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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,016 | OWR-16635-001 | Character Determination from Jantzen’s Sum Formula | How far can Jantzen's sum formula determine the characters of simple representations, beyond the groups where it is already complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | partially_solved | null | 2,018 | 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-16635-001",
"literature-status:partially-solved",
"owr-year:2018"
] | Jantzen's formula reduces the cited low-rank cases to a small number of ambiguities; later periodic-character methods and hand calculations resolve at least the SL5 parameter, but no general characterization follows and higher-rank cases remain difficult. | [
{
"url": "https://ems.press/content/serial-article-files/46794",
"label": "Oberwolfach Report 14/2019"
},
{
"url": "https://arxiv.org/abs/2107.03310",
"label": "Coxeter Combinatorics for Sum Formulas"
},
{
"url": "https://link.springer.com/article/10.1007/s00031-021-09685-6",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | How far can Jantzen's sum formula determine the characters of simple representations, beyond the groups where it is already complete? | How far can Jantzen's sum formula determine the characters of simple representations, beyond the groups where it is already complete? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,017 | OWR-16635-002 | Derived Equivalence of Unipotent Unitary and Linear Representations | Are the categories of unipotent representations of $\operatorname{GU}_n(q)$ and $\operatorname{GL}_n(-q)$ derived equivalent through an equivalence compatible with dominance order, Lusztig’s $a$-function, and the Deligne–Lusztig geometric realizations on both sides? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | open | null | 2,018 | 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-16635-002",
"literature-status:open",
"owr-year:2018"
] | The extracted record is a fragment about a derived self-equivalence and Macdonald-polynomial operators, not a complete formal question; its unresolved status is therefore normalized to open. | [
{
"url": "https://ems.press/content/serial-article-files/46773",
"label": "Oberwolfach Report 52/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | Are the categories of unipotent representations of $\operatorname{GU}_n(q)$ and $\operatorname{GL}_n(-q)$ derived equivalent through an equivalence compatible with dominance order, Lusztig’s $a$-function, and the Deligne–Lusztig geometric realizations on both sides? | Are the categories of unipotent representations of GU_n(q) and GL_n(-q) derived equivalent, with an equivalence compatible with dominance order, the A-function, and the indicated Deligne--Lusztig varieties? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,018 | OWR-16635-003 | Socle Filtrations from Duflo–Serganova Kernels | For $k\leq\min(m,n)$, let $K^k_{m\mid n}$ be generated by the objects annihilated by every Duflo–Serganova functor $\operatorname{DS}_x$ with $x\in X_k$. Is the equality
$$\operatorname{soc}_kK_{m\mid n}=K^k_{m\mid n}$$
valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | partially_solved | null | 2,018 | 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-16635-003",
"literature-status:partially-solved",
"owr-year:2018"
] | The socle filtration and the Duflo--Serganova maps are rigorously described, and the tensor-filtration conjecture is proved for the finite-dimensional direct summand, but the full Conjecture 9 for category O is not resolved. | [
{
"url": "https://arxiv.org/abs/1712.00664",
"label": "Integrable sl-infinity Modules and Category O"
},
{
"url": "https://par.nsf.gov/servlets/purl/10512366",
"label": "The Duflo--Serganova Functor, Vingt Ans Apres"
},
{
"url": "https://ems.press/content/serial-article-files/46773",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | For $k\leq\min(m,n)$, let $K^k_{m\mid n}$ be generated by the objects annihilated by every Duflo–Serganova functor $\operatorname{DS}_x$ with $x\in X_k$. Is the equality
$$\operatorname{soc}_kK_{m\mid n}=K^k_{m\mid n}$$
valid? | For k\le\min(m,n), let K^k_{m|n} be generated by objects annihilated by all DS_x for x\in X_k. Conjecture: \operatorname{soc}_k K_{m|n}=K^k_{m|n}. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,019 | OWR-16635-004 | Quasi-Cuspidal Representations and Generators of Equivariant D-Modules | Let $G$ be connected and reductive, and put $P(V)=D_{\mathfrak g}\otimes_{U\mathfrak g}V$. Characterize the quasi-cuspidal representations $V$ for which $P(V)$ has a cuspidal summand, and find a minimal set of irreducible $V$ whose modules $P(V)$ generate $D\!\operatorname{-mod}(\mathfrak g)^G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | open | null | 2,018 | 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-16635-004",
"literature-status:open",
"owr-year:2018"
] | The extracted questions ask for a general characterization of quasi-cuspidal representations and minimal generators of generalized Springer blocks; the cited report gives examples and partial structure, not a complete solution. | [
{
"url": "https://ems.press/content/serial-article-files/46773",
"label": "Oberwolfach Report 52/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | Let $G$ be connected and reductive, and put $P(V)=D_{\mathfrak g}\otimes_{U\mathfrak g}V$. Characterize the quasi-cuspidal representations $V$ for which $P(V)$ has a cuspidal summand, and find a minimal set of irreducible $V$ whose modules $P(V)$ generate $D\!\operatorname{-mod}(\mathfrak g)^G$. | For a connected reductive G and P(V)=D_{\mathfrak g}\otimes_{U\mathfrak g}V, how can one characterize the quasi-cuspidal representations V for which P(V) has a cuspidal summand, and what is a minimal set of irreducible representations whose P(V)'s generate Dmod(\mathfrak g)^G? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,020 | OWR-16635-008 | Higgs Branches as Associated Varieties of Vertex Algebras | For a four-dimensional $\mathcal N=2$ Argyres–Douglas theory, is its Higgs branch isomorphic to the associated variety of the corresponding vertex algebra under the four-dimensional/two-dimensional duality? This includes algebras of the forms $L_{-h^\vee+h^\vee/q}(\mathfrak g)$ and $W_{-h^\vee+h^\vee/q}(\mathfrak g,f)$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | open | null | 2,018 | 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-16635-008",
"literature-status:open",
"owr-year:2018"
] | The extracted text is an incomplete fragment ending at a conjecture, so no precise mathematical claim can be verified; no authoritative proof or counterexample for the exact fragment was identified. | [
{
"url": "https://doi.org/10.4171/owr/2018/52",
"label": "Oberwolfach report 52"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | For a four-dimensional $\mathcal N=2$ Argyres–Douglas theory, is its Higgs branch isomorphic to the associated variety of the corresponding vertex algebra under the four-dimensional/two-dimensional duality? This includes algebras of the forms $L_{-h^\vee+h^\vee/q}(\mathfrak g)$ and $W_{-h^\vee+h^\vee/q}(\mathfrak g,f)$... | Conjecture: the Higgs branch of a four-dimensional N=2 Argyres--Douglas theory is isomorphic to the associated variety of its corresponding vertex algebra under the 4d/2d duality; typical algebras are L_{-h^\vee+h^\vee/q}(g) and W_{-h^\vee+h^\vee/q}(g,f) for g of type A,D,E. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,021 | OWR-16635-009 | Exceptional Isomorphism of Two W-Algebras | Is
$$W_{-7+7/3}(\mathfrak{sl}_7,f)\cong W_{-4+4/3}(\mathfrak{sl}_4,f'),$$
where $f$ has orbit partition $(3,2^2)$ in $\mathfrak{sl}_7$ and $f'$ has orbit partition $(2^2)$ in $\mathfrak{sl}_4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146](https://doi.org/10.4171/owr/2018/52)
## Literature review (che... | 3 | open | null | 2,018 | 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-16635-009",
"literature-status:open",
"owr-year:2018"
] | The report explicitly labels this specific W-algebra isomorphism a conjecture, and no authoritative primary source located through the cutoff establishes or disproves this exact identification. | [
{
"url": "https://doi.org/10.4171/owr/2018/52",
"label": "Oberwolfach report 52"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/52 | null | null | null | Is
$$W_{-7+7/3}(\mathfrak{sl}_7,f)\cong W_{-4+4/3}(\mathfrak{sl}_4,f'),$$
where $f$ has orbit partition $(3,2^2)$ in $\mathfrak{sl}_7$ and $f'$ has orbit partition $(2^2)$ in $\mathfrak{sl}_4$? | Conjecture: W_{-7+7/3}(\mathfrak{sl}_7,f)\cong W_{-4+4/3}(\mathfrak{sl}_4,f'), where f has orbit partition (3,2^2) in \mathfrak{sl}_7 and f' has orbit partition (2^2) in \mathfrak{sl}_4. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/52, pp. 3081--3146 |
30,004,022 | OWR-16636-004 | Commutator Models for Nonsymmetric Free Random Variables | Extend the available commutator representations for free random variables from symmetric laws $\mu_a,\mu_b$ to arbitrary nonsymmetric laws $\mu_a,\mu_b$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/53, pp. 3147--3215](https://doi.org/10.4171/owr/2018/53)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,018 | 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-16636-004",
"literature-status:open",
"owr-year:2018"
] | The report explicitly identifies the extension to general non-symmetric commutator laws as open, and no authoritative primary source located through the cutoff removes that generality. | [
{
"url": "https://doi.org/10.4171/owr/2018/53",
"label": "Oberwolfach report 53"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/53 | null | null | null | Extend the available commutator representations for free random variables from symmetric laws $\mu_a,\mu_b$ to arbitrary nonsymmetric laws $\mu_a,\mu_b$. | Extend the representations describing commutators of free random variables from symmetric probability measures \mu_a,\mu_b to general nonsymmetric \mu_a,\mu_b. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Free Probability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/53, pp. 3147--3215 |
30,004,023 | OWR-16636-006 | The Quantum Unique Ergodicity Conjecture | On every compact negatively curved manifold, do all high-energy Laplace eigenfunctions equidistribute? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Free Probability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/53, pp. 3147--3215](https://doi.org/10.4171/owr/2018/53)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,018 | 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-16636-006",
"literature-status:open",
"owr-year:2018"
] | The cited arithmetic Hecke cases are proved, but the general quantum unique ergodicity claim remains unresolved; therefore the extracted status is open. | [
{
"url": "https://annals.math.princeton.edu/2006/163-1/p03",
"label": "Lindenstrauss (2006)"
},
{
"url": "https://arxiv.org/abs/0901.4060",
"label": "Soundararajan (2010)"
},
{
"url": "https://doi.org/10.4171/owr/2018/53",
"label": "Oberwolfach report 53"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/53 | null | null | null | On every compact negatively curved manifold, do all high-energy Laplace eigenfunctions equidistribute? | Quantum Unique Ergodicity conjecture: on every compact negatively curved manifold, all high-energy Laplacian eigenfunctions equidistribute. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Free Probability Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/53, pp. 3147--3215 |
30,004,024 | OWR-16637-002 | Covariance Determinant Bounds for Polar Convex Bodies | For every convex body $K\subseteq\mathbb R^n$ with barycenter at the origin and polar body $K^\circ$, does a universal constant $C>0$ exist such that
$$\det\!\bigl(\operatorname{Cov}(K)\operatorname{Cov}(K^\circ)\bigr)\leq(C/n)^{2n}.$$
Does every such $K$ satisfy the displayed bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | solved | null | 2,018 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. B. Klartag (OWR 54/2018, p. 3224) notes that, by the Santaló and Bourgain–Milman inequalities, slicing is equivalent to his inequality (1), the record's bound. Slicing is now proved (see `OWR-12337-001`). | [
"owr",
"oberwolfach-reports",
"OWR-16637-002",
"literature-status:partially-solved",
"owr-year:2018"
] | The main relation in the record is established: isotropic constants and polarity are linked through the covariance determinant and the slicing inequality, now affirmed by Klartag--Lehec; broader trace-based duality relations remain only partial. | [
{
"url": "https://arxiv.org/abs/1710.08084",
"label": "Klartag, isotropic constants and Mahler volumes"
},
{
"url": "https://doi.org/10.1007/s00039-025-00718-w",
"label": "Klartag--Lehec"
},
{
"url": "https://doi.org/10.4171/owr/2018/54",
"label": "Oberwolfach report 54"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For every convex body $K\subseteq\mathbb R^n$ with barycenter at the origin and polar body $K^\circ$, does a universal constant $C>0$ exist such that
$$\det\!\bigl(\operatorname{Cov}(K)\operatorname{Cov}(K^\circ)\bigr)\leq(C/n)^{2n}.$$
Does every such $K$ satisfy the displayed bound? | For every convex body K\subseteq\mathbb{R}^n with barycenter at the origin and polar body K^\circ, does there exist a universal constant C>0 such that det(\operatorname{Cov}(K)\operatorname{Cov}(K^\circ))\leq(C/n)^{2n}? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,025 | OWR-16637-003 | Mahler’s Volume Conjecture | For every convex body $K\subseteq\mathbb R^n$, is its Mahler volume bounded by
$$\bar s(K)=\lvert K\rvert\inf_{x\in K}\lvert(K-x)^\circ\rvert\geq\frac{(n+1)^{n+1}}{(n!)^2},$$
with equality for a simplex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,018 | 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-16637-003",
"literature-status:open",
"owr-year:2018"
] | The displayed local-minimizer and implication results are proved, but the strong slicing conjecture and the general Mahler conjecture remain unresolved beyond known dimensions and special classes; hence the status is open. | [
{
"url": "https://doi.org/10.1016/j.aim.2018.03.009",
"label": "Klartag, isotropic constants and Mahler volumes"
},
{
"url": "https://doi.org/10.1007/s00222-025-01382-5",
"label": "Current Mahler-conjecture survey"
},
{
"url": "https://doi.org/10.4171/owr/2018/54",
"label": "Oberwolf... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For every convex body $K\subseteq\mathbb R^n$, is its Mahler volume bounded by
$$\bar s(K)=\lvert K\rvert\inf_{x\in K}\lvert(K-x)^\circ\rvert\geq\frac{(n+1)^{n+1}}{(n!)^2},$$
with equality for a simplex? | Mahler conjecture: for every convex body K\subseteq\mathbb{R}^n, the Mahler volume \bar{s}(K)=|K|\inf_{x\in K}|(K-x)^\circ| satisfies \bar{s}(K)\geq(n+1)^{n+1}/(n!)^2, with equality for a simplex. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,026 | OWR-16637-004 | Geometric Explanations and Polynomial Pivot Rules for Simplex | For the simplex method for linear programming, can one explain its good practical performance by a geometric property of real-world linear programs, and does there exist a polynomial-time pivot rule? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,018 | 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-16637-004",
"literature-status:open",
"owr-year:2018"
] | The existence of a polynomial-time worst-case simplex pivot rule remains a longstanding open problem; recent work instead gives exponential lower bounds for broad families of rules. | [
{
"url": "https://arxiv.org/abs/2403.04886",
"label": "Recent simplex lower bounds"
},
{
"url": "https://doi.org/10.4171/owr/2018/54",
"label": "Oberwolfach report 54"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For the simplex method for linear programming, can one explain its good practical performance by a geometric property of real-world linear programs, and does there exist a polynomial-time pivot rule? | For the simplex method for linear programming, can one explain its good practical performance by a geometric property of real-world linear programs, and does there exist a polynomial-time pivot rule? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,027 | OWR-16637-005 | Sharp Smoothed Complexity of Simplex Pivot Rules | For smoothed analysis of the simplex method, can the expected number of edges of a projected polyhedron be bounded sharply by $\Theta(d^{3/2}\log n)$ as $\sigma\to\infty$, with a lower bound depending on $\sigma$? What bounds hold if only a random $\varepsilon$-fraction of the entries of $(A,b)$ is perturbed, or if oth... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,018 | 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-16637-005",
"literature-status:open",
"owr-year:2018"
] | The cited work improves Gaussian smoothed bounds, and later papers sharpen upper and lower bounds, but the listed sparse-perturbation and general-pivot-rule questions are not fully resolved; status open. | [
{
"url": "https://doi.org/10.1137/18M1197205",
"label": "Dadush--Huiberts"
},
{
"url": "https://arxiv.org/abs/2211.11860",
"label": "Huiberts--Lee--Zhang"
},
{
