 | OWR-14222-003 | Point Configurations Producing Unexpected Curves | Characterize the finite point sets $Z$ for which a general fat point imposes dependent conditions on the curves containing $Z$, thereby producing unexpected curves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 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-14222-003",
"literature-status:partially-solved",
"owr-year:2016"
] | The broad classification question remains open, but the unexpected-curve criterion is characterized through the splitting type of the dual line arrangement and many explicit families and low-degree cases are known. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1112/S0010437X18007376",
"label": "Cook--Harbourne--Migliore--Nagel"
},
{
"url": "https://doi.org/10.1007/s10711-021-00602-5",
"label": "Dimca--Sticlaru"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Characterize the finite point sets $Z$ for which a general fat point imposes dependent conditions on the curves containing $Z$, thereby producing unexpected curves. | Can one characterize more specifically the finite point sets Z for which a general fat point imposes dependent conditions on the curves containing Z, producing unexpected curves? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,076 | OWR-14222-004 | Cohomology of General Sheaves on Polarized Surfaces | For a general sheaf E in the moduli space $M_H(v)$ on a smooth polarized surface, what is the cohomology of E? In particular, when does E have nonzero cohomology in at most one degree, and if $\chi(v)=0$, does E have no nonzero cohomology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 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-14222-004",
"literature-status:partially-solved",
"owr-year:2016"
] | Weak Brill--Noether gives the general cohomology in substantial cases, including the projective plane and classified families on Hirzebruch surfaces, but the question for general polarized surfaces and Chern characters remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1611.02674",
"label": "Coskun--Huizenga"
},
{
"url": "https://doi.org/10.1093/imrn/rnaf064",
"label": "Coskun--Huizenga--Raha"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | For a general sheaf E in the moduli space $M_H(v)$ on a smooth polarized surface, what is the cohomology of E? In particular, when does E have nonzero cohomology in at most one degree, and if $\chi(v)=0$, does E have no nonzero cohomology? | For a general sheaf E in the moduli space M_H(v) on a smooth polarized surface, what is the cohomology of E? In particular, when does E have nonzero cohomology in at most one degree, and if \chi(v)=0, does E have no nonzero cohomology? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,077 | OWR-14222-005 | Conditions Imposed by Fat Points on Curve Systems | Determine the number of independent conditions imposed by a general collection of fat points on a linear system of curves of fixed degree containing a prescribed finite point set $Z$, possibly with prescribed multiplicities at $Z$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-005",
"literature-status:open",
"owr-year:2016"
] | This is a generalized SHGH-type classification problem for linear subsystems with imposed base points; the classical SHGH problem itself remains unresolved, so the broader proposal is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1112/S0010437X18007376",
"label": "Cook--Harbourne--Migliore--Nagel"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Determine the number of independent conditions imposed by a general collection of fat points on a linear system of curves of fixed degree containing a prescribed finite point set $Z$, possibly with prescribed multiplicities at $Z$. | Determine the number of independent conditions imposed by a general collection of fat points on a linear system of curves of fixed degree containing a prescribed finite point set Z, possibly with prescribed multiplicities at Z. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,078 | OWR-14222-006 | Classification of Unexpected Curves Through Point Sets | Which curves containing a finite point set $Z$ and vanishing to order $m_Z$ at a general point are unexpected curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 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-14222-006",
"literature-status:partially-solved",
"owr-year:2016"
] | Unexpected curves now have a general splitting-type criterion and numerous classified constructions, including supersolvable arrangements and low-degree cases, but there is no complete geometric classification of all such point sets. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1112/S0010437X18007376",
"label": "Cook--Harbourne--Migliore--Nagel"
},
{
"url": "https://arxiv.org/abs/1804.02730",
"label": "Di Marca--Malara--Oneto"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Which curves containing a finite point set $Z$ and vanishing to order $m_Z$ at a general point are unexpected curves? | Which of the curves containing Z and vanishing to order m_Z at a general point are unexpected curves? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,079 | OWR-14222-007 | Terao Conjecture for Line Arrangements | Is Terao's conjecture true for line arrangements; equivalently, is freeness determined by the incidence lattice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-007",
"literature-status:open",
"owr-year:2016"
] | The record identifies deciding Terao's conjecture as a main open problem; later work proves it for additional classes but not for all line arrangements. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1112/jlms.12829",
"label": "Pagaria"
},
{
"url": "https://doi.org/10.1007/s40879-025-00873-2",
"label": "Pokora et al."
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Is Terao's conjecture true for line arrangements; equivalently, is freeness determined by the incidence lattice? | Is Terao's conjecture true for line arrangements; equivalently, is freeness determined by the incidence lattice? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,080 | OWR-14222-008 | Combinatorial Multiplicity Indices and Terao Conjecture | If, for sets of $2k+1$ points, the property of having multiplicity index $m_Z=k$ is combinatorial, does Terao's conjecture follow for line arrangements? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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 (the implication is proved; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (the implication is proved; answered in the source)**. U. Nagel (joint with D. Cook II, B. Harbourne and J. Migliore; OWR 14/2016, p. 685) states, as a corollary of their work, that if having multiplicity index k is a combinatorial property of sets of 2k + 1 points... | [
"owr",
"oberwolfach-reports",
"OWR-14222-008",
"literature-status:open",
"owr-year:2016"
] | The implication from a combinatorial multiplicity-index property to Terao's conjecture is established, but the required property is not known in general, so the resulting route does not settle Terao's conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1602.02300",
"label": "Cook--Harbourne--Migliore--Nagel"
},
{
"url": "https://doi.org/10.1112/jlms.12829",
"label": "Pagaria"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | If, for sets of $2k+1$ points, the property of having multiplicity index $m_Z=k$ is combinatorial, does Terao's conjecture follow for line arrangements? | If, for sets of 2k+1 points, the property of having multiplicity index m_Z=k is combinatorial, does it follow that Terao's conjecture is true for line arrangements? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,081 | OWR-14222-009 | Higher-Dimensional Theory of Unexpected Curves | Develop a higher-dimensional analogue of the logarithmic-vector-field exact sequence used to characterize unexpected plane curves, and determine whether it yields corresponding characterizations of unexpected hypersurfaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-009",
"literature-status:open",
"owr-year:2016"
] | The requested higher-dimensional analogue of the logarithmic-vector-field exact sequence is posed as an open problem; the cited methods establish the plane-curve case only. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1407.3237",
"label": "Schenck--Terao--Yoshinaga"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Develop a higher-dimensional analogue of the logarithmic-vector-field exact sequence used to characterize unexpected plane curves, and determine whether it yields corresponding characterizations of unexpected hypersurfaces. | Can the theorem characterizing unexpected curves via multiplicity indices be extended to higher dimensions using the same methods? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,082 | OWR-14222-010 | Uniform Integral Multiples of Zariski Decompositions | Does every projective surface $X$ admit an integer $m$, depending only on $X$, such that the Zariski decomposition of $mD$ is integral for every effective divisor $D$ on $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-010",
"literature-status:open",
"owr-year:2016"
] | Uniform integrality of a surface-dependent multiple of every effective divisor's Zariski decomposition is equivalent to bounded negativity, which remains open for general smooth complex projective surfaces. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1515/crelle-2015-0058",
"label": "Bauer--Pokora--Schmitz"
},
{
"url": "https://arxiv.org/abs/2306.11292",
"label": "Li"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Does every projective surface $X$ admit an integer $m$, depending only on $X$, such that the Zariski decomposition of $mD$ is integral for every effective divisor $D$ on $X$? | Does there exist an integer m depending only on a surface X such that the Zariski decomposition of mD is integral for every effective divisor D on X? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,083 | OWR-14222-011 | Bounded Negativity Conjecture for Projective Surfaces | Bounded Negativity Conjecture: for every smooth complex projective surface X, there is $b(X)$ such that every irreducible curve C on X satisfies $C^2\geq-b(X)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-011",
"literature-status:open",
"owr-year:2016"
] | The bounded-negativity conjecture over smooth complex projective surfaces remains open in characteristic zero, although it is proved for broad classes of surfaces and bounded-genus families and is false in positive characteristic. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1109.1881",
"label": "Bauer et al."
