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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,316 | OWR-12480-001 | Canonical Dimension of Prime-Power-Split Anisotropic Tori | Is $\operatorname{cdim}(T)=\dim T$ for every anisotropic algebraic torus $T$ split by a Galois extension of prime-power degree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/17, pp. 1025--1085](https://doi.org/10.4171/owr/2013/17)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,013 | 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-12480-001",
"literature-status:open",
"owr-year:2013"
] | The anisotropic-torus canonical-dimension equality remains unresolved in the reviewed primary literature; no proof or counterexample was found. | [
{
"url": "https://doi.org/10.4171/owr/2013/17",
"label": "Oberwolfach algebraic-groups report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/17 | null | null | null | Is $\operatorname{cdim}(T)=\dim T$ for every anisotropic algebraic torus $T$ split by a Galois extension of prime-power degree? | Is the canonical dimension cdim(T) equal to the dimension of T for every anisotropic algebraic torus T split by a Galois extension of prime-power degree? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/17, pp. 1025--1085 |
30,002,317 | OWR-12480-003 | Finite Subgroups and Torsion Primes of Cremona Groups | Write $\operatorname{Aff}_n$ for the affine group, $\operatorname{Cr}_n$ for the Cremona group, and $\operatorname{Tors}(G)$ for the set of torsion primes of a group $G$. Do there exist isomorphic finite subgroups of $\operatorname{Aff}_n$ that are not conjugate in $\operatorname{Cr}_n$? Are the sets $\operatorname{Tor... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/17, pp. 1025--1085](https://doi.org/10.4171/owr/2013/17)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,013 | 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-12480-003",
"literature-status:partially-solved",
"owr-year:2013"
] | Nonconjugate finite-subgroup phenomena and some Cremona torsion information are known, but the affine-conjugacy, automorphism-group torsion, and minimal-prime questions remain open. | [
{
"url": "https://www.math.uni-bielefeld.de/LAG/man/474.pdf",
"label": "Popov, Tori in the Cremona groups"
},
{
"url": "https://doi.org/10.4171/owr/2013/17",
"label": "Oberwolfach algebraic-groups report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/17 | null | null | null | Write $\operatorname{Aff}_n$ for the affine group, $\operatorname{Cr}_n$ for the Cremona group, and $\operatorname{Tors}(G)$ for the set of torsion primes of a group $G$. Do there exist isomorphic finite subgroups of $\operatorname{Aff}_n$ that are not conjugate in $\operatorname{Cr}_n$? Are the sets $\operatorname{Tor... | Are finite isomorphic subgroups of Affine n that are not conjugate in the Cremona group Cr_n possible; are Tors(Cr_n), Tors(Aut(A^n)), and Tors(Aut-star(A^n)) finite; what is the least n for which 7 belongs to one of these torsion-prime sets; and are there analogous or modified properties for these groups? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/17, pp. 1025--1085 |
30,002,318 | OWR-12481-003 | Concentration of Largest Triangular Submatrices in Random Matrices | For an $n\times n$ random matrix with independent identically distributed entries, if $T_n$ is the order of its largest lower-triangular submatrix, is $T_n$ concentrated on at most two values? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-003",
"literature-status:open",
"owr-year:2013"
] | The report poses concentration of the largest triangular submatrix on at most two values as open; the cited asymptotic result does not settle this finer concentration question. | [
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
},
{
"url": "https://doi.org/10.1090/S0002-9939-2014-12301-X",
"label": "Izhakian--Janson--Rhodes, triangular submatrices"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | For an $n\times n$ random matrix with independent identically distributed entries, if $T_n$ is the order of its largest lower-triangular submatrix, is $T_n$ concentrated on at most two values? | For an n by n random matrix with independent identically distributed entries, if T_n is the order of its largest lower triangular submatrix, is T_n concentrated on at most two values? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,319 | OWR-12481-004 | Displacement Exponents for Low-Dimensional Self-Avoiding Walks | For self-avoiding walk in dimensions $d=2$ and $d=3$, prove that there exists $\varepsilon>0$ such that
$$n^{2/d+\varepsilon}\leq \mathbb E_n[\operatorname{Dist}(\gamma_n,0)^2]\leq n^{2-\varepsilon}$$
for all sufficiently large $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-004",
"literature-status:open",
"owr-year:2013"
] | The extracted record contains only an open-problem heading and no identifiable mathematical claim; under the required rule its status is open. | [
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | For self-avoiding walk in dimensions $d=2$ and $d=3$, prove that there exists $\varepsilon>0$ such that
$$n^{2/d+\varepsilon}\leq \mathbb E_n[\operatorname{Dist}(\gamma_n,0)^2]\leq n^{2-\varepsilon}$$
for all sufficiently large $n$. | For self-avoiding walk in dimensions d=2 and d=3, prove that there is an epsilon greater than zero such that, for all sufficiently large n, n^(2/d+epsilon) is less than or equal to the mean-square displacement E_n[Dist(gamma_n,0)^2], which is less than or equal to n^(2-epsilon). | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,320 | OWR-12481-005 | Existence of Random-Graph Coloring Growth Rates | For every integer $k\geq3$ and every average degree $d>0$, does the limit
$$\phi(d)=\lim_{n\to\infty}\mathbb E\bigl[\#\{k\text{-colorings of }G(n,m)\}\bigr]^{1/n}$$
exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-005",
"literature-status:open",
"owr-year:2013"
] | The existence of the normalized expected coloring count limit for every k at every positive density remains unresolved; only a related free-energy limit is established. | [
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol028-approx-random2014/LIPIcs.APPROX-RANDOM.2014.449/LIPIcs.APPROX-RANDOM.2014.449.pdf",
"label": "Bapst--Coja-Oghlan--Hetterich--others, condensation transition"
},
{
"url": "https://doi.org/10.1214/12-AOP816",
"label": "Bayati--Gama... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | For every integer $k\geq3$ and every average degree $d>0$, does the limit
$$\phi(d)=\lim_{n\to\infty}\mathbb E\bigl[\#\{k\text{-colorings of }G(n,m)\}\bigr]^{1/n}$$
exist? | For every integer k greater than or equal to 3 and every average degree d greater than zero, the limit phi(d)=lim as n tends to infinity of the expected nth root of the number of k-colorings of the random graph G(n,m) exists. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,321 | OWR-12481-010 | Large Nonnegative Rank at Bounded Ordinary Rank | Do there exist nonnegative $n\times n$ matrices of bounded ordinary rank whose nonnegative rank is $\Omega(n)$? In particular, do matrices of rank $3$ with nonnegative rank $n$ exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,013 | 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-12481-010",
"literature-status:partially-solved",
"owr-year:2013"
] | Shitov disproved the proposed rank-three nonnegative-rank-equals-n family for sufficiently large n, while the broader bounded-rank linear-growth question is not settled by that result. | [
{
"url": "https://doi.org/10.1016/j.jcta.2013.10.004",
"label": "Shitov, upper bound for nonnegative rank"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Do there exist nonnegative $n\times n$ matrices of bounded ordinary rank whose nonnegative rank is $\Omega(n)$? In particular, do matrices of rank $3$ with nonnegative rank $n$ exist? | Do there exist nonnegative n by n matrices of bounded ordinary rank whose nonnegative rank is of order Omega(n); in particular, do matrices of rank 3 with nonnegative rank n exist? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,322 | OWR-12481-011 | Large Anticomplete Sets in Triangle-Free Graphs | Does there exist a constant $c>0$ such that every triangle-free graph on more than two vertices has disjoint vertex subsets of orders $cn^c$ and $cn$ with no edges between them? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-011",
"literature-status:open",
"owr-year:2013"
] | The triangle case of the Conlon--Fox--Sudakov anticomplete-sets conjecture remains open in the current literature. | [
{
"url": "https://arxiv.org/abs/1810.00058",
"label": "Chudnovsky--Fox--Scott--Seymour--Spirkl, anticomplete sets"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Does there exist a constant $c>0$ such that every triangle-free graph on more than two vertices has disjoint vertex subsets of orders $cn^c$ and $cn$ with no edges between them? | Does there exist a constant c greater than zero such that every triangle-free graph on more than two vertices has disjoint vertex subsets of orders c n^c and c n with no edges between them? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,323 | OWR-12481-012 | Hierarchical Refinement of Symmetric-Group Coset Partitions | If a $t$-coset is a coset of the stabilizer of $t$ points in the symmetric group $S_n$, is every partition of $S_n$ into $t$-cosets a refinement of a partition into $(t-1)$-cosets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,013 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12481-012",
"literature-status:open",
"owr-year:2013"
] | The later OWR 22/2016 report, p. 1217, explicitly credits Gábor Tardos with a counterexample even when t is fixed and n is large. Independently checked the small S4 example from discussion #4: twelve 2-cosets form a partition and refine none of the eight 1-coset partitions.
**What remains.** The universal refinement a... | [
{
"url": "https://doi.org/10.4171/owr/2016/22",
"label": "OWR 22/2016, p. 1217 — Friedgut reports Tardos’s counterexample"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152"
},
{
... | 2026-09-28T00:00:00 | OWR 22/2016, p. 1217 — Friedgut reports Tardos’s counterexample: https://doi.org/10.4171/owr/2016/22
Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152: https://doi.org/10.4171/owr/2013/18 | https://doi.org/10.4171/owr/2013/18 | null | null | null | If a $t$-coset is a coset of the stabilizer of $t$ points in the symmetric group $S_n$, is every partition of $S_n$ into $t$-cosets a refinement of a partition into $(t-1)$-cosets? | If a t-coset is a coset of the stabilizer of t points in the symmetric group S_n, is every partition of S_n into t-cosets a refinement of a partition into (t-1)-cosets? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,324 | OWR-12481-013 | Worst-Case Inputs for Smoothed Caching Complexity | Characterize the input sequences that have the worst performance under the smoothed complexity of the caching problem, whose competitive-ratio complexity is of order $\log k$ for cache size $k$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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"
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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-12481-013",
"literature-status:open",
"owr-year:2013"
] | The characterization of worst inputs for smoothed caching complexity and the analogous increasing-subsequence and binary-search-tree questions remains open in the reviewed literature. | [
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Characterize the input sequences that have the worst performance under the smoothed complexity of the caching problem, whose competitive-ratio complexity is of order $\log k$ for cache size $k$. | Characterize the input sequences that have the worst performance under the smoothed complexity of the caching problem, whose competitive-ratio complexity is of order log k for cache size k. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,325 | OWR-12481-014 | High-Girth Cubic Graph Homomorphisms to the Five-Cycle | Does there exist an integer $\ell$ such that every cubic graph of girth at least $\ell$ admits a graph homomorphism to the cycle $C_5$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-014",
"literature-status:open",
"owr-year:2013"
] | The Pentagon Problem remains open: the Clebsch-graph theorem gives a related high-girth cubic homomorphism result, but not the conjectured homomorphism to C_5. | [
{
"url": "https://kam.mff.cuni.cz/~samal/papers/clebsch/clebsch.pdf",
"label": "DeVos--Šámal, high-girth cubic graphs"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Does there exist an integer $\ell$ such that every cubic graph of girth at least $\ell$ admits a graph homomorphism to the cycle $C_5$? | Does there exist an integer ell such that every cubic graph of girth at least ell admits a graph homomorphism to the cycle C_5? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,326 | OWR-12481-016 | Sublinear Bounds for Disjoint Homometric Vertex Sets | Let $h(n)$ be the largest integer such that every connected $n$-vertex graph has two disjoint homometric vertex subsets, meaning their multisets of pairwise distances agree. Is $h(n)=o(n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-016",
"literature-status:open",
"owr-year:2013"
] | Known bounds for the homometric-set parameter remain far from proving h of n equals o of n, so the question remains open. | [
{
"url": "https://arxiv.org/abs/1203.1158",
"label": "Axenovich--Özkahya, homometric sets"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Let $h(n)$ be the largest integer such that every connected $n$-vertex graph has two disjoint homometric vertex subsets, meaning their multisets of pairwise distances agree. Is $h(n)=o(n)$? | Let h(n) be the largest integer such that every connected n-vertex graph has two disjoint homometric vertex subsets, meaning their multisets of pairwise distances agree. Is h(n)=o(n)? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,327 | OWR-12481-018 | Cryptographic Replacement of Pseudorandom Steganographic Functions | Can the pseudorandom functions used in the steganographic constructions be replaced by cryptographic functions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152](https://doi.org/10.4171/owr/2013/18)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,013 | 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-12481-018",
"literature-status:open",
"owr-year:2013"
] | The later steganography treatment still builds the relevant channel family from pseudorandom functions and does not prove their replacement by cryptographic functions; the question remains open. | [
{
"url": "https://doi.org/10.1016/j.tcs.2017.06.007",
"label": "Liskiewicz--Reischuk--Woelfel, security levels in steganography"
},
{
"url": "https://doi.org/10.4171/owr/2013/18",
"label": "Oberwolfach combinatorics report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/18 | null | null | null | Can the pseudorandom functions used in the steganographic constructions be replaced by cryptographic functions? | Can the pseudorandom functions used in the steganographic constructions be replaced by cryptographic functions? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Combinatorics and Probability (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/18, pp. 1087--1152 |
30,002,328 | OWR-12483-002 | KPZ Boundaries in Cutoff Branching Random Walk | For a branching random walk on $\mathbb Z^2$ with a cutoff rule limiting the number of particles at each site, is the boundary of the occupied set in the KPZ universality class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Extremes in Branching Random Walk and Branching Brownian Motion (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/20, pp. 1205--1251](https://doi.org/10.4171/owr/2013/20)
## Literature rev... | 3 | open | null | 2,013 | 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-12483-002",
"literature-status:open",
"owr-year:2013"
] | The cutoff branching-random-walk KPZ claim remains an explicitly stated conjecture; current search found no proof or disproof for the model as formulated. | [
{
"url": "https://doi.org/10.4171/owr/2013/20",
"label": "Oberwolfach Report 20/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/20 | null | null | null | For a branching random walk on $\mathbb Z^2$ with a cutoff rule limiting the number of particles at each site, is the boundary of the occupied set in the KPZ universality class? | For a branching random walk on Z squared with a cutoff rule limiting the number of particles at each site, is the boundary of the occupied set in the KPZ universality class? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Extremes in Branching Random Walk and Branching Brownian Motion (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/20, pp. 1205--1251 |
30,002,329 | OWR-12484-004 | Global Willmore Minimizers Near the Clifford Torus | For conformal classes sufficiently near that of the Clifford torus, are the constrained Willmore Hopf tori that minimize the constrained energy also the global minimizers of the Willmore energy in their respective conformal classes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Progress in Surface Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/21, pp. 1253--1312](https://doi.org/10.4171/owr/2013/21)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,013 | 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-12484-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Existence and minimization are proved in several rectangular and non-rectangular conformal classes near the Clifford class, but the full local-to-global constrained-Willmore minimizer conjecture remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2021.107804",
"label": "Heller--Ndiaye, First explicit constrained Willmore minimizers of non-rectangular conformal class"
},
{
"url": "https://doi.org/10.1016/j.geomphys.2021.104221",
"label": "Candidates for non-rectangular constrained Willmore minimizer... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/21 | null | null | null | For conformal classes sufficiently near that of the Clifford torus, are the constrained Willmore Hopf tori that minimize the constrained energy also the global minimizers of the Willmore energy in their respective conformal classes? | For conformal classes sufficiently near that of the Clifford torus, are the constrained Willmore Hopf tori that minimize the constrained energy also the global minimizers of the Willmore energy in their respective conformal classes? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Progress in Surface Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/21, pp. 1253--1312 |
30,002,330 | OWR-12484-005 | Convex Spheres with an Isolated Index-Three-Halves Umbilic | Does there exist a strictly convex closed smooth sphere in $\mathbb R^3$ with an isolated umbilic point of index $3/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Progress in Surface Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/21, pp. 1253--1312](https://doi.org/10.4171/owr/2013/21)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,013 | 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-12484-005",
"literature-status:open",