"url": "https://doi.org/10.4171/owr/2018/54",
"label": "Oberwolfach report 54"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For smoothed analysis of the simplex method, can the expected number of edges of a projected polyhedron be bounded sharply by $\Theta(d^{3/2}\log n)$ as $\sigma\to\infty$, with a lower bound depending on $\sigma$? What bounds hold if only a random $\varepsilon$-fraction of the entries of $(A,b)$ is perturbed, or if oth... | Open smoothed-analysis questions for the simplex method include: can the smoothed upper bound on the expected number of edges of a projected polyhedron match the \Theta(d^{3/2}\ln n) bound as \sigma\to\infty, and can one prove a lower bound depending on \sigma; can one analyze perturbing only a random \varepsilon-fract... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,028 | OWR-16637-006 | Planar Log-Brunn–Minkowski After Translation | For planar convex bodies $K,L\in\mathcal K_2$, can the origin be positioned and $L$ translated so that $K$ and the translate satisfy the logarithmic Brunn–Minkowski inequality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,018 | 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-16637-006",
"literature-status:open",
"owr-year:2018"
] | The log-Brunn--Minkowski inequality is proved in planar and several highly symmetric or perturbative settings, but the general position/translation question remains unresolved. | [
{
"url": "https://arxiv.org/abs/2002.12239",
"label": "Log-Brunn--Minkowski under symmetry"
},
{
"url": "https://erdoscenter.renyi.hu/events/focused-workshop-log-brunn-minkowski-conjecture-state-art-and-ramifications",
"label": "Current state-of-the-art workshop"
},
{
"url": "https://doi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For planar convex bodies $K,L\in\mathcal K_2$, can the origin be positioned and $L$ translated so that $K$ and the translate satisfy the logarithmic Brunn–Minkowski inequality? | For planar convex bodies K,L\in\mathcal{K}_2, is there a suitable position of the origin and a suitable translate of L for which K and that translate satisfy the log-Brunn--Minkowski inequality? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,029 | OWR-16637-008 | The $L_p$ Brunn–Minkowski Conjecture | For $0\leq p<1$, origin-symmetric convex bodies $K,C\subseteq\mathbb R^n$, and every $\lambda\in[0,1]$, is
$$V\bigl((1-\lambda)K+_p\lambda C\bigr)\geq V(K)^{1-\lambda}V(C)^\lambda,$$
where $+_p$ denotes the $L_p$-linear combination? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,018 | 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-16637-008",
"literature-status:open",
"owr-year:2018"
] | The record summarizes genuine partial results for symmetric, near-ball, and high-symmetry cases, but the general log-Brunn--Minkowski conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2002.12239",
"label": "Log-Brunn--Minkowski under symmetry"
},
{
"url": "https://erdoscenter.renyi.hu/events/focused-workshop-log-brunn-minkowski-conjecture-state-art-and-ramifications",
"label": "Current state-of-the-art workshop"
},
{
"url": "https://doi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | For $0\leq p<1$, origin-symmetric convex bodies $K,C\subseteq\mathbb R^n$, and every $\lambda\in[0,1]$, is
$$V\bigl((1-\lambda)K+_p\lambda C\bigr)\geq V(K)^{1-\lambda}V(C)^\lambda,$$
where $+_p$ denotes the $L_p$-linear combination? | Lp-Brunn--Minkowski conjecture: for p\in[0,1) and origin-symmetric convex bodies K,C\subseteq\mathbb{R}^n, does V((1-\lambda)K+_p\lambda C)\geq V(K)^{1-\lambda}V(C)^\lambda hold for every \lambda\in[0,1], where +_p is the Lp-linear combination? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,030 | OWR-16637-012 | Ellipsoid Rigidity from Constant Central-Section Products | If an origin-symmetric convex body $K\subseteq\mathbb R^n$, with $n\geq3$, satisfies
$$h_K(\theta)\operatorname{vol}_{n-1}(K\cap\theta^\perp)=c$$
for every $\theta\in S^{n-1}$ and a constant $c$ independent of $\theta$, must $K$ be an ellipsoid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281](https://doi.org/10.4171/owr/2018/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,018 | 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-16637-012",
"literature-status:partially-solved",
"owr-year:2018"
] | The global fifth Busemann--Petty assertion is not known; Alfonseca et al. prove it only for bodies sufficiently close to the Euclidean ball. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870821003595",
"label": "Alfonseca et al., Advances in Mathematics 2021"
},
{
"url": "https://www.birs.ca/workshops/2020/20w5037/report20w5037.pdf",
"label": "BIRS report on Busemann--Petty problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2018/54 | null | null | null | If an origin-symmetric convex body $K\subseteq\mathbb R^n$, with $n\geq3$, satisfies
$$h_K(\theta)\operatorname{vol}_{n-1}(K\cap\theta^\perp)=c$$
for every $\theta\in S^{n-1}$ and a constant $c$ independent of $\theta$, must $K$ be an ellipsoid? | If an origin-symmetric convex body K\subseteq\mathbb{R}^n, n\geq3, satisfies h_K(\theta) \operatorname{vol}_{n-1}(K\cap\theta^\perp)=c for every \theta\in S^{n-1}, with c independent of \theta, must K be an ellipsoid? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Convex Geometry and its Applications (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/54, pp. 3217--3281 |
30,004,031 | OWR-16763-004 | Duplicate Five-Cycle Near-Triangulation Conjecture | For every plane near-triangulation G whose outer face is bounded by a 5-cycle, n_G^\star is a nonnegative linear combination of n_{G_1},\ldots,n_{G_{11}}. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (This extraction repeats the near-triangulation decomposition conjecture represented canonically and with its computational evidence by OWR-1) | [
"OWR-16763-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-004",
"literature-status:open",
"owr-year:2019"
] | The proposed omission of the twelfth ray remains a conjecture; later work gives finite computational verification and obstruction results, not a general proof or counterexample. | [
{
"url": "https://arxiv.org/abs/1907.04066",
"label": "Dvorak and Lidicky, Coloring count cones"
},
{
"url": "https://onlinelibrary.wiley.com/doi/10.1002/jgt.22767",
"label": "Journal of Graph Theory version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | null | For every plane near-triangulation G whose outer face is bounded by a 5-cycle, n_G^\star is a nonnegative linear combination of n_{G_1},\ldots,n_{G_{11}}. | unrecoverable | This extraction repeats the near-triangulation decomposition conjecture represented canonically and with its computational evidence by OWR-16763-005. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,032 | OWR-16763-005 | Five-Cycle Near-Triangulation Decomposition Conjecture | For every plane near-triangulation $G$ whose outer face is bounded by a $5$-cycle, is $n_G^\star$ a nonnegative linear combination of $n_{G_1},\ldots,n_{G_{11}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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... | [
"OWR-16763-004"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-005",
"literature-status:open",
"owr-year:2019"
] | The count-cone conjecture has only finite computational verification and later obstruction results; no general proof or counterexample has resolved it. | [
{
"url": "https://arxiv.org/abs/1907.04066",
"label": "Dvorak and Lidicky, Coloring count cones"
},
{
"url": "https://onlinelibrary.wiley.com/doi/10.1002/jgt.22767",
"label": "Journal of Graph Theory version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For every plane near-triangulation $G$ whose outer face is bounded by a $5$-cycle, is $n_G^\star$ a nonnegative linear combination of $n_{G_1},\ldots,n_{G_{11}}$? | For every plane near-triangulation G whose outer face is bounded by a 5-cycle, n_G^\star is a nonnegative linear combination of n_{G_1},\ldots,n_{G_{11}}; computational evidence verifies this for at most 26 faces. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,033 | OWR-16763-006 | Fractional Coloring of Subcubic Triangle-Free Planar Graphs | Does every planar triangle-free graph with maximum degree at most 3 have fractional chromatic number at most 8/3? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 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-16763-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The fractional extension is incomplete: later work gives improved fractional upper bounds, but the natural 8/3-type analogue remains conjectural. | [
{
"url": "https://doi.org/10.1016/j.ejc.2013.06.006",
"label": "Heckman and Thomas, fractional chromatic number"
},
{
"url": "https://doi.org/10.19086/aic.13667",
"label": "Large independent sets in triangle-free cubic graphs"
},
{
"url": "https://www.advancesincombinatorics.com/article/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Does every planar triangle-free graph with maximum degree at most 3 have fractional chromatic number at most 8/3? | Does every planar triangle-free graph with maximum degree at most 3 have fractional chromatic number at most 8/3? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,034 | OWR-16763-007 | Erdős–Pósa Properties of Induced Subdivisions | For which graphs $H$ do induced $H$-subdivisions have the Erdős–Pósa property? In particular, do even cycles have it, and what happens for $H=K_4$ or for a fan whose path has length $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-007",
"literature-status:open",
"owr-year:2019"
] | Ordinary holes have the Erdos--Posa property, and holes of length at least five do not; the report's induced even-cycle subquestion remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.jctb.2020.05.002",
"label": "Kim and Kwon, Journal of Combinatorial Theory B"
},
{
"url": "https://epubs.siam.org/doi/pdf/10.1137/21M1435239?download=true",
"label": "On the Erdos--Posa property for long holes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For which graphs $H$ do induced $H$-subdivisions have the Erdős–Pósa property? In particular, do even cycles have it, and what happens for $H=K_4$ or for a fan whose path has length $3$? | For which graphs H does the class of induced H-subdivisions have the Erdős--Pósa property; in particular, do even cycles have it, and what happens for H=K_4 or a fan whose path has length 3? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,035 | OWR-16763-008 | Separation Between Higher Graph Equivalence Levels | If graphs $H,H'$ are $2$-equivalent, must they be $3$-equivalent? More generally, can two graphs be $100$-equivalent but not $101$-equivalent? Why do the known pairs that are $3$-equivalent but not $2$-equivalent include a disconnected graph? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-008",
"literature-status:open",
"owr-year:2019"
] | Known equivalences in two colors do not settle the proposed 100 versus 101 case; the general Ramsey-equivalence question remains open. | [
{
"url": "https://arxiv.org/abs/1809.09232",
"label": "Clemens, Liebenau, and Reding, Ramsey equivalence"
},
{
"url": "https://doi.org/10.1002/jgt.22119",
"label": "Conditions on Ramsey Nonequivalence"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/2... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | If graphs $H,H'$ are $2$-equivalent, must they be $3$-equivalent? More generally, can two graphs be $100$-equivalent but not $101$-equivalent? Why do the known pairs that are $3$-equivalent but not $2$-equivalent include a disconnected graph? | For graphs H,H', if they are 2-equivalent must they be 3-equivalent, or can a pair be 100-equivalent but not 101-equivalent; and is it merely coincidental that known pairs which are 3-equivalent but not 2-equivalent include a disconnected graph? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,036 | OWR-16763-009 | Equivalence Hierarchies for Connected Graphs | If connected graphs $H,H'$ are $3$-equivalent, must they be $2$-equivalent? For every $q\geq2$, do nonisomorphic connected $q$-equivalent graphs exist? Which graphs $H$ make $K_k$ and $K_k+H$ Ramsey equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-009",
"literature-status:open",
"owr-year:2019"
] | The connected-graph implication and classification of further q-equivalent graph pairs remain open in the cited literature. | [
{
"url": "https://arxiv.org/abs/1809.09232",
"label": "Clemens, Liebenau, and Reding, Ramsey equivalence"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | If connected graphs $H,H'$ are $3$-equivalent, must they be $2$-equivalent? For every $q\geq2$, do nonisomorphic connected $q$-equivalent graphs exist? Which graphs $H$ make $K_k$ and $K_k+H$ Ramsey equivalent? | For connected graphs H,H' that are 3-equivalent, must they be 2-equivalent; more generally, for each q\geq2 do there exist nonisomorphic connected q-equivalent graphs, and which graphs H satisfy Ramsey equivalence of K_k and K_k+H? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,037 | OWR-16763-010 | Hadwiger’s Coloring Conjecture and Its Odd-Minor Variant | For every integer $t\geq1$, is every graph with no $K_{t+1}$ minor properly $t$-colorable? Is every graph with no odd $K_{t+1}$ minor properly $t$-colorable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-010",
"literature-status:open",
"owr-year:2019"
] | In the report's indexing, cases t at most 5 are known via the Four Color Theorem, but the cases t at least 6 remain open. | [
{
"url": "https://web.math.princeton.edu/~pds/papers/hadwiger/paper.pdf",
"label": "Seymour, Hadwiger survey"
},
{
"url": "https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/improved-lower-bound-for-the-list-chromatic-number-of-graphs-with-no-kt-minor/8132D67EC14... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For every integer $t\geq1$, is every graph with no $K_{t+1}$ minor properly $t$-colorable? Is every graph with no odd $K_{t+1}$ minor properly $t$-colorable? | Hadwiger's conjecture: for every integer t\geq1, every graph with no K_{t+1} minor is properly t-colorable; related open strengthening is that every odd K_{t+1}-minor-free graph is properly t-colorable. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,038 | OWR-16763-011 | Clustered Coloring Without Topological or Odd Clique Minors | For every positive integer $t$, do the $K_{t+1}$-topological-minor-free graphs and the odd-$K_{t+1}$-minor-free graphs admit $t$-colorings whose monochromatic components have uniformly bounded size? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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... | [
"OWR-16763-012"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-011",
"literature-status:open",
"owr-year:2019"
] | Clustered-coloring analogues have substantial partial bounds and special cases, but the full conjectured t-color statement is not proved. | [
{
"url": "https://doi.org/10.1016/j.jctb.2021.09.002",
"label": "Liu and Wood, Clustered variants of Hajos conjecture"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0095895622000764",
"label": "Immersion and clustered coloring"
},
{
"url": "https://doi.org/10.4171/o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For every positive integer $t$, do the $K_{t+1}$-topological-minor-free graphs and the odd-$K_{t+1}$-minor-free graphs admit $t$-colorings whose monochromatic components have uniformly bounded size? | For every positive integer t, every K_{t+1}-topological-minor-free graph and every odd K_{t+1}-minor-free graph admits a vertex coloring with t colors in which every monochromatic component has bounded size. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,039 | OWR-16763-012 | Duplicate Clustered Hadwiger-Type Conjecture | For every positive integer t, the classes of K_{t+1}-topological-minor-free graphs and odd K_{t+1}-minor-free graphs are clustered t-colorable, meaning that all monochromatic components have a size bound independent of the graph. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (This record restates the clustered-coloring conjecture represented canonically by OWR-16763-011. No separate clean statement is promoted; th) | [
"OWR-16763-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-012",
"literature-status:open",
"owr-year:2019"
] | The clustered-coloring conjecture for the two excluded-minor classes remains unresolved; current results establish only partial bounds and special cases. | [
{
"url": "https://doi.org/10.1016/j.jctb.2021.09.002",
"label": "Liu and Wood, Clustered variants of Hajos conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | null | For every positive integer t, the classes of K_{t+1}-topological-minor-free graphs and odd K_{t+1}-minor-free graphs are clustered t-colorable, meaning that all monochromatic components have a size bound independent of the graph. | unrecoverable | This record restates the clustered-coloring conjecture represented canonically by OWR-16763-011. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,040 | OWR-16763-014 | Maximum Clique in Proper Vertex-Minor-Closed Classes | Let $\mathcal F$ be a proper graph class closed under isomorphism and vertex minors. Is there a polynomial-time algorithm that, given $G\in\mathcal F$, computes the clique number of $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-014",