},
{
"url": "https://arxiv.org/abs/1708.09463",
"label": "Laface--Pokora"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Bounded Negativity Conjecture: for every smooth complex projective surface X, there is $b(X)$ such that every irreducible curve C on X satisfies $C^2\geq-b(X)$. | Bounded Negativity Conjecture: for every smooth complex projective surface X, there is b(X) such that every irreducible curve C on X satisfies C^2\geq-b(X). | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,084 | OWR-14222-012 | Wiseman–Wilson Theorem for Complex Conics | Let $P\subset\mathbb{P}^2(\mathbb{C})$ be a finite point set not contained in a conic. Must there be a conic determined by exactly five points of $P$ and containing no other point of $P$, as in the real Wiseman–Wilson theorem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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-14222-012",
"literature-status:open",
"owr-year:2016"
] | The extracted lead-in is an incomplete higher-degree Sylvester--Gallai question; no general theorem settles the intended statement beyond the low-degree cases. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1016/j.ejc.2022.103509",
"label": "Boys--Valculescu--De Zeeuw"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Let $P\subset\mathbb{P}^2(\mathbb{C})$ be a finite point set not contained in a conic. Must there be a conic determined by exactly five points of $P$ and containing no other point of $P$, as in the real Wiseman–Wilson theorem? | Do counterexamples to the Wiseman--Wilson theorem exist for complex conics, or does the theorem hold in the complex projective plane? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,085 | OWR-14222-013 | Ordinary Degree-d Curves Through Finite Point Sets | For a finite set $P\subset\mathbb{P}^2(\mathbb{R})$ and a positive integer $d$, must either $P$ lie on a degree-$d$ curve or some degree-$d$ curve contain exactly $(d^2+3d)/2$ points of $P$ and be uniquely determined by them? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 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-14222-013",
"literature-status:partially-solved",
"owr-year:2016"
] | The real-plane conjecture is proved in the conic case and a cubic analogue is proved for sufficiently large point sets, but the all-degree statement and the sharp finite-set formulation remain open. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://doi.org/10.1016/j.ejc.2022.103509",
"label": "Boys--Valculescu--De Zeeuw"
},
{
"url": "https://numdam.org/item/10.4171/RSMUP/136-13.pdf",
"label": "Czapliński et al."
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | For a finite set $P\subset\mathbb{P}^2(\mathbb{R})$ and a positive integer $d$, must either $P$ lie on a degree-$d$ curve or some degree-$d$ curve contain exactly $(d^2+3d)/2$ points of $P$ and be uniquely determined by them? | Conjecture: for a finite set P\subset\mathbb{P}^2(\mathbb{R}) and a positive integer d, either P lies on a degree-d curve, or some degree-d curve contains exactly (d^2+3d)/2 points of P and is uniquely determined by them. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,086 | OWR-14222-014 | Absolute Linear Harbourne Constants | Determine or estimate the absolute linear Harbourne constant $H(d)$, defined as the minimum of $H(K,L)$ over all fields $K$ and all configurations $L$ of $d$ lines. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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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-14222-014",
"literature-status:partially-solved",
"owr-year:2016"
] | The value and bounds of absolute linear Harbourne constants are known through 31 lines and for finite-projective-plane sizes, but the general value problem highlighted by the extracted conjectural passage remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1507.04080",
"label": "Dumnicki--Harrer--Szpond"
},
{
"url": "https://doi.org/10.1016/j.ffa.2018.03.001",
"label": "Dumnicki--Harrer--Szpond 2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | Determine or estimate the absolute linear Harbourne constant $H(d)$, defined as the minimum of $H(K,L)$ over all fields $K$ and all configurations $L$ of $d$ lines. | Determine or estimate the absolute linear Harbourne constant H(d), the minimum of H(K,L) over all fields K and configurations L of d lines. | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,087 | OWR-14222-015 | Explicit Formula for Absolute Linear Harbourne Constants | For $d\geq 2$, let $q=q(d)$ be the least prime power satisfying $d\leq q^2+q+1$, and put $i=q^2+q+1-d$. Define $m_1(i)=q+1-i$, $m_2(i)=2q+1-i$, $\varepsilon_1(i)=1$ for $0\leq i\leq q-1$ and $0$ otherwise, and $\varepsilon_2(i)=1$ for $i>q+1$ and $0$ otherwise. Also define $t_{q-1}(i)=qi-q^2-q$ for $i>q+1$ and $0$ othe... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | partially_solved | null | 2,016 | 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,
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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-14222-015",
"literature-status:partially-solved",
"owr-year:2016"
] | The displayed formula is verified for all d up to 31 and for d=q^2+q+1 with q a prime power, while the remaining cases covered by the conjecture are not settled. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1507.04080",
"label": "Dumnicki--Harrer--Szpond"
},
{
"url": "https://doi.org/10.1016/j.ffa.2018.03.001",
"label": "Dumnicki--Harrer--Szpond 2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | For $d\geq 2$, let $q=q(d)$ be the least prime power satisfying $d\leq q^2+q+1$, and put $i=q^2+q+1-d$. Define $m_1(i)=q+1-i$, $m_2(i)=2q+1-i$, $\varepsilon_1(i)=1$ for $0\leq i\leq q-1$ and $0$ otherwise, and $\varepsilon_2(i)=1$ for $i>q+1$ and $0$ otherwise. Also define $t_{q-1}(i)=qi-q^2-q$ for $i>q+1$ and $0$ othe... | Conjecture: for d\geq2, let q=q(d), i=q^2+q+1-d, and let h(d) be the explicit piecewise expression in the report; if i\leq2q-2, then H(d)=h(d), with the stated special formula when i=2q-1. | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,088 | OWR-14222-016 | Chern Slope Accumulation for Complex Line Arrangements | What are the accumulation points of the logarithmic Chern-slope ratio $\bar c_1^2/\bar c_2$ satisfying $5/2<\bar c_1^2/\bar c_2\leq 8/3$ for strictly complex line arrangements, and are they related to the fields of definition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,016 | 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,
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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,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14222-016",
"literature-status:open",
"owr-year:2016"
] | Known constructions give dense accumulation ranges up to 5/2 over the reals and finite-field analogues, but accumulation points in the strictly complex interval ]5/2,8/3] remain an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2016/14",
"label": "OWR report 14/2016"
},
{
"url": "https://arxiv.org/abs/1511.03879",
"label": "Czapliński--Pokora"
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{
"url": "https://www.scielo.cl/pdf/proy/v41n2/0716-0917-proy-41-02-517.pdf",
