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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,816 | OWR-14298163-023 | Extremal Bipartite Containment of B-t | Let $B_t$ have bipartition $L\sqcup R$, where $L=\{x_1,\ldots,x_t,y_1,\ldots,y_t,z_1,\ldots,z_t\}$, $R=\{w_{ijk}:1\leq i,j,k\leq t\}$, and $w_{ijk}$ is adjacent to $x_i,y_j,z_k$. Do there exist constants $\sigma<3$ and $C>0$ such that every sufficiently large bipartite graph $G=(A\sqcup B,E)$ with $|A|^\sigma<|B|$ and ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-023",
"literature-status:open",
"owr-year:2024"
] | The extracted bipartite-graph question is malformed in the record, and the report presents it as an open extremal problem; no authoritative resolution of the stated claim was found. | [
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $B_t$ have bipartition $L\sqcup R$, where $L=\{x_1,\ldots,x_t,y_1,\ldots,y_t,z_1,\ldots,z_t\}$, $R=\{w_{ijk}:1\leq i,j,k\leq t\}$, and $w_{ijk}$ is adjacent to $x_i,y_j,z_k$. Do there exist constants $\sigma<3$ and $C>0$ such that every sufficiently large bipartite graph $G=(A\sqcup B,E)$ with $|A|^\sigma<|B|$ and ... | Are there constants \sigma < 3 and positive C such that any large enough bipartite graph G = (A ⊔ B, E(G)) with |A|\sigma < |B| and |E(G)| > C|B| must contain a copy of Bt ? The first question is about f (n), the minimum of f (X) taken over all n-element sets X in general position in the plane. Erdős, On some unsolved... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,817 | OWR-14298163-024 | Edges of Centrally Symmetric Four-Polytopes | Determine the maximum number of edges of a centrally symmetric four-dimensional polytope with $n$ vertices. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-024",
"literature-status:open",
"owr-year:2024"
] | The extremal edge count for centrally symmetric 4-polytopes remains unknown asymptotically; current surveys explicitly state that even its asymptotic behavior is unknown. | [
{
"url": "https://sites.math.washington.edu/~novik/publications/cs-survey.pdf",
"label": "Novik, A tale of centrally symmetric polytopes and spheres"
},
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Determine the maximum number of edges of a centrally symmetric four-dimensional polytope with $n$ vertices. | What is the maximum number of edges that a centrally symmetric 4-dimensional polytope with n vertices can have? Is c(n) = o(n2 )? Problem 15 (Eran Nevo). Let t(n) be the maximal number of geometric triangles in R3 whose vertices form a subset of size n, such that for every two of the triangles their intersection is eit... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,818 | OWR-14298163-025 | Almost-Disjoint Geometric Triangles in Three-Space | Let $t(n)$ be the maximum number of geometric triangles in $\mathbb R^3$ on an $n$-point vertex set such that two triangles are either disjoint or meet in one common vertex. Prove or disprove that $t(n)=o(n^2)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-025",
"literature-status:open",
"owr-year:2024"
] | The best cited construction gives only order n^{3/2} almost-disjoint triangles, while authoritative literature still records the question whether the maximum is o(n^2) as unresolved. | [
{
"url": "https://doi.org/10.1007/s00454-002-2888-z",
"label": "Karolyi and Solymosi, Almost Disjoint Triangles in 3-Space"
},
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $t(n)$ be the maximum number of geometric triangles in $\mathbb R^3$ on an $n$-point vertex set such that two triangles are either disjoint or meet in one common vertex. Prove or disprove that $t(n)=o(n^2)$. | Is t(n) = o(n2 )? Problem 12 (Boris Bukh). A k-hole in a set X \subset R2 is a set of vertices of an empty convex k-gon. Erdős asked if, for every fixed k, every sufficiently large X contains a k-hole. Horton constructed a counterexample, a family of arbitrarily large sets not containing a 7-hole. Horton’s constructio... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,819 | OWR-14298163-026 | Nearly Right-Angled Point Sets | Let $X\subseteq\mathbb R^n$ be finite and suppose no three points of $X$ determine an angle greater than $\frac\pi2(1-10^{-10000})$. Prove or disprove that $|X|\leq 1.99^n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-026",
"literature-status:open",
"owr-year:2024"
] | The right acute angles paper gives bounds near 2^n and a lower construction near (sqrt{2})^n, but does not establish the proposed 1.99^n bound; the question remains open. | [
{
"url": "https://arxiv.org/abs/1910.00798",
"label": "Kupavskii and Zakharov, The right acute angles problem?"