"literature-status:open",
"owr-year:2019"
] | The polynomial-time maximum-clique conjecture remains open beyond special classes such as circle graphs and bounded rank-width. | [
{
"url": "https://dspacemainprd01.lib.uwaterloo.ca/server/api/core/bitstreams/a3790341-2224-4c60-b8a6-34dc44a88c07/content",
"label": "McCarty, Local Structure for Vertex-Minors"
},
{
"url": "https://sangiloum.github.io/legacy/2024/03/2023vertexminors-survey-revised.pdf",
"label": "Vertex-minors... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Let $\mathcal F$ be a proper graph class closed under isomorphism and vertex minors. Is there a polynomial-time algorithm that, given $G\in\mathcal F$, computes the clique number of $G$? | Let F be a proper graph class closed under isomorphism and vertex minors. Is there a polynomial-time algorithm that, given G\in F, computes the size of a maximum clique of G? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,041 | OWR-16763-015 | Finite Obstruction Sets for Vertex-Minor-Closed Graph Classes | Let $\mathcal F$ be a proper graph class closed under isomorphism and vertex minors. Does $\mathcal F$ have only finitely many excluded vertex minors, up to isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-015",
"literature-status:open",
"owr-year:2019"
] | The conjectured finite forbidden-vertex-minor characterization remains open; current surveys list it as a central unresolved problem. | [
{
"url": "https://sangiloum.github.io/legacy/2024/03/2023vertexminors-survey-revised.pdf",
"label": "Vertex-minors survey"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Let $\mathcal F$ be a proper graph class closed under isomorphism and vertex minors. Does $\mathcal F$ have only finitely many excluded vertex minors, up to isomorphism? | Let F be a proper graph class closed under isomorphism and vertex minors. Are there, up to isomorphism, only finitely many excluded vertex minors for F? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,042 | OWR-16763-016 | Weak Coloring Numbers Excluding Complete Bipartite Minors | What is the asymptotically sharp bound on the weak coloring number $\operatorname{wcol}_r(G)$ for graphs $G$ excluding $K_{3,t}$ as a minor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 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-16763-016",
"literature-status:partially-solved",
"owr-year:2019"
] | For K3,t-minor-free graphs, current primary results give polynomial upper and lower bounds for weak coloring numbers with a remaining exponent or logarithmic gap, so the exact bound is not settled. | [
{
"url": "https://arxiv.org/abs/2407.04588",
"label": "Weak coloring numbers of minor-closed graph classes"
},
{
"url": "https://doi.org/10.1137/1.9781611978322.107",
"label": "SODA 2025 weak coloring numbers"
},
{
"url": "https://arxiv.org/abs/2603.13097",
"label": "Centered colorin... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | What is the asymptotically sharp bound on the weak coloring number $\operatorname{wcol}_r(G)$ for graphs $G$ excluding $K_{3,t}$ as a minor? | What is the asymptotically sharp bound on the r-th weak coloring number \operatorname{wcol}_r(G) for graphs excluding K_{3,t} as a minor? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,043 | OWR-16763-017 | Oberwolfach Decompositions into Prescribed Two-Factors | Given an odd integer $n$ and a $2$-regular graph $F$ on $n$ vertices, can $K_n$ be decomposed into edge-disjoint copies of $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 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-16763-017",
"literature-status:partially-solved",
"owr-year:2019"
] | The generalized Oberwolfach problem is proved for all sufficiently large orders, but the remaining finite small-order cases are not all resolved. | [
{
"url": "https://doi.org/10.1016/j.jctb.2021.09.007",
"label": "The generalised Oberwolfach problem"
},
{
"url": "https://web.mat.bham.ac.uk/D.Kuehn/OW.pdf",
"label": "Resolution of the Oberwolfach problem"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Repo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Given an odd integer $n$ and a $2$-regular graph $F$ on $n$ vertices, can $K_n$ be decomposed into edge-disjoint copies of $F$? | Given an odd integer n and a 2-regular graph F on n vertices, can K_n be decomposed into edge-disjoint copies of F; equivalently, can n people be seated around round tables for (n-1)/2 meals so that every pair sits next to each other exactly once? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,044 | OWR-16763-018 | Universal Decomposition of Complete Graphs into Bounded-Degree Factors | For every $\Delta$, does an $n_0$ exist such that, whenever $n\geq n_0$ and the $n$-vertex graphs $F_1,\ldots,F_t$ are $r_i$-regular with $r_i\leq\Delta$ and $\sum_i r_i=n-1$, the complete graph $K_n$ decomposes into copies of $F_1,\ldots,F_t$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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... | [
"OWR-16931-017"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-018",
"literature-status:open",
"owr-year:2019"
] | The bounded-degree regular-factorization conjecture remains open; known theorems cover important special regimes but not arbitrary bounded-degree factor families. | [
{
"url": "https://web.mat.bham.ac.uk/D.Kuehn/OW.pdf",
"label": "Resolution of the Oberwolfach problem"
},
{
"url": "https://eprints.lse.ac.uk/126935/1/978-3-98547-564-3-volume-6-chapter-5567.pdf",
"label": "Recent survey on decomposition problems"
},
{
"url": "https://doi.org/10.4171/owr... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For every $\Delta$, does an $n_0$ exist such that, whenever $n\geq n_0$ and the $n$-vertex graphs $F_1,\ldots,F_t$ are $r_i$-regular with $r_i\leq\Delta$ and $\sum_i r_i=n-1$, the complete graph $K_n$ decomposes into copies of $F_1,\ldots,F_t$? | For every maximum degree bound \Delta, does there exist n_0 such that for all n\geq n_0, whenever n-vertex graphs F_1,\ldots,F_t are r_i-regular with r_i\leq\Delta and \sum_{i=1}^t r_i=n-1, the complete graph K_n decomposes into F_1,\ldots,F_t? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,045 | OWR-16763-019 | Asymptotic Enumeration of Rank-Three Matroids | Let $p(n,3)$ count rank-$3$ matroids and $p'(n,3)$ count rank-$3$ paving matroids with no hyperplane larger than $4$. Is there a constant $c>-2$ such that
$$\log p(n,3)\sim\log p'(n,3)=\frac1{n-2}\binom n3\bigl(\log(n-2)+c\bigr)$$
as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-019",
"literature-status:open",
"owr-year:2019"
] | Coarse rank-three enumeration is known, but the finer conjecture comparing all rank-three matroids with the specified paving subclass and its constant remains unresolved. | [
{
"url": "https://arxiv.org/abs/1811.11810",
"label": "Tighter enumeration of matroids of fixed rank"
},
{
"url": "https://arxiv.org/abs/2112.03788",
"label": "Enumerating Matroids and Linear Spaces"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/201... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Let $p(n,3)$ count rank-$3$ matroids and $p'(n,3)$ count rank-$3$ paving matroids with no hyperplane larger than $4$. Is there a constant $c>-2$ such that
$$\log p(n,3)\sim\log p'(n,3)=\frac1{n-2}\binom n3\bigl(\log(n-2)+c\bigr)$$
as $n\to\infty$? | Let p(n,3) count rank-3 matroids and let p'(n,3) count rank-3 paving matroids with no hyperplane larger than 4. Is there a constant c>-2 such that \ln p(n,3)\sim\ln p'(n,3)=\frac{1}{n-2}\binom{n}{3}(\ln(n-2)+c) as n\to\infty? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,046 | OWR-16763-020 | Simultaneously Localized List-Coloring Bounds | For localized list-coloring theorems, what happens when the local clique number $\omega(v)$ is close to the degree $d(v)$? Is an at-most-exponential range of degrees necessary, and can the bounds be localized simultaneously? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-020",
"literature-status:open",
"owr-year:2019"
] | Several local list-coloring extensions are proved, but the listed questions about near-clique degree, degree range, and simultaneous localization remain open. | [
{
"url": "https://doi.org/10.1016/j.jctb.2022.06.002",
"label": "Bonamy, Kelly, Nelson, and Postle, local coloring"
},
{
"url": "https://arxiv.org/abs/1911.02672",
"label": "A local epsilon version of Reed conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For localized list-coloring theorems, what happens when the local clique number $\omega(v)$ is close to the degree $d(v)$? Is an at-most-exponential range of degrees necessary, and can the bounds be localized simultaneously? | For local list versions of graph-coloring theorems, what happens when the local clique number \omega(v) is close to the degree d(v); is an at most exponential range of degrees necessary; and can these versions be simultaneously localized? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,047 | OWR-16763-021 | Two-Step Path Density in Tripartite Graphs | Let $A,B,C$ be disjoint nonempty vertex sets. Suppose every vertex of $A$ has at least $x\lvert B\rvert$ neighbors in $B$ and every vertex of $B$ has at least $y\lvert C\rvert$ neighbors in $C$. Let $\phi(x,y)$ be the largest $z$ such that some vertex of $C$ is joined by two-edge paths to at least $z\lvert A\rvert$ ver... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-021",
"literature-status:open",
"owr-year:2019"
] | The published study retains the x greater than 1 over 3 threshold question as open and proves only a weaker lower bound, so the queried assertion is unresolved. | [
{
"url": "https://doi.org/10.37236/8451",
"label": "Chudnovsky et al., Concatenating bipartite graphs"
},
{
"url": "https://arxiv.org/abs/1902.10878",
"label": "Concatenating bipartite graphs preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Let $A,B,C$ be disjoint nonempty vertex sets. Suppose every vertex of $A$ has at least $x\lvert B\rvert$ neighbors in $B$ and every vertex of $B$ has at least $y\lvert C\rvert$ neighbors in $C$. Let $\phi(x,y)$ be the largest $z$ such that some vertex of $C$ is joined by two-edge paths to at least $z\lvert A\rvert$ ver... | Let A,B,C be disjoint nonempty vertex sets in a graph, with every vertex of A having at least x|B| neighbors in B and every vertex of B at least y|C| neighbors in C, and let \phi(x,y) be the largest z such that some vertex of C is joined to at least z|A| vertices of A by two-edge paths. Is \phi(x,x)\geq1/2 for x>1/3, a... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,048 | OWR-16763-022 | Symmetry of Bidirectional Two-Step Path Density | Let $A,B,C$ be disjoint nonempty vertex sets in a graph. Suppose every vertex of $A$ has at least $x\lvert B\rvert$ neighbors in $B$, every vertex of $B$ has at least $x\lvert A\rvert$ neighbors in $A$ and at least $y\lvert C\rvert$ neighbors in $C$, and every vertex of $C$ has at least $y\lvert B\rvert$ neighbors in $... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-022",
"literature-status:open",
"owr-year:2019"
] | The biconstrained function is known to satisfy several lower bounds, but symmetry psi(x,y)=psi(y,x) was left unresolved in the primary paper. | [
{
"url": "https://doi.org/10.37236/8451",
"label": "Chudnovsky et al., Concatenating bipartite graphs"
},
{
"url": "https://arxiv.org/abs/1902.10878",
"label": "Concatenating bipartite graphs preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Let $A,B,C$ be disjoint nonempty vertex sets in a graph. Suppose every vertex of $A$ has at least $x\lvert B\rvert$ neighbors in $B$, every vertex of $B$ has at least $x\lvert A\rvert$ neighbors in $A$ and at least $y\lvert C\rvert$ neighbors in $C$, and every vertex of $C$ has at least $y\lvert B\rvert$ neighbors in $... | In the preceding setup, additionally require every vertex of B to have at least x|A| neighbors in A and every vertex of C at least y|B| neighbors in B, and define \psi(x,y) as the corresponding maximum two-edge-path density. Is \psi(x,y)=\psi(y,x) for all x,y? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,049 | OWR-16763-023 | Strong Erdős–Hajnal Phenomena in Sparse H-Free Graphs | For which graphs $H$ does some $\varepsilon>0$ have the following property? Every $n$-vertex, $\varepsilon$-sparse, $H$-free graph $G$, with $n>1$, contains sets $A,B$ that are complete or anticomplete to each other and satisfy at least one of
$$\lvert A\rvert,\lvert B\rvert\geq\varepsilon n;\qquad
\lvert A\rvert\geq\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-023",
"literature-status:open",
"owr-year:2019"
] | The sparse H-free pure-pair questions are solved for important classes and variants, but no general classification of H is known. | [
{
"url": "https://doi.org/10.1002/jgt.22556",
"label": "Pure pairs III"
},
{
"url": "https://arxiv.org/abs/2201.04062",
"label": "Pure pairs VIII, Excluding a sparse graph"
},
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Oberwolfach Report 1/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | For which graphs $H$ does some $\varepsilon>0$ have the following property? Every $n$-vertex, $\varepsilon$-sparse, $H$-free graph $G$, with $n>1$, contains sets $A,B$ that are complete or anticomplete to each other and satisfy at least one of
$$\lvert A\rvert,\lvert B\rvert\geq\varepsilon n;\qquad
\lvert A\rvert\geq\... | For which graphs H does there exist \varepsilon>0 such that every n-vertex \varepsilon-sparse H-free graph G with n>1 contains sets A,B satisfying one of: (a) |A|,|B|\geq\varepsilonn; (b) |A|\geq\varepsilonn and |B|\geqn^{\varepsilon}; or (c) |A|,|B|\geqn^{\varepsilon}; with A complete or anticomplete to B? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,050 | OWR-16763-024 | Disjoint Transversal Bases from a Family of Matroid Bases | Given a rank-$n$ matroid and bases $B_1,\ldots,B_n$, do there exist $n$ pairwise disjoint transversal bases, each choosing one representative from every $B_i$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,019 | 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-16763-024",
"literature-status:open",
"owr-year:2019"
] | Rota's basis conjecture remains open even for general vector spaces; recent results are asymptotic, random, or special-case advances rather than a full proof. | [
{
"url": "https://ems.press/content/serial-article-files/53597?nt=1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2508.05601",
"label": "Montgomery and Sauermann, asymptotically-tight packing"
},
{
"url": "https://arxiv.org/abs/1810.07462",
"label": "Halfw... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Given a rank-$n$ matroid and bases $B_1,\ldots,B_n$, do there exist $n$ pairwise disjoint transversal bases, each choosing one representative from every $B_i$? | For any rank-n matroid and bases B_1,\ldots,B_n, do there exist n pairwise disjoint transversal bases, each choosing one representative from every B_i? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,051 | OWR-16763-025 | Kahn’s Matroidal Rota Basis Conjecture | Given a rank-$n$ matroid and bases $B_{i,j}$ for $1\leq i,j\leq n$, can representatives $b_{i,j}\in B_{i,j}$ be chosen so that every column $\{b_{1,j},\ldots,b_{n,j}\}$ and every row $\{b_{i,1},\ldots,b_{i,n}\}$ is a basis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 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-16763-025",
"literature-status:partially-solved",
"owr-year:2019"
] | The full Kahn basis conjecture remains unresolved; Bucić, Kwan, Pokrovskiy, and Sudakov prove only a roughly half-row partial result, while later work gives asymptotically many transversal bases in the Rota special case. | [
{
"url": "https://arxiv.org/abs/1810.07464",
"label": "Bucić--Kwan--Pokrovskiy--Sudakov"
},
{
"url": "https://doi.org/10.1090/proc/16581",
"label": "Pokrovskiy, asymptotic Rota basis conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Given a rank-$n$ matroid and bases $B_{i,j}$ for $1\leq i,j\leq n$, can representatives $b_{i,j}\in B_{i,j}$ be chosen so that every column $\{b_{1,j},\ldots,b_{n,j}\}$ and every row $\{b_{i,1},\ldots,b_{i,n}\}$ is a basis? | Kahn's conjecture: given a rank-n matroid and bases B_{i,j} for 1\leqi,j\leqn, can one choose b_{i,j}\inB_{i,j} so that every column set \{b_{1,j},\ldots,b_{n,j}\} and every row set \{b_{i,1},\ldots,b_{i,n}\} is a basis? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,052 | OWR-16763-026 | Duplicate Latin-Square Transversal Conjecture | Every Latin square of order n has a partial transversal of size n-1, and if n is odd it has a transversal. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (This record repeats the Latin-square transversal conjecture represented canonically and with its matching formulation by OWR-16763-027. No s) | [
"OWR-16763-027"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-026",
"literature-status:partially-solved",
"owr-year:2019"
] | Duplicate extraction; the canonical question is OWR-16763-027. This record repeats the Latin-square transversal conjecture represented canonically and with its matching formulation by OWR-16763-027. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance.