"label": "Urzúa survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/14 | null | null | null | What are the accumulation points of the logarithmic Chern-slope ratio $\bar c_1^2/\bar c_2$ satisfying $5/2<\bar c_1^2/\bar c_2\leq 8/3$ for strictly complex line arrangements, and are they related to the fields of definition? | What are the accumulation points of the logarithmic Chern-slope ratio \bar c_1^2/\bar c_2 in (5/2,8/3] for strictly complex line arrangements, and are they related to the fields of definition? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/14, pp. 653--702 |
30,003,089 | OWR-14224-001 | Detection Gaps Between Parametric and Kernel Tests | To what extent is the gap between the $n^{-1/2}$ detection boundary of the standard maximum-mean-discrepancy goodness-of-fit test and the $n^{-1}$ boundary typical of parametric tests intrinsic to nonparametric testing, rather than a consequence of the suboptimality of the standard statistic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796](https://doi.org/10.4171/owr/2016/16)
## Literature ... | 3 | partially_solved | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. K. Balasubramanian (joint with M. Yuan; OWR 16/2016, p. 749) asks to what extent the gap between the n^{−1/2} detection boundary of the MMD goodness-of-fit test and the parametric n^{−1} is intrinsic, and answers that much of it is due t... | [
"owr",
"oberwolfach-reports",
"OWR-14224-001",
"literature-status:partially-solved",
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] | For kernel-MMD testing, later minimax and moderated-MMD analyses show that much of the parametric--nonparametric detection gap is due to test suboptimality, while the general attribution question remains model-dependent. | [
{
"url": "https://doi.org/10.4171/owr/2016/16",
"label": "OWR report 16/2016"
},
{
"url": "https://www.jmlr.org/papers/volume22/17-570/17-570.pdf",
"label": "Balasubramanian et al."
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/16 | null | null | null | To what extent is the gap between the $n^{-1/2}$ detection boundary of the standard maximum-mean-discrepancy goodness-of-fit test and the $n^{-1}$ boundary typical of parametric tests intrinsic to nonparametric testing, rather than a consequence of the suboptimality of the standard statistic? | To what extent can the gap between the relevant statistical procedures be attributed to the fundamental difference between parametric and nonparametric testing problems? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796 |
30,003,090 | OWR-14224-002 | Adaptive Honest Confidence Intervals Under Moderate Sparsity | In the moderate-sparsity regime, is it possible to construct a valid confidence interval for $\beta_i$, and can one construct an adaptive honest confidence interval that does not depend on the unknown sparsity k? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796](https://doi.org/10.4171/owr/2016/16)
## Literature ... | 3 | partially_solved | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. T. Cai (joint with Z. Guo; OWR 16/2016, pp. 756–757) asks whether, for sparsity √n/log p ≪ k ≪ n/log p, a valid confidence interval for β_i exists and whether an honest one can adapt to unknown k, and answers both there. Cai–Guo, [Ann. S... | [
"owr",
"oberwolfach-reports",
"OWR-14224-002",
"literature-status:partially-solved",
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] | Cai and Guo establish valid minimax intervals across sparsity regimes and show that honest adaptation independent of k is possible only in the ultra-sparse region and impossible more generally. | [
{
"url": "https://doi.org/10.4171/owr/2016/16",
"label": "OWR report 16/2016"
},
{
"url": "https://doi.org/10.1214/16-AOS1461",
"label": "Cai--Guo"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/16 | null | null | null | In the moderate-sparsity regime, is it possible to construct a valid confidence interval for $\beta_i$, and can one construct an adaptive honest confidence interval that does not depend on the unknown sparsity k? | In the moderate-sparsity regime, is it possible to construct a valid confidence interval for \beta_i, and can one construct an adaptive honest confidence interval that does not depend on the unknown sparsity k? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796 |
30,003,091 | OWR-14224-003 | Oracle Quality Confidence Intervals with Unknown Sparsity | Without knowing the sparsity $k$, can one construct a confidence interval as accurate as one constructed when $k$ is known? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796](https://doi.org/10.4171/owr/2016/16)
## Literature ... | 3 | partially_solved | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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 | Answered in the source or not an open problem (solved (no in general; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no in general; answered in the source)**. In the same talk (OWR 16/2016, p. 757), T. Cai and Z. Guo ask whether a confidence interval built without knowing the sparsity k can be as accurate as one that uses k, and show that it cannot in general: for β_i only when ... | [
"owr",
"oberwolfach-reports",
"OWR-14224-003",
"literature-status:partially-solved",
"owr-year:2016"
] | The oracle-rate comparison is resolved conditionally: adaptation to unknown sparsity is achievable in the ultra-sparse range but incurs a provable cost or fails in the moderate-sparse range. | [
{
"url": "https://doi.org/10.4171/owr/2016/16",
"label": "OWR report 16/2016"
},
{
"url": "https://doi.org/10.1214/16-AOS1461",
"label": "Cai--Guo"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/16 | null | null | null | Without knowing the sparsity $k$, can one construct a confidence interval as accurate as one constructed when $k$ is known? | Without knowing the sparsity k, can one construct a confidence interval as good as one constructed when k is known? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796 |
30,003,092 | OWR-14224-004 | Extremal Difficulty of Tree Flow Estimation | For least-squares estimation of noisy tree flows, is the path the hardest flow-estimation problem and the star the easiest? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796](https://doi.org/10.4171/owr/2016/16)
## Literature ... | 3 | partially_solved | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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-14224-004",
"literature-status:partially-solved",
"owr-year:2016"
] | The tree-flow study gives rigorous bounds for path-like and logarithmic-depth regimes and analyzes interpolating trees, with evidence that path and star are not extremal, but it leaves a minimax gap and no complete ordering of tree difficulties. | [
{
"url": "https://doi.org/10.4171/owr/2016/16",
"label": "OWR report 16/2016"
},
{
"url": "https://doi.org/10.1109/TIT.2017.2782369",
"label": "Chatterjee--Lafferty"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/16 | null | null | null | For least-squares estimation of noisy tree flows, is the path the hardest flow-estimation problem and the star the easiest? | For least-squares estimation of noisy tree flows, is the path the hardest flow-estimation problem and the star the easiest? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Computationally and Efficient Inference for Complex Large-scale Data (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/16, pp. 741--796 |