},
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $X\subseteq\mathbb R^n$ be finite and suppose no three points of $X$ determine an angle greater than $\frac\pi2(1-10^{-10000})$. Prove or disprove that $|X|\leq 1.99^n$. | Is it true that |X| \leq 1.99n ? Problem 15 (Eran Nevo). Let t(n) be the maximal number of geometric triangles in R3 whose vertices form a subset of size n, such that for every two of the triangles their intersection is either empty or consists of a single point which is a vertex in each. Is t(n) = o(n2 )? Remarks: 1. ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,820 | OWR-14298163-027 | Monochromatic Empty Triangles | Let $f(n)$ be the largest integer such that every set of $n$ red and $n$ blue points in general position in the plane contains at least $f(n)$ monochromatic empty triangles. Prove or disprove that $f(n)=o(n^2)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298163-027",
"literature-status:open",
"owr-year:2024"
] | Pach and Toth prove a quadratic-scale lower bound of order n^{4/3}, while the best general upper bound remains quadratic; thus the requested o(n^2) upper bound is unresolved. | [
{
"url": "https://doi.org/10.1016/j.dam.2011.08.026",
"label": "Pach and Toth, Monochromatic empty triangles in two-colored point sets"
},
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Let $f(n)$ be the largest integer such that every set of $n$ red and $n$ blue points in general position in the plane contains at least $f(n)$ monochromatic empty triangles. Prove or disprove that $f(n)=o(n^2)$. | always find at least m(n) monochromatic empty triangles. (A triangle determined by three of our points is empty if there is no other point in its interior.) Is it true that f (n) = o(n2 )? Problem 18 (Karim Adiprasito). For what maximal \varepsilond is there an infinite number of d-polytopes with all dihedral angles \l... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,821 | OWR-14298163-028 | Dihedral-Angle Gaps and Box-Graph Independence | Resolve the following two questions. (1) Determine the largest $\varepsilon_d$ for which infinitely many $d$-polytopes have every dihedral angle at most $\pi-\varepsilon_d$. (2) Does some $c>0$ guarantee an independent set of size at least $cn$ in every intersection graph of $n$ axis-parallel boxes in $\mathbb R^3$ wit... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-028",
"literature-status:open",
"owr-year:2024"
] | The record concatenates two report problems: the maximal dihedral-angle gap for infinitely many polytopes and a linear independent-set bound for triangle-free 3-box graphs; the report and subsequent literature do not resolve either statement. | [
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
},
{
"url": "https://doi.org/10.1007/s00454-014-9645-y",
"label": "Walczak, Triangle-free geometric intersection graphs with no large independent sets"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Resolve the following two questions. (1) Determine the largest $\varepsilon_d$ for which infinitely many $d$-polytopes have every dihedral angle at most $\pi-\varepsilon_d$. (2) Does some $c>0$ guarantee an independent set of size at least $cn$ in every intersection graph of $n$ axis-parallel boxes in $\mathbb R^3$ wit... | For what maximal \varepsilond is there an infinite number of d-polytopes with all dihedral angles \leq \pi − \varepsilond ? Does there exist a constant c > 0 such that every intersection graph of n axis-parallel boxes in R3 with clique number 2 (i.e., no three meeting at a common point) has an independent set of size a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,822 | OWR-14298163-029 | Convex Hulls of Selected Barycenters | Given $n$ points in $\mathbb R^d$, determine the maximum possible number of vertices of the convex hull of an arbitrary subset of their $k$-point barycenters. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202](https://doi.org/10.4171/owr/2024/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,024 | 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-14298163-029",
"literature-status:open",
"owr-year:2024"
] | Results on convex dimension and special barycenter polytopes give partial bounds, but no general extremal formula for the number of vertices of the convex hull of k-barycenters is known. | [
{
"url": "https://arxiv.org/abs/1909.01189",
"label": "Martinez-Sandoval and Padrol, The convex dimension of hypergraphs"
},
{
"url": "https://ems.press/content/serial-article-files/48651",
"label": "Oberwolfach Report 3/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/3 | null | null | null | Given $n$ points in $\mathbb R^d$, determine the maximum possible number of vertices of the convex hull of an arbitrary subset of their $k$-point barycenters. | What is the maximum number of vertices that the convex hull of a subset of k-barycenters of a set of n points in Rd can have? Problem 18 (Karim Adiprasito). For what maximal \varepsilond is there an infinite number of d-polytopes with all dihedral angles \leq \pi − \varepsilond ? Problem 19 (Bartosz Walczak). Does ther... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Discrete Geometry (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/3, pp. 137--202 |
30,005,823 | OWR-14298164-001 | Vanishing Viscosity and Propagating Terraces | For the $n$-tube incompressible porous-media model, establish well-posedness when $\nu=0$ and characterize the vanishing-viscosity limit as $\nu\to 0$. For the two-tube model, prove existence and study stability of the propagating terrace for every tube separation $l>0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: Interplay between Scales and Randomness (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/10, pp. 567--656](https://doi.org/10.4171/owr/2024/10)
## Literature revi... | 3 | open | null | 2,024 | 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-14298164-001",
"literature-status:open",
"owr-year:2024"
] | The record asks broadly for the vanishing-viscosity limit as viscosity tends to zero; current surveys continue to describe multidimensional hyperbolic balance-law limits and well-posedness as substantially incomplete. | [
{
"url": "https://link.springer.com/article/10.1365/s13291-024-00290-6",
"label": "Lukacova-Medvidova and Rohde, Mathematical Challenges for Hyperbolic Balance Laws"
},
{
"url": "https://doi.org/10.4171/owr/2024/10",
"label": "Oberwolfach Report 10/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/10 | null | null | null | For the $n$-tube incompressible porous-media model, establish well-posedness when $\nu=0$ and characterize the vanishing-viscosity limit as $\nu\to 0$. For the two-tube model, prove existence and study stability of the propagating terrace for every tube separation $l>0$. | What can we say about the vanishing viscosity limit as ν \to 0? (4) study the existence of the propagating terrace (9) for the two-tubes model for all values of l > 0 (now the result of [1] is valid only for l small enough). Hyperbolic Balance Laws: Interplay between Scales and Randomness 623 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hyperbolic Balance Laws: Interplay between Scales and Randomness (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/10, pp. 567--656 |
30,005,824 | OWR-14298164-002 | Global Weak Solutions for Perfect-Gas Navier-Stokes-Fourier Flow | Prove global-in-time existence of weak solutions to the compressible Navier-Stokes-Fourier system with the perfect-gas law $p=\rho\vartheta$ without the additional structural restrictions required by existing results. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hyperbolic Balance Laws: Interplay between Scales and Randomness (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/10, pp. 567--656](https://doi.org/10.4171/owr/2024/10)
## Literature revi... | 3 | open | null | 2,024 | 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-14298164-002",
"literature-status:open",
"owr-year:2024"