**Wha... | [
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-u... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | null | Every Latin square of order n has a partial transversal of size n-1, and if n is odd it has a transversal. | unrecoverable | This record repeats the Latin-square transversal conjecture represented canonically and with its matching formulation by OWR-16763-027. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,053 | OWR-16763-027 | Ryser–Brualdi–Stein Transversals in Latin Squares | Does every Latin square of order $n$ have a partial transversal of size $n-1$, and a full transversal when $n$ is odd? Equivalently, does every proper $n$-edge-coloring of $K_{n,n}$ contain a rainbow matching of size $n-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16763-026",
"OWR-16763-028",
"OWR-10252930-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-027",
"literature-status:partially-solved",
"owr-year:2019"
] | Montgomery proves a partial transversal of size n-1 for every sufficiently large Latin square, settling the near-transversal part asymptotically; the assertion of a full transversal for every odd order is still unresolved. | [
{
"url": "https://arxiv.org/abs/2310.19779",
"label": "Montgomery, large even orders"
},
{
"url": "https://doi.org/10.1090/btran/92",
"label": "new bounds for Ryser's conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | Does every Latin square of order $n$ have a partial transversal of size $n-1$, and a full transversal when $n$ is odd? Equivalently, does every proper $n$-edge-coloring of $K_{n,n}$ contain a rainbow matching of size $n-1$? | Every Latin square of order n has a partial transversal of size n-1 and, when n is odd, a transversal; equivalently, every proper n-coloring of K_{n,n} has a rainbow matching of size n-1. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,054 | OWR-16763-028 | Composite Duplicate of Two Rainbow-Matching Conjectures | Conjectures: every Latin square of order n has a partial transversal of size n-1 and, if n is odd, a transversal; and every properly n-edge-colored bipartite multigraph with at least n+1 edges of each color has a rainbow matching using every color. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (The first clause is represented canonically by OWR-16763-027 and the second by OWR-16763-030. This composite extraction adds no distinct pro) | [
"OWR-16763-027",
"OWR-16763-030"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-028",
"literature-status:partially-solved",
"owr-year:2019"
] | Duplicate extraction; the canonical question is OWR-16763-027, OWR-16763-030. The first clause is represented canonically by OWR-16763-027 and the second by OWR-16763-030. This composite extraction adds no distinct problem. No separate clean statement is promoted; the original record remains publicly visible and retain... | [
{
"url": "https://doi.org/10.4171/owr/2019/1",
"label": "Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updates and follow-u... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | null | Conjectures: every Latin square of order n has a partial transversal of size n-1 and, if n is odd, a transversal; and every properly n-edge-colored bipartite multigraph with at least n+1 edges of each color has a rainbow matching using every color. | unrecoverable | The first clause is represented canonically by OWR-16763-027 and the second by OWR-16763-030. This composite extraction adds no distinct problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,055 | OWR-16763-030 | Full Rainbow Matchings in Densely Colored Bipartite Multigraphs | If a bipartite multigraph is properly edge-colored with $n$ colors and has at least $n+1$ edges of each color, must it have a rainbow matching using every color? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63](https://doi.org/10.4171/owr/2019/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16763-028",
"OWR-9790352-023"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16763-030",
"literature-status:partially-solved",
"owr-year:2019"
] | This is the exact Aharoni--Berger conjecture: asymptotic n+o(n) results and near-perfect rainbow matchings are known, but a rainbow matching using every colour under the stated n+1 threshold is not known in general. | [
{
"url": "https://doi.org/10.1016/j.aim.2018.05.036",
"label": "Pokrovskiy, approximate conjecture"
},
{
"url": "https://arxiv.org/abs/1710.03041",
"label": "Keevash--Yepremyan, rainbow matchings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/1 | null | null | null | If a bipartite multigraph is properly edge-colored with $n$ colors and has at least $n+1$ edges of each color, must it have a rainbow matching using every color? | If a bipartite multigraph is properly edge-colored with n colors and has at least n+1 edges of each color, then it has a rainbow matching using every color. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/1, pp. 5--63 |
30,004,056 | OWR-16764-001 | Integral Models of Parahoric Shimura Varieties | Determine the existence and characterize the uniqueness of integral models of Shimura varieties with parahoric level structure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131](https://doi.org/10.4171/owr/2019/2)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16764-001",
"literature-status:open",
"owr-year:2019"
] | The record poses a broad existence, characterization, and uniqueness question rather than a single theorem; integral models are constructed in major cases, but no general uniqueness-and-characterization result resolves the stated problem. | [
{
"url": "https://arxiv.org/abs/1512.01149",
"label": "Kisin--Pappas, parahoric integral models"
},
{
"url": "https://arxiv.org/abs/2409.03689",
"label": "Kisin--Pappas--Zhou, integral models II"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/2 | null | null | null | Determine the existence and characterize the uniqueness of integral models of Shimura varieties with parahoric level structure. | Determine the existence and characterize the uniqueness of integral models of Shimura varieties with parahoric level structure. | 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 | Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131 |
30,004,057 | OWR-16764-002 | Theta Operators for Unitary Shimura Varieties | Develop, for unitary Shimura varieties, analogues of the characteristic-$p$ modular-form structures involving the Hasse invariant, the theta derivation, and theta cycles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131](https://doi.org/10.4171/owr/2019/2)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16764-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The stated goal has substantial realizations: theta operators are constructed for unitary groups of arbitrary signature in the inert case and more broadly at unramified primes, but a complete theory for all unitary Shimura settings is not established. | [
{
"url": "https://doi.org/10.2140/ant.2019.13.1829",
"label": "de Shalit--Goren, theta operators"
},
{
"url": "https://arxiv.org/abs/2002.09450",
"label": "Eischen--Mantovan, entire theta operators"
},
{
"url": "https://arxiv.org/abs/2209.03717",
"label": "La Porta, generalized theta... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/2 | null | null | null | Develop, for unitary Shimura varieties, analogues of the characteristic-$p$ modular-form structures involving the Hasse invariant, the theta derivation, and theta cycles. | Develop for unitary Shimura varieties analogues of the characteristic-p modular-form structures involving the Hasse invariant, the theta derivation, and theta cycles. | 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 | Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131 |
30,004,058 | OWR-16764-003 | Filtration along Modular Theta Cycles | If $\tau(f),\ldots,\tau^p(f)$ is the theta cycle of a modular form $f$, how does the filtration of $f$ change along this cycle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131](https://doi.org/10.4171/owr/2019/2)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16764-003",
"literature-status:partially-solved",
"owr-year:2019"
] | For signature (n,1), de Shalit and Goren give an explicit theta-cycle filtration formula, and later work constructs further weight-shifting operators; the general filtration behavior across unitary Shimura varieties remains open. | [
{
"url": "https://doi.org/10.2140/ant.2019.13.1829",
"label": "de Shalit--Goren, theta cycles"
},
{
"url": "https://arxiv.org/abs/2209.03717",
"label": "La Porta, generalized theta operators"
},
{
"url": "https://academic.oup.com/imrn/article/2022/21/16405/6326546",
"label": "Eischen... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/2 | null | null | null | If $\tau(f),\ldots,\tau^p(f)$ is the theta cycle of a modular form $f$, how does the filtration of $f$ change along this cycle? | If \tau(f),\ldots,\tau^{p}(f) is the theta cycle of a modular form f, how does the filtration of f change along its theta cycle? | 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 | Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131 |
30,004,059 | OWR-16764-005 | Equality of Automorphic Weight Cones | Let $C_{\mathrm{zip}}$ be the cone of automorphic weights defined by global sections on the $G$-zip stack, and let $C_K(\mathbb F_p)$ be the corresponding cone for the special fiber of the Shimura variety. Is
$$
\langle C_{\mathrm{zip}}\rangle=\langle C_K(\mathbb F_p)\rangle
$$
? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131](https://doi.org/10.4171/owr/2019/2)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16764-005",
"literature-status:partially-solved",
"owr-year:2019"
] | The saturated-cone equality between automorphic weights and G-zip weights remains a conjecture in general; inclusions, representation-theoretic descriptions, and several group or Shimura-variety cases are proved. | [
{
"url": "https://arxiv.org/abs/2211.16817",
"label": "Koskivirta, divisibility and the cone"
},
{
"url": "https://arxiv.org/abs/1810.05255",
"label": "Irving--Koskivirta, automorphic forms on G-zips"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/2 | null | null | null | Let $C_{\mathrm{zip}}$ be the cone of automorphic weights defined by global sections on the $G$-zip stack, and let $C_K(\mathbb F_p)$ be the corresponding cone for the special fiber of the Shimura variety. Is
$$
\langle C_{\mathrm{zip}}\rangle=\langle C_K(\mathbb F_p)\rangle
$$
? | For the cones of automorphic weights defined by global sections on the G-zip stack and on the special fiber of the Shimura variety, is \langle C_{\mathrm{zip}}\rangle=\langle C_K(\mathbb{F}_p)\rangle? | 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 | Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131 |
30,004,060 | OWR-16764-006 | Newton Strata Meeting Weakly Admissible Loci | For which $[b']\in B(G)$ does the Newton stratum $\mathcal{F}(G,b,\mu)^{[b']}$ intersect the weakly admissible locus $\mathcal{F}(G,b,\mu)^{wa}$ nontrivially? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131](https://doi.org/10.4171/owr/2019/2)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,019 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16764-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The question is answered for important basic and Hodge--Newton-decomposable cases, but the report explicitly leaves other Newton strata unresolved; later structure theorems do not give the requested complete classification of intersections. | [
{
"url": "https://arxiv.org/abs/1710.06935",
"label": "Chen--Fargues--Shen, p-adic period domains"
},
{
"url": "https://doi.org/10.4171/OWR/2019/2",
"label": "Oberwolfach report on arithmetic of Shimura varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/2 | null | null | null | For which $[b']\in B(G)$ does the Newton stratum $\mathcal{F}(G,b,\mu)^{[b']}$ intersect the weakly admissible locus $\mathcal{F}(G,b,\mu)^{wa}$ nontrivially? | For which [b']\inB(G) does the Newton stratum \mathcal F(G,b,\mu)^{[b']} intersect the weakly admissible locus \mathcal F(G,b,\mu)^{wa} nontrivially? | 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 | Arithmetic of Shimura Varieties (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/2, pp. 65--131 |
30,004,061 | OWR-16765-002 | Convergence of Finite-Element Mean-Curvature Flow | Prove convergence of Dziuk's method or related evolving finite-element methods for mean-curvature flow of closed two-dimensional surfaces or higher-dimensional hypersurfaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/3, pp. 133--207](ht... | 3 | partially_solved | null | 2,019 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open 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-16767-005"
] | null | Answered in the source or not an open problem (solved (yes, as posed; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] and its duplicate `OWR-16767-005` → **solved (yes, as posed; answered in the source)**. This updates Follow-up 11, which named the wrong record as the flagged duplicate. C. Lubich (OWR 3/2019, pp. 162–163) calls convergence of Dziuk's method "or related" evolving FEMs for c... | [
"owr",
"oberwolfach-reports",
"OWR-16765-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The historical gap is closed for closed two-dimensional surfaces in several evolving finite-element formulations, and direct semidiscrete convergence of Dziuk's method is proved for high-order elements; the broad higher-dimensional and fully general formulation remains incomplete. | [
{
"url": "https://doi.org/10.1137/20M136935X",
"label": "Li, convergence of Dziuk's method"
},
{
"url": "https://doi.org/10.1007/s00211-019-01074-2",
"label": "Kovács--Li--Lubich, evolving finite elements"
},
{
"url": "https://doi.org/10.4171/IFB/493",
"label": "Binz--Kovács, arbitra... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/3 | null | null | null | Prove convergence of Dziuk's method or related evolving finite-element methods for mean-curvature flow of closed two-dimensional surfaces or higher-dimensional hypersurfaces. | Prove convergence of Dziuk's method or related evolving finite-element methods for mean-curvature flow of closed two-dimensional surfaces or higher-dimensional hypersurfaces. | 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 | Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, non-local and discrete structures (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/3, pp. 133--207 |
30,004,062 | OWR-16766-001 | Tomographic Reconstruction near Discontinuities | For reconstruction of functions with discontinuities from discrete tomographic data, what is the reconstruction behavior near singularities, what is the effect of remote singularities, and why can discontinuous functions be reconstructed accurately? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303](https://doi.org/10.4171/owr/2019/4)
## Literature review (checked 2... | 3 | partially_solved | null | 2,019 | 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-16766-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Discrete Radon and related tomographic reconstructions now have precise asymptotic descriptions near jumps and results on remote singularities in several two- and three-dimensional models, but the general discontinuous discrete-tomography problem remains unresolved. | [
{
"url": "https://doi.org/10.1137/21M1466712",
"label": "Katsevich, nonsmooth edges in discrete Radon data"
},
{
"url": "https://arxiv.org/abs/1903.08216",
"label": "Katsevich, three-dimensional jump discontinuities"
},
{
"url": "https://arxiv.org/abs/2001.05774",
"label": "Katsevich... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/4 | null | null | null | For reconstruction of functions with discontinuities from discrete tomographic data, what is the reconstruction behavior near singularities, what is the effect of remote singularities, and why can discontinuous functions be reconstructed accurately? | For reconstruction of functions with discontinuities from discrete tomographic data, what is the reconstruction behavior near singularities, what is the effect of remote singularities, and why can discontinuous functions be reconstructed accurately? | 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 | Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303 |
30,004,063 | OWR-16766-002 | Exact Recovery by Lagrangian-Dual Binary Tomography | In noiseless binary tomography, if the tomographic problem has a unique solution, does the proposed Lagrangian-dual approach retrieve that solution? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303](https://doi.org/10.4171/owr/2019/4)
## Literature review (checked 2... | 3 | open | null | 2,019 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this is a partial duplicate of the binary-tomography recovery conjecture retained in OWR-16766-003. No separa) | [
"OWR-16766-003"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16766-002",
"literature-status:open",
"owr-year:2019"
] | The dual method is only supported by exhaustive small-image experiments; the primary paper states that the relaxation is not generally guaranteed to recover an optimal binary solution and does not prove the conjectured uniqueness or intersection property. | [
{
"url": "https://doi.org/10.1109/TCI.2019.2898333",
"label": "Kadu--van Leeuwen, convex binary tomography"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/4 | null | null | null | null | In noiseless binary tomography, if the tomographic problem has a unique solution, does the proposed Lagrangian-dual approach retrieve that solution? | unrecoverable | The official report shows that this is a partial duplicate of the binary-tomography recovery conjecture retained in OWR-16766-003. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303 |
30,004,064 | OWR-16766-003 | Dual Recovery of Binary Tomography Solution Intersections | Let $A\in\mathbb R^{m\times n}$, let $x\in\{-1,1\}^n$ produce noiseless data $y=Ax$, and let $\mu^*$ minimize
$$
\frac12\lVert\mu-y\rVert_2^2+\lVert A^T\mu\rVert_1.
$$
With $\widehat x=\operatorname{sign}(A^T\mu^*)$, must $\widehat x$ recover $x$ whenever the binary tomography problem has a unique solution? When it has... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303](https://doi.org/10.4171/owr/2019/4)
## Literature review (checked 2... | 3 | open | null | 2,019 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16766-002",
"OWR-16766-004"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16766-003",
"literature-status:open",
"owr-year:2019"
] | The extracted sentence introduces the binary-tomography conjecture, whose two assertions remain empirical rather than theorem-level; no primary source located proves them in the stated generality. | [
{
"url": "https://doi.org/10.1109/TCI.2019.2898333",
"label": "Kadu--van Leeuwen, convex binary tomography"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/4 | null | null | null | Let $A\in\mathbb R^{m\times n}$, let $x\in\{-1,1\}^n$ produce noiseless data $y=Ax$, and let $\mu^*$ minimize
$$
\frac12\lVert\mu-y\rVert_2^2+\lVert A^T\mu\rVert_1.