30,003,093 | OWR-14225-001 | Attainment of Constrained Domain-Wall Energies | For the domain-wall minimization problem, is the constrained infimum attained for every $0<\theta\leq\pi/2$ and every $q\in\mathbb{Z}$, when $q$ is the degree or winding number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Mechanics of Interfaces and Evolving Microstructure (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/17, pp. 797--867](https://doi.org/10.4171/owr/2016/17)
## Lite... | 3 | open | null | 2,016 | 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"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14225-001",
"literature-status:open",
"owr-year:2016"
] | The cited papers treat the unconstrained and small-angle domain-wall problems, but do not establish attainment of the Dirichlet infimum for every degree or winding number q\in\mathbb Z; the arbitrary-q question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/17",
"label": "OWR 2016 report"
},
{
"url": "https://doi.org/10.4171/JEMS/464",
"label": "Döring--Ignat--Otto"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/17 | null | null | null | For the domain-wall minimization problem, is the constrained infimum attained for every $0<\theta\leq\pi/2$ and every $q\in\mathbb{Z}$, when $q$ is the degree or winding number? | For the domain-wall minimization problem, is the constrained infimum attained for every \theta\in(0,\pi/2] and every q\in\mathbb{Z}, when q is the degree or winding number? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Mechanics of Materials: Mechanics of Interfaces and Evolving Microstructure (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/17, pp. 797--867 |
30,003,094 | OWR-14226-001 | Low-Rank Splitting Error Analysis for Discretized PDEs | Extend the error analysis of the dynamical low-rank splitting scheme to spatial discretizations of partial differential equations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948](https://doi.org/10.4171/owr/2016/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14226-001",
"literature-status:open",
"owr-year:2016"
] | The report states that the estimate depends on a Lipschitz constant and fails for spatial discretisations of PDEs; no authoritative later result located supplies the missing general error analysis. | [
{
"url": "https://doi.org/10.4171/owr/2016/18",
"label": "OWR 2016 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/18 | null | null | null | Extend the error analysis of the dynamical low-rank splitting scheme to spatial discretizations of partial differential equations. | Extend the error analysis of the dynamical low-rank splitting scheme to spatial discretizations of partial differential equations. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948 |
30,003,095 | OWR-14226-002 | Efficient Numerical Transport between Smooth Densities | How can the density transport problem, namely finding a diffeomorphism that transports one smooth density to another, be solved numerically in an efficient way? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948](https://doi.org/10.4171/owr/2016/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,016 | 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-14226-002",
"literature-status:partially-solved",
"owr-year:2016"
] | Optimal information transport supplies efficient numerical algorithms for smooth density matching, but the broad numerical density-transport challenge is not solved in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2016/18",
"label": "OWR 2016 report"
},
{
"url": "https://doi.org/10.1137/151006238",
"label": "Bauer--Joshi--Modin"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/18 | null | null | null | How can the density transport problem, namely finding a diffeomorphism that transports one smooth density to another, be solved numerically in an efficient way? | How can the density transport problem, namely finding a diffeomorphism that transports one smooth density to another, be solved numerically in an efficient way? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948 |
30,003,096 | OWR-14226-003 | Pluri-Lagrangian Integrability of Discrete Variational Systems | Can integrability of discrete variational systems be characterized by the pluri-Lagrangian property that a field on a multi-time space is critical for the action of a $d$-form on every $d$-dimensional multi-time manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948](https://doi.org/10.4171/owr/2016/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,016 | 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-14226-003",
"literature-status:partially-solved",
"owr-year:2016"
] | Pluri-Lagrangian systems give a successful notion and solve important one-dimensional and special lattice cases, while classification and the relation to standard integrability remain incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2016/18",
"label": "OWR 2016 report"
},
{
"url": "https://doi.org/10.1098/rspa.2013.0550",
"label": "Boll--Petrera--Suris"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/18 | null | null | null | Can integrability of discrete variational systems be characterized by the pluri-Lagrangian property that a field on a multi-time space is critical for the action of a $d$-form on every $d$-dimensional multi-time manifold? | What is integrability of discrete variational systems? More specifically, can it be characterized by the pluri-Lagrangian property that a field on a multi-time space is critical for the action of a d-form on every d-dimensional multi-time manifold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Geometric Numerical Integration (2016), Oberwolfach Reports, DOI 10.4171/owr/2016/18, pp. 869--948 |
30,003,097 | OWR-14601-002 | Multistationarity and Permanence in MESSI Reaction Networks | For MESSI mass-action biochemical systems, characterize when a stoichiometric compatibility class can contain more than one positive steady state with the same conserved quantities, and determine the related permanence and invariant-subspace properties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026](https://doi.org/10.4171/owr/2016/19)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,016 | 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-14601-002",
"literature-status:partially-solved",
"owr-year:2016"
] | MESSI theory gives structural criteria and algorithms for toric subclasses, and later work treats reduced and extended networks, but multistationarity is not characterized for all MESSI systems. | [
{
"url": "https://doi.org/10.4171/owr/2016/19",
"label": "OWR 2016 report"
},
{
"url": "https://doi.org/10.1137/17M1113722",
"label": "Pérez Millán--Dickenstein"
},
{
"url": "https://doi.org/10.1007/s00285-024-02115-7",
"label": "Later MESSI analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/19 | null | null | null | For MESSI mass-action biochemical systems, characterize when a stoichiometric compatibility class can contain more than one positive steady state with the same conserved quantities, and determine the related permanence and invariant-subspace properties. | For MESSI mass-action biochemical systems, characterize when a stoichiometric compatibility class can contain more than one positive steady state with the same conserved quantities, and determine the related permanence and invariant-subspace properties. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026 |