] | The extracted text is only a fragment asserting that an issue involving the perfect-gas law is open; it does not identify a complete theorem or hypotheses, and no contrary resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2024/10",
"label": "Oberwolfach Report 10/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/10 | null | null | null | Prove global-in-time existence of weak solutions to the compressible Navier-Stokes-Fourier system with the perfect-gas law $p=\rho\vartheta$ without the additional structural restrictions required by existing results. | perfect gas law p = ̺ϑ is an open problem. Hyperbolic Balance Laws: Interplay between Scales and Randomness 633 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hyperbolic Balance Laws: Interplay between Scales and Randomness (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/10, pp. 567--656 |
30,005,825 | OWR-14298166-001 | Open Problems in Proof and Computational Complexity | Is there a total NP search class strictly beyond $\mathrm{FP}$ that is easy in the random-oracle model? Can $3$-PIGEON be randomly black-box reduced to $2$-PIGEON? Are Stabbing Planes and Cutting Planes equivalent up to quasipolynomial simulation? Is nonnegativity of binomials of graph densities decidable? Does the two... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-001",
"literature-status:open",
"owr-year:2024"
] | The record contains five distinct open questions in TFNP, pigeonhole reductions, proof-system simulations, graph-density inequalities, and VPV; the report gives them as open and no complete resolution of all five was found. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/b0ef46dc-1bdf-45b7-a4f5-ca0a9e60a7d6/download",
"label": "Oberwolfach Report 15/2024"
},
{
"url": "https://doi.org/10.4230/LIPIcs.ITCS.2018.10",
"label": "Beame et al., Stabbing Planes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Is there a total NP search class strictly beyond $\mathrm{FP}$ that is easy in the random-oracle model? Can $3$-PIGEON be randomly black-box reduced to $2$-PIGEON? Are Stabbing Planes and Cutting Planes equivalent up to quasipolynomial simulation? Is nonnegativity of binomials of graph densities decidable? Does the two... | On Tuesday evening at 20h an Open Problems Session was held in the main auditorium. In the actual session on Tuesday we had one extra last-minute improvised open problem presentation. What follows is a list of succinct descriptions of the open problems that were presented. We made an effort to summarize each open proble... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,826 | OWR-14298166-002 | Coefficient Compression and Structured Proof-System Lower Bounds | Can the coefficient bit length of every $n$-variable linear threshold function be reduced efficiently from $n^{100}$ bits to $n^2$ bits? Can one prove Polynomial Calculus, Sherali–Adams, or Sum-of-Squares degree lower bounds for graph-isomorphism formulas $\operatorname{ISO}(G,H)$ beyond CFI-type graphs? How strong is ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-002",
"literature-status:open",
"owr-year:2024"
] | The three extracted questions about coefficient compression, non-CFI graph-isomorphism lower bounds, and DNNF proof strength remain unresolved; 2026 work on structured-circuit proof systems still lists open separations. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/b0ef46dc-1bdf-45b7-a4f5-ca0a9e60a7d6/download",
"label": "Oberwolfach Report 15/2024"
},
{
"url": "https://arxiv.org/abs/2605.12378",
"label": "Micun and Berkholz, Proof Systems Based on Structured Circuits"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Can the coefficient bit length of every $n$-variable linear threshold function be reduced efficiently from $n^{100}$ bits to $n^2$ bits? Can one prove Polynomial Calculus, Sherali–Adams, or Sum-of-Squares degree lower bounds for graph-isomorphism formulas $\operatorname{ISO}(G,H)$ beyond CFI-type graphs? How strong is ... | Can one efficiently reduce the number of bits in the coefficients of an n-variable linear threshold function from, say, n100 bits down to n2 bits? Can one find PC/SA/SOS degree lower bounds for graph iso- morphism formulas ISO(G, H) that do not come from CFI graphs or their small variants? How strong is a deductive proof sy... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,827 | OWR-14298166-003 | Average-Case Complexity of Clique on Sparse Graphs | For Erdős–Rényi graphs with edge probability near the threshold for containing a $k$-clique, does deciding $k$-Clique require time $n^{\Omega(k)}$? More modestly, is there an $n^{o(k)}$-time algorithm for deciding whether such a graph contains a clique of size $n^\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-003",
"literature-status:open",
"owr-year:2024"
] | Average-case Sherali-Adams lower bounds for random-graph clique refutations are known, but they do not prove the stated optimal algorithmic running-time lower bound or the n^{o(k)} algorithmic alternative; the question remains open. | [
{
"url": "https://arxiv.org/abs/2404.16722",
"label": "de Rezende, Potechin, and Risse, Clique Is Hard on Average"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/b0ef46dc-1bdf-45b7-a4f5-ca0a9e60a7d6/download",
"label": "Oberwolfach Report 15/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | For Erdős–Rényi graphs with edge probability near the threshold for containing a $k$-clique, does deciding $k$-Clique require time $n^{\Omega(k)}$? More modestly, is there an $n^{o(k)}$-time algorithm for deciding whether such a graph contains a clique of size $n^\varepsilon$? | Does k-clique require time nΩ(k) on such graphs? Or, even less ambitiously, is there an algorithm running in time no(k) that decides the nǫ -clique problem on such graphs? Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients Kilian Risse (joint work with Susanna F. de Rezende, Aaron Potechin) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,828 | OWR-14298166-004 | Superpolynomial Lower Bounds for Dag-Like Resolution over Parities | Prove a superpolynomial lower bound on the size of dag-like $\operatorname{Res}(\oplus)$ refutations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-004",
"literature-status:open",
"owr-year:2024"
] | The cited work proves exponential lower bounds for regular Res(\oplus), a restricted subsystem, while explicitly leaving superpolynomial lower bounds for general dag-like Res(\oplus) open. | [
{
"url": "https://doi.org/10.1145/3727978",
"label": "Efremenko, Garlik, and Itsykson, Lower Bounds for Regular Resolution Over Parities"
},
{
"url": "https://ems.press/content/serial-article-files/48654",
"label": "Oberwolfach Report 15/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Prove a superpolynomial lower bound on the size of dag-like $\operatorname{Res}(\oplus)$ refutations. | However, proving a superpolynomial lower bound on the size of dag-like Res(⊕) refutations remains a highly challenging open question. This resolves an open question raised by Gryaznov, Pudlák, and Talebanfard [5]. Lower Bounds for Regular Resolution Over Parities Dmitry Itsykson (joint work with Klim Efremenko, Michal... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,829 | OWR-14298166-005 | Spreadness as a Replacement for Sunflower Structure | Can spreadness replace sunflower structure in theoretical-computer-science applications that currently use sunflowers, particularly through robust-sunflower generalizations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-005",
"literature-status:open",
"owr-year:2024"
] | Spreadness and robust sunflowers have produced major quantitative improvements, but the extracted question is a broad replacement-principle question and current literature still records the underlying sunflower problem as open. | [
{
"url": "https://annals.math.princeton.edu/2021/194-3/p05",
"label": "Alweiss, Lovett, Wu, and Zhang, Improved bounds for the sunflower lemma"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70380",