$$
With $\widehat x=\operatorname{sign}(A^T\mu^*)$, must $\widehat x$ recover $x$ whenever the binary tomography problem has a unique solution? When it has... | For a binary tomography problem with noiseless projections, does the dual approach retrieve the unique solution when it is unique, and the intersection of all solutions when multiple solutions exist? | 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 | Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303 |
30,004,065 | OWR-16766-004 | Binary Tomography Recovery Conjecture | Conjecture: for a binary tomography problem with noiseless projections, the dual approach retrieves the unique solution when it is unique and retrieves the common intersection of all solutions when multiple solutions exist. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303](https://doi.org/10.4171/owr/2019/4)
## Literature review (checked 2... | 3 | open | null | 2,019 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23110494",
"checked_at": "2026-10-02",
"kind": "claim",
"evidence": "unrefereed_claim"
} | Duplicate/merged OWR extraction (The official report confirms that this is a second complete duplicate of the binary-tomography recovery conjecture retained in OWR-16766-003) | [
"OWR-16766-003"
] | null | [Discussion #4 unrefereed claim, 2026-10-02] I have released an unrefereed preprint, **A Negative Answer to the Kadu–van Leeuwen Conjecture on Dual Binary Tomography** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23110494) | [
"owr",
"oberwolfach-reports",
"OWR-16766-004",
"literature-status:open",
"owr-year:2019"
] | The explicit conjecture is still open in general: the published work reports exhaustive verification only for small images and presents the dual formulation as a relaxation without a general recovery theorem. | [
{
"url": "https://doi.org/10.1109/TCI.2019.2898333",
"label": "Kadu--van Leeuwen, convex binary tomography"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/4 | null | null | null | null | Conjecture: for a binary tomography problem with noiseless projections, the dual approach retrieves the unique solution when it is unique and retrieves the common intersection of all solutions when multiple solutions exist. | unrecoverable | The official report confirms that this is a second complete duplicate of the binary-tomography recovery conjecture retained in OWR-16766-003. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303 |
30,004,066 | OWR-16766-005 | Strong Duality and Multilevel Discrete Tomography | Does strong duality hold between the binary-tomography primal problem and its Lagrangian dual? Can an analogous dual formulation be developed for discrete tomography with more than two gray levels? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303](https://doi.org/10.4171/owr/2019/4)
## Literature review (checked 2... | 3 | open | null | 2,019 | 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-16766-005",
"literature-status:open",
"owr-year:2019"
] | The listed strong-duality question, conjecture-proof request, and extension to more grey levels remain open; the source records them as open questions and supplies only small-scale computational evidence. | [
{
"url": "https://doi.org/10.1109/TCI.2019.2898333",
"label": "Kadu--van Leeuwen, convex binary tomography"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/4 | null | null | null | Does strong duality hold between the binary-tomography primal problem and its Lagrangian dual? Can an analogous dual formulation be developed for discrete tomography with more than two gray levels? | For the binary-tomography primal and dual formulations, does strong duality hold; can the preceding unique-solution/intersection conjecture be proved; and does the approach extend to discrete tomography with more than two gray levels? | 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 | Tomographic Inverse Problems: Theory and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/4, pp. 209--303 |
30,004,067 | OWR-16767-001 | Energy Transfer Among Modes in Resonant Evolution | For the cubic resonant system
$$i\frac{d\alpha_n}{d\tau}=\sum_{n+j=k+l}S_{njkl}\overline{\alpha_j}\alpha_k\alpha_l,$$
how is the conserved energy $E=\sum_{n\geq0}E_n\lvert\alpha_n\rvert^2$ distributed among modes during evolution? In particular, under what conditions does energy flow from low to high modes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | open | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16767-001",
"literature-status:open",
"owr-year:2019"
] | The resonant-system analysis gives conservation laws, scaling asymptotics, and numerical evidence for high-frequency transfer in dimensions at least 7, but it does not determine the general mode-energy dynamics or prove a universal cascade statement. | [
{
"url": "https://doi.org/10.4171/OWR/2019/5",
"label": "Oberwolfach report on nonlinear evolution equations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | For the cubic resonant system
$$i\frac{d\alpha_n}{d\tau}=\sum_{n+j=k+l}S_{njkl}\overline{\alpha_j}\alpha_k\alpha_l,$$
how is the conserved energy $E=\sum_{n\geq0}E_n\lvert\alpha_n\rvert^2$ distributed among modes during evolution? In particular, under what conditions does energy flow from low to high modes? | For the resonant evolution system under discussion, how is the energy of the initial data distributed among the modes during evolution, and does energy flow from low to high modes? | corrected_verified | The official report was checked. The reconstruction restores the cubic resonant equation and the conserved modal energy referred to by the extracted question. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,068 | OWR-16767-002 | Symplectic Nonsqueezing in Infinite-Dimensional Hilbert Spaces | Does the finite-dimensional symplectic non-squeezing theorem extend to symplectomorphisms of infinite-dimensional Hilbert symplectic spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | partially_solved | null | 2,019 | 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-16767-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Infinite-dimensional non-squeezing is proved for convex images, Hilbert-scale regular symplectomorphisms, and several Hamiltonian PDE flows, but the unrestricted Hilbert-space analogue stated in the record remains unproved. | [
{
"url": "https://arxiv.org/abs/1405.3200",
"label": "Abbondandolo--Majer, convex Hilbert images"
},
{
"url": "https://arxiv.org/abs/1411.3989",
"label": "Sukhov--Tumanov, Hilbert-space theorem"
},
{
"url": "https://hdl.handle.net/20.500.11811/9440",
"label": "Cicmilović, infinite-di... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | Does the finite-dimensional symplectic non-squeezing theorem extend to symplectomorphisms of infinite-dimensional Hilbert symplectic spaces? | Does the finite-dimensional symplectic non-squeezing theorem extend to symplectomorphisms of infinite-dimensional Hilbert symplectic spaces? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,069 | OWR-16767-003 | Direct Proofs of Hilbert-Space Symplectic Nonsqueezing | Does there exist a direct proof of symplectic non-squeezing in Hilbert space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | partially_solved | null | 2,019 | 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-16767-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Direct proofs exist under substantial geometric or Hilbert-scale regularity assumptions, including the Sukhov--Tumanov theorem, but no direct proof for arbitrary symplectomorphisms of a Hilbert space is established. | [
{
"url": "https://arxiv.org/abs/1411.3989",
"label": "Sukhov--Tumanov, Hilbert-space theorem"
},
{
"url": "https://arxiv.org/abs/1405.3200",
"label": "Abbondandolo--Majer, convex Hilbert images"
},
{
"url": "https://hdl.handle.net/20.500.11811/9440",
"label": "Cicmilović, infinite-di... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | Does there exist a direct proof of symplectic non-squeezing in Hilbert space? | Does there exist a direct proof of symplectic non-squeezing in Hilbert space? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,070 | OWR-16767-004 | Optimal Fourier Restriction Estimates on Submanifolds | For the Fourier restriction operator $R$ to a submanifold $C\subset\mathbb R^{1+n}$, determine the optimal exponents $p,q$ for which
$$\lVert Rf\rVert_{L^p(C)}\lesssim\lVert f\rVert_{L^q(\mathbb R^{1+n})}$$
holds. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-16767-004",
"literature-status:open",
"owr-year:2019"
] | The record is the cone Fourier-restriction estimate in its conjectured optimal exponent range; sharp results cover several dimensions and bilinear subranges, but the full optimal range remains open in higher dimensions. | [
{
"url": "https://doi.org/10.1093/imrn/rnw223",
"label": "Guth--Hickman-- Iliopoulou, bilinear restriction"
},
{
"url": "https://doi.org/10.4171/OWR/2019/5",
"label": "Oberwolfach report on Fourier restriction"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | For the Fourier restriction operator $R$ to a submanifold $C\subset\mathbb R^{1+n}$, determine the optimal exponents $p,q$ for which
$$\lVert Rf\rVert_{L^p(C)}\lesssim\lVert f\rVert_{L^q(\mathbb R^{1+n})}$$
holds. | For the Fourier restriction operator R to a submanifold C of \mathbb{R}^{1+n}, prove an estimate \|Rf\|_{L^p(C)}\lesssim\|f\|_{L^q(\mathbb{R}^{1+n})} throughout the optimal range of p and q determined by C. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,071 | OWR-16767-005 | Duplicate Finite-Element Mean-Curvature-Flow Problem | For mean-curvature flow of closed two-dimensional surfaces, or higher-dimensional hypersurfaces, does Dziuk's finite-element method or a related evolving finite-element method converge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | partially_solved | null | 2,019 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 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 | Answered in the source or not an open problem (solved (yes, as posed; answered in the source)) | [
"OWR-16765-002"
] | null | [Discussion #4 literature review, 2026-09-30] and its duplicate `OWR-16767-005` → **solved (yes, as posed; answered in the source)**. This updates Follow-up 11, which named the wrong record as the flagged duplicate. C. Lubich (OWR 3/2019, pp. 162–163) calls convergence of Dziuk's method "or related" evolving FEMs for c... | [
"owr",
"oberwolfach-reports",
"OWR-16767-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Convergence is now proved for Dziuk's semidiscrete method on closed two-dimensional surfaces with high-order elements and for several related evolving-surface schemes, while the broad higher-dimensional formulation in the record is not fully settled. | [
{
"url": "https://doi.org/10.1137/20M136935X",
"label": "Li, convergence of Dziuk's method"
},
{
"url": "https://doi.org/10.1007/s00211-019-01074-2",
"label": "Kovács--Li--Lubich, evolving finite elements"
},
{
"url": "https://doi.org/10.4171/IFB/493",
"label": "Binz--Kovács, arbitra... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | null | For mean-curvature flow of closed two-dimensional surfaces, or higher-dimensional hypersurfaces, does Dziuk's finite-element method or a related evolving finite-element method converge? | unrecoverable | This record repeats the convergence problem for Dziuk’s method and related evolving finite-element methods represented canonically by the earlier OWR-16765-002. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,072 | OWR-16767-006 | Long-Time Dynamics of Randomized Mass-Subcritical NLS | Let $d\geq1$, $2/d<p<4/d$, and $\phi\in L^2(\mathbb R^d)$. For
$$i\partial_tu-\Delta u=\lvert u\rvert^pu,\qquad u(0)=\phi^\omega,$$
what is the long-time asymptotic behavior beyond free scattering profiles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | open | null | 2,019 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16767-006",
"literature-status:open",
"owr-year:2019"
] | The cited randomized Cauchy problem has global solutions in the stated regime, but the requested asymptotic behavior remains unresolved in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2019/5",
"label": "Oberwolfach Report 5/2019"
},
{
"url": "https://arxiv.org/abs/1203.4027",
"label": "Chatterjee on soliton resolution"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | Let $d\geq1$, $2/d<p<4/d$, and $\phi\in L^2(\mathbb R^d)$. For
$$i\partial_tu-\Delta u=\lvert u\rvert^pu,\qquad u(0)=\phi^\omega,$$
what is the long-time asymptotic behavior beyond free scattering profiles? | Let d\geq 1, 2/d<p<4/d, and \phi\in L^2(\mathbb{R}^d). For the randomized mass-subcritical nonlinear Schrödinger problem i\partial_tu-\Delta u=|u|^pu with u(0)=\phi^\omega, what is the asymptotic behavior as t\to\infty, beyond the free scattering profiles? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,073 | OWR-16767-007 | Soliton Resolution for Randomized Mass-Subcritical NLS | Let $2/d<p<4/d$ and $\phi\in L^2(\mathbb{R}^d)$. For almost every $\omega$, does the solution of $i\partial_tu-\Delta u=|u|^pu$, $u(0)=\phi^\omega$, admit solitons $u_j(t,x)=e^{it a_j+i x\cdot k_j}\phi_j(x-c_jt)$ and a free profile $e^{-it\Delta}\phi$ such that $\left\|u(t)-\sum_j u_j(t)-e^{-it\Delta}\phi\right\|_{L^2(... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-16767-007",
"literature-status:open",
"owr-year:2019"
] | The randomized soliton-resolution assertion is still open; existing work gives global solutions or statistical and special-case results, not the stated almost-sure decomposition. | [
{
"url": "https://doi.org/10.4171/owr/2019/5",
"label": "Oberwolfach Report 5/2019"
},
{
"url": "https://arxiv.org/abs/1203.4027",
"label": "Chatterjee on soliton resolution"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | Let $2/d<p<4/d$ and $\phi\in L^2(\mathbb{R}^d)$. For almost every $\omega$, does the solution of $i\partial_tu-\Delta u=|u|^pu$, $u(0)=\phi^\omega$, admit solitons $u_j(t,x)=e^{it a_j+i x\cdot k_j}\phi_j(x-c_jt)$ and a free profile $e^{-it\Delta}\phi$ such that $\left\|u(t)-\sum_j u_j(t)-e^{-it\Delta}\phi\right\|_{L^2(... | Let 2/d<p<4/d and \phi\in L^2(\mathbb{R}^d). For almost every \omega, does the solution of i\partial_tu-\Delta u=|u|^pu, u(0)=\phi^\omega, admit solitons u_j(t,x)=e^{it a_j+i x\cdot k_j}\phi_j(x-c_jt) and a free profile e^{-it\Delta}\phi such that \left\|u(t)-\sum_j u_j(t)-e^{-it\Delta}\phi\right\|_{L^2(\mathbb{R}^d)}\... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,074 | OWR-16767-008 | Critical Self-Similar Profiles for Focusing Cubic Wave Blowup | For the focusing cubic wave equation in dimensions $d\geq5$, is $f^*$ a critical self-similar profile describing threshold solutions and their intermediate-time behavior between stable blowup and global existence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405](https://doi.org/10.4171/owr/2019/5)
## Literature review (checked 20... | 3 | open | null | 2,019 | 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-16767-008",
"literature-status:open",
"owr-year:2019"
] | Primary work constructs the nontrivial self-similar profile and proves stability in cases, but its role as the complete threshold between blowup and global existence remains analytically open. | [
{
"url": "https://doi.org/10.1016/j.aim.2021.107930",
"label": "Glogic--Schoerkhuber"
},
{
"url": "https://doi.org/10.1088/1361-6544/ab6f4d",
"label": "Glogic--Maliborski--Schoerkhuber"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/5 | null | null | null | For the focusing cubic wave equation in dimensions $d\geq5$, is $f^*$ a critical self-similar profile describing threshold solutions and their intermediate-time behavior between stable blowup and global existence? | For the focusing cubic wave equation in dimensions d\geq 5, is f^* a critical self-similar profile describing solutions at, and during at least some intermediate times near, the threshold between stable blowup and global existence? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Nonlinear Evolution Equations: Analysis and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/5, pp. 305--405 |
30,004,075 | OWR-16768-003 | Localization of Finitistic Test Ideals | Let $R$ be an $F$-finite Noetherian domain of characteristic $p>0$, let $\mathfrak a\neq0$ be an ideal, let $t>0$, and let $S\subset R$ be multiplicatively closed. Is
$$S^{-1}\tau_{\mathrm{fg}}(\mathfrak a^t)=\tau_{\mathrm{fg}}\bigl((S^{-1}\mathfrak a)^t\bigr).$$
Does this equality hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16768-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-003",
"literature-status:open",
"owr-year:2019"
] | The Stückrad--Vogel conjecture mentioned in the record is solved, but the extracted localization compatibility question for finitistic test ideals remains unresolved beyond additional hypotheses. | [
{
"url": "https://doi.org/10.1016/j.aim.2019.02.029",
"label": "St\\\"uckrad--Vogel resolution"
},
{
"url": "https://doi.org/10.1090/S0002-9947-01-02643-5",
"label": "Lyubeznik--Smith on localization"
},
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/20... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Let $R$ be an $F$-finite Noetherian domain of characteristic $p>0$, let $\mathfrak a\neq0$ be an ideal, let $t>0$, and let $S\subset R$ be multiplicatively closed. Is
$$S^{-1}\tau_{\mathrm{fg}}(\mathfrak a^t)=\tau_{\mathrm{fg}}\bigl((S^{-1}\mathfrak a)^t\bigr).$$
Does this equality hold? | For an F-finite Noetherian domain R of characteristic p>0, a nonzero ideal a, t>0, and a multiplicative subset S of R, is the formation of finitistic test ideals compatible with localization, namely S^{-1}\tau_{\mathrm{fg}}(a^t)=\tau_{\mathrm{fg}}((S^{-1}a)^t)? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,076 | OWR-16768-006 | Smooth Varieties with Squarefree Gröbner Degenerations | Let $I$ be a homogeneous ideal in a standard graded polynomial ring $S$ over a field $K$. Suppose $I$ defines a nonsingular projective variety and has a square-free initial ideal for some monomial order. Must $S/I$ be Cohen–Macaulay with negative $a$-invariant? For curves, must every such nonsingular projective curve h... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-006",
"literature-status:open",
"owr-year:2019"
] | The conjecture is proved for degree-reverse-lexicographic order and the curve case has since been settled, but the full assertion for arbitrary square-free initial ideals remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://arxiv.org/abs/2512.00584",