"owr-year:2013"
] | The bound \operatorname{Index}\le 3/2 is known, but existence of a smooth convex umbilic of index 3/2 remains unproved; no counterexample was found. | [
{
"url": "https://arxiv.org/abs/1207.5994",
"label": "Guilfoyle--Klingenberg, An index bound for smooth umbilic points"
},
{
"url": "https://doi.org/10.1007/s00025-023-02003-4",
"label": "Roots of Polynomials and Umbilics of Surfaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/21 | null | null | null | Does there exist a strictly convex closed smooth sphere in $\mathbb R^3$ with an isolated umbilic point of index $3/2$? | Does there exist a strictly convex closed smooth sphere in three-dimensional Euclidean space with an isolated umbilic point of index 3/2? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Progress in Surface Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/21, pp. 1253--1312 |
30,002,331 | OWR-12485-001 | Spectra of Multi-Crossing Knot Numbers | For the spectrum of multi-crossing numbers of a knot, what is its behavior, which knot families arise naturally from it, what braids arise from petal projections, and how do these invariants relate to traditional knot invariants? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,013 | 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-12485-001",
"literature-status:partially-solved",
"owr-year:2013"
] | Multi-crossing spectra have monotonicity, composition results, and extensive computations, but the general spectrum behavior and the resulting braid classification asked here remain open. | [
{
"url": "https://doi.org/10.1017/S0305004116000906",
"label": "Adams et al., Multi-crossing Number for Knots and the Kauffman Bracket Polynomial"
},
{
"url": "https://doi.org/10.4171/owr/2013/22",
"label": "Oberwolfach Report 22/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | For the spectrum of multi-crossing numbers of a knot, what is its behavior, which knot families arise naturally from it, what braids arise from petal projections, and how do these invariants relate to traditional knot invariants? | For the spectrum of multi-crossing numbers of a knot, what is its behavior, which knot families arise naturally from it, what braids arise from petal projections, and how do these invariants relate to traditional knot invariants? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,332 | OWR-12485-003 | Linear Ropelength Bounds in Crossing Number | For every knot $K$, is its ropelength $O(\operatorname{Cr}(K))$, where $\operatorname{Cr}(K)$ is the crossing number? If not, do infinitely many knots have faster growth? Do alternating knots have a ropelength lower bound of linear order in crossing number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** open... | 3 | partially_solved | null | 2,013 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1017/S0305004124000288",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. Y. Diao (OWR 22/2013, §6 of his abstract and problem-session item (3), p. 1354) asks whether ropelength is O(Cr(K)) for every knot, whether infinitely many knots grow faster, and whether alternating knots have a lower bound linear in Cr(K). The last is... | [
"owr",
"oberwolfach-reports",
"OWR-12485-003",
"literature-status:open",
"owr-year:2013"
] | The best general theorem located is O(\operatorname{Cr}(K)\log^5\operatorname{Cr}(K)); the linear O(\operatorname{Cr}(K)) bound and the listed family questions remain unresolved. | [
{
"url": "https://arxiv.org/abs/0912.3282",
"label": "Diao--Ernst--Por--Ziegler, The ropelength of a knot"
},
{
"url": "https://doi.org/10.4171/owr/2013/22",
"label": "Oberwolfach Report 22/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | For every knot $K$, is its ropelength $O(\operatorname{Cr}(K))$, where $\operatorname{Cr}(K)$ is the crossing number? If not, do infinitely many knots have faster growth? Do alternating knots have a ropelength lower bound of linear order in crossing number? | For every knot K, is its ropelength bounded above by O(Cr(K)), where Cr(K) is crossing number; equivalently, do infinitely many knots have faster growth, and do alternating knots have a linear-order ropelength lower bound? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,333 | OWR-12485-005 | Symplectic Measure of Two-Component Link Types | For a two-component link type $[L]$, let $A([L])$ be the infimum of the symplectic measure $A(K_1,K_2)$ over its representatives. Determine $A([L])$. Is it positive for every hyperbolic link? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** open... | 3 | open | null | 2,013 | 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-12485-005",
"literature-status:open",
"owr-year:2013"
] | O'Hara characterized the zero minimum for a fixed geometric link and known zero-infimum classes, but positivity of A([L]) for hyperbolic links remains open. | [
{
"url": "https://doi.org/10.2748/tmj/1378991024",
"label": "O'Hara, Measure of a 2-component link"
},
{
"url": "https://doi.org/10.4171/owr/2013/22",
"label": "Oberwolfach Report 22/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | For a two-component link type $[L]$, let $A([L])$ be the infimum of the symplectic measure $A(K_1,K_2)$ over its representatives. Determine $A([L])$. Is it positive for every hyperbolic link? | For a two-component link type [L], with A([L]) the infimum of the symplectic measure A(K1,K2) over representatives, what is A([L]), and is it positive for every hyperbolic link? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,334 | OWR-12485-006 | Critical Integral Menger Curvature | For the integral Menger curvature $M_p$ of a fixed-length space curve, is the round circle the unique minimizer? Does $M_3(\gamma)<\infty$ imply that $\gamma'$ exists everywhere? What regularity do local minimizers and stationary points have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,013 | 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-12485-006",
"literature-status:partially-solved",
"owr-year:2013"
] | Supercritical regularity and several variational results are known for Menger-curvature energies, but the critical M_3 questions, circle uniqueness, and full minimizer or stationary-point regularity remain open. | [
{
"url": "https://doi.org/10.1016/j.topol.2013.05.022",
"label": "Strzelecki--von der Mosel, On some knot energies involving Menger curvature"
},
{
"url": "https://www.numdam.org/item/ASNSP_2010_5_9_1_145_0.pdf",
"label": "Strzelecki--Szumanska--von der Mosel, Regularizing and self-avoidance eff... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | For the integral Menger curvature $M_p$ of a fixed-length space curve, is the round circle the unique minimizer? Does $M_3(\gamma)<\infty$ imply that $\gamma'$ exists everywhere? What regularity do local minimizers and stationary points have? | For integral Menger curvature Mp of a fixed-length space curve, is the round circle the unique minimizer, does M3(γ)<∞ imply that γ' exists everywhere, and what regularity do local minimizers and stationary points have? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,335 | OWR-12485-007 | End Angles of Tight Open Knots | What mathematical model describes a tight open knot whose released ends form a characteristic angle, and how does that angle depend on the knot type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** open... | 3 | open | null | 2,013 | 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-12485-007",
"literature-status:open",
"owr-year:2013"
] | Existence and C^{1,1} regularity of closed ropelength minimizers are known, but no general model or formula determines the end angle of a tight open knotted rope from its knot type. | [
{
"url": "https://arxiv.org/abs/math/0103224",
"label": "Cantarella--Kusner--Sullivan, On the Minimum Ropelength of Knots and Links"
},
{
"url": "https://doi.org/10.4171/owr/2013/22",
"label": "Oberwolfach Report 22/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | What mathematical model describes a tight open knot whose released ends form a characteristic angle, and how does that angle depend on the knot type? | What mathematical model describes a tight open knot whose released ends form a characteristic angle, and how does that angle depend on the knot type? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,336 | OWR-12485-008 | Ropelength, Menger Energy, and Loop-Number Problems | Can a ropelength-minimizing or ropelength-critical knot be described explicitly, and is the minimizing trefoil piecewise $C^2$ or piecewise smooth? Which geometric quantities or topological invariants are bounded by higher-dimensional integral Menger energies $M_p(\Sigma)$? For an unknot diagram $D$ with writhe $w(D)$,... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,013 | 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-12485-008",
"literature-status:partially-solved",
"owr-year:2013"
] | Minimizers exist and several ropelength bounds and energy estimates are known, including a linear lower bound for alternating knots, but explicit nontrivial minimizers, smoothness of the trefoil, and the remaining invariant questions are unresolved. | [
{
"url": "https://arxiv.org/abs/math/0103224",
"label": "Cantarella--Kusner--Sullivan, On the Minimum Ropelength of Knots and Links"
},
{
"url": "https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/ropelength-conjecture-of-alternating-knots... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | Can a ropelength-minimizing or ropelength-critical knot be described explicitly, and is the minimizing trefoil piecewise $C^2$ or piecewise smooth? Which geometric quantities or topological invariants are bounded by higher-dimensional integral Menger energies $M_p(\Sigma)$? For an unknot diagram $D$ with writhe $w(D)$,... | Can any ropelength-minimal or ropelength-critical knot be explicitly described, and is the minimizing trefoil piecewise C2 or piecewise smooth; are there knot families with ropelength more than linear in crossing number or with a better alternating-knot lower bound; what quantities are controlled by higher-dimensional ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,337 | OWR-12485-009 | Geometric, Energetic, and Probabilistic Knot Problems | Can complexity methods prove the existence of nontrivial local minima for knot energies? Are the spaces of embedded equilateral arms and unknotted equilateral polygons connected? How many knot types have a given stick number? What are the limiting torsion laws for confined equilateral walks and polygons? Does mutation ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358](https://doi.org/10.4171/owr/2013/22)
## Literature review (checked 2026-08-21)
**Status:** part... | 3 | partially_solved | null | 2,013 | 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-12485-009",
"literature-status:partially-solved",
"owr-year:2013"
] | Several components have partial answers, including random-polymer knotting and computational studies of equilateral knot spaces, while the general local-minimum, connectivity, enumeration, torsion, and arc-index questions remain unresolved. | [
{
"url": "https://doi.org/10.1016/j.topol.2013.05.022",
"label": "On some knot energies involving Menger curvature"
},
{
"url": "https://doi.org/10.1142/S0218216594000307",
"label": "Diao--Pippenger--Sumners, On Random Knots"
},
{
"url": "https://doi.org/10.4171/owr/2013/22",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/22 | null | null | null | Can complexity methods prove the existence of nontrivial local minima for knot energies? Are the spaces of embedded equilateral arms and unknotted equilateral polygons connected? How many knot types have a given stick number? What are the limiting torsion laws for confined equilateral walks and polygons? Does mutation ... | Can complexity methods prove nontrivial local minima for knot energies; are spaces of embedded equilateral arms and unknotted equilateral polygons connected; how many knot types have a given stick number; what are the limiting torsion laws for confined equilateral walks and polygons; does mutation preserve arc index; a... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Knot Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/22, pp. 1313--1358 |
30,002,338 | OWR-12486-002 | High-Dimensional Limits of Metric-Measure Spaces | How should sequences of Riemannian or metric-measure spaces be studied when their dimensions tend to infinity, particularly with respect to concentration convergence, curvature-dimension conditions, and Laplacian eigenvalues? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/23, pp. 1359--1443](https://doi.org/10.4171/owr/2013/23)
## Literature revi... | 3 | open | null | 2,013 | 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-12486-002",
"literature-status:open",
"owr-year:2013"
] | Convergence and stability theories for metric-measure spaces already cover important diverging-dimension cases, but the broad infinite-dimensional concentration, Ricci, and spectral program in the extracted record is not a single settled theorem. | [
{
"url": "https://doi.org/10.1112/plms/pdv047",
"label": "Gigli--Mondino--Savare, Convergence of pointed non-compact metric measure spaces"
},
{
"url": "https://doi.org/10.4171/owr/2013/23",
"label": "Oberwolfach Report 23/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/23 | null | null | null | How should sequences of Riemannian or metric-measure spaces be studied when their dimensions tend to infinity, particularly with respect to concentration convergence, curvature-dimension conditions, and Laplacian eigenvalues? | How should sequences of Riemannian or metric-measure spaces be studied when their dimensions tend to infinity, particularly with respect to concentration convergence, curvature-dimension conditions, and Laplacian eigenvalues? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/23, pp. 1359--1443 |
30,002,339 | OWR-12487-001 | Expository Automorphic Spectral Decomposition | For a reductive group G, how does the automorphic representation L2(G(Z)\backslash G(R)) decompose, including its discrete and continuous spectra and their multiplicities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494](https://doi.org/10.4171/owr/2013/24)
## Literature ... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 | Unrecoverable OWR statement (The official report presents this as expository background and immediately gives the discrete–continuous decomposition, finite-multiplicity ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12487-001",
"literature-status:open",
"owr-year:2013"
] | The Langlands spectral theorem gives the general cusp, residual, and continuous framework for L^2(G(\mathbb{Z})\backslash G(\mathbb{R})), but the extracted broad request for its representation-theoretic description is not fully resolved in general. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC2747161/",
"label": "Arthur, The spectral side of Arthur's trace formula"
},
{
"url": "https://doi.org/10.1016/j.aim.2023.109107",
"label": "Delorme, On the spectral theorem of Langlands"
},
{
"url": "https://doi.org/10.4171/owr/2013/24"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/24 | null | null | null | null | For a reductive group G, how does the automorphic representation L2(G(Z)\backslash G(R)) decompose, including its discrete and continuous spectra and their multiplicities? | unrecoverable | The official report presents this as expository background and immediately gives the discrete–continuous decomposition, finite-multiplicity discrete sum, and Eisenstein-series description of the continuous part. It does not formulate the extracted sentence as an unresolved problem. No separate clean statement is promot... | null | null | null | null | null | Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494 |
30,002,340 | OWR-12487-002 | Expository Transition to Adelic Hecke Operators | What is known about the Hecke algebra associated with the arithmetic group G(Z), including its action on L2(G(Z)\backslash G(R))? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494](https://doi.org/10.4171/owr/2013/24)
## Literature ... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The source’s “What does one know?” is a rhetorical transition in an introductory account; the following paragraphs answer it by passing to t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12487-002",
"literature-status:open",
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] | The report poses a broad question about the Hecke algebra for the discrete automorphic spectrum; general Satake and spherical-variety theories give important cases, but no general description settles the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2013/24",
"label": "Oberwolfach Report 2013/24"
},
{
"url": "https://arxiv.org/abs/1203.0039",
"label": "Sakellaridis--Venkatesh, Periods and harmonic analysis on spherical varieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/24 | null | null | null | null | What is known about the Hecke algebra associated with the arithmetic group G(Z), including its action on L2(G(Z)\backslash G(R))? | unrecoverable | The source’s “What does one know?” is a rhetorical transition in an introductory account; the following paragraphs answer it by passing to the adelic framework. No definite unresolved mathematical claim is stated. No separate clean statement is promoted; the original record remains publicly visible and retained for pro... | null | null | null | null | null | Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494 |
30,002,341 | OWR-12487-003 | Spherical Hecke Modules on Homogeneous Schemes | For a homogeneous spherical $G$-scheme $X$ over the integers of a nonarchimedean local field, describe the module structure of the $K$-invariant compactly supported functions $C_c^\infty(X)^K$ over the spherical Hecke algebra $\mathcal H(G,K)$, including a description of $\mathcal H(G,K)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494](https://doi.org/10.4171/owr/2013/24)
## Literature ... | 3 | partially_solved | null | 2,013 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12487-003",
"literature-status:partially-solved",
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] | Generalized Satake transforms and substantial spherical-variety cases describe the Hecke-module structure, but the requested uniform basis and module description for arbitrary spherical X is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2013/24",
"label": "Oberwolfach Report 2013/24"
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{
"url": "https://arxiv.org/abs/1203.0039",
"label": "Sakellaridis--Venkatesh, Periods and harmonic analysis on spherical varieties"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/24 | null | null | null | For a homogeneous spherical $G$-scheme $X$ over the integers of a nonarchimedean local field, describe the module structure of the $K$-invariant compactly supported functions $C_c^\infty(X)^K$ over the spherical Hecke algebra $\mathcal H(G,K)$, including a description of $\mathcal H(G,K)$. | For a homogeneous spherical G-scheme X over the integers of a non-archimedean local field, describe the module structure of the K-invariant compactly supported functions Cc∞(X)K over the spherical Hecke algebra H(G,K), including the description of H(G,K). | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Spherical Varieties and Automorphic Representations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/24, pp. 1445--1494 |