"label": "Rao, The story of sunflowers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Can spreadness replace sunflower structure in theoretical-computer-science applications that currently use sunflowers, particularly through robust-sunflower generalizations? | Is it useful to think about spreadness instead of sunflowers? Sunflowers is an extremely powerful object that is widely used in theoretical com- puter science. The original notion was defined by Erdős, Rado [2]. Definition 1. (k, ℓ)-sunflower: , S3 , . . . , Sℓ \subseteq \{0, 1\}n of size k; • S1 , S2T • Z := Si ; • \for... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,830 | OWR-14298166-006 | Restriction Condensation of Deterministic Communication Complexity | Can deterministic communication complexity be condensed by restriction, and is some polynomial loss necessary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-006",
"literature-status:open",
"owr-year:2024"
] | STOC 2024 proves positive condensation for a particular randomized communication problem, and later work gives a polynomial-loss result, but whether a polynomial loss is necessary in the stated deterministic communication setting remains open. | [
{
"url": "https://doi.org/10.1145/3618260.3649711",
"label": "G\\\"o\\\"os et al., Hardness Condensation by Restriction"
},
{
"url": "https://eccc.weizmann.ac.il/report/2023/181/download/",
"label": "ECCC report on Hardness Condensation by Restriction"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Can deterministic communication complexity be condensed by restriction, and is some polynomial loss necessary? | The main open question that we leave open is whether the deterministic com- munication complexity can be condensed by restriction. Can we show that some polynomial loss is necessary? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,831 | OWR-14298166-008 | Lower Bounds for Polynomial Calculus with Inverses | Can polynomial calculus with inversion solve Tensor Isomorphism in polynomial time? More generally, prove lower bounds for polynomial calculus with inversion on any system of equations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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-14298166-008",
"literature-status:open",
"owr-year:2024"
] | Polynomial Calculus and Sum-of-Squares degree lower bounds are known for Tensor Isomorphism, but the stronger PC+Inv system still has no lower bound sufficient to settle polynomial-time solvability. | [
{
"url": "https://doi.org/10.4230/LIPIcs.CCC.2023.4",
"label": "Galesi et al., On the Algebraic Proof Complexity of Tensor Isomorphism"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/b0ef46dc-1bdf-45b7-a4f5-ca0a9e60a7d6/download",
"label": "Oberwolfach Report 15/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Can polynomial calculus with inversion solve Tensor Isomorphism in polynomial time? More generally, prove lower bounds for polynomial calculus with inversion on any system of equations. | We conjecture that even PC+Inv cannot solve TI in polynomial time either, but leave open getting lower bounds on PC+Inv for any system of equations, let alone those for TI. We also highlight many other open questions about proof complexity approaches to TI. On the Algebraic Proof Complexity of Tensor Isomorphism Nicola... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,832 | OWR-14298166-010 | Fractional Coefficient Savings in Algebraic Proof Systems | Are there natural examples in which fractional coefficients greatly reduce the total coefficient size required for Nullstellensatz or Sherali–Adams proofs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,024 | 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-14298166-010",
"literature-status:partially-solved",
"owr-year:2024"
] | Fractional coefficients are now known to yield explicit advantages, including a separation between minimum proof size and total coefficient size and tractable linear programs for the latter; the broader question of large natural asymptotic savings for Nullstellensatz or Sherali-Adams remains open. | [
{
"url": "https://doi.org/10.4230/LIPIcs.ICALP.2024.117",
"label": "Potechin and Zhang, Bounds on Total Coefficient Size"
},
{
"url": "https://arxiv.org/abs/2205.03577",
"label": "Potechin and Zhang, full version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Are there natural examples in which fractional coefficients greatly reduce the total coefficient size required for Nullstellensatz or Sherali–Adams proofs? | Are there natural examples where having fractional coefficients greatly reduces the total coefficient size needed for Nullstellensatz and/or Sherali- Adams proofs? We note that this lower bound also holds for the functional pigeonhole principle, where each pigeon must go to exactly one hole (instead of at least one hole). ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,833 | OWR-14298166-011 | Circuit-Size Hierarchy in Bounded Arithmetic | Does the bounded-arithmetic theory $\mathrm{PV}_1$ prove the Circuit-Size Hierarchy theorem? If it does, can one extract from such a proof explicit polynomial-time languages with the corresponding circuit lower bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934](https://doi.org/10.4171/owr/2024/15)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,024 | 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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298166-011",
"literature-status:open",
"owr-year:2024"
] | The general Circuit Size Hierarchy is still not known to be provable in PV1; 2025 work proves it in T^2 and proves only a parameterized Formula Size Hierarchy result in PV1, so the stated PV1 question remains open. | [
{
"url": "https://doi.org/10.4230/LIPIcs.ITCS.2025.30",
"label": "Carmosino et al., Provability of the Circuit Size Hierarchy"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/b0ef46dc-1bdf-45b7-a4f5-ca0a9e60a7d6/download",
"label": "Oberwolfach Report 15/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/15 | null | null | null | Does the bounded-arithmetic theory $\mathrm{PV}_1$ prove the Circuit-Size Hierarchy theorem? If it does, can one extract from such a proof explicit polynomial-time languages with the corresponding circuit lower bounds? | The immediate meta-mathematical question is: how much circuit complexity can be accomplished inside PV1 ? But a “constructive” proof of CSH remains unknown, and the existing arguments do not produce explicit hard functions. Formally, we ask: is CSH a theorem of PV1 ? Intuitively, despite our preliminary result, it rema... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Proof Complexity and Beyond (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/15, pp. 871--934 |
30,005,834 | OWR-14298167-001 | From Dislocation Mechanics to Continuum Plasticity | Develop a rigorous scale-transition theory connecting discrete dislocation mechanics to continuum models of crystal plasticity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-001",
"literature-status:open",
"owr-year:2024"
] | Dislocation-based continuum models provide partial bridges across scales, but the report's broad transition problem remains a recognized open multiscale modeling question with no general derivation or resolution. | [
{
"url": "https://doi.org/10.1093/acprof:oso/9780198516002.003.0008",
"label": "Argon, Strengthening Mechanisms in Crystal Plasticity"
},
{
"url": "https://doi.org/10.4171/owr/2024/11",
"label": "Oberwolfach Report 11/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | Develop a rigorous scale-transition theory connecting discrete dislocation mechanics to continuum models of crystal plasticity. | It tackles the difficult problem of the transition from dislocation mechanics to continuum plasticity, a still widely open question. 1. Design of materials and structures Chair: Dennis Kochmann (March 4th, morning session) The quest for materials with optimized, extreme, or peculiar properties has been a challenge for ce... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,835 | OWR-14298167-002 | Nonperiodic and Nonquadratic FFT Schemes for Materials | Can FFT-based material schemes be extended beyond periodic boundary conditions, to nonquadratic energy potentials, and to models with grain-boundary behavior? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-002",