"label": "Huang--Tarasova--Varbaro--Witt"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Let $I$ be a homogeneous ideal in a standard graded polynomial ring $S$ over a field $K$. Suppose $I$ defines a nonsingular projective variety and has a square-free initial ideal for some monomial order. Must $S/I$ be Cohen–Macaulay with negative $a$-invariant? For curves, must every such nonsingular projective curve h... | Let I be a homogeneous ideal in a standard graded polynomial ring S over K, with square-free initial ideal for some monomial order, and suppose I defines a nonsingular projective variety. Must S/I be Cohen--Macaulay with negative a-invariant? Equivalently for curves, must every such nonsingular projective curve have ge... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,077 | OWR-16768-009 | Coordinate Realization of Characteristic-Polyhedron Multiplicity | Let $R$ be an excellent regular local ring with regular parameters $(u,y)$, and let $f\in R\setminus\langle u\rangle$. Write $m=m(f)$ and let $\operatorname{in}_0(f)\in k[Y_1,\ldots,Y_r]$ be its degree-$m$ initial form. Assume there is no proper $k$-subspace $T\subset k[Y_1,\ldots,Y_r]_1$ with $\operatorname{in}_0(f)\i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-009",
"literature-status:open",
"owr-year:2019"
] | The exact extension question for excellent rings remains open; related characteristic-polyhedron results require additional G-ring, Henselian, or similar hypotheses. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://arxiv.org/abs/1411.2522",
"label": "Cossart--Schober"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Let $R$ be an excellent regular local ring with regular parameters $(u,y)$, and let $f\in R\setminus\langle u\rangle$. Write $m=m(f)$ and let $\operatorname{in}_0(f)\in k[Y_1,\ldots,Y_r]$ be its degree-$m$ initial form. Assume there is no proper $k$-subspace $T\subset k[Y_1,\ldots,Y_r]_1$ with $\operatorname{in}_0(f)\i... | Let R be an excellent regular local ring with regular system of parameters (u,y), let f\in R with f\notin\langle u\rangle, and let m=m(f) be defined from the characteristic polyhedron. Assuming the initial-form condition (*) and f\in\langle\widehat y\rangle^m for coordinates \widehat y_j=y_j+\varphi_j with \varphi_j\in... | corrected_verified | The official report was checked. The reconstruction replaces the dangling initial-form condition with its explicit no-proper-linear-subspace hypothesis and restores the completion notation. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,078 | OWR-16768-010 | Duplicate Localization Conjecture for Finitistic Test Ideals | For an F-finite Noetherian domain R of characteristic p>0, a nonzero ideal a, t>0, and any multiplicative subset S of R, does S^{-1}\tau_{\mathrm{fg}}(a^t)=\tau_{\mathrm{fg}}((S^{-1}a)^t) hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record repeats the localization-compatibility problem represented canonically by OWR-16768-003. No separate clean statement is promoted) | [
"OWR-16768-003"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-010",
"literature-status:open",
"owr-year:2019"
] | The finitistic and big test ideal equality in the extracted conjecture remains unresolved in general, although important special cases including numerically Q-Gorenstein settings are proved. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2018.08.003",
"label": "Takagi, finitistic test ideals"
},
{
"url": "https://doi.org/10.1016/j.aim.2024.109559",
"label": "Aberbach--Huneke--Polstra"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | null | For an F-finite Noetherian domain R of characteristic p>0, a nonzero ideal a, t>0, and any multiplicative subset S of R, does S^{-1}\tau_{\mathrm{fg}}(a^t)=\tau_{\mathrm{fg}}((S^{-1}a)^t) hold? | unrecoverable | This record repeats the localization-compatibility problem represented canonically by OWR-16768-003. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,079 | OWR-16768-011 | Equality of Finitistic and Big Test Ideals | For an $F$-finite Noetherian domain $R$ of characteristic $p>0$, a nonzero ideal $\mathfrak a$, and $t>0$, is
$$\tau_{\mathrm{fg}}(\mathfrak a^t)=\tau_b(\mathfrak a^t).$$
Does this equality hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-011",
"literature-status:open",
"owr-year:2019"
] | Known cases establish the equality of finitistic and big test ideals under additional hypotheses, but the general conjecture recorded here remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2018.08.003",
"label": "Takagi, finitistic test ideals"
},
{
"url": "https://doi.org/10.1016/j.aim.2024.109559",
"label": "Aberbach--Huneke--Polstra"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | For an $F$-finite Noetherian domain $R$ of characteristic $p>0$, a nonzero ideal $\mathfrak a$, and $t>0$, is
$$\tau_{\mathrm{fg}}(\mathfrak a^t)=\tau_b(\mathfrak a^t).$$
Does this equality hold? | For an F-finite Noetherian domain R of characteristic p>0, a nonzero ideal a, and t>0, is the finitistic test ideal equal to the big test ideal, namely \tau_{\mathrm{fg}}(a^t)=\tau_b(a^t)? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,080 | OWR-16768-012 | Big Test Ideals from Plus Closure | Let $R$ be a localization of a numerically $\mathbb Q$-Gorenstein normal domain of finite type over an $F$-finite field, and set
$$P(R)=\bigcap_{I\subseteq R}(I:I^+),\qquad I^+=IR^+\cap R.$$
Is the big test ideal $\tau_b(R)$ equal to $P(R)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-012",
"literature-status:open",
"owr-year:2019"
] | The exact conjectural equality between the big test ideal and the plus-closure ideal remains unproved; known inclusions and related special-case equalities do not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2018.08.003",
"label": "Takagi, finitistic test ideals"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Let $R$ be a localization of a numerically $\mathbb Q$-Gorenstein normal domain of finite type over an $F$-finite field, and set
$$P(R)=\bigcap_{I\subseteq R}(I:I^+),\qquad I^+=IR^+\cap R.$$
Is the big test ideal $\tau_b(R)$ equal to $P(R)$? | Let R be a localization of a numerically Q-Gorenstein normal domain of finite type over an F-finite field, and let P(R)=\bigcap_{I\subseteq R}(I:I^+) with I^+=IR^+\cap R. Is the big test ideal of R equal to P(R), namely \tau_b(R)=P(R)? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,081 | OWR-16768-013 | Finiteness of Singular-Centered Arc-Space Components | If $X$ is an irreducible variety over a perfect field of characteristic $p>0$, does the subspace of the arc space $X_\infty$ consisting of arcs centered in $\operatorname{Sing}(X)$ have finitely many irreducible components? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-013",
"literature-status:open",
"owr-year:2019"
] | In positive characteristic it remains unknown in arbitrary dimension whether the singular arc space has finitely many irreducible components; surface and local-uniformization cases do not prove the general statement. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2022.107110",
"label": "Benito--Piltant--Reguera"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2017.08.012",
"label": "Piltant--Reguera"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | If $X$ is an irreducible variety over a perfect field of characteristic $p>0$, does the subspace of the arc space $X_\infty$ consisting of arcs centered in $\operatorname{Sing}(X)$ have finitely many irreducible components? | If X is an irreducible variety over a perfect field of characteristic p>0, does the arc space of X consisting of arcs centered at Sing(X) have finitely many irreducible components? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,082 | OWR-16768-014 | Birational Models with Irreducible Arc Spaces | Given a variety $X$, does there exist a proper birational morphism $Y\to X$ such that the arc space $Y_\infty$ is irreducible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-014",
"literature-status:open",
"owr-year:2019"
] | The existence of a proper birational model with irreducible arc space remains open in general; the known positive result only gives a birationally equivalent projective variety under a characteristic bound. | [
{
"url": "https://doi.org/10.1016/j.jpaa.2022.107110",
"label": "Benito--Piltant--Reguera"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Given a variety $X$, does there exist a proper birational morphism $Y\to X$ such that the arc space $Y_\infty$ is irreducible? | Given a variety X, does there exist a birational proper morphism Y\to X such that the arc space Y_\infty is irreducible? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,083 | OWR-16768-015 | Local-Cohomology Obstructions to Regular Maps and Projections | Can local-cohomology obstructions rule out injective or $k$-regular maps of complex varieties, or low-dimensional projections defined by separating invariants? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-015",
"literature-status:open",
"owr-year:2019"
] | The record gives only a broad title-level question about injections; primary work supplies lower bounds and examples but no general answer, so the question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
},
{
"url": "https://arxiv.org/abs/1905.11306",
"label": "G\\\"orlach, Injection dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Can local-cohomology obstructions rule out injective or $k$-regular maps of complex varieties, or low-dimensional projections defined by separating invariants? | For the problem of constructing injective or k-regular maps of complex varieties and low-dimensional separating-invariant projections, can local cohomology obstruct the existence of such injections? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,084 | OWR-16768-016 | Injective Projective Maps of Curves and Segre–Veronese Varieties | Can every smooth complex projective curve be injected into $\mathbb P^2$? More generally, can every smooth $d$-dimensional projective variety be injected into $\mathbb P^{2d}$? Can every Segre–Veronese variety be injectively projected into a projective space of twice its dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-016",
"literature-status:open",
"owr-year:2019"
] | The universal injection questions for smooth curves and Segre--Veronese varieties remain open; the literature establishes only positive families, bounds, and examples. | [
{
"url": "https://doi.org/10.1007/s11565-020-00343-5",
"label": "Ballico--Ventura"
},
{
"url": "https://arxiv.org/abs/1905.11306",
"label": "G\\\"orlach, Injection dimensions"
},
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Can every smooth complex projective curve be injected into $\mathbb P^2$? More generally, can every smooth $d$-dimensional projective variety be injected into $\mathbb P^{2d}$? Can every Segre–Veronese variety be injectively projected into a projective space of twice its dimension? | Can every smooth complex projective curve be injected into \mathbb{P}^2? Can every Segre--Veronese variety be injectively projected into a projective space of twice its dimension? | corrected_verified | The official report was checked. The omitted general smooth-variety question was restored alongside the curve and Segre–Veronese special cases. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,085 | OWR-16768-017 | Optimal Dimensions for Complex k-Regular Maps | Does a continuous $k$-regular map $\mathbb C^m\to\mathbb C^N$ exist if and only if $N\geq m(k-1)+1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-017",
"literature-status:open",
"owr-year:2019"
] | The proposed exact threshold for continuous k-regular maps is not known in general; current primary work gives lower bounds and constructions whose ranges do not universally coincide. | [
{
"url": "https://arxiv.org/abs/1511.05707",
"label": "Buczynski--Januszkiewicz--Jelisiejew--Michalek"
},
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach Report 6/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Does a continuous $k$-regular map $\mathbb C^m\to\mathbb C^N$ exist if and only if $N\geq m(k-1)+1$? | There exists a continuous k-regular map \mathbb{C}^m\to\mathbb{C}^N if and only if N\geq m(k-1)+1. | corrected_verified | The official report labels this assertion as Conjecture 5; it has been recast as a question without changing the dimensional threshold. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,086 | OWR-16768-023 | Simplicity of Differential-Operator Rings on Invariant Rings | Let $G$ be a linearly reductive group acting linearly on a polynomial ring $R$ over $\mathbb C$. Is the differential-operator ring $D_{\mathbb C}(R^G)$ simple? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464](https://doi.org/10.4171/owr/2019/6)
## Literature review (ch... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16768-023",
"literature-status:open",
"owr-year:2019"
] | The simplicity of the ring of differential operators on invariants is established in important cases, but the stated general characteristic-zero conjecture for all linearly reductive groups remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2023.109276",
"label": "Jeffries--Singh on invariant rings"
},
{
"url": "https://doi.org/10.4171/owr/2019/6",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/6 | null | null | null | Let $G$ be a linearly reductive group acting linearly on a polynomial ring $R$ over $\mathbb C$. Is the differential-operator ring $D_{\mathbb C}(R^G)$ simple? | Let G be a linearly reductive group acting linearly on a polynomial ring R over \mathbb{C}. Is the ring of differential operators D_{\mathbb{C}}(R^G) simple? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Singularities and Homological Aspects of Commutative Algebra (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/6, pp. 407--464 |
30,004,087 | OWR-16769-001 | Variance Feedback in Cloud Boundary-Layer Models | For Reynolds-averaged equations modeling the variances of liquid-water potential temperature and total-water mixing ratio in a precipitating cloudy atmospheric boundary layer, can the equations represent explicitly the slow positive feedback that produces the variance without an additional stochastic submodel? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Moist Processes in the Atmosphere (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/7, pp. 465--512](https://doi.org/10.4171/owr/2019/7)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,019 | 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-16769-001",
"literature-status:open",
"owr-year:2019"
] | Reynolds averaging leaves unresolved subgrid covariances and feedback terms; stochastic and deterministic parameterization research has not supplied a general closure without an additional submodel. | [
{
"url": "https://journals.ametsoc.org/view/journals/bams/98/3/bams-d-15-00268.1.xml",
"label": "Stochastic parameterization review"
},
{
"url": "https://doi.org/10.4171/owr/2019/7",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/7 | null | null | null | For Reynolds-averaged equations modeling the variances of liquid-water potential temperature and total-water mixing ratio in a precipitating cloudy atmospheric boundary layer, can the equations represent explicitly the slow positive feedback that produces the variance without an additional stochastic submodel? | For Reynolds-averaged equations modeling the variances of liquid-water potential temperature and total-water mixing ratio in a precipitating cloudy atmospheric boundary layer, can the equations represent explicitly the slow positive feedback that produces the variance without an additional stochastic submodel? | 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 | Moist Processes in the Atmosphere (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/7, pp. 465--512 |
30,004,088 | OWR-16770-001 | Cohomology of the Drinfeld Tower | For the Drinfeld tower $\mathcal M_\infty$ over a $p$-adic field, describe its $p$-adic étale cohomology and coherent cohomology, beyond the known compactly supported $\ell$-adic étale cohomology. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-001",
"literature-status:open",
"owr-year:2019"
] | Important cases of Drinfeld-tower etale and coherent cohomology are known, but the general cohomological description, admissibility, and finite-length assertions in the record remain unresolved. | [
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/factorisation-de-la-cohomologie-etale-padique-de-la-tour-de-drinfeld/79733067FC7CB7574B408744E4387F91",
"label": "Drinfeld-tower etale cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwol... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | For the Drinfeld tower $\mathcal M_\infty$ over a $p$-adic field, describe its $p$-adic étale cohomology and coherent cohomology, beyond the known compactly supported $\ell$-adic étale cohomology. | For the Drinfeld tower M_\infty over a p-adic field, what can be said about its cohomology groups other than compactly supported l-adic etale cohomology, in particular its p-adic etale cohomology and coherent cohomology? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,089 | OWR-16770-002 | Admissibility and Finite Length on the Drinfeld Tower | Let $F$ be a $p$-adic field, let $G=\operatorname{GL}_2(F)$, and let $\Sigma_n$ be the level-$n$ space in the Drinfeld tower. For every $n\geq0$, is $\mathcal O(\Sigma_n)^*$ an admissible locally analytic representation of $G$, and does it have finite length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16770-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Admissibility is proved for all levels when the base field is Qp and at the first level for arbitrary fields, while finite length is known at the first level; the full all-field all-level conjecture remains open. | [
{
"url": "https://annals.math.princeton.edu/2017/186-2/p01",
"label": "Dospinescu--Le Bras"
},
{
"url": "https://arxiv.org/abs/1201.3646",
"label": "Patel--Schmidt--Strauch"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | Let $F$ be a $p$-adic field, let $G=\operatorname{GL}_2(F)$, and let $\Sigma_n$ be the level-$n$ space in the Drinfeld tower. For every $n\geq0$, is $\mathcal O(\Sigma_n)^*$ an admissible locally analytic representation of $G$, and does it have finite length? | For the Drinfeld tower over a p-adic field F with G=GL_2(F), is O(\Sigma_n)^* an admissible locally analytic representation of G for every n\geq 0, and does it always have finite length? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,090 | OWR-16770-003 | Admissibility and Finite Length on the Drinfeld Tower | For the Drinfeld tower over a p-adic field F with G=GL_2(F), is O(\Sigma_n)^* an admissible locally analytic representation of G for every n\geq 0, and does it always have finite length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,019 | 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 contains a single two-part conjecture on admissibility and finite length; this extraction duplicates the complete statem) | [