30,002,342 | OWR-12490-002 | Étale Covers of Smooth Loci of Singular Varieties | For a singular complex algebraic variety $X$, what obstructs extension of finite étale covers of its smooth locus $X_{\mathrm{reg}}$ to $X$, and how do the étale fundamental groups of $X$ and $X_{\mathrm{reg}}$ differ? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627](https://doi.org/10.4171/owr/2013/27)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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"oberwolfach-reports",
"OWR-12490-002",
"literature-status:partially-solved",
"owr-year:2013"
] | For klt spaces, finite quasi-etale covers can be chosen so that the fundamental groups of the cover and its smooth locus agree, and local algebraic fundamental groups are finite; the full direct comparison and obstruction theory asked in the record is not known in general. | [
{
"url": "https://arxiv.org/abs/1307.5718",
"label": "Greb--Kebekus--Peternell, Etale fundamental groups of klt spaces"
},
{
"url": "https://arxiv.org/abs/1210.5564",
"label": "Xu, Finiteness of algebraic fundamental groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/27 | null | null | null | For a singular complex algebraic variety $X$, what obstructs extension of finite étale covers of its smooth locus $X_{\mathrm{reg}}$ to $X$, and how do the étale fundamental groups of $X$ and $X_{\mathrm{reg}}$ differ? | For a singular complex algebraic variety X, what obstructs extending finite étale covers of its smooth locus Xreg to X, and how do the étale fundamental groups of X and Xreg differ? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627 |
30,002,343 | OWR-12490-003 | Optimal Pluricanonical Bounds for Stable Log Surfaces | For a stable log surface $(X,\Delta)$ with Gorenstein locus $U$, what is the optimal integer $r$ such that $rK_U$ induces a birational map or an embedding? Does there exist a stable log surface for which $5I(K_X+\Delta)$ is not very ample? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627](https://doi.org/10.4171/owr/2013/27)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,013 | 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-12490-003",
"literature-status:open",
"owr-year:2013"
] | Pluricanonical bounds are known: 4I is base-point free and 8I is very ample, with stronger results for semi-canonical surfaces; the optimal uniform r and the proposed 5I counterexample question remain unresolved. | [
{
"url": "https://arxiv.org/abs/1211.1291",
"label": "Liu--Rollenske, Pluricanonical maps of stable log surfaces"
},
{
"url": "https://doi.org/10.1016/j.aim.2014.03.009",
"label": "Advances in Mathematics publication"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/27 | null | null | null | For a stable log surface $(X,\Delta)$ with Gorenstein locus $U$, what is the optimal integer $r$ such that $rK_U$ induces a birational map or an embedding? Does there exist a stable log surface for which $5I(K_X+\Delta)$ is not very ample? | For a stable log surface (X,Δ) with Gorenstein locus U, what is the optimal integer r such that rKU induces a birational map or an embedding, and does there exist a stable log surface for which 5I(KX+Δ) is not very ample? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627 |
30,002,344 | OWR-12490-004 | Torus Quotients among Simple Compact Kähler Threefolds | Let $X$ be either a smooth compact Kähler threefold or a normal $\mathbb Q$-factorial compact Kähler threefold with at most terminal singularities. If no positive-dimensional subvariety passes through a very general point, must $X$ be bimeromorphic to $T/G$ for a torus $T$ and a finite group $G$ acting on it? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627](https://doi.org/10.4171/owr/2013/27)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,013 | 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-12490-004",
"literature-status:partially-solved",
"owr-year:2013"
] | The restricted terminal threefold statement without divisors is proved, including a finite cover by a torus; the broader simple compact Kahler threefold torus-quotient assertion still has an acknowledged proof gap and is not settled uniformly. | [
{
"url": "https://math.univ-cotedazur.fr/u/hoering/articles/a26-abundance.pdf",
"label": "Campana--Horing--Peternell, Abundance for Kahler threefolds"
},
{
"url": "https://math.univ-cotedazur.fr/~hoering/articles/erratum-addendum-abundance.pdf",
"label": "Erratum and addendum on the abundance pr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/27 | null | null | null | Let $X$ be either a smooth compact Kähler threefold or a normal $\mathbb Q$-factorial compact Kähler threefold with at most terminal singularities. If no positive-dimensional subvariety passes through a very general point, must $X$ be bimeromorphic to $T/G$ for a torus $T$ and a finite group $G$ acting on it? | If X is a smooth compact Kähler threefold, or a normal Q-factorial compact Kähler threefold with at most terminal singularities, and no positive-dimensional subvariety passes through a very general point, must X be bimeromorphic to T/G for a torus T and a finite group G acting on T? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627 |
30,002,345 | OWR-12490-005 | Hodge Algebras of Conjugate Varieties | For which subfields $K\subset\mathbb C$ is the graded algebra of $K$-rational Hodge classes $H^{*,*}(X,K)$ isomorphic to $H^{*,*}(X^\sigma,K)$ for every pair of conjugate varieties $X$ and $X^\sigma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627](https://doi.org/10.4171/owr/2013/27)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,013 | 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-12490-005",
"literature-status:partially-solved",
"owr-year:2013"
] | Schreieder proved that fields not contained in an imaginary quadratic field admit conjugate varieties with different rational (p,p)-class algebras; the remaining imaginary-quadratic cases reduce to the Hodge conjecture and are unresolved. | [
{
"url": "https://arxiv.org/abs/1304.5146",
"label": "Schreieder, Multiplicative sub-Hodge structures of conjugate varieties"
},
{
"url": "https://doi.org/10.1017/fms.2013.7",
"label": "Forum of Mathematics Sigma publication"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/27 | null | null | null | For which subfields $K\subset\mathbb C$ is the graded algebra of $K$-rational Hodge classes $H^{*,*}(X,K)$ isomorphic to $H^{*,*}(X^\sigma,K)$ for every pair of conjugate varieties $X$ and $X^\sigma$? | For which subfields K of C is the graded algebra of K-rational Hodge classes H*,*(X,K) isomorphic to H*,*(Xσ,K) for every pair of conjugate varieties X and Xσ? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627 |
30,002,346 | OWR-12490-008 | Wild McKay Identity for Crepant Resolutions | Let $X$ be a quotient by a faithful linear action of a finite group $\Gamma$, and let $Y\to X$ be a crepant resolution with exceptional fiber $E$ over the origin. Is the wild McKay identity $\#E(\kappa)=M(K,\Gamma,-w)$ valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627](https://doi.org/10.4171/owr/2013/27)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,013 | 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-12490-008",
"literature-status:partially-solved",
"owr-year:2013"
] | The wild McKay equality is proved in important p-cyclic and symmetric-group or Hilbert-scheme cases, but the stated general motivic equality for arbitrary wild quotient data remains conjectural. | [
{
"url": "https://arxiv.org/abs/1208.0132",
"label": "Yasuda, The p-cyclic McKay correspondence via motivic integration"
},
{
"url": "https://doi.org/10.1093/imrn/rnv074",
"label": "Wood--Yasuda, Mass formulas and quotient singularities"
},
{
"url": "https://arxiv.org/abs/2107.07073",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/27 | null | null | null | Let $X$ be a quotient by a faithful linear action of a finite group $\Gamma$, and let $Y\to X$ be a crepant resolution with exceptional fiber $E$ over the origin. Is the wild McKay identity $\#E(\kappa)=M(K,\Gamma,-w)$ valid? | Let X be a quotient by a faithful linear action of a finite group Γ and let Y→X be a crepant resolution with exceptional fiber E over the origin; is the wild McKay identity #E(κ)=M(K,Γ,−w) valid? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Complex Algebraic Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/27, pp. 1563--1627 |
30,002,347 | OWR-12491-001 | Growth Functions of Finitely Generated Groups | Which functions occur, up to growth equivalence, as the growth function $v_G$ of a finitely generated group $G$? How far can $\inf_S v_{G,S}$ differ from $v_G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/28, pp. 1629--1675](https://doi.org/10.4171/owr/2013/28)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,013 | 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-12491-001",
"literature-status:open",
"owr-year:2013"
] | Growth types and rates are understood in many classes, with constructions realizing broad intermediate-growth families and examples of non-uniform exponential growth; the requested classification and the general relation between infimal and ordinary growth functions remain open. | [
{
"url": "https://arxiv.org/abs/1110.3650",
"label": "Bartholdi--Erschler, Groups of given intermediate word growth"
},
{
"url": "https://annals.math.princeton.edu/2004/160-3/p09",
"label": "Erschler, Boundary behavior for groups of subexponential growth"
},
{
"url": "https://arxiv.org/a... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/28 | null | null | null | Which functions occur, up to growth equivalence, as the growth function $v_G$ of a finitely generated group $G$? How far can $\inf_S v_{G,S}$ differ from $v_G$? | Which functions occur, up to growth equivalence, as the growth type vG of a finitely generated group G, and how far can the infimal growth function infS vG,S differ from vG? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Structures in Group Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/28, pp. 1629--1675 |
30,002,348 | OWR-12491-002 | Minimal-Genus Surface Subgroups of Random Groups | For random groups at density $D<1/2$, do the simplest homologically essential closed surface subgroups have genus $O(n/\log n)$ as the relator length $n$ tends to infinity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/28, pp. 1629--1675](https://doi.org/10.4171/owr/2013/28)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,013 | 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-12491-002",
"literature-status:open",
"owr-year:2013"
] | Random groups admit essential surface subgroups of genus bounded linearly in the relator length, but the conjectured optimal order n divided by log n for the simplest essential surfaces has not been proved. | [
{
"url": "https://arxiv.org/abs/1304.2188",
"label": "Calegari--Walker, Random groups contain surface subgroups"
},
{
"url": "https://arxiv.org/abs/1212.2618",
"label": "Calegari--Walker, Surface subgroups from linear programming"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/28 | null | null | null | For random groups at density $D<1/2$, do the simplest homologically essential closed surface subgroups have genus $O(n/\log n)$ as the relator length $n$ tends to infinity? | For random groups at density D<1/2, do the simplest homologically essential closed surface subgroups have genus O(n/log n) as the relator length n tends to infinity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Geometric Structures in Group Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/28, pp. 1629--1675 |
30,002,349 | OWR-12493-003 | Characteristic-Zero Lifts of Local Galois Extensions | Let $k$ be an algebraically closed field of characteristic $p$, let $L/k((t))$ be a Galois extension with group $G$, and let $A$ be the integral closure of $k[[t]]$ in $L$. Does there exist a complete discrete valuation ring $R$ of characteristic zero with residue field $k$ and a $G$-Galois lift whose reduction is $k[[... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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-12493-003",
"literature-status:open",
"owr-year:2013"
] | The local lifting problem is solved for cyclic groups by the Oort conjecture theorem, but the extracted question asks for arbitrary G and its additional ring-control refinement; those general assertions remain unresolved. | [
{
"url": "https://annals.math.princeton.edu/2014/180-1/p06",
"label": "Pop, The Oort conjecture on lifting covers of curves"
},
{
"url": "https://annals.math.princeton.edu/2014/180-1/p05",
"label": "Obus--Wewers, Cyclic extensions and the local lifting problem"
},
{
"url": "https://doi.o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | Let $k$ be an algebraically closed field of characteristic $p$, let $L/k((t))$ be a Galois extension with group $G$, and let $A$ be the integral closure of $k[[t]]$ in $L$. Does there exist a complete discrete valuation ring $R$ of characteristic zero with residue field $k$ and a $G$-Galois lift whose reduction is $k[[... | Given an algebraically closed field k of characteristic p, a k((t))-extension with Galois group G, and its integral closure A of k[[t]], does there exist a characteristic-zero complete discrete valuation ring R with residue field k and a Galois lift whose reduction is k[[t]]-isomorphic to A? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,350 | OWR-12493-004 | Dihedral Groups as Oort Groups | For an odd prime $p$ and $n\geq1$, is the dihedral group $D_{p^n}$ of order $2p^n$ an Oort group; that is, does every local Galois extension with this group lift to characteristic zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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-12493-004",
"literature-status:open",
"owr-year:2013"
] | Cyclic Oort groups and several noncyclic cases are known, including D4, but the classification of all Oort groups and the conjectured odd-prime dihedral family are not settled. | [
{
"url": "https://arxiv.org/abs/1502.07623",
"label": "Obus, A generalization of the Oort conjecture"
},
{
"url": "https://arxiv.org/abs/1706.03751",
"label": "The local lifting problem for D4"
},
{
"url": "https://annals.math.princeton.edu/2014/180-1/p06",
"label": "Pop, The Oort co... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | For an odd prime $p$ and $n\geq1$, is the dihedral group $D_{p^n}$ of order $2p^n$ an Oort group; that is, does every local Galois extension with this group lift to characteristic zero? | For odd p and n≥1, are the dihedral groups Dpn of order 2pn Oort groups, meaning that every local Galois extension with this group lifts to characteristic zero? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,351 | OWR-12493-005 | Merkurjev–Suslin Theory for Higher Massey Products | Can the Merkurjev–Suslin theorem be generalized from the twofold cup product to $n$-fold Massey products? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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-12493-005",
"literature-status:open",
"owr-year:2013"
] | The requested all-n generalization is not proved: triple Massey products vanish for absolute Galois groups and substantial four-fold and higher special cases are known, but the general Massey-vanishing and Merkurjev--Suslin-type statement remains open. | [
{
"url": "https://arxiv.org/abs/1412.7265",
"label": "Efrat--Matzri, Triple Massey products and absolute Galois groups"
},
{
"url": "https://arxiv.org/abs/1711.07711",
"label": "Guillot--Minac, Extensions of unipotent groups and Massey products"
},
{
"url": "https://doi.org/10.1016/j.aim... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | Can the Merkurjev–Suslin theorem be generalized from the twofold cup product to $n$-fold Massey products? | Can the Merkurjev--Suslin theorem be generalized from the two-fold cup product to n-fold Massey products? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,352 | OWR-12493-006 | Duplicate: Valuative Form of Grothendieck's Section Conjecture | For a number field k and a hyperbolic curve X over k, is every Galois section of π1(X)→Gal(k) induced, up to conjugacy, by a suitable k-valuation of the function field of X? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (Comparison with the official report and OWR-12493-007 confirms that this is another extraction of the same valuative section conjecture. No ) | [
"OWR-12493-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12493-006",
"literature-status:open",
"owr-year:2013"
] | The extracted record is only a section heading and introductory fragment about a valuative viewpoint, not a complete claim whose truth can be tested; it is therefore classified open under the rule for unclear records. | [
{
"url": "https://doi.org/10.4171/owr/2013/30",
"label": "The Arithmetic of Fields, Oberwolfach Reports"
},
{
"url": "https://www.math.uni-frankfurt.de/~stix/research/preprints/owr-STIX-Jun13.pdf",
"label": "Stix, On Galois sections for hyperbolic p-adic curves"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | null | For a number field k and a hyperbolic curve X over k, is every Galois section of π1(X)→Gal(k) induced, up to conjugacy, by a suitable k-valuation of the function field of X? | unrecoverable | Comparison with the official report and OWR-12493-007 confirms that this is another extraction of the same valuative section conjecture. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,353 | OWR-12493-007 | Valuative Form of Grothendieck's Section Conjecture | Let $k$ be a number field and $X/k$ a hyperbolic curve. Is every Galois section $s:G_k\to\pi_1(X)$ induced, up to conjugacy, by a suitable $k$-valuation of the function field $k(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12493-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12493-007",
"literature-status:open",
"owr-year:2013"
] | The number-field Grothendieck section conjecture remains unresolved; valuative and p-adic analogues are proved, and conditional reductions over finitely generated fields do not establish the number-field assertion. | [
{
"url": "https://www.math.uni-frankfurt.de/~stix/research/preprints/owr-STIX-Jun13.pdf",
"label": "Stix, On Galois sections for hyperbolic p-adic curves"
},
{
"url": "https://arxiv.org/abs/1111.1354",
"label": "Pop--Stix, Arithmetic in the fundamental group of a p-adic curve"
},
{
"url"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | Let $k$ be a number field and $X/k$ a hyperbolic curve. Is every Galois section $s:G_k\to\pi_1(X)$ induced, up to conjugacy, by a suitable $k$-valuation of the function field $k(X)$? | Grothendieck's section conjecture: if k is a number field and X/k is a hyperbolic curve, every Galois section s:G_k\to\pi_1(X) is induced by a suitable k-valuation w of the function field of X. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,354 | OWR-12493-009 | Pythagoras Numbers of Real Function Fields | For the function field $F$ of a variety over a real closed field, determine its Pythagoras number $p(F)$, or obtain good lower bounds, where $p(F)$ is the least $n$ such that every sum of squares in $F$ is a sum of $n$ squares. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818](https://doi.org/10.4171/owr/2013/30)