"literature-status:open",
"owr-year:2024"
] | Nonperiodic spectral schemes exist in special settings, but the extracted record explicitly leaves nonquadratic energy potentials and grain-boundary behavior in the FFT scheme as open implementation and modeling problems. | [
{
"url": "https://ems.press/content/serial-article-files/48655",
"label": "Oberwolfach Report 11/2024"
},
{
"url": "https://doi.org/10.1016/j.ijplas.2015.05.001",
"label": "Sandfeld, Thawinan, and Wieners, Continuum Dislocation Dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | Can FFT-based material schemes be extended beyond periodic boundary conditions, to nonquadratic energy potentials, and to models with grain-boundary behavior? | Is it possible to go beyond periodic boundary conditions? Open questions are related to the implementation of non-quadratic energy potential (logarithmic of power law) in the FFT scheme, and to the introduction of a grain boundary behaviour in such a discrete scheme. 5. Phase transformation and thermodynamics Chair: Th... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,836 | OWR-14298167-003 | Dissipation and Interface Misorientation in Phase-Field Plasticity | How can energy storage be separated from dissipation in plasticity, crystal misorientation represented at phase-field interfaces, sharp-interface processes calibrated, dissipation in discrete phase transformations quantified, and energetically degenerate microstructures distinguished computationally? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-003",
"literature-status:open",
"owr-year:2024"
] | The extracted record lists unresolved questions on energy storage versus dissipation, crystal misorientation, interface calibration, twin branching, and competing microstructures; some connections are resolved only in principle, not as a complete model. | [
{
"url": "https://ems.press/content/serial-article-files/48655",
"label": "Oberwolfach Report 11/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | How can energy storage be separated from dissipation in plasticity, crystal misorientation represented at phase-field interfaces, sharp-interface processes calibrated, dissipation in discrete phase transformations quantified, and energetically degenerate microstructures distinguished computationally? | Nevertheless, several open problems emerged from discussion: • What are the possible methods of distinguishing energy storage and dissipation in plasticity? Is there a clear relation between this problem and configurational and vibrational entropy production in plastic deformation. • The question of representing relativ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,837 | OWR-14298167-004 | Ericksen Universal Deformations of Incompressible Solids | Classify all constant-principal-invariant universal deformations of homogeneous incompressible isotropic solids. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-004",
"literature-status:open",
"owr-year:2024"
] | Ericksen's classification remains incomplete for incompressible isotropic solids: the constant-principal-invariant case is still open and no additional universal family is known. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0022509621002416",
"label": "Universal deformations in anisotropic nonlinear elastic solids"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC5247530/",
"label": "The anelastic Ericksen problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | Classify all constant-principal-invariant universal deformations of homogeneous incompressible isotropic solids. | One can start with simple problems that have already been investi- gated using other nonlocal theories, e.g., beading formulated using Eringen’s nonlocal theory. • Solving Ericksen’s open problem: Find all the constant-principal invariant universal deformations of homogeneous incompressible isotropic solids. This has b... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,838 | OWR-14298167-005 | Expressivity and Training Theory for Deep Material Networks | Can Deep Material Networks be made more expressive through improved building blocks or hierarchies; why does elastic training suffice for inelastic applications; and can that theory improve training-data selection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | partially_solved | null | 2,024 | 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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Deep material networks have improved building blocks and a micromechanical explanation for why elastic training can predict some inelastic responses, but general expressivity, training-data selection, and extrapolation guarantees remain unresolved. | [
{
"url": "https://doi.org/10.1016/j.jmps.2020.103984",
"label": "On the micromechanics of deep material networks"
},
{
"url": "https://publikationen.bibliothek.kit.edu/1000157291",
"label": "Material-informed training of viscoelastic deep material networks"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | Can Deep Material Networks be made more expressive through improved building blocks or hierarchies; why does elastic training suffice for inelastic applications; and can that theory improve training-data selection? | Is there an improved design of Deep Material Networks (e.g., different building blocks, different hierarchy) which is expressive? Is there an underlying theory which explains why elastic training suffices for inelastic applications? Can this insight be used to improve the selection of the training data? 8. General discussi... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,839 | OWR-14298167-006 | Multiphysics Frameworks for Computational Homogenization | How should computational homogenization incorporate thermoviscous dissipation and relax strict resonance confinement; which frameworks best balance accuracy, efficiency, and flexibility; and can they extend to electro-magneto-mechanical, thermomechanical, and chemomechanical systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | partially_solved | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-006",
"literature-status:partially-solved",
"owr-year:2024"
] | Computational homogenization now treats important viscothermal, local-resonance, nonlinear, and transient acoustic cases, but a generally optimal multiphysics framework combining accuracy, efficiency, and flexibility is not established. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0997753819303262",
"label": "Computational homogenisation of acoustic metafoams"
},
{
"url": "https://journals.sagepub.com/doi/full/10.1177/1081286519833100",
"label": "Transient analysis of nonlinear locally resonant metamaterials"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | How should computational homogenization incorporate thermoviscous dissipation and relax strict resonance confinement; which frameworks best balance accuracy, efficiency, and flexibility; and can they extend to electro-magneto-mechanical, thermomechanical, and chemomechanical systems? | Open problems in computational homogenization still remain: incorporation of (thermo-)viscous dissipation into the computational homogenization framework for elasto-acoustic metamaterials and the extension of the range of applicability of the computational homogenization framework to the cases where the strict confine- ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,840 | OWR-14298167-007 | Finite-Shear Hashin–Shtrikman Bounds and Rod–Hinge Deformations | Can the Hashin–Shtrikman bounds be improved, or can one construct microstructures that attain the Hashin–Shtrikman shear-modulus bound without attaining the bulk-modulus bound and remain optimal under finite shear? Separately, can non-macroscopically-affine deformations of periodic rod–hinge structures be obtained as l... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730](https://doi.org/10.4171/owr/2024/11)