"OWR-16770-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-003",
"literature-status:partially-solved",
"owr-year:2019"
] | The conjecture has substantial partial results, including admissibility for the Qp tower and first-level results over general fields, but its simultaneous admissibility and finite-length claims at every level and field are not proved. | [
{
"url": "https://annals.math.princeton.edu/2017/186-2/p01",
"label": "Dospinescu--Le Bras"
},
{
"url": "https://arxiv.org/abs/1201.3646",
"label": "Patel--Schmidt--Strauch"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | null | For the Drinfeld tower over a p-adic field F with G=GL_2(F), is O(\Sigma_n)^* an admissible locally analytic representation of G for every n\geq 0, and does it always have finite length? | unrecoverable | The official report contains a single two-part conjecture on admissibility and finite length; this extraction duplicates the complete statement retained as OWR-16770-002. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,091 | OWR-16770-007 | Dual Complexes of Maximally Degenerate Hyperkähler Varieties | Let $\mathcal X$ be a maximally unipotent good minimal dlt degeneration of compact hyperkähler manifolds over $\mathbb C((t))$. Is the dual complex of its special fiber homeomorphic to $\mathbb P^n(\mathbb C)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-007",
"literature-status:open",
"owr-year:2019"
] | For type-III hyper-Kahler degenerations the dual complex is known to be a closed pseudomanifold with the rational homology of complex projective space, but the stronger homeomorphism claim remains open beyond special cases. | [
{
"url": "https://aif.centre-mersenne.org/item/AIF_2018__68_7_2837_0/",
"label": "Degenerations of hyper-Kahler manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | Let $\mathcal X$ be a maximally unipotent good minimal dlt degeneration of compact hyperkähler manifolds over $\mathbb C((t))$. Is the dual complex of its special fiber homeomorphic to $\mathbb P^n(\mathbb C)$? | Let X be a maximally unipotent good minimal dlt degeneration of compact hyper-Kähler manifolds over \mathbb{C}((t)). Is the dual complex of the special fibre of X homeomorphic to \mathbb{P}^n(\mathbb{C})? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,092 | OWR-16770-008 | Tropical Dolbeault Cohomology of Non-Archimedean Varieties | For a variety $X$ over an algebraically closed complete non-Archimedean field, determine the tropical Dolbeault cohomology groups $H^{p,q}(X^{\mathrm{an}})$ and characterize their finiteness, duality, and relation to tropicalizations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,019 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-008",
"literature-status:open",
"owr-year:2019"
] | There are substantial computations and curve results for tropical Dolbeault cohomology, but the general Hodge-number and duality questions remain unsettled; the original theory can even be infinite-dimensional and fail Poincare duality. | [
{
"url": "https://arxiv.org/abs/1909.12633",
"label": "Tropical Hodge theory"
},
{
"url": "https://arxiv.org/abs/2111.05747",
"label": "Weakly smooth tropical cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | For a variety $X$ over an algebraically closed complete non-Archimedean field, determine the tropical Dolbeault cohomology groups $H^{p,q}(X^{\mathrm{an}})$ and characterize their finiteness, duality, and relation to tropicalizations. | For a variety X over an algebraically closed complete non-Archimedean field, what can be said about its tropical Dolbeault cohomology groups H^{p,q}(X^{\mathrm{an}})? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,093 | OWR-16770-010 | Formal Group Models for Commuting p-Adic Power Series | Let $(f,u)$ be a pair of commuting stable power series over a $p$-adic field $K$, with $f$ noninvertible, $u$ invertible, and $f\not\equiv0\pmod{\mathfrak m_K}$. Does there exist a formal group $S$ such that $f$ and $u$ are semiconjugate to endomorphisms of $S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575](https://doi.org/10.4171/owr/2019/8)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16770-010",
"literature-status:partially-solved",
"owr-year:2019"
] | Lubin's conjecture is proved for substantial families and height-one systems, but the general assertion that every relevant commuting p-adic dynamical system is semiconjugate to a formal-group system remains open. | [
{
"url": "https://arxiv.org/abs/1702.06037",
"label": "Berger on Lubin's conjecture"
},
{
"url": "https://arxiv.org/abs/2607.03257",
"label": "Height-one Lubin conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/8 | null | null | null | Let $(f,u)$ be a pair of commuting stable power series over a $p$-adic field $K$, with $f$ noninvertible, $u$ invertible, and $f\not\equiv0\pmod{\mathfrak m_K}$. Does there exist a formal group $S$ such that $f$ and $u$ are semiconjugate to endomorphisms of $S$? | Given a Lubin pair (f,u) of commuting stable power series over a p-adic field K, with f noninvertible and u invertible and f\not\equiv0\pmod{\mathfrak m_K}, does there exist a formal group S such that f and u are semiconjugate to endomorphisms of S? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/8, pp. 513--575 |
30,004,094 | OWR-16772-001 | Higher-Order Failure of the Quantum Linear Boltzmann Limit | For the quantum Lorentz gas with scatterers placed periodically on $\mathbb Z^d$, does the Boltzmann–Grad limit agree with the linear Boltzmann equation through second order in the coupling constant but disagree at every order greater than four? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/10, pp. 617--661](https://doi.org/10.4171/owr/2019/10)
## Literat... | 3 | open | null | 2,019 | 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-16772-001",
"literature-status:open",
"owr-year:2019"
] | For the periodic quantum Lorentz gas the agreement with the linear Boltzmann equation is proved only through second order; the predicted disagreement at all orders greater than four remains an unproved conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2019/10",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2201.08229",
"label": "Quantum Lorentz gas limits"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/10 | null | null | null | For the quantum Lorentz gas with scatterers placed periodically on $\mathbb Z^d$, does the Boltzmann–Grad limit agree with the linear Boltzmann equation through second order in the coupling constant but disagree at every order greater than four? | For the quantum Lorentz gas with scatterers placed periodically on \mathbb{Z}^d, does the Boltzmann--Grad limit agree with the linear Boltzmann equation through second order in the coupling constant but disagree at every order greater than four? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/10, pp. 617--661 |
30,004,095 | OWR-16772-002 | Duplicate Random Lorentz Gas Invariance Principle | For the random Lorentz gas in the Boltzmann--Grad limit, does the diffusively rescaled trajectory converge weakly to a Wiener process as the time scale tends to infinity, both in the quenched setting for a typical Poisson configuration with initial-velocity averaging and in the average-quenched setting with averaging o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/10, pp. 617--661](https://doi.org/10.4171/owr/2019/10)
## Literat... | 3 | partially_solved | null | 2,019 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record repeats the quenched and averaged-quenched random-Lorentz-gas invariance-principle question represented canonically by OWR-16416) | [
"OWR-16416-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16772-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Annealed invariance principles and finite-time Boltzmann--Grad limits are known, and recent work gives a semi-quenched three-dimensional result along extractor sequences, but the full long-time quenched and average-quenched problem remains open. | [
{
"url": "https://link.springer.com/article/10.1007/s00220-020-03852-8",
"label": "Lutsko--Toth invariance principle"
},
{
"url": "https://arxiv.org/abs/2501.00519",
"label": "Semi-quenched Lorentz process"
},
{
"url": "https://doi.org/10.4171/owr/2019/10",
"label": "Oberwolfach repo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/10 | null | null | null | null | For the random Lorentz gas in the Boltzmann--Grad limit, does the diffusively rescaled trajectory converge weakly to a Wiener process as the time scale tends to infinity, both in the quenched setting for a typical Poisson configuration with initial-velocity averaging and in the average-quenched setting with averaging o... | unrecoverable | This record repeats the quenched and averaged-quenched random-Lorentz-gas invariance-principle question represented canonically by OWR-16416-001. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/10, pp. 617--661 |
30,004,096 | OWR-16773-002 | Artin–Schelter Gorenstein Property of Noetherian Hopf Algebras | Is every noetherian Hopf algebra Artin–Schelter Gorenstein? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693](https://doi.org/10.4171/owr/2019/11)
## Literature revi... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16773-002",
"literature-status:open",
"owr-year:2019"
] | The universal assertion that every noetherian Hopf algebra is AS-Gorenstein remains open; many important classes are known, but no general proof or counterexample has been established. | [
{
"url": "https://arxiv.org/abs/2605.00774",
"label": "Report on AS-Gorenstein Hopf algebras"
},
{
"url": "https://doi.org/10.4171/owr/2019/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/11 | null | null | null | Is every noetherian Hopf algebra Artin–Schelter Gorenstein? | Is every noetherian Hopf algebra AS-Gorenstein? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693 |
30,004,097 | OWR-16773-003 | Inner Automorphisms in the Fourth Antipode Formula | Let $H$ be an Artin–Schelter Gorenstein Hopf algebra. Determine the inner automorphism $\gamma$ in the fourth-antipode identity $$S^4=\gamma\circ\tau_{\chi_\ell}\circ\tau_{\chi_r}^{-1}$$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693](https://doi.org/10.4171/owr/2019/11)
## Literature revi... | 3 | open | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16773-003",
"literature-status:open",
"owr-year:2019"
] | In the general noetherian AS-Gorenstein setting only existence of the inner automorphism is known; identifying it explicitly remains open, beyond special finite-dimensional situations where the distinguished grouplike gives a formula. | [
{
"url": "https://arxiv.org/abs/2605.00774",
"label": "Report on AS-Gorenstein Hopf algebras"
},
{
"url": "https://doi.org/10.4171/owr/2019/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/11 | null | null | null | Let $H$ be an Artin–Schelter Gorenstein Hopf algebra. Determine the inner automorphism $\gamma$ in the fourth-antipode identity $$S^4=\gamma\circ\tau_{\chi_\ell}\circ\tau_{\chi_r}^{-1}$$. | For an AS-Gorenstein Hopf algebra H, determine the inner automorphism gamma in the identity S^4=gamma\circ tau_{chi_ell}\circ tau_{chi_r}^{-1}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693 |
30,004,098 | OWR-16773-004 | Duality Invariance of Finite Type Tensor Categories | Is the finite-type property of finite tensor categories preserved under duality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693](https://doi.org/10.4171/owr/2019/11)
## Literature revi... | 3 | partially_solved | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16773-004",
"literature-status:partially-solved",
"owr-year:2019"
] | Finite-type cohomology is preserved under duality in several broad settings, including suitable exact module categories and important braided examples, but the unrestricted finite-tensor-category conjecture remains open. | [
{
"url": "https://doi.org/10.1090/tran/8548",
"label": "Cohomology and duality for finite tensor categories"
},
{
"url": "https://arxiv.org/abs/1807.08854",
"label": "Negron--Plavnik preprint"
},
{
"url": "https://doi.org/10.4171/owr/2019/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/11 | null | null | null | Is the finite-type property of finite tensor categories preserved under duality? | Is the finite-type property for finite tensor categories preserved under duality? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693 |
30,004,099 | OWR-16773-005 | Finite Generation of Noncocommutative Hopf Algebra Cohomology | Is the cohomology of every finite-dimensional noncocommutative Hopf algebra finitely generated? In particular, for odd characteristic $p$, is finite generation valid for the remaining algebra $A_5(0)$ among the connected Hopf algebras of dimension $p^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693](https://doi.org/10.4171/owr/2019/11)
## Literature revi... | 3 | partially_solved | null | 2,019 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16773-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Finite-generation results cover the connected Hopf algebras of dimension p cubed except the A5(0) case for odd p; the A5(beta) cases with nonzero beta are settled, leaving the stated general problem unresolved. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2019.02.030",
"label": "Finite-generation for connected Hopf algebras"
},
{
"url": "https://arxiv.org/abs/1904.04533",
"label": "Erdmann on A5 beta"
},
{
"url": "https://doi.org/10.4171/owr/2019/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/11 | null | null | null | Is the cohomology of every finite-dimensional noncocommutative Hopf algebra finitely generated? In particular, for odd characteristic $p$, is finite generation valid for the remaining algebra $A_5(0)$ among the connected Hopf algebras of dimension $p^3$? | Determine whether the cohomology of finite-dimensional noncocommutative Hopf algebras is finitely generated; in particular, resolve the remaining A5(beta) family in characteristic p>2, including the beta=0 case. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Cohomology of Hopf Algebras and Tensor Categories (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/11, pp. 663--693 |
30,004,100 | OWR-16774-001 | Adaptive Moment Selection Without Reconstruction Overfitting | How should the number $R$ of moments be selected in practical reconstruction algorithms so that overestimation does not cause overfitting or inaccurate reconstructions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uncertainty Quantification (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/12, pp. 695--772](https://doi.org/10.4171/owr/2019/12)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16774-001",
"literature-status:open",
"owr-year:2019"
] | Convergence as the number of moments grows is understood, but there is no generally valid finite-sample rule for choosing the truncation order while controlling approximation error, estimation error, and overfitting. | [
{
"url": "https://doi.org/10.4171/owr/2019/12",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/12 | null | null | null | How should the number $R$ of moments be selected in practical reconstruction algorithms so that overestimation does not cause overfitting or inaccurate reconstructions? | How should the number R of moments be selected in practical computations so that overestimation does not cause overfitting and inaccurate reconstructions? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Uncertainty Quantification (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/12, pp. 695--772 |
30,004,101 | OWR-16775-003 | Sequential Decoding of Nonbinary Convolutional Codes | How do nonbinary convolutional codes perform with sequential decoders on channels with errors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840](https://doi.org/10.4171/owr/2019/13)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 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-16775-003",
"literature-status:open",
"owr-year:2019"
] | Concrete nonbinary sequential decoders exist for several synchronization and substitution-error models, but general performance and optimality, together with the proposed broader applications, remain open research questions. | [
{
"url": "https://arxiv.org/abs/2201.11935",
"label": "Sequential decoding for synchronization errors"
},
{
"url": "https://doi.org/10.1109/TCOMM.2024.3405322",
"label": "Multi-sequence sequential decoding"
},
{
"url": "https://doi.org/10.4171/owr/2019/13",
"label": "Oberwolfach repo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/13 | null | null | null | How do nonbinary convolutional codes perform with sequential decoders on channels with errors? | How do nonbinary convolutional codes perform with sequential decoders on channels with errors? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840 |
30,004,102 | OWR-16775-004 | Convolutional Codes for Retrieval, Sensing, and Rank Metrics | Can convolutional codes exploit sliding-window properties for private information retrieval or compressed sensing, and can they attain strong rank-metric properties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840](https://doi.org/10.4171/owr/2019/13)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 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-16775-004",
"literature-status:open",
"owr-year:2019"
] | The 2019 Oberwolfach report presents convolutional PIR and convolutional rank-metric codes as open directions; later work gives constructions but no general resolution of the three questions. | [
{
"url": "https://doi.org/10.4171/owr/2019/13",
"label": "Oberwolfach coding theory report"
},
{
"url": "https://arxiv.org/abs/1404.7251",
"label": "Convolutional rank-metric codes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/13 | null | null | null | Can convolutional codes exploit sliding-window properties for private information retrieval or compressed sensing, and can they attain strong rank-metric properties? | Can convolutional codes exploit sliding-window properties for private information retrieval or compressed sensing, and can convolutional codes achieve good rank-metric properties, while nonbinary codes are evaluated with sequential decoding on channels with errors? | corrected_verified | The clause about sequential decoding duplicated OWR-16775-003 and was removed; the two distinct convolutional-code questions were retained. | null | null | null | null | null | Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840 |