## Literature review (checked 2026-08-21)
**Status:** o... | 3 | open | null | 2,013 | 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-12493-009",
"literature-status:open",
"owr-year:2013"
] | The general lower bound p(F) at least d+1 is proved, and further special cases are known, but the exact value and sharp general bounds remain open. | [
{
"url": "https://doi.org/10.4171/CMH/356",
"label": "Grimm, Lower bounds for Pythagoras numbers"
},
{
"url": "https://arxiv.org/abs/2302.11425",
"label": "Pythagoras number in two variables"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/30 | null | null | null | For the function field $F$ of a variety over a real closed field, determine its Pythagoras number $p(F)$, or obtain good lower bounds, where $p(F)$ is the least $n$ such that every sum of squares in $F$ is a sum of $n$ squares. | For the function field F of a variety over a real closed field, determine the exact Pythagoras number p(F), or obtain good lower bounds, where p(F) is the least n such that every sum of squares in F is a sum of n squares. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Arithmetic of Fields (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/30, pp. 1771--1818 |
30,002,355 | OWR-12494-001 | Local–Global Isotropy over Function Fields | Let $X$ be an integral scheme on which $2$ is invertible, let $K$ be its function field, and let $\Omega$ be the set of rank-one discrete valuations of $K$. If a nondegenerate quadratic form $q$ over $K$ is isotropic over the completion $K_v$ for every $v\in\Omega$, must $q$ be isotropic over $K$? More specifically, do... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,013 | 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-12494-001",
"literature-status:partially-solved",
"owr-year:2013"
] | The local-global principle holds in global fields and several low-dimensional cases, while counterexamples are known over surface and higher-transcendence-degree fields; no general classification for a given function field is known. | [
{
"url": "https://math.dartmouth.edu/~auel/papers/docs/AUEL_MFO2013.pdf",
"label": "Auel, Parimala and Suresh, local-global principle"
},
{
"url": "https://doi.org/10.2140/ant.2024.18.1497",
"label": "Auel and Suresh, quadratic-form counterexamples"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | Let $X$ be an integral scheme on which $2$ is invertible, let $K$ be its function field, and let $\Omega$ be the set of rank-one discrete valuations of $K$. If a nondegenerate quadratic form $q$ over $K$ is isotropic over the completion $K_v$ for every $v\in\Omega$, must $q$ be isotropic over $K$? More specifically, do... | For a function field K with rank-one discrete valuations v and completions K_v, determine whether the local-global principle for quadratic-form isotropy holds: if a nondegenerate quadratic form q over K is isotropic over every K_v, must q be isotropic over K? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,356 | OWR-12494-002 | Cohomological Invariants of Simple Algebraic Groups | For a simple algebraic group $G$ and a Galois module $M$, compute the group of normalized cohomological invariants $\operatorname{Inv}^n(G,M)^{\mathrm{norm}}$, including the basic case $M=\mathbb Z/2\mathbb Z$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,013 | 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-12494-002",
"literature-status:partially-solved",
"owr-year:2013"
] | The general computation remains open, but degree-three cohomological invariants are classified in major families, including adjoint inner-type groups; this is substantial partial progress rather than a complete computation. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/75e13110-0aa1-46a6-8c43-3bf00c863bc2/content",
"label": "Oberwolfach report on cohomological invariants"
},
{
"url": "https://doi.org/10.4171/JEMS/599",
"label": "Merkurjev, degree-three invariants"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | For a simple algebraic group $G$ and a Galois module $M$, compute the group of normalized cohomological invariants $\operatorname{Inv}^n(G,M)^{\mathrm{norm}}$, including the basic case $M=\mathbb Z/2\mathbb Z$. | For a simple algebraic group G and a Galois module M, compute the group of normalized cohomological invariants Inv^n(G,M)^{norm}, even in the simplest case where G is simple and M=\mathbb{Z}/2. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,357 | OWR-12494-003 | Pythagoras Numbers of Real Function Fields | For a real function field $F$, determine its Pythagoras number $p(F)$, or obtain effective lower bounds for it, where $p(F)$ is the least integer such that every sum of squares in $F$ is a sum of at most $p(F)$ squares. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | open | null | 2,013 | 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-12494-003",
"literature-status:open",
"owr-year:2013"
] | The general exact-value problem for the Pythagoras number remains open, despite lower bounds and results for important special classes of function fields. | [
{
"url": "https://doi.org/10.4171/CMH/356",
"label": "Grimm, lower bounds for Pythagoras numbers"
},
{
"url": "https://arxiv.org/abs/2302.11425",
"label": "Pythagoras number in two variables"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | For a real function field $F$, determine its Pythagoras number $p(F)$, or obtain effective lower bounds for it, where $p(F)$ is the least integer such that every sum of squares in $F$ is a sum of at most $p(F)$ squares. | For a real function field F, determine the exact Pythagoras number p(F), or obtain good lower bounds, where p(F) is the least number of squares needed to represent every sum of squares in F. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,358 | OWR-12494-004 | Possible Values of Characteristic-Two Quadratic-Form Invariants | Let $F$ be a field of characteristic $2$, let $Q'(F)$ be the set of anisotropic quadratic forms over $F$ that are not totally singular, and let $\operatorname{rdim}(\varphi)$ and $\operatorname{ql}(\varphi)$ denote the regular dimension and quasilinear part of $\varphi$. Determine the possible values of
$$\widetilde u... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,013 | 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-12494-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Many realizability and exclusion results are known for the three u-invariants, but their complete value sets and all relations remain unresolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/75e13110-0aa1-46a6-8c43-3bf00c863bc2/content",
"label": "Oberwolfach report on u-invariants"
},
{
"url": "https://www.math.uni-bielefeld.de/LAG/man/229.pdf",
"label": "Vishik, fields of u-invariant"
},
{
"url": "https://www.ma... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | Let $F$ be a field of characteristic $2$, let $Q'(F)$ be the set of anisotropic quadratic forms over $F$ that are not totally singular, and let $\operatorname{rdim}(\varphi)$ and $\operatorname{ql}(\varphi)$ denote the regular dimension and quasilinear part of $\varphi$. Determine the possible values of
$$\widetilde u... | For fields F, determine the possible values of the invariants u-tilde(F), u_r(F), and u-tilde-sub-s(F), defined using dimensions of anisotropic quadratic forms outside the totally singular forms. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,359 | OWR-12494-005 | The Value Nine and Universality for Quadratic-Form Invariants | Does there exist a field $F$ of characteristic $2$ with $\widetilde u(F)=9$? If $u(F)<\infty$, is every anisotropic nonsingular quadratic form over $F$ of dimension $u(F)$ universal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | open | null | 2,013 | 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-12494-005",
"literature-status:open",
"owr-year:2013"
] | The existence of a field with tilde u equal to 9 remains unresolved, and the universality question for arbitrary finite u-invariant is not settled; later work treats important special classes only. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/75e13110-0aa1-46a6-8c43-3bf00c863bc2/content",
"label": "Oberwolfach report on quadratic-form questions"
},
{
"url": "https://arxiv.org/abs/2309.00689",
"label": "Universal quadratic forms over semi-global fields"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | Does there exist a field $F$ of characteristic $2$ with $\widetilde u(F)=9$? If $u(F)<\infty$, is every anisotropic nonsingular quadratic form over $F$ of dimension $u(F)$ universal? | Does there exist a field F with u-tilde(F)=9, and, when u(F) is finite, is every anisotropic nonsingular F-quadratic form of dimension u(F) universal? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,360 | OWR-12494-006 | Grothendieck–Serre Conjecture for Regular Local Rings | Let $R$ be a regular local ring with fraction field $K$, and let $G$ be a reductive group scheme over $R$. If a principal $G$-bundle over $R$ becomes trivial over $K$, must it already be trivial over $R$? Equivalently, does $H^1_{\mathrm{\acute et}}(R,G)\to H^1_{\mathrm{\acute et}}(K,G)$ have trivial kernel? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859](https://doi.org/10.4171/owr/2013/31)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,013 | 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-12494-006",
"literature-status:partially-solved",
"owr-year:2013"
] | The conjecture is proved for regular local rings containing a field, but the full mixed-characteristic statement for arbitrary reductive group schemes remains open; only substantial mixed-characteristic subcases are known. | [
{
"url": "https://doi.org/10.1007/s10240-015-0075-z",
"label": "Fedorov and Panin, Grothendieck--Serre conjecture"
},
{
"url": "https://doi.org/10.1070/IM8982",
"label": "Panin, reductive group schemes over local rings"
},
{
"url": "https://doi.org/10.1090/tran/8490",
"label": "Fedor... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/31 | null | null | null | Let $R$ be a regular local ring with fraction field $K$, and let $G$ be a reductive group scheme over $R$. If a principal $G$-bundle over $R$ becomes trivial over $K$, must it already be trivial over $R$? Equivalently, does $H^1_{\mathrm{\acute et}}(R,G)\to H^1_{\mathrm{\acute et}}(K,G)$ have trivial kernel? | Grothendieck-Serre conjecture: if R is a regular local ring with fraction field K, G is a reductive group scheme over R, and a principal G-bundle over R becomes trivial over K, then it is already trivial over R; equivalently, H^1_et(R,G)\to H^1_et(K,G) has trivial kernel. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Quadratic Forms and Linear Algebraic Groups (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/31, pp. 1819--1859 |
30,002,361 | OWR-12495-001 | Lott Secondary Index and Transfer Compatibility | Does there exist a natural transformation $KR^0\to KR_{\mathbb R/\mathbb Z}^{-1}$ under which analytic push-forward corresponds to the Becker–Gottlieb–Dold transfer? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,013 | 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-12495-001",
"literature-status:partially-solved",
"owr-year:2013"
] | The natural transformation required by Lott's conjecture is constructed, but compatibility of analytic push-forward with the Becker--Gottlieb--Dold transfer remains unproved. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on differential algebraic K-theory"
},
{
"url": "https://arxiv.org/abs/1306.0247",
"label": "Bunke and Gepner, differential K-theory transfer"
},
{
"url": "https://bookstore.ams.org/MEMO/26... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | Does there exist a natural transformation $KR^0\to KR_{\mathbb R/\mathbb Z}^{-1}$ under which analytic push-forward corresponds to the Becker–Gottlieb–Dold transfer? | Lott's secondary-index conjecture: there is a natural transformation KR^0\to KR_{\mathbb{R}/\mathbb{Z}}^{-1} under which the analytic push-forward corresponds to the Becker-Gottlieb-Dold transfer. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,362 | OWR-12495-002 | Secondary K-Theory Comparison Map | Lott's secondary K-group admits a well-defined map to differential algebraic K-theory, KR^0(M)\to KR_d^0(M)\cong KR_{\mathbb{R}/\mathbb{Z}}^{-1}(M), sending a generator (V,g_V,eta) to cycl(V,g_V)-a(eta). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The extracted sentence states a construction and result proved in the source, rather than a) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12495-002",
"literature-status:partially-solved",
"owr-year:2013"
] | The existence part of Lott's conjecture is settled by the differential algebraic K-theory theorem, while the transfer-compatibility part remains unproved. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on Lott's conjecture"
},
{
"url": "https://arxiv.org/abs/1306.0247",
"label": "Bunke and Gepner, differential K-theory transfer"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | null | Lott's secondary K-group admits a well-defined map to differential algebraic K-theory, KR^0(M)\to KR_d^0(M)\cong KR_{\mathbb{R}/\mathbb{Z}}^{-1}(M), sending a generator (V,g_V,eta) to cycl(V,g_V)-a(eta). | unrecoverable | Checked against the official Oberwolfach report. The extracted sentence states a construction and result proved in the source, rather than an unresolved question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,363 | OWR-12495-003 | Lefschetz Classes and the Tate and Hodge Conjectures | For CM-type abelian varieties, the Lefschetz-class property that all Tate classes on all powers of a reduction, respectively all Hodge classes on all powers over the complex numbers, are generated by degree-one classes is a sufficient condition for the Tate, respectively Hodge, conjecture. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The extracted sentence is an explanatory sufficient-condition statement, not an open proble) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12495-003",
"literature-status:open",
"owr-year:2013"
] | The record refers to Tate and Hodge conjecture questions; Sugiyama proves criteria and special cases for Lefschetz classes, but no general resolution is known. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on Lefschetz classes"
},
{
"url": "https://doi.org/10.1016/j.jnt.2012.09.023",
"label": "Sugiyama, Lefschetz classes"
},
{
"url": "https://jmilne.org/math/articles/1999a.html",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | null | For CM-type abelian varieties, the Lefschetz-class property that all Tate classes on all powers of a reduction, respectively all Hodge classes on all powers over the complex numbers, are generated by degree-one classes is a sufficient condition for the Tate, respectively Hodge, conjecture. | unrecoverable | Checked against the official Oberwolfach report. The extracted sentence is an explanatory sufficient-condition statement, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,364 | OWR-12495-004 | Lefschetz-Class Properties Under CM Reduction | Let $A$ be a CM-type abelian variety over $\overline{\mathbb Q}$, and let $A_0$ be a reduction of $A$. Does the property that all Hodge classes on all powers of $A$ are Lefschetz classes imply that all Tate classes on all powers of $A_0$ are Lefschetz classes? Is there a class of CM-type abelian varieties for which the... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,013 | 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-12495-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Sugiyama proves equivalence for simple CM abelian varieties with an abelian CM field under explicit reduction hypotheses, but the questions for arbitrary primes and CM varieties remain open. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on CM reductions"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3363/OWR_2013_32.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach report on Lefschetz classes"
},
{
"url": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | Let $A$ be a CM-type abelian variety over $\overline{\mathbb Q}$, and let $A_0$ be a reduction of $A$. Does the property that all Hodge classes on all powers of $A$ are Lefschetz classes imply that all Tate classes on all powers of $A_0$ are Lefschetz classes? Is there a class of CM-type abelian varieties for which the... | For a CM-type abelian variety A over the algebraic numbers, does the Lefschetz-class property for A imply the same property for every reduction A_0, and is there a class of such A for which the property for A_0 implies the property for A? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,365 | OWR-12495-005 | Tate and Hodge Classes on CM Abelian Varieties | For a simple CM-type abelian variety A and a reduction A_0, study the property that all Tate classes on all powers of A_0, respectively all Hodge classes on all powers of A, are Lefschetz classes, and determine its relation to the Tate and Hodge conjectures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The extraction paraphrases background already represented by the adjacent source questions ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12495-005",
"literature-status:partially-solved",
"owr-year:2013"
] | A conditional equivalence is proved for simple CM varieties with abelian CM field and suitable unramified degree-one primes, while the unrestricted property questions remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on Tate and Hodge properties"
},
{
"url": "https://doi.org/10.1016/j.jnt.2012.09.023",
"label": "Sugiyama, Lefschetz classes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | null | For a simple CM-type abelian variety A and a reduction A_0, study the property that all Tate classes on all powers of A_0, respectively all Hodge classes on all powers of A, are Lefschetz classes, and determine its relation to the Tate and Hodge conjectures. | unrecoverable | Checked against the official Oberwolfach report. The extraction paraphrases background already represented by the adjacent source questions and does not isolate a distinct unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,366 | OWR-12495-006 | Unstable Motivic Homotopy Exact-Sequence Conjecture | For every $n\geq 4$, is there an exact sequence of strictly $\mathbb A^1$-invariant sheaves
$$K^M_{n+2}/24\longrightarrow \pi_n^{\mathbb A^1}(\mathbb A^n\setminus\{0\})\longrightarrow GW_{n+1}^n,$$
which becomes short exact after $n$-fold contraction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2306.04631",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] keep **partially_solved**, but update the literature note. A. Asok (joint with J. Fasel; OWR 32/2013, pp. 1892–1895, Conjecture 7) conjectures, over perfect fields of characteristic ≠ 2 and for n ≥ 4, an exact sequence K^M_{n+2}/24 → π_n^{A¹}(A^n∖0) → GW^n_{n+1}, short exac... | [
"owr",
"oberwolfach-reports",
"OWR-12495-006",
"literature-status:partially-solved",
"owr-year:2013"