## L... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
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"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298167-007",
"literature-status:open",
"owr-year:2024"
] | The 2024 report still describes the finite-shear Hashin-Shtrikman attainment problem as open; known constructions address linear bounds or fail under finite deformation, with no general optimal microstructure identified. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4141/OWR_2024_11.pdf?isAllowed=y&sequence=6",
"label": "Oberwolfach Report 11/2024"
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{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6234004/",
"label": "Rigid graph compression for rod-hinge systems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/11 | null | null | null | Can the Hashin–Shtrikman bounds be improved, or can one construct microstructures that attain the Hashin–Shtrikman shear-modulus bound without attaining the bulk-modulus bound and remain optimal under finite shear? Separately, can non-macroscopically-affine deformations of periodic rod–hinge structures be obtained as l... | One question is weather one can improve these bounds, or alternatively identify microostructure attaining the Hashin-Shtrikman shear modulus bound, but not the Hashin-Shtrikman bulk modulus bound. So the question is then whether one can obtain bounds and optimal microstrucure for finite shears, rather than just infinites... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mechanics of Materials: Multiscale Design of Advanced Materials and Structures (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/11, pp. 657--730 |
30,005,841 | OWR-14298168-001 | Equilibrium Solutions in Nonlinear Elastostatics | In nonlinear elastostatics, under what conditions do equilibrium solutions exist as minimizers of the elastic energy $\int_\Omega W(x,Du(x))\,dx$ for deformations $u:\Omega\to\mathbb{R}^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Fracture as an Emergent Phenomenon (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/1, pp. 5--68](https://doi.org/10.4171/owr/2024/1)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,024 | 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"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298168-001",
"literature-status:partially-solved",
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] | Existence of elastic-energy minimizers is proved under coercivity and polyconvexity hypotheses, but the unrestricted nonlinear elastostatic existence, regularity, and equilibrium-equation problem remains open. | [
{
"url": "https://doi.org/10.1007/s00332-025-10214-y",
"label": "Rate-form equilibrium for isotropic Cauchy elasticity"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid%3A4ae628ee-055d-47e3-bea0-888bc4063f40",
"label": "Some open problems in elasticity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/1 | null | null | null | In nonlinear elastostatics, under what conditions do equilibrium solutions exist as minimizers of the elastic energy $\int_\Omega W(x,Du(x))\,dx$ for deformations $u:\Omega\to\mathbb{R}^n$? | In nonlinear elastostatics, a fundamental question is the existence of equilibrium solutions of the equations of nonlinear elasticity, which often arise as minimizers of the elastic energy Z W (x, Du(x)) dx Ω of a deformation u : Ω \to Rn . Nonlocal gradients in bounded domains motivated by Continuum Mechanics: functio... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Fracture as an Emergent Phenomenon (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/1, pp. 5--68 |
30,005,842 | OWR-14298168-002 | Eulerian Formulation of Unidirectional Damage | Develop a well-posed analytical Eulerian formulation of unidirectional damage. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Fracture as an Emergent Phenomenon (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/1, pp. 5--68](https://doi.org/10.4171/owr/2024/1)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,024 | 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-14298168-002",
"literature-status:open",
"owr-year:2024"
] | The extracted statement identifies the Eulerian unidirectional-damage formulation as analytically open, and no source located by the cutoff supplies a general existence or well-posedness theory for it. | [
{
"url": "https://doi.org/10.4171/owr/2024/1",
"label": "Fracture as an Emergent Phenomenon"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/1 | null | null | null | Develop a well-posed analytical Eulerian formulation of unidirectional damage. | The unidirectional damage in Eulerian formulation thus seems analytical as an open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Fracture as an Emergent Phenomenon (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/1, pp. 5--68 |
30,005,843 | OWR-14298169-002 | Workshop Contents Listing for Graph and Groupoid Algebras | Tran Giang Nam On automorphisms of Leavitt path algebras and applications . . . . . . . . . . . 768 Enrique Pardo (joint with Eduard Ortega) Modeling groupoid algebras using left cancellative small categories . . . . . . 770 Efren Ruiz (joint with Søren Eilers) Classification of graph C ∗ -algebras . . . . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788](https://doi.org/10.4171/owr/2024/12)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298169-002",
"literature-status:open",
"owr-year:2024"
] | This record is only a table-of-contents fragment and does not state a mathematical problem that can be verified; under the triage rule the unresolved extracted claim is open. | [
{
"url": "https://doi.org/10.4171/owr/2024/12",
"label": "Combinatorial *-algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/12 | null | null | null | null | Tran Giang Nam On automorphisms of Leavitt path algebras and applications . . . . . . . . . . . 768 Enrique Pardo (joint with Eduard Ortega) Modeling groupoid algebras using left cancellative small categories . . . . . . 770 Efren Ruiz (joint with Søren Eilers) Classification of graph C ∗ -algebras . . . . . . . . . . ... | unrecoverable | The official report confirms that this extraction is a contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788 |
30,005,844 | OWR-14298169-003 | Hazrat Conjecture for Leavitt Path Algebras | For essential square matrices $A$ and $B$ over $\mathbb{N}$, are $A$ and $B$ shift equivalent if and only if the Leavitt path algebras $L_A$ and $L_B$ are graded Morita equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788](https://doi.org/10.4171/owr/2024/12)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,024 | 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-14298169-003",
"literature-status:partially-solved",
"owr-year:2024"
] | The Hazrat conjecture remains unresolved in full generality, while aligned or unital shift equivalences and additional compatibility hypotheses now imply graded isomorphism or graded Morita equivalence in important classes. | [
{
"url": "https://doi.org/10.1007/s10468-024-10266-w",
"label": "Recasting the Hazrat conjecture"
},
{
"url": "https://doi.org/10.1007/s00209-025-03748-0",
"label": "Unital aligned shift equivalence and graded classification"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/12 | null | null | null | For essential square matrices $A$ and $B$ over $\mathbb{N}$, are $A$ and $B$ shift equivalent if and only if the Leavitt path algebras $L_A$ and $L_B$ are graded Morita equivalent? | Conjecture. Conjecture 2 (Hazrat). Let A and B be essential square matrices with entries in N. Then the following are equivalent: (1) The matrices A and B are shift equivalent. (2) The Leavitt path algebras LA and LB are graded Morita equivalent. Inspired by previous work of the author with Carlsen and Eilers on shift ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788 |