30,003,098 | OWR-14601-005 | Gorenstein Secants, Normal Ball Polytopes, and Gradient Images | Is the affine cone over the second secant variety of $(P^1)^5$ Gorenstein? Is the convex hull of all lattice points in any ball a normal polytope? For a homogeneous polynomial $f$ in $n+1$ variables and a generic subspace $L$ of $P^n$, is $L^\perp$ intersected with the gradient image of $L$ empty? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026](https://doi.org/10.4171/owr/2016/19)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 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 | {
"source_url": "https://zenodo.org/records/23377176",
"checked_at": "2026-10-14",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-14] I have released an unrefereed preprint, **The Affine Cone over the Second Secant Variety of (P^1)^5 Is Gorenstein: On Three Questions of Michałek** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23377176) | [
"owr",
"oberwolfach-reports",
"OWR-14601-005",
"literature-status:open",
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] | The identifiable secant-cone question is answered affirmatively for (P^1)^5, but the same record also contains a truncated second conjecture; the full extracted claim is therefore unclear and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2016/19",
"label": "OWR 2016 report"
},
{
"url": "https://doi.org/10.1093/imrn/rnu056",
"label": "Michalek--Oeding--Zwiernik"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/19 | null | null | null | Is the affine cone over the second secant variety of $(P^1)^5$ Gorenstein? Is the convex hull of all lattice points in any ball a normal polytope? For a homogeneous polynomial $f$ in $n+1$ variables and a generic subspace $L$ of $P^n$, is $L^\perp$ intersected with the gradient image of $L$ empty? | Is the affine cone over the second secant variety of (P^1)^5 Gorenstein? Is the convex hull of all lattice points in any ball a normal polytope? For a homogeneous polynomial f in n+1 variables and a generic subspace L of P^n, is L^perp intersected with the gradient image of L empty? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026 |
30,003,099 | OWR-14601-006 | Toric Local Uniformization Without Embedded Resolution | When embedded resolution is not known to exist for a variety $X$, how can one find local re-embeddings and toric birational maps that uniformize a chosen valuation, making the strict transform of $X$ nonsingular and transverse to the toric boundary at the valuation-selected point? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026](https://doi.org/10.4171/owr/2016/19)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 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-14601-006",
"literature-status:open",
"owr-year:2016"
] | The report presents valuation-based toric uniformization as a possible approach when embedded resolution is unavailable, not as a general solution; the question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/19",
"label": "OWR 2016 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/19 | null | null | null | When embedded resolution is not known to exist for a variety $X$, how can one find local re-embeddings and toric birational maps that uniformize a chosen valuation, making the strict transform of $X$ nonsingular and transverse to the toric boundary at the valuation-selected point? | When embedded resolution is not known to exist for a variety X, how can one find suitable local re-embeddings and toric birational maps that uniformize a chosen valuation, making the strict transform of X nonsingular and transverse to the toric boundary at the valuation-selected point? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026 |
30,003,100 | OWR-14601-007 | Minimal Rational Curves on Almost Homogeneous Varieties | Describe the minimal families of rational curves on every smooth projective almost homogeneous variety $X$, meaning a variety equipped with an action of a connected linear algebraic group having an open orbit. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026](https://doi.org/10.4171/owr/2016/19)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,016 | 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-14601-007",
"literature-status:partially-solved",
"owr-year:2016"
] | Toric and complete symmetric or wonderful cases have been described, but a description for every smooth projective almost homogeneous variety remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2016/19",
"label": "OWR 2016 report"
},
{
"url": "https://arxiv.org/abs/2303.03013",
"label": "Brion--Perrin--Kim"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/19 | null | null | null | Describe the minimal families of rational curves on every smooth projective almost homogeneous variety $X$, meaning a variety equipped with an action of a connected linear algebraic group having an open orbit. | Describe the minimal families of rational curves on every smooth projective almost homogeneous variety X, namely a variety equipped with an action of a connected linear algebraic group having an open orbit. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Toric Geometry (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/19, pp. 963--1026 |
30,003,101 | OWR-14602-002 | Existence of Irreducible Hecke Eigensheaves | For every irreducible local system $E$ for the Langlands dual group on a smooth projective curve, does there exist a nonzero Hecke eigensheaf $F$ on $\operatorname{Bun}_G$ with eigenvalue $E$ whose restriction to every irreducible component of $\operatorname{Bun}_G$ is an irreducible perverse sheaf? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098](https://doi.org/10.4171/owr/2016/20)
## Literature review (che... | 3 | open | null | 2,016 | 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-14602-002",
"literature-status:open",
"owr-year:2016"
] | In the finite-field l-adic setting of the record, the general reductive-group eigensheaf assertion remains unresolved; later characteristic-zero geometric Langlands results do not by themselves settle this exact claim. | [
{
"url": "https://doi.org/10.4171/owr/2016/20",
"label": "OWR 2016 report"
},
{
"url": "https://arxiv.org/abs/2409.09856",
"label": "Gaitsgory--Raskin 2024"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/20 | null | null | null | For every irreducible local system $E$ for the Langlands dual group on a smooth projective curve, does there exist a nonzero Hecke eigensheaf $F$ on $\operatorname{Bun}_G$ with eigenvalue $E$ whose restriction to every irreducible component of $\operatorname{Bun}_G$ is an irreducible perverse sheaf? | For every irreducible local system E for the Langlands dual group on a smooth projective curve, does there exist a nonzero Hecke eigensheaf F on Bun_G with eigenvalue E whose restriction to every irreducible component of Bun_G is an irreducible perverse sheaf? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098 |
30,003,102 | OWR-14602-009 | Refined Local Langlands Parametrization of Tempered Packets | For a quasi-split connected reductive group G over a local field, does every tempered L-packet admit an injective Whittaker-dependent parametrization by irreducible representations of the component group of its centralizer, bijective in the p-adic case, with a unique Whittaker-generic constituent and the expected endos... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098](https://doi.org/10.4171/owr/2016/20)
## Literature review (che... | 3 | open | null | 2,016 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report shows that this record is a second extraction of the refined local Langlands conjecture retained as OWR-14602-010. No se) | [
"OWR-14602-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14602-009",