] | The stable 2-primary statement over fields of 2-cohomological dimension at most 2 and several low-dimensional splitting cases are proved, but the full unstable conjecture and its secondary obstruction remain open. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on motivic splitting"
},
{
"url": "https://ems.press/content/book-chapter-files/33191?nt=1",
"label": "Asok and Fasel, vector bundles"
},
{
"url": "https://msp.org/obs/2025/6-1/obs-v6-n1-p0... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | For every $n\geq 4$, is there an exact sequence of strictly $\mathbb A^1$-invariant sheaves
$$K^M_{n+2}/24\longrightarrow \pi_n^{\mathbb A^1}(\mathbb A^n\setminus\{0\})\longrightarrow GW_{n+1}^n,$$
which becomes short exact after $n$-fold contraction? | For every integer n>=4, conjecturally there is an exact sequence of sheaves K^{A1}_{n+2}/24\to pi_n^{A1}(A^n\setminus 0)\to GW_{n+1}, becoming short exact after n-fold contraction. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,367 | OWR-12495-007 | Topological Nilpotence Degree of Finite-Group Chow Rings | For a finite group $G$, is the topological nilpotence degree $d_0(CH_G^*)$ of its mod-$p$ Chow ring equal to the largest integer $d$ such that $CH_G^*$, as a module over the Steenrod algebra, contains the $d$th suspension of a nonzero unstable module? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913](https://doi.org/10.4171/owr/2013/32)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,013 | 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-12495-007",
"literature-status:open",
"owr-year:2013"
] | The detection bound d0 of the Chow ring is bounded and computed for many finite groups, but the proposed equality with the maximal Steenrod-module suspension remains an open conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/46461?nt=1",
"label": "Oberwolfach report on Chow detection"
},
{
"url": "https://arxiv.org/abs/math/9802097",
"label": "Totaro, Chow ring of a classifying space"
},
{
"url": "https://doi.org/10.1016/j.aim.2004.07.009",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/32 | null | null | null | For a finite group $G$, is the topological nilpotence degree $d_0(CH_G^*)$ of its mod-$p$ Chow ring equal to the largest integer $d$ such that $CH_G^*$, as a module over the Steenrod algebra, contains the $d$th suspension of a nonzero unstable module? | For a finite group G, conjecturally the topological nilpotence degree d_0(CH_G^*) of its mod-p Chow ring equals the largest d for which CH_G^*, as a module over the Steenrod algebra, contains the dth suspension of a nonzero unstable module. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Algebraic K-theory and Motivic Cohomology (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/32, pp. 1861--1913 |
30,002,368 | OWR-12581-001 | Geometric Decomposition from Long-Time Ricci Flow | For a Ricci flow with surgery on a closed $3$-manifold that exists for all sufficiently large times, determine whether and how its behavior as $t\to\infty$ realizes the full geometric decomposition of the manifold. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974](https://doi.org/10.4171/owr/2013/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,013 | 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-12581-001",
"literature-status:open",
"owr-year:2013"
] | Bamler proves finite surgery and curvature control for arbitrary closed 3-manifolds and obtains a qualitative asymptotic description, but the record's stronger question about the full geometric decomposition exhibited by the flow remains unresolved. | [
{
"url": "https://arxiv.org/abs/1310.4483",
"label": "Bamler, long-time analysis III"
},
{
"url": "https://arxiv.org/abs/1411.6658",
"label": "Bamler, long-time behavior introduction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/33 | null | null | null | For a Ricci flow with surgery on a closed $3$-manifold that exists for all sufficiently large times, determine whether and how its behavior as $t\to\infty$ realizes the full geometric decomposition of the manifold. | For a Ricci flow with surgery on a closed 3-manifold that exists for infinite time, determine whether and how its long-time behavior realizes the full geometric decomposition of the manifold as t\to\infty; the finite-surgery part of Perelman's conjecture is known. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974 |
30,002,369 | OWR-12581-002 | Auslander Conjecture for Complete Affine Manifolds | Is every closed complete affine manifold finitely covered by a complete affine solvmanifold $G/\Gamma$, where $G$ is a closed solvable subgroup of the affine group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974](https://doi.org/10.4171/owr/2013/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,013 | 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-12581-002",
"literature-status:open",
"owr-year:2013"
] | The Auslander conjecture remains open in general; it is proved in dimensions below seven and other special cases, while the compact affine statement is not settled. | [
{
"url": "https://arxiv.org/abs/2011.12788",
"label": "Abels, Margulis and Soifer, Auslander conjecture"
},
{
"url": "https://cm.episciences.org/9522/pdf",
"label": "Burde, affine crystallographic groups"
},
{
"url": "https://math.umd.edu/~wmg/icm.pdf",
"label": "Goldman, affine mani... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/33 | null | null | null | Is every closed complete affine manifold finitely covered by a complete affine solvmanifold $G/\Gamma$, where $G$ is a closed solvable subgroup of the affine group? | Auslander conjecture: every closed complete affine manifold is finitely covered by a complete affine solvmanifold G/Gamma, for a closed solvable subgroup G of the affine group. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974 |
30,002,370 | OWR-12581-003 | Einstein Metric Gluing by Reverse Bubbling | Can Einstein metrics be glued across connected-sum pieces by starting from a limit space and attaching a bubble, thereby producing a critical point of a Riemannian functional that generalizes the Einstein–Hilbert functional? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974](https://doi.org/10.4171/owr/2013/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,013 | 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-12581-003",
"literature-status:partially-solved",
"owr-year:2013"
] | Gursky and Viaclovsky construct critical metrics on several connected sums using gluing, but the general reverse-bubbling existence question is not solved. | [
{
"url": "https://arxiv.org/abs/1303.0827",
"label": "Gursky and Viaclovsky, gluing critical metrics"
},
{
"url": "https://doi.org/10.1016/j.aim.2015.11.054",
"label": "Gursky and Viaclovsky, connected-sum metrics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/33 | null | null | null | Can Einstein metrics be glued across connected-sum pieces by starting from a limit space and attaching a bubble, thereby producing a critical point of a Riemannian functional that generalizes the Einstein–Hilbert functional? | Can one glue Einstein metrics on connected-sum pieces, starting from a limit space and attaching a bubble, to produce a critical point of a Riemannian functional generalizing the Einstein-Hilbert functional? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974 |
30,002,371 | OWR-12581-004 | Complex Extension Conjecture for Polyhedral Kähler Manifolds | Let $M^{2n}$ be a polyhedral Kähler manifold. Does its flat complex structure away from the metric singularities extend across all of $M$, making $M$ a normal complex analytic variety whose complex singularities have codimension $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974](https://doi.org/10.4171/owr/2013/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,013 | 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-12581-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Panov proves the extension and complex-surface structure in real dimension four, with further special constructions in higher dimensions, but the all-dimensional complex conjecture remains open. | [
{
"url": "https://doi.org/10.2140/gt.2009.13.2205",
"label": "Panov, polyhedral Kahler manifolds"
},
{
"url": "https://arxiv.org/abs/2510.17447",
"label": "de Borbon and Panov, polyhedral Kahler metrics"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/2771cf96-e925-492b-... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/33 | null | null | null | Let $M^{2n}$ be a polyhedral Kähler manifold. Does its flat complex structure away from the metric singularities extend across all of $M$, making $M$ a normal complex analytic variety whose complex singularities have codimension $3$? | Complex conjecture: if M^{2n} is a polyhedral Kaehler manifold, its flat complex structure away from the metric singularities extends over all of M so that M becomes a normal complex analytic variety with complex singularities in codimension 3. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974 |
30,002,372 | OWR-12581-005 | Polyhedral Frankel Conjecture | Is every orientable nonnegatively curved polyhedral manifold with irreducible holonomy and $b_2(M)>0$ biholomorphic to $\mathbb{CP}^n$ in a natural holomorphic structure, with a singular Kähler metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974](https://doi.org/10.4171/owr/2013/33)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,013 | 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-12581-005",
"literature-status:partially-solved",
"owr-year:2013"
] | The polyhedral Frankel problem is known in low dimensions through the complex-extension results, but the general all-dimensional classification by CP^n remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46372?nt=1",
"label": "Oberwolfach report on polyhedral Frankel conjecture"
},
{
"url": "https://doi.org/10.2140/gt.2009.13.2205",
"label": "Panov, polyhedral Kahler manifolds"
},
{
"url": "https://ems.press/content/serial-article-... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/33 | null | null | null | Is every orientable nonnegatively curved polyhedral manifold with irreducible holonomy and $b_2(M)>0$ biholomorphic to $\mathbb{CP}^n$ in a natural holomorphic structure, with a singular Kähler metric? | Polyhedral Frankel conjecture: an orientable non-negatively curved polyhedral manifold with irreducible holonomy and b_2(M)>0 is biholomorphic to CP^n in a natural holomorphic structure, and its metric is singular Kaehler. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Differentialgeometrie im Großen (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/33, pp. 1929--1974 |
30,002,373 | OWR-12582-001 | Persistence of KdV Solutions Under Quasilinear Perturbations | Let $N_4(x,u,u_x,u_{xx},u_{xxx})$ be a Hamiltonian quasilinear term vanishing to fourth order at the origin. For the perturbed equations on $\mathbb T$
$$u_t+u_{xxx}-\partial_x(u^2)+N_4(x,u,u_x,u_{xx},u_{xxx})=0$$
and
$$u_t+u_{xxx}\pm\partial_x(u^3)+N_4(x,u,u_x,u_{xx},u_{xxx})=0,$$
do the periodic, quasiperiodic, o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12582-001",
"literature-status:partially-solved",
"owr-year:2013"
] | KAM theory proves persistence and stability of Cantor families of small quasi-periodic solutions for broad Hamiltonian quasi-linear KdV perturbations, but persistence of all periodic, quasi-periodic, or almost periodic solutions under arbitrary small perturbations remains open. | [
{
"url": "https://www.numdam.org/item/AIHPC_2016__33_6_1589_0/",
"label": "Baldi, Berti and Montalto, autonomous quasi-linear KdV"
},
{
"url": "https://arxiv.org/abs/1211.6672",
"label": "Baldi, Berti and Montalto, forced KdV"
},
{
"url": "https://arxiv.org/abs/1908.08768",
"label": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | Let $N_4(x,u,u_x,u_{xx},u_{xxx})$ be a Hamiltonian quasilinear term vanishing to fourth order at the origin. For the perturbed equations on $\mathbb T$
$$u_t+u_{xxx}-\partial_x(u^2)+N_4(x,u,u_x,u_{xx},u_{xxx})=0$$
and
$$u_t+u_{xxx}\pm\partial_x(u^3)+N_4(x,u,u_x,u_{xx},u_{xxx})=0,$$
do the periodic, quasiperiodic, o... | Do the periodic, quasi-periodic, or almost periodic solutions of the integrable KdV and modified KdV equations persist under small Hamiltonian quasi-linear perturbations of the displayed equations? | corrected_verified | The two KdV-type equations and the order condition on the Hamiltonian quasilinear perturbation were restored from the official report, eliminating the missing display reference. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,374 | OWR-12582-002 | The Hofer–Zehnder Periodic-Orbit Conjecture | Hofer–Zehnder conjecture: A Hamiltonian diffeomorphism with more than the necessary number of fixed points—in particular, more than $n+1$ on $\mathbb{CP}^n$ in the expected case—has infinitely many periodic orbits. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.4007/annals.2022.195.3.1",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] keep **partially_solved**, but **update the note**. V. Ginzburg (joint with B. Gürel; OWR 34/2013, p. 1986) recalls the Hofer–Zehnder conjecture: a Hamiltonian diffeomorphism with more fixed points than necessary (more than n + 1 on CPⁿ) has infinitely many periodic points,... | [
"owr",
"oberwolfach-reports",
"OWR-12582-002",
"literature-status:partially-solved",
"owr-year:2013"
] | Franks's two-dimensional theorem and higher-dimensional results for hyperbolic fixed points establish substantial special cases and motivate the HZ-conjecture, but the proposed extension from hyperbolic to general non-elliptic fixed points remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/34",
"label": "Oberwolfach Report 34/2013"
},
{
"url": "https://doi.org/10.1016/j.aim.2025.110709",
"label": "Invariant sets and hyperbolic closed Reeb orbits"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | Hofer–Zehnder conjecture: A Hamiltonian diffeomorphism with more than the necessary number of fixed points—in particular, more than $n+1$ on $\mathbb{CP}^n$ in the expected case—has infinitely many periodic orbits. | HZ-conjecture: a Hamiltonian diffeomorphism with more than the necessary number of fixed points, in particular more than n+1 on CP^n in the expected case, has infinitely many periodic orbits. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,375 | OWR-12582-004 | Global Rigidity of Diophantine Pseudo-Rotations | Are Diophantine pseudo-rotations always globally conjugate to a rotation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12582-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Diophantine pseudo-rotations are globally conjugate to rotations in perturbative and other restricted regimes, but the general global-conjugacy question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/34",
"label": "Oberwolfach Report 34/2013"
},
{
"url": "https://www.numdam.org/articles/10.24033/asens.2093/",
"label": "Herman's last geometric theorem"
},
{
"url": "https://webusers.imj-prg.fr/~bassam.fayad/ICM_FayadKrikorian-cor.pdf",
"la... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | Are Diophantine pseudo-rotations always globally conjugate to a rotation? | Are Diophantine pseudo-rotations always globally conjugate to a rotation? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,376 | OWR-12582-006 | Recovering Three-Manifold Topology from Contact Dynamics | Can the diffeomorphism type of a closed connected 3-manifold be determined from dynamical properties of a flow defined on it, viewed as a contact-type energy level, together with its induced contact structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,013 | 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-12582-006",
"literature-status:partially-solved",
"owr-year:2013"
] | A dynamical characterization is proved for standard tight lens spaces, including the three-sphere, using a distinguished Reeb orbit and index/linking data; no characterization of every closed connected three-manifold is known. | [
{
"url": "https://arxiv.org/abs/1306.6617",
"label": "A dynamical characterization of universally tight lens spaces"
},
{
"url": "https://doi.org/10.4171/owr/2013/34",
"label": "Oberwolfach Report 34/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | Can the diffeomorphism type of a closed connected 3-manifold be determined from dynamical properties of a flow defined on it, viewed as a contact-type energy level, together with its induced contact structure? | Can the diffeomorphism type of a closed connected 3-manifold be determined from dynamical properties of a flow defined on it, viewed as a contact-type energy level, together with its induced contact structure? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,377 | OWR-12582-008 | Dynamics of Large-Coupling Quasiperiodic Schrödinger Cocycles | For the quasiperiodic Schrödinger cocycle with $f:\mathbb T\to\mathbb R$ of class $C^2$, exactly two nondegenerate critical points, Diophantine frequency $\omega$, and sufficiently large coupling $\lambda$, describe the dynamics of the induced projective map $\Phi_E:\mathbb T^2\to\mathbb T^2$ for every $E\in\mathbb R$ ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12582-008",
"literature-status:open",
"owr-year:2013"
] | The report explicitly leaves the dynamics of \Phi_{E} under more general assumptions on f open; available results cover analytic, Gevrey, and selected differentiable classes rather than the requested generality. | [
{
"url": "https://doi.org/10.4171/owr/2013/34",
"label": "Oberwolfach Report 34/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | For the quasiperiodic Schrödinger cocycle with $f:\mathbb T\to\mathbb R$ of class $C^2$, exactly two nondegenerate critical points, Diophantine frequency $\omega$, and sufficiently large coupling $\lambda$, describe the dynamics of the induced projective map $\Phi_E:\mathbb T^2\to\mathbb T^2$ for every $E\in\mathbb R$ ... | For the quasi-periodic Schrödinger cocycle with f:\mathbb T\to\mathbb R of class C^2, exactly two non-degenerate critical points, Diophantine frequency \omega, and sufficiently large coupling \lambda, describe the dynamics of the induced projective map \Phi_E:\mathbb T^2\to\mathbb T^2 for every E\in\mathbb R under more... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,378 | OWR-12582-009 | The Tits Alternative for Analytic Surface Symplectomorphisms | Tits-alternative conjecture: For every compact surface $M$, every finitely generated subgroup of the real-analytic area-preserving diffeomorphism group $\operatorname{Symp}^\omega_\mu(M)$ is either virtually solvable or contains a nonabelian free group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033](https://doi.org/10.4171/owr/2013/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12582-009",
"literature-status:open",
"owr-year:2013"
] | The full Tits-alternative assertion for finitely generated subgroups of real-analytic circle diffeomorphisms remains unresolved; later results give weaker dynamical or probabilistic alternatives, not the stated theorem. | [
{
"url": "https://doi.org/10.4171/owr/2013/34",
"label": "Oberwolfach Report 34/2013"
},
{
"url": "https://arxiv.org/abs/2412.08779",