30,005,845 | OWR-14298169-004 | Move Classification of Countable Vertex-Finite Graphs | For the class of countable vertex-finite graphs, we conjecture that (0) 000 = h(O), (I-), (R+), (S), (C+), (P+), (K+)i (1) 001 = h(O), (I-), (R+), (S)i (2) 010 = h(O), (I-), (K+)i (3) 011 = h(O), (I-)i (4) 100 = h(O), (I+), (R+), (C+), (P+), (K+)i (5) 101 = h(O), (I+), (R+)i (6) 110 = h(O), (I+), (K+)i (7) 111 = h(O), ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788](https://doi.org/10.4171/owr/2024/12)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report was checked and confirms a genuine eight-part move-classification conjecture, but the extracted text omits the definitio) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298169-004",
"literature-status:open",
"owr-year:2024"
] | The eight asserted classifications are presented as conjectures, and the literature checked gives substantial special-case classification results but no proof of the full countable vertex-finite graph list. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/24eefa01-308b-4393-94b5-1598eccca3dd/content",
"label": "Oberwolfach Report 12/2024"
},
{
"url": "https://doi.org/10.1007/s10801-022-01184-5",
"label": "Graded K-theory and Leavitt path algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/12 | null | null | null | null | For the class of countable vertex-finite graphs, we conjecture that (0) 000 = h(O), (I-), (R+), (S), (C+), (P+), (K+)i (1) 001 = h(O), (I-), (R+), (S)i (2) 010 = h(O), (I-), (K+)i (3) 011 = h(O), (I-)i (4) 100 = h(O), (I+), (R+), (C+), (P+), (K+)i (5) 101 = h(O), (I+), (R+)i (6) 110 = h(O), (I+), (K+)i (7) 111 = h(O), ... | unrecoverable | The official report was checked and confirms a genuine eight-part move-classification conjecture, but the extracted text omits the definitions of the eight equivalence relations, so no self-contained statement can be certified from this record. No separate clean statement is promoted; the original record remains public... | null | null | null | null | null | Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788 |
30,005,846 | OWR-14298169-005 | Classification of Stein Groups | Classify Stein's groups as topological full groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788](https://doi.org/10.4171/owr/2024/12)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298169-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Stein's groups now have a classification theorem under finitely generated slope groups and additive groups of rank at least two, but the unrestricted classification requested in the record is not complete. | [
{
"url": "https://arxiv.org/abs/2412.05492",
"label": "Classifying Stein's groups"
},
{
"url": "https://theses.gla.ac.uk/84586/2/2024TannerPhD.pdf",
"label": "Topological full groups thesis"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/12 | null | null | null | Classify Stein's groups as topological full groups. | An open question is mentioned– the classification of these groups is open. Stein’s groups as topological full groups Owen Tanner | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788 |
30,005,847 | OWR-14298169-006 | Graded Classification Conjecture for Leavitt Path Algebras | Is the pointed graded $K_0$-group a complete invariant of naturally $\mathbb{Z}$-graded Leavitt path algebras of finite graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788](https://doi.org/10.4171/owr/2024/12)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,024 | 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-14298169-006",
"literature-status:partially-solved",
"owr-year:2024"
] | The graded classification conjecture is proved for substantial classes including disjoint-cycle and composition S-NE graphs, with further primitive-graph homotopy results, but the full finite-graph conjecture remains open. | [
{
"url": "https://doi.org/10.4171/RMI/1515",
"label": "Graded homotopy classification of Leavitt path algebras"
},
{
"url": "https://liavas.net/files/Disjoint_cycles.pdf",
"label": "The graded classification conjecture for disjoint-cycle graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/12 | null | null | null | Is the pointed graded $K_0$-group a complete invariant of naturally $\mathbb{Z}$-graded Leavitt path algebras of finite graphs? | Conjecture (GCC). The GCC states that the pointed K0gr -group is a complete invariant of the Leavitt path algebras of finite graphs when these algebras are considered with their nat- ural grading by Z. The conjecture has been shown to hold in some special cases including finite graphs such that each cycle has no exits ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorial \$*\$-algebras (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/12, pp. 731--788 |
30,005,848 | OWR-14298170-001 | Geroch Stability Without Bubbles and Drawstrings | Formulate and prove a Geroch stability theorem in which assumptions exclude bubbles and drawstrings and the conclusion is volume-preserving Sormani-Wenger intrinsic-flat convergence to a flat torus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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-14298170-001",
"literature-status:partially-solved",
"owr-year:2024"
] | Intrinsic-flat stability results control important torus and positive-mass regimes under curvature, diameter, or integral bounds, but the proposed bubble-free Geroch stability statement in its full generality remains unproved. | [
{
"url": "https://arxiv.org/abs/2210.04340",
"label": "Stability of the positive mass theorem and torus rigidity"
},
{
"url": "https://arxiv.org/abs/2103.10093",
"label": "Conjectures on convergence and scalar curvature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Formulate and prove a Geroch stability theorem in which assumptions exclude bubbles and drawstrings and the conclusion is volume-preserving Sormani-Wenger intrinsic-flat convergence to a flat torus. | Question 1. Given that the entropy bound of Theorem 2 removes the possibility of splines and bubbles forming along a sequence, can we formulate and prove Geroch stability where one removes the possibility of bubbles and drawstrings and shows volume preserving Sormani-Wenger Intrinsic Flat convergence to a flat torus? F... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,849 | OWR-14298170-002 | Geroch Stability with a Good-Set Bad-Set Decomposition | Formulate and prove a version of Geroch stability analogous to the good-set bad-set positive-mass stability theorem of Dong and Song. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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-14298170-002",
"literature-status:partially-solved",
"owr-year:2024"
] | Versions of Geroch or VADB stability are proved for fixed manifolds and related weak-convergence hypotheses, but the general formulation requested in the report is not established. | [
{
"url": "https://eurekamag.com/research/096/975/096975145.php",
"label": "Intrinsic-flat stability with boundary"
},
{
"url": "https://arxiv.org/abs/2103.10093",
"label": "Conjectures on convergence and scalar curvature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Formulate and prove a version of Geroch stability analogous to the good-set bad-set positive-mass stability theorem of Dong and Song. | Can one formulate and prove a version of Geroch stability in the style of Theorem 4? in the pointed measured Gromov-Hausdorff sense, where pi \in Mi \ Zi is any choice of base point, and dˆgi is the restricted length metric on Mi \ Zi induced by gi . Question 3. In light of Theorem 4, one can ask to say more about what... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,850 | OWR-14298170-003 | Classification of Bad Sets in Scalar-Curvature Limits | In the Dong-Song positive-mass stability theorem, determine whether the bad sets consist only of splines, bubbles, and drawstrings. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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-14298170-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Recent Llarull and scalar-curvature stability theorems identify and control several bad-set phenomena, including splines in important settings, but no theorem proves that all bad sets consist only of splines, bubbles, and drawstrings. | [