30,004,103 | OWR-16775-005 | The Generalized Hamada p-Rank Conjecture | Among all combinatorial designs with the same parameters as a subspace design
$$t\text{-}(v,k,\lambda)_q,$$
does the induced design with parameters
$$2\text{-}\left(\binom{v}{1}_q,\binom{k}{1}_q,\lambda\right)$$
have minimum $p$-rank? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840](https://doi.org/10.4171/owr/2019/13)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 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-16775-005",
"literature-status:open",
"owr-year:2019"
] | Recent work proves rank results for important families of subspace designs, but explicitly continues to describe the generalized Hamada conjecture as open; equal-rank nongeometric examples do not settle the conjecture. | [
{
"url": "https://arxiv.org/abs/2404.06513",
"label": "Recent subspace-design rank results"
},
{
"url": "https://digitalcommons.mtu.edu/math-fp/97/",
"label": "Equal-rank subspace designs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/13 | null | null | null | Among all combinatorial designs with the same parameters as a subspace design
$$t\text{-}(v,k,\lambda)_q,$$
does the induced design with parameters
$$2\text{-}\left(\binom{v}{1}_q,\binom{k}{1}_q,\lambda\right)$$
have minimum $p$-rank? | Generalized Hamada conjecture: a t-(v,k,lambda)_q subspace design, viewed as a combinatorial design with parameters 2-(binom(v,1)_q,binom(k,1)_q,lambda), has p-rank minimal among all combinatorial designs with the same parameters. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840 |
30,004,104 | OWR-16775-007 | $q$-Analogues of Quadrilaterals | What should be regarded as a $q$-analogue of a quadrilateral? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840](https://doi.org/10.4171/owr/2019/13)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 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-16775-007",
"literature-status:open",
"owr-year:2019"
] | The q-analogues literature still treats the appropriate notion of a quadrilateral and related q-Fano-type incidence structures as unresolved design questions; no canonical general construction or classification was found. | [
{
"url": "https://arxiv.org/abs/1305.6126",
"label": "q-analogues of designs"
},
{
"url": "https://arxiv.org/abs/1504.06688",
"label": "q-Fano plane existence"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/13 | null | null | null | What should be regarded as a $q$-analogue of a quadrilateral? | What should be regarded as a q-analog of a quadrilateral? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840 |
30,004,105 | OWR-16775-009 | Theta Invariants and New Families of MRD Codes | Can the theta-dimension and theta-increment invariants of rank-metric codes characterize families of MRD codes other than Gabidulin codes, or yield new code constructions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840](https://doi.org/10.4171/owr/2019/13)
## Literature review (checked 2026-08-22)
**Status:** o... | 3 | open | null | 2,019 | 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-16775-009",
"literature-status:open",
"owr-year:2019"
] | MRD codes and several convolutional rank-metric families are known, but the report's classification and construction questions for other MRD families remain unresolved in the literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2019/13",
"label": "Oberwolfach coding theory report"
},
{
"url": "https://arxiv.org/abs/1404.7251",
"label": "Convolutional rank-metric codes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/13 | null | null | null | Can the theta-dimension and theta-increment invariants of rank-metric codes characterize families of MRD codes other than Gabidulin codes, or yield new code constructions? | Can the theta-dimension and theta-increment invariants of rank-metric codes characterize families of MRD codes other than Gabidulin codes, or yield new code constructions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Contemporary Coding Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/13, pp. 773--840 |
30,004,106 | OWR-16776-002 | Symmetry of Completed Finite-Group Representation Rings | Let $G$ be a finite group and let $k$ be a field of characteristic $p$. Write $a_{\mathbb C}(G)=\mathbb C\otimes_{\mathbb Z}a(G)$ for the complexified Green ring of finite-dimensional $kG$-modules, give $\sum_i a_i[M_i]$ the norm $\sum_i|a_i|\dim M_i$, and let $\widehat a(G)$ be its completion with involution induced b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-002",
"literature-status:open",
"owr-year:2019"
] | The modular representation-ring question is still explicitly recorded in the primary reference as unknown; no later source located here establishes that the Banach star-algebra is always symmetric. | [
{
"url": "https://homepages.abdn.ac.uk/d.j.benson/pages/papers/b/benson/banach-book.pdf",
"label": "Benson on modular representation rings"
},
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | Let $G$ be a finite group and let $k$ be a field of characteristic $p$. Write $a_{\mathbb C}(G)=\mathbb C\otimes_{\mathbb Z}a(G)$ for the complexified Green ring of finite-dimensional $kG$-modules, give $\sum_i a_i[M_i]$ the norm $\sum_i|a_i|\dim M_i$, and let $\widehat a(G)$ be its completion with involution induced b... | Is the completion a-hat(G) of the representation ring of a finite group G, with its stated norm and involution, always a symmetric Banach star-algebra? | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,107 | OWR-16776-003 | Combinatorial Formula for Kronecker Coefficients | Give an efficient combinatorial description of the Kronecker coefficients $g(\lambda,\mu,\nu)$ analogous to the Littlewood–Richardson rule. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-003",
"literature-status:open",
"owr-year:2019"
] | Efficient combinatorial descriptions of Kronecker coefficients remain a central open problem; known dominance and positivity results do not provide the requested general description. | [
{
"url": "https://doi.org/10.5802/alco.434",
"label": "Kronecker coefficients and Saxl's conjecture"
},
{
"url": "https://doi.org/10.1016/j.disc.2015.04.027",
"label": "Dominance for Kronecker products"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | Give an efficient combinatorial description of the Kronecker coefficients $g(\lambda,\mu,\nu)$ analogous to the Littlewood–Richardson rule. | Give an efficient combinatorial description of the Kronecker coefficients g(lambda,mu,nu), analogous to the Littlewood--Richardson rule. | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,108 | OWR-16776-006 | Blockwise Chain Cancellation for Finite Groups | For a finite group $G$, a prime $p$, and a positive-defect block idempotent $b$ of $\mathbb{Z}_pG$, does the alternating sum over conjugacy classes of chains of nontrivial $p$-subgroups, $\sum_{\sigma\in[\mathcal{P}(G)/G]}(-1)^{|\sigma|}\operatorname{Mat}_{|G:G_\sigma|}(\mathbb{Q}G_\sigma b_\sigma)$, equal zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The report's block-algebra conjecture has substantial verified cases and reductions in the cited literature, but no general theorem covering all finite groups and the full stated p-adic assertion was found. | [
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | For a finite group $G$, a prime $p$, and a positive-defect block idempotent $b$ of $\mathbb{Z}_pG$, does the alternating sum over conjugacy classes of chains of nontrivial $p$-subgroups, $\sum_{\sigma\in[\mathcal{P}(G)/G]}(-1)^{|\sigma|}\operatorname{Mat}_{|G:G_\sigma|}(\mathbb{Q}G_\sigma b_\sigma)$, equal zero? | For a finite group G, a prime p, and a positive-defect block idempotent b of Z_p G, does the alternating sum over conjugacy classes of chains of nontrivial p-subgroups, sum_{sigma in [P(G)/G]} (-1)^{|sigma|} Mat_{|G:G_sigma|}(Q G_sigma b_sigma), equal zero? | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,109 | OWR-16776-007 | Character-Counting Chain Cancellation in Blocks | For a positive-defect block idempotent $b$ of $\mathcal{O}G$ and every admissible parameter tuple $(d,r,L,h)$, does the alternating sum over conjugacy classes of chains of nontrivial $p$-subgroups, $\sum_{\sigma\in[\mathcal{P}(G)/G]}(-1)^{|\sigma|}|\operatorname{Irr}_K(G_\sigma,b_\sigma,d,r,L,h)|$, equal zero? Here $\o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The extracted Turull-special-case conjecture has proved cases and structural reductions reported in the primary literature, but the general conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | For a positive-defect block idempotent $b$ of $\mathcal{O}G$ and every admissible parameter tuple $(d,r,L,h)$, does the alternating sum over conjugacy classes of chains of nontrivial $p$-subgroups, $\sum_{\sigma\in[\mathcal{P}(G)/G]}(-1)^{|\sigma|}|\operatorname{Irr}_K(G_\sigma,b_\sigma,d,r,L,h)|$, equal zero? Here $\o... | For a positive-defect block idempotent b of O G and every admissible parameter tuple (d,r,L,h), does the alternating sum over conjugacy classes of chains of nontrivial p-subgroups, sum_{sigma in [P(G)/G]} (-1)^{|sigma|} |Irr_K(G_sigma,b_sigma,d,r,L,h)|, equal zero? Here Irr_K denotes the irreducible K-characters in the... | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,110 | OWR-16776-008 | Robinson's Defect Conjecture and Commuting Sylow Subgroups | Robinson's conjecture asserts that for a character chi in a p-block with defect group D, pdef(chi) is at least |Z(D)|, with equality exactly when D is abelian; additionally, for primes p and q, a finite group G has commuting Sylow p- and q-subgroups if and only if every character in the principal p-block has degree pri... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 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 | Unrecoverable OWR statement (The official report shows that this extraction concatenates two independent conjectures: Robinson's defect conjecture and a criterion for co) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-008",
"literature-status:partially-solved",
"owr-year:2019"
] | Robinson's conjecture is proved for odd primes and for all 2-blocks of quasi-simple classical groups, while the principal-block statement has only conditional general results; the full extracted claim is not settled. | [
{
"url": "https://doi.org/10.1515/jgth-2018-0177",
"label": "Robinson conjecture paper"
},
{
"url": "https://agag-malle.math.rptu.de/~malle/download/robconj.pdf",
"label": "Odd-prime and principal-block results"
},
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | null | Robinson's conjecture asserts that for a character chi in a p-block with defect group D, pdef(chi) is at least |Z(D)|, with equality exactly when D is abelian; additionally, for primes p and q, a finite group G has commuting Sylow p- and q-subgroups if and only if every character in the principal p-block has degree pri... | unrecoverable | The official report shows that this extraction concatenates two independent conjectures: Robinson's defect conjecture and a criterion for commuting Sylow subgroups. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,111 | OWR-16776-009 | Geck's Unitriangularity Conjecture | Let $G$ be a finite reductive group and let $\ell$ be a very good prime. Can the unipotent decomposition matrix be ordered by unipotent classes so that it is block lower triangular, with identity diagonal blocks indexed by the relevant families of unipotent characters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-009",
"literature-status:partially-solved",
"owr-year:2019"
] | Geck's unitriangularity conjecture is proved in broad good-characteristic settings, but the general conjecture in the extracted record, including the remaining bad-characteristic cases, is not fully resolved. | [
{
"url": "https://doi.org/10.4007/annals.2020.192.2.7",
"label": "Geck unitriangularity theorem"
},
{
"url": "https://arxiv.org/abs/2402.17616",
"label": "Extensions of unitriangularity"
},
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory re... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | Let $G$ be a finite reductive group and let $\ell$ be a very good prime. Can the unipotent decomposition matrix be ordered by unipotent classes so that it is block lower triangular, with identity diagonal blocks indexed by the relevant families of unipotent characters? | Geck's Unitriangularity Conjecture: for a finite reductive group G and a very good prime ell, the unipotent decomposition matrix can be ordered by unipotent classes so that it is block lower triangular with identity diagonal blocks indexed by the relevant unipotent-character families. | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,112 | OWR-16776-011 | Character Bounds beyond Split Levi Subgroups | Can character bounds currently available for split Levi subgroups be extended to non-split Levi subgroups? Can useful bounds be obtained for every $g\in G^F$ and every $\chi\in\operatorname{Irr}(G^F)$ when $G$ is simple and is not of type $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-011",
"literature-status:open",
"owr-year:2019"
] | The extracted questions ask for extensions to non-split Levi subgroups and uniform character bounds beyond the established simple type-A and restricted cases; no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | Can character bounds currently available for split Levi subgroups be extended to non-split Levi subgroups? Can useful bounds be obtained for every $g\in G^F$ and every $\chi\in\operatorname{Irr}(G^F)$ when $G$ is simple and is not of type $A$? | Can the character-bound theorem be extended to non-split Levi subgroups, and can one obtain good character bounds for every g in G^F and every chi in Irr(G^F) when G is simple and not of type 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,113 | OWR-16776-012 | Character Determination by Jantzen's Sum Formula | How far does Jantzen's sum formula determine the characters of simple highest-weight modules for reductive groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895](https://doi.org/10.4171/owr/2019/14)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16776-012",
"literature-status:partially-solved",
"owr-year:2019"
] | Jantzen's sum formula resolves the relevant questions in several low-rank types and reduces further cases to finite ambiguities, but the report records additional higher-rank complications and no general solution. | [
{
"url": "https://doi.org/10.4171/owr/2019/14",
"label": "Oberwolfach representation theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/14 | null | null | null | How far does Jantzen's sum formula determine the characters of simple highest-weight modules for reductive groups? | How far does Jantzen's sum formula determine the characters of simple highest-weight modules for reductive groups? | 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 | Representations of Finite Groups (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/14, pp. 841--895 |
30,004,114 | OWR-16927-004 | Formal Hyperplanes in Periodic Bordism | For periodic bordism $MP$, does there exist a formal group with underlying formal hyperplane $MP[[t]]$ whose induced formal group over $\pi_0(MP)$ is additive, and do the three formal hyperplanes corepresented by $MP[t^{\pm1}]$ completed at $t^{-1}$, $MP[[t]]$, and $MP^{\mathbb{CP}^\infty}$ agree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Elliptic Cohomology according to Lurie (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/15, pp. 911--1001](https://doi.org/10.4171/owr/2019/15)
## Literature review (... | 3 | open | null | 2,019 | 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-16927-004",
"literature-status:open",
"owr-year:2019"
] | The report formulates the two formal-hyperplane questions for MP, and no authoritative later source located here proves either the additive pi-zero claim or the asserted comparison of the three hyperplanes. | [
{
"url": "https://doi.org/10.4171/owr/2019/15",
"label": "Oberwolfach elliptic and chromatic report"
},
{
"url": "http://www.math.harvard.edu/~lurie/papers/Elliptic-II.pdf",
"label": "Lurie, Elliptic Cohomology II"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/15 | null | null | null | For periodic bordism $MP$, does there exist a formal group with underlying formal hyperplane $MP[[t]]$ whose induced formal group over $\pi_0(MP)$ is additive, and do the three formal hyperplanes corepresented by $MP[t^{\pm1}]$ completed at $t^{-1}$, $MP[[t]]$, and $MP^{\mathbb{CP}^\infty}$ agree? | For periodic bordism M P, does there exist a formal group with underlying formal hyperplane M P[[t]] whose induced formal group over pi_0(M P) is additive, and do the three formal hyperplanes corepresented by M P[t^{+-1}] completed at t^{-1}, M P[[t]], and M P^{CP-infinity} agree? | 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 | Arbeitsgemeinschaft: Elliptic Cohomology according to Lurie (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/15, pp. 911--1001 |
30,004,115 | OWR-16929-001 | Infinite Families of Nonarithmetic Complex-Hyperbolic Lattices | For every $n\geq2$, are there infinitely many commensurability classes of nonarithmetic lattices in $\operatorname{PU}(n,1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070](https://doi.org/10.4171/owr/2019/17)
## Literature review (chec... | 3 | open | null | 2,019 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16929-001",
"literature-status:open",
"owr-year:2019"
] | The complex-hyperbolic-lattice literature continues to identify the existence and number of commensurability classes of non-arithmetic lattices in PU(n,1) as major open questions, especially in higher dimensions. | [
{
"url": "https://doi.org/10.1016/j.topol.2019.106918",
"label": "Non-arithmetic complex hyperbolic lattices"
},
{
"url": "https://doi.org/10.4171/owr/2019/17",
"label": "Oberwolfach reflection-group report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/17 | null | null | null | For every $n\geq2$, are there infinitely many commensurability classes of nonarithmetic lattices in $\operatorname{PU}(n,1)$? | Are there infinitely many commensurability classes of non-arithmetic lattices in PU(n,1) for n at least 2? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070 |
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