"literature-status:open",
"owr-year:2016"
] | The extracted record ends inside a refined local-Langlands remark and does not contain a complete proposition; its status is therefore unclear and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2016/20",
"label": "OWR 2016 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/20 | null | null | null | null | For a quasi-split connected reductive group G over a local field, does every tempered L-packet admit an injective Whittaker-dependent parametrization by irreducible representations of the component group of its centralizer, bijective in the p-adic case, with a unique Whittaker-generic constituent and the expected endos... | unrecoverable | The official report shows that this record is a second extraction of the refined local Langlands conjecture retained as OWR-14602-010. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098 |
30,003,103 | OWR-14602-010 | Refined Local Langlands Correspondence for Quasi-Split Groups | For a quasi-split connected reductive group $G$ over a local field and a tempered Langlands parameter $\varphi$, does the associated packet admit an injective Whittaker-dependent parametrization by the irreducible representations of the component group of the centralizer of $\varphi$, bijective over non-Archimedean loc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098](https://doi.org/10.4171/owr/2016/20)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 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... | [
"OWR-14602-009"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14602-010",
"literature-status:partially-solved",
"owr-year:2016"
] | The refined local Langlands assertions are proved in substantial cases such as GL_n, real groups, and important classical groups, but the full quasi-split p-adic statement with all endoscopic identities remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2016/20",
"label": "OWR 2016 report"
},
{
"url": "https://annals.math.princeton.edu/2016/184-2/p06",
"label": "Kaletha"
},
{
"url": "https://arxiv.org/abs/2008.04472",
"label": "Kaletha"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/20 | null | null | null | For a quasi-split connected reductive group $G$ over a local field and a tempered Langlands parameter $\varphi$, does the associated packet admit an injective Whittaker-dependent parametrization by the irreducible representations of the component group of the centralizer of $\varphi$, bijective over non-Archimedean loc... | For a quasi-split connected reductive group G over a local field, there is an injective map from each tempered L-packet to the irreducible representations of the component group of the parameter centralizer, bijective over p-adic fields, with a unique Whittaker-generic constituent corresponding to the trivial represent... | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098 |
30,003,104 | OWR-14602-011 | Langlands Packets Across Extended Pure Inner Forms | For a discrete Langlands parameter and all extended pure inner twists of a quasi-split group $G$, should the union of the associated $L$-packets be parametrized by irreducible representations of the parameter centralizer, compatibly with Kottwitz's bijection between basic isocrystals and the character group of the dual... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098](https://doi.org/10.4171/owr/2016/20)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 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-14602-011",
"literature-status:partially-solved",
"owr-year:2016"
] | The extended-pure-inner-form refinement has major case-by-case results and precise conjectural formulations, but the general packet parametrization and endoscopic identities are not fully proved. | [
{
"url": "https://doi.org/10.4171/owr/2016/20",
"label": "OWR 2016 report"
},
{
"url": "https://annals.math.princeton.edu/2016/184-2/p06",
"label": "Kaletha"
},
{
"url": "https://arxiv.org/abs/2008.04472",
"label": "Kaletha"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/20 | null | null | null | For a discrete Langlands parameter and all extended pure inner twists of a quasi-split group $G$, should the union of the associated $L$-packets be parametrized by irreducible representations of the parameter centralizer, compatibly with Kottwitz's bijection between basic isocrystals and the character group of the dual... | For a discrete Langlands parameter and all extended pure inner twists of a quasi-split group G, the union of the associated L-packets should be parametrized by the irreducible representations of the parameter centralizer, compatibly with Kottwitz's bijection between basic isocrystals and the character group of the dual... | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098 |
30,003,105 | OWR-14602-015 | Fargues–Fontaine Hecke Eigensheaves for General Linear Groups | For a discrete Weil parameter $\varphi:W_{\mathbb{Q}_p}\to GL_n$, does there exist, up to shifts and twists, a sheaf $F_{\varphi}$ on $\operatorname{Bun}_{GL_n}$ in the Fargues–Fontaine setting whose Hecke transform is $F_{\varphi}\otimes\varphi$ and whose pullbacks to the basic points correspond to the local Langlands... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098](https://doi.org/10.4171/owr/2016/20)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 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-14602-015",
"literature-status:partially-solved",
"owr-year:2016"
] | The GL_n cuspidal or irreducible case is proved by Anschuetz--Le Bras and Hansen, while the full discrete-parameter statement represented here is not established. | [
{
"url": "https://ems.press/content/serial-article-files/46624",
"label": "OWR report"
},
{
"url": "https://www.cambridge.org/core/journals/journal-of-the-institute-of-mathematics-of-jussieu/article/averaging-functors-in-fargues-program-for-mathrm-gln/471BA6B4BB71261287EC350F1C8DECA2",
"label": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/20 | null | null | null | For a discrete Weil parameter $\varphi:W_{\mathbb{Q}_p}\to GL_n$, does there exist, up to shifts and twists, a sheaf $F_{\varphi}$ on $\operatorname{Bun}_{GL_n}$ in the Fargues–Fontaine setting whose Hecke transform is $F_{\varphi}\otimes\varphi$ and whose pullbacks to the basic points correspond to the local Langlands... | For a discrete Weil parameter phi from W_Qp to GL_n, does there exist a sheaf F_phi on Bun_GLn over the Fargues-Fontaine setting, up to shifts and twists, whose Hecke transform is F_phi tensor phi and whose pullbacks to the basic points correspond to the local Langlands representations attached to phi? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Arbeitsgemeinschaft: The Geometric Langlands Conjecture (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/20, pp. 1027--1098 |
30,003,106 | OWR-14603-003 | Algebraic Values and Relations of Mahler Functions | Given a vector of $q$-Mahler functions and an algebraic point $\alpha$ inside the unit disk that is nonsingular for the defining system, determine the algebraic points at which a transcendental Mahler function takes an algebraic value, and more generally determine the corresponding value relations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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 | Answered in the source or not an open problem (solved (answered in the source; made effective by Adamczewski–Faverjon)) | null | null | [Discussion #4 literature review, 2026-10-02] **solved (answered in the source; made effective by Adamczewski–Faverjon)**. P. Philippon (OWR 21/2016, pp. 1109–1111) asks how to find the algebraic points where a transcendental Mahler function takes algebraic values, and answers it at non-singular points with his main th... | [