"label": "Probabilistic Tits alternative for circle diffeomorphisms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/34 | null | null | null | Tits-alternative conjecture: For every compact surface $M$, every finitely generated subgroup of the real-analytic area-preserving diffeomorphism group $\operatorname{Symp}^\omega_\mu(M)$ is either virtually solvable or contains a nonabelian free group. | Tits-alternative conjecture: for every compact surface M, every finitely generated subgroup of the real-analytic area-preserving diffeomorphism group \operatorname{Symp}^{\omega}_{\mu}(M) is either virtually solvable or contains a non-abelian free group. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Dynamische Systeme (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/34, pp. 1975--2033 |
30,002,379 | OWR-12583-002 | Rational Points on Prime-Level Modular Curves | For every prime $p>37$, are the rational points on $X_0^+(p)$, $X_{\mathrm{sp}}^+(p)$, and $X_{\mathrm{ns}}^+(p)$ only cusps and points arising from elliptic curves with complex multiplication? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,013 | 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 | [Discussion #4 literature review, 2026-09-29] the record writes X_0⁺(p) in its title and statement, but the source (Bilu–Parent–Rebolledo, OWR 35/2013, p. 2041) has X_0(p). | [
"owr",
"oberwolfach-reports",
"OWR-12583-002",
"literature-status:partially-solved",
"owr-year:2013"
] | The rational-point problem is solved for the Borel and split-Cartan cases in the required large-prime range, while the corresponding nonsplit-Cartan rational-point problem remains a central obstruction to uniformity; hence the combined problem is only partially solved. | [
{
"url": "https://doi.org/10.4171/owr/2013/35",
"label": "Oberwolfach Report 35/2013"
},
{
"url": "https://annals.math.princeton.edu/2011/173-1/p13",
"label": "Serre's uniformity problem in the split Cartan case"
},
{
"url": "https://arxiv.org/abs/2305.17780",
"label": "Serre's unifo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | For every prime $p>37$, are the rational points on $X_0^+(p)$, $X_{\mathrm{sp}}^+(p)$, and $X_{\mathrm{ns}}^+(p)$ only cusps and points arising from elliptic curves with complex multiplication? | For every prime p>37, the rational points on X_0^+(p),X_{\mathrm{sp}}^+(p), and X_{\mathrm{ns}}^+(p) are only the cusps and the points arising from elliptic curves with complex multiplication (CM-points). | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,380 | OWR-12583-003 | Serre's Uniformity Problem for Elliptic Curves | Does there exist a constant $p_0$ such that, for every elliptic curve $E/\mathbb Q$ without complex multiplication and every prime $p>p_0$, the representation
$$\rho_{E,p}:\operatorname{Gal}(\overline{\mathbb Q}/\mathbb Q)\longrightarrow\operatorname{GL}_2(\mathbb F_p)$$
is surjective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,013 | 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-12583-003",
"literature-status:partially-solved",
"owr-year:2013"
] | Serre's uniformity conjecture remains open in general, although the Borel and split-Cartan obstructions are controlled for primes above explicit bounds and recent work narrows the remaining nonsplit-Cartan possibilities. | [
{
"url": "https://annals.math.princeton.edu/2011/173-1/p13",
"label": "Serre's uniformity problem in the split Cartan case"
},
{
"url": "https://doi.org/10.1007/s00209-018-2189-8",
"label": "Some cases of Serre's uniformity problem"
},
{
"url": "https://arxiv.org/abs/2305.17780",
"la... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | Does there exist a constant $p_0$ such that, for every elliptic curve $E/\mathbb Q$ without complex multiplication and every prime $p>p_0$, the representation
$$\rho_{E,p}:\operatorname{Gal}(\overline{\mathbb Q}/\mathbb Q)\longrightarrow\operatorname{GL}_2(\mathbb F_p)$$
is surjective? | Serre’s uniformity problem: does there exist a positive constant p_0 such that for every elliptic curve E/\mathbb Q without complex multiplication and every prime p>p_0, the representation \rho_{E,p}:\operatorname{Gal}_{\mathbb Q}\to\operatorname{GL}_2(\mathbb F_p) is surjective? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,381 | OWR-12583-004 | Efficient Relation Generation for Curve Class Groups | Can the heuristic expected running time
$$\exp\!\left(O\!\left(\max\{\log q,\,n(\log q)^{1/2}\}\right)\right)$$
for relation generation in the discrete-logarithm algorithm be achieved for broader families of elliptic curves, or for curves of any fixed genus, by weakening or removing the hypothesis $n\leq C\log q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12583-004",
"literature-status:open",
"owr-year:2013"
] | For fixed genus greater than one, the required efficient algorithm that outputs a degree-zero class-group generating system with certainty is still not established; randomized potential generating systems do not resolve the stated guarantee. | [
{
"url": "https://doi.org/10.4171/owr/2013/35",
"label": "Oberwolfach Report 35/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | Can the heuristic expected running time
$$\exp\!\left(O\!\left(\max\{\log q,\,n(\log q)^{1/2}\}\right)\right)$$
for relation generation in the discrete-logarithm algorithm be achieved for broader families of elliptic curves, or for curves of any fixed genus, by weakening or removing the hypothesis $n\leq C\log q$? | Can the heuristic expected running time for relation generation in the discrete-logarithm algorithm be achieved for larger input classes of elliptic curves, or for curves of any fixed genus, by weakening or removing the condition n\le C\log q? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,382 | OWR-12583-005 | Abelian Galois Groups of Imaginary Quadratic Fields | For density one of the imaginary quadratic fields of prime class number, is the absolute abelian Galois group isomorphic to
$$A_0=\widehat{\mathbb Z}^{\times}\times\prod_{n\geq1}\mathbb Z/n\mathbb Z$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,013 | 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-12583-005",
"literature-status:open",
"owr-year:2013"
] | The universal-group description is proved for many imaginary quadratic fields and supported numerically for prime class number, but the claimed density-one statement has no proof. | [
{
"url": "https://arxiv.org/abs/1209.6005",
"label": "Imaginary quadratic fields with isomorphic abelian Galois groups"
},
{
"url": "https://doi.org/10.4171/owr/2013/35",
"label": "Oberwolfach Report 35/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | For density one of the imaginary quadratic fields of prime class number, is the absolute abelian Galois group isomorphic to
$$A_0=\widehat{\mathbb Z}^{\times}\times\prod_{n\geq1}\mathbb Z/n\mathbb Z$$? | Conjecture: for 100\% (density one) of imaginary quadratic fields of prime class number, the absolute abelian Galois group is isomorphic to A_0=\widehat{\mathbb Z}^{\times}\times\prod_{n\ge1}\mathbb Z/n\mathbb Z. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,383 | OWR-12583-010 | Unbounded Symmetric and Alternating Extensions with Restricted Ramification | Let $P$ be a finite set of primes containing every prime dividing the order of some finite nonabelian simple group, and let $F_P(m)$ count degree-$m$ number fields with Galois group $A_m$ or $S_m$ that ramify only at primes in $P$. Is the sequence $F_P(m)$ unbounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,013 | 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-12583-010",
"literature-status:partially-solved",
"owr-year:2013"
] | Roberts's geometric fullness theorem and explicit Hurwitz-field examples support the Unboundedness Conjecture, but the required arithmetic specialization statement proving unbounded F_{P}(m) remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/35",
"label": "Oberwolfach Report 35/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | Let $P$ be a finite set of primes containing every prime dividing the order of some finite nonabelian simple group, and let $F_P(m)$ count degree-$m$ number fields with Galois group $A_m$ or $S_m$ that ramify only at primes in $P$. Is the sequence $F_P(m)$ unbounded? | Unboundedness conjecture: if P is a finite set of primes containing all primes dividing the order of some finite non-abelian simple group, and F_P(m) counts degree-m number fields with Galois group A_m or S_m ramified only at primes in P, then the sequence F_P(m) is unbounded. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,384 | OWR-12583-011 | Unbounded Torsion and Selmer Groups in Quadratic Extensions | Let $\ell$ be a prime, $K$ a number field, and $A/K$ an abelian variety. As quadratic extensions $L/K$ vary, are $\#\operatorname{Pic}(\mathcal O_L)[\ell]$ and $\#\operatorname{Sel}_\ell(A_L)$ unbounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082](https://doi.org/10.4171/owr/2013/35)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,013 | 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-12583-011",
"literature-status:partially-solved",
"owr-year:2013"
] | The class-group conjecture is known for \ell=2 and the corresponding Selmer statement in several \ell=2 cases, while both number-field conjectures remain open for every odd \ell; function-field analogues provide additional positive cases. | [
{
"url": "https://doi.org/10.1112/S0010437X14007441",
"label": "Selmer groups and class groups"
},
{
"url": "https://arxiv.org/abs/1307.4261",
"label": "Selmer groups and class groups"
},
{
"url": "https://doi.org/10.4171/owr/2013/35",
"label": "Oberwolfach Report 35/2013"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/35 | null | null | null | Let $\ell$ be a prime, $K$ a number field, and $A/K$ an abelian variety. As quadratic extensions $L/K$ vary, are $\#\operatorname{Pic}(\mathcal O_L)[\ell]$ and $\#\operatorname{Sel}_\ell(A_L)$ unbounded? | Let l be a prime, K a number field, and A/K an abelian variety. As quadratic extensions L/K vary, the conjectures are that \#\operatorname{Pic}(\mathcal O_L)[l] is unbounded and that \#\operatorname{Sel}_l(A_L) is unbounded. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Explicit Methods in Number Theory (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/35, pp. 2035--2082 |
30,002,385 | OWR-12584-002 | Spectral Measures of Perturbed Isospectral Tori | Characterize the spectral measures of all $\ell^2$ perturbations of points in the isospectral torus $T_E$. Do such perturbations preserve the absolutely continuous spectrum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Direct and Inverse Spectral Theory of Almost Periodic Operators (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/36, pp. 2083--2117](https://doi.org/10.4171/owr/2013/36)
##... | 3 | open | null | 2,013 | 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-12584-002",
"literature-status:open",
"owr-year:2013"
] | Although important finite-gap Szego and perturbation theorems are known, a general characterization of spectral measures for all \ell^{2} perturbations of the isospectral torus, including preservation of absolutely continuous spectrum, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/36",
"label": "Oberwolfach Report 36/2013"
},
{
"url": "https://arxiv.org/abs/1108.0183",
"label": "Finite Gap Jacobi Matrices III"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/36 | null | null | null | Characterize the spectral measures of all $\ell^2$ perturbations of points in the isospectral torus $T_E$. Do such perturbations preserve the absolutely continuous spectrum? | How can one characterize the spectral measures of all \ell^2 perturbations of points in the isospectral torus T_E, and do such perturbations preserve the absolutely continuous spectrum? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Direct and Inverse Spectral Theory of Almost Periodic Operators (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/36, pp. 2083--2117 |
30,002,386 | OWR-12584-004 | Fluctuation Order in First-Passage Percolation | Determine the order of the fluctuations of the first-passage-percolation metric
$$\rho(x,y)=\inf_{(u_j):x\leadsto y}\sum_j W(u_j)$$
on $\mathbb Z^d$, where the vertex or edge weights $W(u_j)$ are random and nonnegative. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Direct and Inverse Spectral Theory of Almost Periodic Operators (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/36, pp. 2083--2117](https://doi.org/10.4171/owr/2013/36)
##... | 3 | open | null | 2,013 | 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-12584-004",
"literature-status:open",
"owr-year:2013"
] | The order of passage-time fluctuations in first-passage percolation is still not determined in general; later work improves lower bounds but does not identify the conjectured fluctuation exponent. | [
{
"url": "https://doi.org/10.4171/owr/2013/36",
"label": "Oberwolfach Report 36/2013"
},
{
"url": "https://arxiv.org/abs/1810.08270",
"label": "Lower bounds for fluctuations in first-passage percolation"
},
{
"url": "https://arxiv.org/abs/2511.06166",
"label": "Lower bounds on non-ra... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/36 | null | null | null | Determine the order of the fluctuations of the first-passage-percolation metric
$$\rho(x,y)=\inf_{(u_j):x\leadsto y}\sum_j W(u_j)$$
on $\mathbb Z^d$, where the vertex or edge weights $W(u_j)$ are random and nonnegative. | Determine the order of fluctuations of the first-passage-percolation metric \rho(x,y)=\inf_{(u_j):x\leadsto y}\sum_j W(u_j) on \mathbb Z^d with random nonnegative weights. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Mini-Workshop: Direct and Inverse Spectral Theory of Almost Periodic Operators (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/36, pp. 2083--2117 |
30,002,387 | OWR-12588-003 | Existence of Solutions to the Inverse $\sigma_k$ Equation | Given a compact Kähler manifold $(M,\omega)$, a Kähler metric $\chi$, and the associated topological constant $c_k$, is there a metric $\widetilde\chi\in[\chi]$ for which
$$c_k\widetilde\chi^n=\binom nk\widetilde\chi^{n-k}\wedge\omega^k$$
holds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/40, pp. 2259--2319](https://doi.org/10.4171/owr/2013/40)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,013 | 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... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. H. Fang (OWR 40/2013, p. 2274, Question 0.1) asks when [χ] contains χ̃ with c_k χ̃ⁿ = C(n, k) χ̃^{n−k} ∧ ωᵏ, and says that [FLM] solves it: Fang–Lai–Ma, [J. reine angew. Math. 653 (2011)](https://doi.org/10.1515/crelle.2011.027) ([arXiv:... | [
"owr",
"oberwolfach-reports",
"OWR-12588-003",
"literature-status:partially-solved",
"owr-year:2013"
] | Fang, Lai, and Ma proved solvability under the cone condition, while the report explicitly leaves the failure-of-cone-condition case open; the unrestricted question is only partially settled. | [
{
"url": "https://doi.org/10.4171/owr/2013/40",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/40 | null | null | null | Given a compact Kähler manifold $(M,\omega)$, a Kähler metric $\chi$, and the associated topological constant $c_k$, is there a metric $\widetilde\chi\in[\chi]$ for which
$$c_k\widetilde\chi^n=\binom nk\widetilde\chi^{n-k}\wedge\omega^k$$
holds? | Given a compact Kähler manifold (M,\omega), a Kähler metric \chi, and the associated topological constant c_k, does the class [\chi] contain a metric \widetilde\chi satisfying c_k\widetilde\chi^n=\binom{n}{k}\widetilde\chi^{,n-k}\wedge\omega^k? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Partial Differential Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/40, pp. 2259--2319 |
30,002,388 | OWR-12588-006 | Gauss–Bonnet–Chern Positive Mass and Penrose Inequalities | Do the Positive Mass Theorem and the Penrose Inequality for the Gauss–Bonnet–Chern mass hold for asymptotically flat manifolds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/40, pp. 2259--2319](https://doi.org/10.4171/owr/2013/40)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,013 | 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-12588-006",
"literature-status:open",
"owr-year:2013"
] | Positive mass and Penrose results are known for graphs and conformally flat manifolds, but the conjectured general asymptotically flat theorem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2013/40",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1211.3645",
"label": "Ge--Wang--Wu primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/40 | null | null | null | Do the Positive Mass Theorem and the Penrose Inequality for the Gauss–Bonnet–Chern mass hold for asymptotically flat manifolds? | Do the Positive Mass Theorem and the Penrose Inequality for the Gauss--Bonnet--Chern mass hold for asymptotically flat manifolds? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Partial Differential Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/40, pp. 2259--2319 |
30,002,389 | OWR-12589-001 | All-Time Soliton Resolution for Equivariant Wave Maps | For the finite-energy equivariant wave-map equation, can soliton resolution be proved for all times rather than only along a sequence of times? Can one construct a solution with at least two bubbles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/41, pp. 2321--2374](https://doi.org/10.4171/owr/2013/41)
## Literature review (checked 2026-08-21... | 3 | solved | null | 2,013 | 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 | {
"source_url": "https://doi.org/10.1007/s00220-022-04330-z",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes to both)**. R. Côte (OWR 41/2013, p. 2333) proves soliton resolution along a sequence of times for finite-energy corotational wave maps and lists as open problems resolution for all times and the construction of a solution with J ≥ 2 bubbles. All times: Duycka... | [
"owr",
"oberwolfach-reports",
"OWR-12589-001",
"literature-status:open",
"owr-year:2013"
] | The report explicitly identifies all-time soliton resolution and construction of solutions with at least two bubbles as open problems. | [
{
"url": "https://doi.org/10.4171/owr/2013/41",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/41 | null | null | null | For the finite-energy equivariant wave-map equation, can soliton resolution be proved for all times rather than only along a sequence of times? Can one construct a solution with at least two bubbles? | For the finite-energy equivariant wave-map equation, can one prove soliton resolution for all times rather than only along a sequence of times, and can one construct a solution whose number J of bubbles satisfies J\ge2? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Nonlinear Waves and Dispersive Equations (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/41, pp. 2321--2374 |
30,002,390 | OWR-12590-003 | Hyperbolic Limit Sets and Fibered Four-Manifolds | Does there exist a hyperbolic $3$-manifold group $\Gamma<\operatorname{Isom}(\mathbb H^4)$ whose limit set has Hausdorff dimension arbitrarily close to $3$? Does there exist a real hyperbolic $4$-manifold fibering over a surface with surface fiber? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Theory, Measure, and Asymptotic Invariants (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/42, pp. 2375--2422](https://doi.org/10.4171/owr/2013/42)