"owr",
"oberwolfach-reports",
"OWR-14603-003",
"literature-status:open",
"owr-year:2016"
] | The q-Mahler transcendence-degree theorem does not determine the requested higher-order relation points, and no general determination procedure is established in the record or checked literature. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Given a vector of $q$-Mahler functions and an algebraic point $\alpha$ inside the unit disk that is nonsingular for the defining system, determine the algebraic points at which a transcendental Mahler function takes an algebraic value, and more generally determine the corresponding value relations. | Given a vector of q-Mahler functions and an algebraic point alpha inside the unit disk that is nonsingular for the defining system, how can one determine the algebraic points at which a transcendental Mahler function takes an algebraic value, or more generally determine the corresponding value relations? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,107 | OWR-14603-004 | Kawaguchi–Silverman Arithmetic Degree Conjecture | Let $f$ be a dominant self-map of a smooth projective variety $X$ over a number field, and let $P\in X(\overline{\mathbb Q})$. If the forward orbit of $P$ is Zariski dense in $X$, must the arithmetic degree $\alpha(f,P)$ equal the dynamical degree $\delta(f)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,016 | 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-14603-004",
"literature-status:partially-solved",
"owr-year:2016"
] | This is the Kawaguchi--Silverman conjecture: the abelian-variety case in the record is proved, and later work adds polarized, int-amplified, and other cases, but the general dominant-map claim remains open. | [
{
"url": "https://arxiv.org/abs/1208.0815",
"label": "Kawaguchi--Silverman"
},
{
"url": "https://www.numdam.org/item/JTNB_2017__29_1_151_0/",
"label": "Silverman on abelian varieties"
},
{
"url": "https://arxiv.org/abs/2408.00566",
"label": "Meng--Zhong"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Let $f$ be a dominant self-map of a smooth projective variety $X$ over a number field, and let $P\in X(\overline{\mathbb Q})$. If the forward orbit of $P$ is Zariski dense in $X$, must the arithmetic degree $\alpha(f,P)$ equal the dynamical degree $\delta(f)$? | Let f be a dominant self-map of a smooth projective variety X over a number field and let P be an algebraic point. If the forward orbit of P is Zariski dense in X, then the arithmetic degree alpha(f,P) equals the dynamical degree delta(f). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,108 | OWR-14603-006 | Lang–Silverman Height Bounds for Simple Abelian Varieties | For every integer $g\geq1$ and number field $K$, does there exist $c_2(K,g)>0$ such that every simple abelian variety $A/K$ of dimension $g$, every ample symmetric line bundle $L$ on $A$, and every nontorsion point $P\in A(K)$ satisfy
$$\widehat h_{A,L}(P)\geq c_2(K,g)\max\{h_F(A/K),1\}$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,016 | 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-14603-006",
"literature-status:partially-solved",
"owr-year:2016"
] | The Lang--Silverman conjecture is open in general, although important special cases and conditional consequences are known, including elliptic and bounded-Szpiro regimes. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://swc-math.github.io/aws/2024/2024SilvermanNotes.pdf",
"label": "Silverman notes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | For every integer $g\geq1$ and number field $K$, does there exist $c_2(K,g)>0$ such that every simple abelian variety $A/K$ of dimension $g$, every ample symmetric line bundle $L$ on $A$, and every nontorsion point $P\in A(K)$ satisfy
$$\widehat h_{A,L}(P)\geq c_2(K,g)\max\{h_F(A/K),1\}$$? | For every integer g at least 1 and number field K, there is a constant c2(K,g)>0 such that every simple abelian variety A over K of dimension g, every ample symmetric line bundle L on A, and every nontorsion point P in A(K) satisfy the Néron-Tate height inequality hhat_A,L(P) >= c2(K,g) max{h_F(A/K),1}. | corrected_verified | The official report was checked. This is its Lang–Silverman conjecture with all quantifiers, hypotheses, and notation restored. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,109 | OWR-14603-007 | Regulator Finiteness from Lang–Silverman Heights | Assume the Lang–Silverman height conjecture. For a fixed number field $K$ and integer $g\geq1$, are there only finitely many $\mathbb Q$-isomorphism classes of simple abelian varieties over $K$ of dimension $g$, bounded positive Mordell–Weil rank, and bounded regulator? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-007",
"literature-status:open",
"owr-year:2016"
] | The displayed proposition is a proved conditional implication, but its Lang--Silverman hypothesis is unresolved; therefore the corresponding unconditional extracted problem remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://swc-math.github.io/aws/2024/2024SilvermanNotes.pdf",
"label": "Silverman notes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Assume the Lang–Silverman height conjecture. For a fixed number field $K$ and integer $g\geq1$, are there only finitely many $\mathbb Q$-isomorphism classes of simple abelian varieties over $K$ of dimension $g$, bounded positive Mordell–Weil rank, and bounded regulator? | Assuming the Lang-Silverman height conjecture, for fixed K, g, and Mordell-Weil rank m at least 1, there are only finitely many Q-isomorphism classes of simple abelian varieties A over K of dimension g, bounded rank m, and bounded regulator. | corrected_verified | The official report was checked. The clean statement is the source theorem conditional on Lang–Silverman, with the rank condition expressed without the extraction ambiguity. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,110 | OWR-14603-008 | Regulator Finiteness for Elliptic Curves from ABC | Assume the ABC conjecture. Over a fixed number field $K$, are there only finitely many $\mathbb Q$-isomorphism classes of elliptic curves with bounded positive Mordell–Weil rank and bounded regulator? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-008",
"literature-status:open",
"owr-year:2016"
] | The theorem recorded here is conditional on Lang--Silverman; its special consequences are established, but the unresolved hypothesis leaves the extracted claim open. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://swc-math.github.io/aws/2024/2024SilvermanNotes.pdf",
"label": "Silverman notes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Assume the ABC conjecture. Over a fixed number field $K$, are there only finitely many $\mathbb Q$-isomorphism classes of elliptic curves with bounded positive Mordell–Weil rank and bounded regulator? | Assuming the Lang-Silverman conjecture, the Q-isomorphism classes of simple abelian varieties over a fixed number field K with fixed dimension, bounded positive Mordell-Weil rank, and bounded regulator form a finite set; assuming the ABC conjecture, the analogous finiteness holds for elliptic curves. | corrected_verified | The official report was checked. The duplicated Lang–Silverman consequence, represented by OWR-14603-007, was removed; this record now preserves only the distinct ABC consequence for elliptic curves. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,111 | OWR-14603-010 | Root Separation and Rational Values of Littlewood Polynomials | Let