## Literature review (checked 20... | 3 | partially_solved | null | 2,013 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1215/00127094-2871415",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. L. Bowen (OWR 42/2013, p. 2393) notes that convex cocompact surface groups in Isom(H³) deform to limit sets of dimension near 2, and asks whether a hyperbolic 3-manifold group in Isom(H⁴) can have limit set of dimension close to 3, and whether a real h... | [
"owr",
"oberwolfach-reports",
"OWR-12590-003",
"literature-status:open",
"owr-year:2013"
] | Bowen proves a uniform upper bound for the relevant conical limit-set dimension, while the requested near-3 construction and the related hyperbolic-four-manifold fibration problem remain open. | [
{
"url": "https://arxiv.org/abs/1303.5963",
"label": "Bowen primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/42 | null | null | null | Does there exist a hyperbolic $3$-manifold group $\Gamma<\operatorname{Isom}(\mathbb H^4)$ whose limit set has Hausdorff dimension arbitrarily close to $3$? Does there exist a real hyperbolic $4$-manifold fibering over a surface with surface fiber? | Does there exist a hyperbolic 3-manifold group \Gamma<\operatorname{Isom}(\mathbb H^4) whose limit set has Hausdorff dimension arbitrarily close to 3; and does there exist a real hyperbolic 4-manifold fibering over a surface with surface fiber? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Group Theory, Measure, and Asymptotic Invariants (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/42, pp. 2375--2422 |
30,002,391 | OWR-12590-005 | Typical Properties of Marked Grigorchuk Groups | For the compact family $G_p$ of marked Grigorchuk groups parametrized by sequences over $\{0,1,\ldots,p\}$, which group-theoretic properties, especially growth rates, are typical in the invariant-measure sense and in the Baire-category sense? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Theory, Measure, and Asymptotic Invariants (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/42, pp. 2375--2422](https://doi.org/10.4171/owr/2013/42)
## Literature review (checked 20... | 3 | partially_solved | null | 2,013 | 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-12590-005",
"literature-status:partially-solved",
"owr-year:2013"
] | The report establishes measure-typical and Baire-typical growth results in G_p, but the broader question about all typical group-theoretic properties is not exhausted. | [
{
"url": "https://doi.org/10.4171/owr/2013/42",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/42 | null | null | null | For the compact family $G_p$ of marked Grigorchuk groups parametrized by sequences over $\{0,1,\ldots,p\}$, which group-theoretic properties, especially growth rates, are typical in the invariant-measure sense and in the Baire-category sense? | For the compact family G_p of marked Grigorchuk groups parametrized by sequences over \{0,1,\ldots,p\} ext{, which group-theoretic properties, especially growth rates, are typical in the invariant-measure sense and in the Baire-category sense?} | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Group Theory, Measure, and Asymptotic Invariants (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/42, pp. 2375--2422 |
30,002,392 | OWR-12591-001 | Rigidity of Completely Close $C^*$-Algebras | For $C^*$-algebras $A,B\subseteq B(H)$, what structural properties and invariants are forced by small completely bounded Kadison–Kastler distance $d_{\mathrm{cb}}(A,B)$, and must sufficiently close algebras be isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-001",
"literature-status:open",
"owr-year:2013"
] | The record asks an open-ended perturbation question; results such as K-theory and nuclear-case stability cover important classes but do not give a general answer for close operator algebras. | [
{
"url": "https://doi.org/10.4171/owr/2013/43",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s11511-012-0075-5",
"label": "Christensen et al. primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | For $C^*$-algebras $A,B\subseteq B(H)$, what structural properties and invariants are forced by small completely bounded Kadison–Kastler distance $d_{\mathrm{cb}}(A,B)$, and must sufficiently close algebras be isomorphic? | For C^*-algebras A,B\subseteq B(H), what structural properties and invariants are forced by small completely bounded Kadison--Kastler distance d_{\mathrm{cb}}(A,B), and must sufficiently close algebras be isomorphic? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,393 | OWR-12591-002 | Bounded Maps Between Close Operator Algebras | What methods produce bounded linear maps between close, or completely close, operator algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-002",
"literature-status:open",
"owr-year:2013"
] | The record asks for general methods rather than stating a settled theorem; bounded-map constructions are known in special perturbation settings, but the general problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2013/43",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s11511-012-0075-5",
"label": "Christensen et al. primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | What methods produce bounded linear maps between close, or completely close, operator algebras? | What methods produce bounded linear maps between close, or completely close, operator algebras? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,394 | OWR-12591-003 | Generalized Pimsner–Voiculescu Embeddings | Can the Pimsner–Voiculescu embedding of an irrational rotation algebra be generalized to higher-dimensional noncommutative tori or more general discrete abelian groups; can spectra of unitary generators be broken in more general crossed products by locally compact abelian groups; and which properties such as maximality... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-003",
"literature-status:open",
"owr-year:2013"
] | The report presents higher-dimensional and more general crossed-product extensions as future questions, with no general construction resolving them. | [
{
"url": "https://doi.org/10.4171/owr/2013/43",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | Can the Pimsner–Voiculescu embedding of an irrational rotation algebra be generalized to higher-dimensional noncommutative tori or more general discrete abelian groups; can spectra of unitary generators be broken in more general crossed products by locally compact abelian groups; and which properties such as maximality... | Can the Pimsner--Voiculescu embedding of an irrational rotation algebra be generalized to higher-dimensional noncommutative tori or more general discrete abelian groups; can spectra of unitary generators be broken in more general crossed products by locally compact abelian groups; and which properties such as maximalit... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,395 | OWR-12591-005 | Dini Spaces as Primitive Spectra of Amenable $C^*$-Algebras | Is every Dini space homeomorphic to the primitive spectrum of a separable amenable $C^*$-algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-005",
"literature-status:open",
"owr-year:2013"
] | The 2024 inverse-problem work gives a topological characterization of realizable primitive spectra but does not show that every Dini space satisfies it; the stated universal question remains open. | [
{
"url": "https://arxiv.org/abs/2401.05917",
"label": "Harnisch--Kirchberg primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | Is every Dini space homeomorphic to the primitive spectrum of a separable amenable $C^*$-algebra? | Is every Dini space homeomorphic to the primitive spectrum of a separable amenable C^*-algebra? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,396 | OWR-12591-009 | Regularity Properties of Nuclear $C^*$-Algebras | For a separable unital simple nuclear stably finite infinite-dimensional $C^*$-algebra $A$, are the following equivalent: $\mathcal Z$-stability ($A\cong A\otimes\mathcal Z$), strict comparison, and finite decomposition rank? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** partially solv... | 3 | partially_solved | null | 2,013 | 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-12591-009",
"literature-status:partially-solved",
"owr-year:2013"
] | Finite nuclear dimension and Z-stability are equivalent and Z-stability implies strict comparison, but strict comparison implying Z-stability remains open in general; the conjecture is only partially solved. | [
{
"url": "https://arxiv.org/abs/1403.0747",
"label": "Sato--White--Winter primary paper"
},
{
"url": "https://arxiv.org/abs/1912.04207",
"label": "Castillejos et al. primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | For a separable unital simple nuclear stably finite infinite-dimensional $C^*$-algebra $A$, are the following equivalent: $\mathcal Z$-stability ($A\cong A\otimes\mathcal Z$), strict comparison, and finite decomposition rank? | For a separable unital simple nuclear stably finite infinite-dimensional C*-algebra A, are Z-stability (A is isomorphic to A tensor Z), strict comparison, and finite decomposition rank equivalent? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,397 | OWR-12591-010 | Atomlessness from Operator-Valued Cauchy Transforms | For a selfadjoint polynomial in free variables without atoms, can the absence of atoms in its distribution, and similar qualitative results, be derived from the operator-valued Cauchy-transform and linearization description? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-010",
"literature-status:open",
"owr-year:2013"
] | The extracted statement is too vague to identify a precise theorem or conjecture, and the cited report does not establish a resolution. | [
{
"url": "https://doi.org/10.4171/owr/2013/43",
"label": "Oberwolfach Report 43"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | For a selfadjoint polynomial in free variables without atoms, can the absence of atoms in its distribution, and similar qualitative results, be derived from the operator-valued Cauchy-transform and linearization description? | For a selfadjoint polynomial in free variables without atoms, can the absence of atoms in its distribution, and similar qualitative results, be derived from the operator-valued Cauchy-transform and linearization description? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,398 | OWR-12591-011 | Nuclear Dimension and Z-Stability Beyond Simple Algebras | For $C^*$-algebras in which no ideal has a type-I representation, are finite nuclear dimension and amenability together with $\mathcal Z$-stability equivalent even without assuming simplicity and unitality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500](https://doi.org/10.4171/owr/2013/43)
## Literature review (checked 2026-08-21)
**Status:** open
**Assess... | 3 | open | null | 2,013 | 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-12591-011",
"literature-status:open",
"owr-year:2013"
] | The general non-simple Toms--Winter implication remains open; available results prove important special classes but not the stated generality. | [
{
"url": "https://ems.press/content/serial-article-files/46475",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/1308.2941",
"label": "Robert--Tikuisis"
},
{
"url": "https://arxiv.org/abs/2503.18088",
"label": "Enstad--Vilalta"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/43 | null | null | null | For $C^*$-algebras in which no ideal has a type-I representation, are finite nuclear dimension and amenability together with $\mathcal Z$-stability equivalent even without assuming simplicity and unitality? | For C*-algebras in which no ideal has a type I representation, are finite nuclear dimension and amenability together with Z-stability equivalent even without assuming simplicity and unitality? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | C*-Algebren (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/43, pp. 2423--2500 |
30,002,399 | OWR-12592-001 | Uniqueness and Existence of Link-Invariant Categorifications | Do categorifications of a given link invariant become unique, and does the Kauffman polynomial admit a categorification? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552](https://doi.org/10.4171/owr/2013/44)
## Literature review (che... | 3 | open | null | 2,013 | 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-12592-001",
"literature-status:open",
"owr-year:2013"
] | Uniqueness is proved for restricted tensor-product categorification axioms, but the broader uniqueness question for the stated link invariant, including the indicated case, is not settled. | [
{
"url": "https://ems.press/content/serial-article-files/46474",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/1303.1336",
"label": "Losev--Webster"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/44 | null | null | null | Do categorifications of a given link invariant become unique, and does the Kauffman polynomial admit a categorification? | Do categorifications of a given link invariant become unique, and does the Kauffman polynomial admit a categorification? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552 |
30,002,400 | OWR-12592-002 | Entropy of Serre Functors and Algebraicity | For general categories of graded matrix factorizations, what is the geometric interpretation of the entropy $h_t(S)$ of the Serre functor $S$? More generally, is $\exp(h_0(F))$ always algebraic, and under what conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552](https://doi.org/10.4171/owr/2013/44)
## Literature review (che... | 3 | open | null | 2,013 | 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-12592-002",
"literature-status:open",
"owr-year:2013"
] | Special computations relate entropy of Serre functors to categorical growth, but no general geometric interpretation for the broader class of categories in the extracted question is established. | [
{
"url": "https://ems.press/content/serial-article-files/46474",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/2201.00302",
"label": "Higher hereditary algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/44 | null | null | null | For general categories of graded matrix factorizations, what is the geometric interpretation of the entropy $h_t(S)$ of the Serre functor $S$? More generally, is $\exp(h_0(F))$ always algebraic, and under what conditions? | For general categories of graded matrix factorizations, what is the geometric interpretation of the entropy h_t(S) of the Serre functor S; more generally, is exp(h_0(F)) always algebraic, and under what conditions? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552 |
30,002,401 | OWR-12592-003 | Mass Growth Versus Categorical Entropy | For an exact endofunctor $F$ of a triangulated category equipped with a Bridgeland stability condition $\sigma$, under what natural hypotheses does the mass-growth entropy $h_\sigma(F)$ equal the categorical entropy $h_0(F)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552](https://doi.org/10.4171/owr/2013/44)
## Literature review (che... | 3 | partially_solved | null | 2,013 | 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-12592-003",
"literature-status:partially-solved",
"owr-year:2013"
] | Equality of the relevant categorical growth quantities is proved in several important settings, while the natural general hypotheses guaranteeing equality remain open. | [
{
"url": "https://ems.press/content/serial-article-files/46474",
"label": "Oberwolfach Report"
},
{
"url": "https://link.springer.com/article/10.1007/s00229-023-01533-z",
"label": "Mass growth of triangulated autoequivalences"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/44 | null | null | null | For an exact endofunctor $F$ of a triangulated category equipped with a Bridgeland stability condition $\sigma$, under what natural hypotheses does the mass-growth entropy $h_\sigma(F)$ equal the categorical entropy $h_0(F)$? | For general categories of graded matrix factorizations, what is the geometric interpretation of the entropy h_t(S) of the Serre functor S, and under what conditions does the associated entropy behavior hold? | corrected_verified | The official report first proves the inequality between mass growth and categorical entropy, then asks for natural conditions under which equality holds. The clean statement isolates that distinct question instead of repeating the preceding Serre-functor problem. | null | null | null | null | null | Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552 |
30,002,402 | OWR-12592-004 | D-Brane Equivalence Across Calabi–Yau Phases | For the compact Calabi-Yau threefolds and their Pfaffian, determinantal, or hybrid Landau-Ginzburg phases constructed from the non-abelian linear sigma models, are the corresponding D-brane categories equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552](https://doi.org/10.4171/owr/2013/44)
## Literature review (che... | 3 | partially_solved | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-12592-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12592-004",
"literature-status:partially-solved",
"owr-year:2013"
] | The phase construction gives predictions of equivalent D-brane categories and later work proves selected examples, but the broad conjecture for the stated exotic Calabi--Yau families is not proved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3375/OWR_2013_44.pdf?sequence=1",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1308.6265",
"label": "Hori--Knapp"
},
{
"url": "https://doi.org/10.1007/s11401-017-1103-8",
"label": "Grade restriction rul... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/44 | null | null | null | For the compact Calabi-Yau threefolds and their Pfaffian, determinantal, or hybrid Landau-Ginzburg phases constructed from the non-abelian linear sigma models, are the corresponding D-brane categories equivalent? | For the compact Calabi-Yau threefolds and their Pfaffian, determinantal, or hybrid Landau-Ginzburg phases constructed from the non-abelian linear sigma models, are the corresponding D-brane categories equivalent? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552 |
30,002,403 | OWR-12592-005 | Duplicate Linear $\sigma$-Model Phase Equivalence | For each pair of respective phases in the constructed one-parameter linear sigma models, are the categories associated to those phases equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552](https://doi.org/10.4171/owr/2013/44)
## Literature review (che... | 3 | open | null | 2,013 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report states one conjecture that the D-brane categories associated with the respective phases of the constructed nonabelian li) | [
"OWR-12592-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12592-005",
"literature-status:open",
"owr-year:2013"
] | The extracted phase-equivalence claim is stated at broad, underspecified generality; the primary source presents predictions and selected constructions rather than a general proof. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3375/OWR_2013_44.pdf?sequence=1",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1308.6265",
"label": "Hori--Knapp"
},
{
"url": "https://doi.org/10.1007/s11401-017-1103-8",
"label": "Grade restriction rul... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/44 | null | null | null | null | For each pair of respective phases in the constructed one-parameter linear sigma models, are the categories associated to those phases equivalent? | unrecoverable | The official report states one conjecture that the D-brane categories associated with the respective phases of the constructed nonabelian linear sigma models are equivalent. This record restates the conjecture represented more fully by OWR-12592-004. No separate clean statement is promoted; the original record remains ... | null | null | null | null | null | Matrix Factorizations in Algebra, Geometry, and Physics (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/44, pp. 2501--2552 |
30,002,404 | OWR-12593-002 | Controlled K-Theory for Farrell–Jones Assembly Maps | Let $\Gamma$ act asymptotically properly on a compact space $X$. Can controlled $K$-theory prove split injectivity of the Farrell–Jones assembly map in algebraic $K$-theory and thereby establish the Farrell–Jones conjecture for such an action? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,013 | 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-12593-002",
"literature-status:open",
"owr-year:2013"
] | The report explicitly says that the Farrell--Jones results were only outlined and were still being written and checked; no authoritative completed proof of the extracted claim was located. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Let $\Gamma$ act asymptotically properly on a compact space $X$. Can controlled $K$-theory prove split injectivity of the Farrell–Jones assembly map in algebraic $K$-theory and thereby establish the Farrell–Jones conjecture for such an action? | For an asymptotically proper action Gamma acting on a compact space X, can controlled K-theory arguments give split injectivity of the Farrell-Jones assembly map in algebraic K-theory and imply the Farrell-Jones conjecture? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,405 | OWR-12593-003 | Furstenberg Classification of Times-$p$ and Times-$q$ Invariant Measures | Let $p,q\geq 2$ be multiplicatively independent. Are the probability measures on $\mathbb R/\mathbb Z$ invariant under both $T_p(x)=px\pmod 1$ and $T_q(x)=qx\pmod 1$ precisely the finitely supported invariant measures, Lebesgue measure, and their convex combinations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12593-003",
"literature-status:open",
"owr-year:2013"
] | The full classification of invariant measures for the times-two and times-three action remains an open Furstenberg problem; positive-entropy rigidity does not settle the zero-entropy case. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
},
{
"url": "https://annals.math.princeton.edu/wp-content/uploads/annals-v189-n2-p01-s.pdf",
"label": "Furstenberg intersection paper"
},
{
"url": "https://arxiv.org/abs/2410.22701",
"label... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Let $p,q\geq 2$ be multiplicatively independent. Are the probability measures on $\mathbb R/\mathbb Z$ invariant under both $T_p(x)=px\pmod 1$ and $T_q(x)=qx\pmod 1$ precisely the finitely supported invariant measures, Lebesgue measure, and their convex combinations? | For multiplicatively independent integers p,q at least 2, are the only probability measures on the circle invariant under both T_p(x)=px mod 1 and T_q(x)=qx mod 1 the finitely supported invariant measures, Lebesgue measure, and their convex combinations? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,406 | OWR-12593-004 | Zero Entropy Measures for Higher Rank Toral Actions | Can invariant measures for higher-rank toral actions, including those in the Furstenberg–Rudolph setting, be partially classified under a hypothesis weaker than positive entropy, particularly in the zero-entropy case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,013 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12593-004",
"literature-status:partially-solved",
"owr-year:2013"
] | Rudolph's theorem gives the principal positive-entropy classification, while the requested zero-entropy or broader generalizations remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
},
{
"url": "https://doi.org/10.1017/S0143385700005629",
"label": "Rudolph"
},
{
"url": "https://people.math.ethz.ch/~einsiedl/E-ICM2010.pdf",
"label": "Einsiedler survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Can invariant measures for higher-rank toral actions, including those in the Furstenberg–Rudolph setting, be partially classified under a hypothesis weaker than positive entropy, particularly in the zero-entropy case? | Can one obtain a partial classification of invariant measures for higher-rank toral actions, including the Furstenberg-Rudolph setting, under an assumption replacing positive entropy, especially for zero-entropy measures? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,407 | OWR-12593-005 | Intrinsic Criteria for Expected L-Function Properties | Which intrinsic properties of an arithmetic or geometric object $M$ ensure that its $L$-function has the expected local-to-global properties: an Euler product, an archimedean factor, meromorphic continuation, and a functional equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,013 | 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-12593-005",
"literature-status:open",
"owr-year:2013"
] | This is a broad foundational question rather than a precise proposition; the extracted record supplies no criterion whose truth has been established or refuted. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Which intrinsic properties of an arithmetic or geometric object $M$ ensure that its $L$-function has the expected local-to-global properties: an Euler product, an archimedean factor, meromorphic continuation, and a functional equation? | What intrinsic properties of an arithmetic or geometric object M ensure that its L-function has the expected local-to-global interpolation properties, including an Euler product, an archimedean factor, meromorphic continuation, and a functional equation? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,408 | OWR-12593-006 | Global L-Functions from Adelic Cyclic Homology | Can Connes–Consani cyclic homology with adelic coefficients be extended to give a global definition of the completed $L$-function $\Lambda(s,M)$, including analytic continuation, local epsilon factors, and a global duality that yields the functional equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** pa... | 3 | partially_solved | null | 2,013 | 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-12593-006",
"literature-status:partially-solved",
"owr-year:2013"
] | Cyclic-homology constructions recover important archimedean local factors, but a complete global definition of the completed L-function requested in the record is not established. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/1211.4239",
"label": "Connes--Consani"
},
{
"url": "https://doi.org/10.1017/is014006012jkt270",
"label": "Published version"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Can Connes–Consani cyclic homology with adelic coefficients be extended to give a global definition of the completed $L$-function $\Lambda(s,M)$, including analytic continuation, local epsilon factors, and a global duality that yields the functional equation? | Can a version of Connes-Consani cyclic homology with adelic coefficients provide a global definition of the completed L-function Lambda(s,M), together with analytic continuation, local epsilon factors, and a global duality yielding the functional equation? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,409 | OWR-12593-007 | Noncommutative Geometry of Automorphic Function Spaces | Can noncommutative geometry clarify the analytic spaces of automorphic cusp forms and Eisenstein series, possibly through an appropriate noncommutative boundary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629](https://doi.org/10.4171/owr/2013/45)
## Literature review (checked 2026-08-21)
**Status:** op... | 3 | open | null | 2,013 | 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-12593-007",
"literature-status:open",
"owr-year:2013"
] | The extracted question asks broadly whether noncommutative geometry supplies a better analytic-space interpretation, without a precise conjecture or a demonstrated general construction. | [
{
"url": "https://ems.press/content/serial-article-files/46476",
"label": "Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/45 | null | null | null | Can noncommutative geometry clarify the analytic spaces of automorphic cusp forms and Eisenstein series, possibly through an appropriate noncommutative boundary? | Can noncommutative geometry provide a better understanding of automorphic spaces of cusp forms and Eisenstein series as analytic spaces, perhaps through a noncommutative boundary? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Noncommutative Geometry (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/45, pp. 2553--2629 |
30,002,410 | OWR-12595-001 | Involutions and Accuracy in Constrained PDE Methods | For involution-constrained PDEs in magnetohydrodynamics and nonlinear elasticity, how can the proper involutions be identified; what is the relation between enforcing involutions and using higher-order methods; and are lower-order methods with involution constraints sufficient? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747](https://doi.org/10.4171/owr/2013/47)... | 3 | open | null | 2,013 | 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-12595-001",
"literature-status:open",
"owr-year:2013"
] | Numerical methods exist for particular curl-involution systems, but the extracted questions ask for broad structural and constructive answers that remain unsettled. | [
{
"url": "https://ems.press/content/serial-article-files/46478",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/2003.02799",
"label": "Dumbser--Chiocchetti--Peshkov"
},
{
"url": "https://doi.org/10.2140/camcos.2021.16.1.59",
"label": "Balsara--Kumar--Chandrashekar"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/47 | null | null | null | For involution-constrained PDEs in magnetohydrodynamics and nonlinear elasticity, how can the proper involutions be identified; what is the relation between enforcing involutions and using higher-order methods; and are lower-order methods with involution constraints sufficient? | For involution-constrained PDEs in magnetohydrodynamics and nonlinear elasticity, how can the proper involutions be identified; what is the relation between enforcing involutions and using higher-order methods; and are lower-order methods with involution constraints sufficient? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747 |
30,002,411 | OWR-12595-002 | Constraint-Preserving Methods for Maxwell-Coupled Systems | Can high-resolution numerical methodology for involution-constrained systems be applied to equations coupled with Maxwell's equations, such as elastodynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747](https://doi.org/10.4171/owr/2013/47)... | 3 | partially_solved | null | 2,013 | 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-12595-002",
"literature-status:partially-solved",
"owr-year:2013"
] | Differential-form and mimetic formulations provide a route for coupled elastodynamic systems, and curl-preserving schemes exist, but no general methodology covering the extracted question is established. | [
{
"url": "https://ems.press/content/serial-article-files/46478",
"label": "Oberwolfach Report"
},
{
"url": "https://arxiv.org/abs/2003.02799",
"label": "Dumbser--Chiocchetti--Peshkov"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/47 | null | null | null | Can high-resolution numerical methodology for involution-constrained systems be applied to equations coupled with Maxwell's equations, such as elastodynamics? | Can high-resolution numerical methodology for involution-constrained systems be applied to equations coupled with Maxwell's equations, such as elastodynamics? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747 |
30,002,412 | OWR-12595-003 | Involution Structure and Stability of MHD Solvers | What is the role of the involution structure in numerical calculations, and can it influence the stability of Riemann solvers for ideal magnetohydrodynamics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747](https://doi.org/10.4171/owr/2013/47)... | 3 | partially_solved | null | 2,013 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "analysis",
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"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12595-003",
"literature-status:partially-solved",
"owr-year:2013"
] | The effect of involution violations on MHD stability is documented and constraint-preserving solvers have been developed, but a complete general characterization of the role requested remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46478",
"label": "Oberwolfach Report"
},
{
"url": "https://www.math.ntnu.no/conservation/2010/018.html",
"label": "Kemm"
},
{
"url": "https://doi.org/10.1016/j.jcp.2004.11.016",
"label": "Gardiner--Stone"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/47 | null | null | null | What is the role of the involution structure in numerical calculations, and can it influence the stability of Riemann solvers for ideal magnetohydrodynamics? | What is the role of the involution structure in numerical calculations, and can it influence the stability of Riemann solvers for ideal magnetohydrodynamics? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | High-Resolution Mathematical and Numerical Analysis of Involution-Constrained PDEs (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/47, pp. 2691--2747 |
30,002,413 | OWR-12596-001 | Specification Testing for Higher-Order GARCH Models | Can the specification-testing theory for $\operatorname{GARCH}(1,1)$ models, including its asymptotic and bootstrap results, be extended to higher-order and augmented GARCH processes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Inference for Complex Time Series Data (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/48, pp. 2749--2823](https://doi.org/10.4171/owr/2013/48)
## Literature review (checked ... | 3 | partially_solved | null | 2,013 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12596-001",
"literature-status:partially-solved",
"owr-year:2013"
] | The GARCH(1,1) specification-test theory is established and related higher-order or augmented-GARCH results exist, but the exact conjectured generalization is not proved in full. | [
{
"url": "https://ems.press/content/serial-article-files/46479",
"label": "Oberwolfach Report"
},
{
"url": "https://madoc.bib.uni-mannheim.de/35107/1/Leucht_%26_Neumann_%26_Kreiss_13-11.pdf",
"label": "Leucht--Neumann--Kreiss"
},
{
"url": "https://doi.org/10.1016/S0304-4076(97)00009-2",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/48 | null | null | null | Can the specification-testing theory for $\operatorname{GARCH}(1,1)$ models, including its asymptotic and bootstrap results, be extended to higher-order and augmented GARCH processes? | Can the proposed specification-testing theory for GARCH(1,1), including its asymptotic and bootstrap results, be generalized to higher-order GARCH models and augmented GARCH processes? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Statistical Inference for Complex Time Series Data (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/48, pp. 2749--2823 |
30,002,414 | OWR-12596-002 | Stationarity of a GARCH Recurrence | For the recurrence h_t=omega_0+h_{t-1}(alpha_0 Z_{t-1}^2+beta_0), why does E[log(alpha_0 Z_t^2+beta_0)]<0 imply a stationary ergodic solution and convergence of solutions from different initial conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Inference for Complex Time Series Data (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/48, pp. 2749--2823](https://doi.org/10.4171/owr/2013/48)
## Literature review (checked ... | 3 | open | null | 2,013 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (Checked against the official Oberwolfach report. The source presents the implication as a standard explanatory step establishing stationarit) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-12596-002",
"literature-status:open",
"owr-year:2013"
] | The record contains only the fragment Why does this hold and omits its antecedent, so the claimed statement cannot be identified or verified. | [
{
"url": "https://ems.press/content/serial-article-files/46479",
"label": "Oberwolfach Report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/48 | null | null | null | null | For the recurrence h_t=omega_0+h_{t-1}(alpha_0 Z_{t-1}^2+beta_0), why does E[log(alpha_0 Z_t^2+beta_0)]<0 imply a stationary ergodic solution and convergence of solutions from different initial conditions? | unrecoverable | Checked against the official Oberwolfach report. The source presents the implication as a standard explanatory step establishing stationarity and initial-condition stability, not as an unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Statistical Inference for Complex Time Series Data (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/48, pp. 2749--2823 |
30,002,415 | OWR-12723-001 | Sharp Multidimensional Star-Discrepancy Asymptotics | Determine the sharp asymptotic order, as $N\to\infty$, of the minimum star discrepancy, equivalently the minimum $L^\infty$ discrepancy, of $N$-point sets in the unit half-open $s$-cube for $s\geq3$, and clarify its relation to the small-ball conjecture and Kolmogorov entropy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917](https://doi.org/10.4171/owr/2013/49)
## Literature review (checked 2026-0... | 3 | open | null | 2,013 | 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-12723-001",
"literature-status:open",
"owr-year:2013"
] | The sharp asymptotic order of finite-point-set star discrepancy in the relevant higher-dimensional regime remains unresolved despite substantial lower bounds and constructions. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3380/OWR_2013_49.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 49"
},
{
"url": "https://doi.org/10.1007/s00013-021-01688-9",
"label": "Kritzinger--Pillichshammer"
},
{
"url": "https://www.sciencedirect.com/science/art... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2013/49 | null | null | null | Determine the sharp asymptotic order, as $N\to\infty$, of the minimum star discrepancy, equivalently the minimum $L^\infty$ discrepancy, of $N$-point sets in the unit half-open $s$-cube for $s\geq3$, and clarify its relation to the small-ball conjecture and Kolmogorov entropy. | Determine the sharp asymptotic order, as N tends to infinity, of the minimum star discrepancy, equivalently the L-infinity discrepancy, of N-point sets in [0,1)^s for s at least 3, and clarify its relation to the small-ball conjecture and Kolmogorov entropy. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Uniform Distribution Theory and Applications (2014), Oberwolfach Reports, DOI 10.4171/owr/2013/49, pp. 2837--2917 |
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