$$\mathcal P_d=\{a_dx^d+\cdots+a_0:a_i\in\{-1,0,1\}\}.$$
Is the minimum nonzero distance between roots of two polynomials in $\mathcal P_d$ bounded below by $\exp(-Cd)$ for some absolute $C>0$? For a fixed rational $p/q\in[9/10,19/20]$, can the trivial lower bound on $\min_{P\in\mathcal P_d}\lvert P(p/q)\rvert$ b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-010",
"literature-status:open",
"owr-year:2016"
] | The record contains Hochman's root-separation question and the rational-evaluation minimum; the cited literature gives only Mahler's exponential-in-d log d bound and the trivial q^{-d} bound, with the requested improvement unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1610.09154",
"label": "Breuillard--Varju"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Let
$$\mathcal P_d=\{a_dx^d+\cdots+a_0:a_i\in\{-1,0,1\}\}.$$
Is the minimum nonzero distance between roots of two polynomials in $\mathcal P_d$ bounded below by $\exp(-Cd)$ for some absolute $C>0$? For a fixed rational $p/q\in[9/10,19/20]$, can the trivial lower bound on $\min_{P\in\mathcal P_d}\lvert P(p/q)\rvert$ b... | For P_d consisting of degree-at-most-d polynomials with coefficients in {-1,0,1}, what is the minimum nonzero distance between two roots of two such polynomials, and what is the minimum of |P(p/q)| over P in P_d for a fixed rational p/q? | corrected_verified | The official report was checked. The reconstruction restores the polynomial family and the explicit exponential bounds requested in its first and third questions. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,112 | OWR-14603-011 | Duplicate Small-Value Sparsity Question for Littlewood Polynomials | For every rational p/q in [9/10,19/20], is there a constant c_p,q such that, for some absolute constant C, the number of P in P_d with |P(p/q)| < c_p,q exp(-Cd) is less than exp(d/100)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report contains this small-value counting question once; OWR-14603-013 gives its complete formula and is the canonical clean re) | [
"OWR-14603-013"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14603-011",
"literature-status:open",
"owr-year:2016"
] | No proof of the stated rational-point counting and separation question was located; it remains an open Diophantine problem. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1608.04210",
"label": "Varju"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | null | For every rational p/q in [9/10,19/20], is there a constant c_p,q such that, for some absolute constant C, the number of P in P_d with |P(p/q)| < c_p,q exp(-Cd) is less than exp(d/100)? | unrecoverable | The official report contains this small-value counting question once; OWR-14603-013 gives its complete formula and is the canonical clean record. This entry repeats the same question. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,113 | OWR-14603-012 | Absolute Continuity Parameters for Bernoulli Convolutions | For $\lambda\in(0,1)$, let $\mu_\lambda$ be the distribution of $\sum_{n\geq0}A_n\lambda^n$, where the $A_n$ are independent unbiased random variables taking values $\pm1$. Determine the set of parameters $\lambda$ for which $\mu_\lambda$ is absolutely continuous. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-012",
"literature-status:open",
"owr-year:2016"
] | The parameter set for absolute continuity of Bernoulli convolutions is still not characterized; known results cover almost-every parameter and important algebraic or near-one regimes only. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1602.00261",
"label": "Varju"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | For $\lambda\in(0,1)$, let $\mu_\lambda$ be the distribution of $\sum_{n\geq0}A_n\lambda^n$, where the $A_n$ are independent unbiased random variables taking values $\pm1$. Determine the set of parameters $\lambda$ for which $\mu_\lambda$ is absolutely continuous. | For the Bernoulli convolution mu_lambda, the distribution of the random series sum_{n>=0} A_n lambda^n with independent unbiased plus-or-minus-one variables and lambda in (0,1), determine the set of parameters lambda for which mu_lambda is absolutely continuous. | corrected_verified | The official report was checked. The clean statement preserves its Bernoulli-convolution definition and long-standing parameter-classification problem. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,114 | OWR-14603-013 | Exponential Small-Value Bounds for Littlewood Polynomials | Let $\mathcal P_d=\{a_dx^d+\cdots+a_0:a_i\in\{-1,0,1\}\}$. For every rational $p/q\in[9/10,19/20]$, does there exist an absolute $C>0$ such that $\#\{P\in\mathcal P_d:|P(p/q)|<c_{p,q}e^{-Cd}\}<e^{d/100}$ for some constant $c_{p,q}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-011"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14603-013",
"literature-status:open",
"owr-year:2016"
] | This record is a conditional application of the still-open Question 4 and does not state a separately resolved theorem. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1608.04210",
"label": "Varju"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | Let $\mathcal P_d=\{a_dx^d+\cdots+a_0:a_i\in\{-1,0,1\}\}$. For every rational $p/q\in[9/10,19/20]$, does there exist an absolute $C>0$ such that $\#\{P\in\mathcal P_d:|P(p/q)|<c_{p,q}e^{-Cd}\}<e^{d/100}$ for some constant $c_{p,q}$? | Let P_d=\{a_dx^d+\cdots+a_0:a_i\in\{-1,0,1\}\}. For every rational p/q\in[9/10,19/20], does there exist an absolute C>0 such that \#\{P\in P_d:|P(p/q)|<c_{p,q}e^{-Cd}\}<e^{d/100} for some constant c_{p,q}? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
30,003,115 | OWR-14603-014 | Dense Multiplicative Orbits on the Two-Torus | If $1,x,y$ are multiplicatively independent over $\mathbb Q$ and $a,b$ are relatively prime positive integers, is $\{a^n b^k(x,y)\bmod 1:n,k\in\mathbb N\}$ dense in $[0,1]^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187](https://doi.org/10.4171/owr/2016/21)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,016 | 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-14603-014",
"literature-status:open",
"owr-year:2016"
] | The two-generator Furstenberg density question for multiplicatively independent x and y remains open; known density theorems require stronger hypotheses such as three pairwise coprime multipliers. | [
{
"url": "https://ems.press/content/serial-article-files/46625?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/21 | null | null | null | If $1,x,y$ are multiplicatively independent over $\mathbb Q$ and $a,b$ are relatively prime positive integers, is $\{a^n b^k(x,y)\bmod 1:n,k\in\mathbb N\}$ dense in $[0,1]^2$? | If 1,x,y are multiplicatively independent over \mathbb Q and a,b are relatively prime positive integers, is \{a^n b^k(x,y)\bmod 1:n,k\in\mathbb N\} dense in [0,1]^2? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Diophantische Approximationen (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/21, pp. 1099--1187 |
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