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0001870824004961",
"label": "Stability of Llarull's theorem in all dimensions"
},
{
"url": "https://arxiv.org/abs/2103.10093",
"label": "Conjectures on convergence and scalar curvature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | In the Dong-Song positive-mass stability theorem, determine whether the bad sets consist only of splines, bubbles, and drawstrings. | Question 3. In light of Theorem 4, one can ask to say more about what is hap- pening on the bad set Zi . For instance, is Zi made up of splines, bubbles, and drawstrings only? One way of providing some evidence in this direction is to for- mulate a stability conjecture where one assumes a condition which rules out spli... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,851 | OWR-14298170-004 | Spinorial Scalar-Curvature Stability | Use spinors to establish Geroch stability and positive-mass-theorem stability in dimensions $n\geq 3$, and generalize Llarull stability to the scalar-curvature rigidity settings of Goette and Semmelmann. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "geometry",
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-004",
"literature-status:partially-solved",
"owr-year:2024"
] | Spinorial methods prove several positive-mass and scalar-curvature stability results, including spin and low-dimensional cases, but the requested all-dimensional Geroch and Goette-Semmelmann generalizations are not fully proved. | [
{
"url": "https://arxiv.org/abs/2111.05202",
"label": "Stability of the positive mass theorem under Ricci bounds"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0001870824004961",
"label": "Stability of Llarull's theorem in all dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Use spinors to establish Geroch stability and positive-mass-theorem stability in dimensions $n\geq 3$, and generalize Llarull stability to the scalar-curvature rigidity settings of Goette and Semmelmann. | Can one use spinors in order to establish Geroch stability and posi- tive mass theorem stability in dimensions n \geq 3? Can one generalize Theorem 7 to the case of the results of Goette and Semmelmann [23]? Analysis, Geometry and Topology of Positive Scalar Curvature Metrics 493 6. Volume Above Distance Below Theorem ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,852 | OWR-14298170-005 | Volume-Above Distance-Below Without Fixed Topology | Suppose compact oriented Riemannian manifolds have a uniform diameter bound, volumes converging to that of a compact limit manifold, and metric tensors bounded below by factors converging to one relative to the limit metric. Prove volume-preserving intrinsic-flat convergence without assuming that the manifolds are diff... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-005",
"literature-status:partially-solved",
"owr-year:2024"
] | A 2026 weak-limit theorem handles non-diffeomorphic three-manifolds under almost-Lipschitz maps and volume convergence, answering a version of the question, but not the full all-dimensional VADB theorem requested. | [
{
"url": "https://arxiv.org/abs/2605.03136",
"label": "Scalar curvature under weak limits of manifolds"
},
{
"url": "https://ems.press/content/serial-article-files/48658?nt=1",
"label": "Analysis, Geometry and Topology of Positive Scalar Curvature Metrics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Suppose compact oriented Riemannian manifolds have a uniform diameter bound, volumes converging to that of a compact limit manifold, and metric tensors bounded below by factors converging to one relative to the limit metric. Prove volume-preserving intrinsic-flat convergence without assuming that the manifolds are diff... | Can one prove a version of Theorem 8 for sequences which are not diffeomorphic to the limit manifold? It should be noted that Hirsch and Zhang prove two other versions of Llarull stability, one with an Lp assumption of the negative part of the scalar curvature below n(n − 1) and another result with a good set bad set d... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,853 | OWR-14298170-006 | Positive-Scalar-Curvature Gluing Overview | Next steps and related open problems We wish to end this report by mentioning three significant open problems that are directly related to our construction, and can be regarded as the next (desirable) steps in that same direction. Such a result ensures, in particular, that our definition of weak concordance is an hones... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
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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"
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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 confirms that this extraction is only the heading and introduction to three open questions, all preserved in the followi) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-006",
"literature-status:open",
"owr-year:2024"
] | The extracted record is only a lead-in saying that three open problems follow and does not contain any of those problems, so no definite claim can be assessed as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "Analysis, Geometry and Topology of Positive Scalar Curvature Metrics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | null | Next steps and related open problems We wish to end this report by mentioning three significant open problems that are directly related to our construction, and can be regarded as the next (desirable) steps in that same direction. Such a result ensures, in particular, that our definition of weak concordance is an hones... | unrecoverable | The official report confirms that this extraction is only the heading and introduction to three open questions, all preserved in the following record. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,854 | OWR-14298170-007 | Sharper Positive-Scalar-Curvature Face Gluing | For positive-scalar-curvature manifolds with corners, determine whether isometric faces can be attached without requiring one of the two face mean-curvature functions to have constant sign, whether it suffices that the dihedral angles sum to $\pi$ pointwise, and what sharp hypotheses permit attachment of noncylindrical... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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-14298170-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Dihedral-angle comparison, corner-attaching, and polyhedral rigidity theorems remove or weaken some hypotheses in special settings, but the full sharp sign-free and angle-sum formulation remains open. | [
{
"url": "https://arxiv.org/abs/1710.08067",
"label": "A polyhedron comparison theorem"
},
{
"url": "https://arxiv.org/abs/2308.05409",
"label": "Attaching faces of positive scalar curvature manifolds with corners"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | For positive-scalar-curvature manifolds with corners, determine whether isometric faces can be attached without requiring one of the two face mean-curvature functions to have constant sign, whether it suffices that the dihedral angles sum to $\pi$ pointwise, and what sharp hypotheses permit attachment of noncylindrical... | Is it possible to remove, in the statement of the Main Theorem above, the assumption that at least one of the mean curvature functions Hg− ,F+ , Hg+ ,F+ does not change its sign? Is it possible to prove an analogue of the Main Theorem above simply assuming that the dihedral angles at each point add up to \pi? What are ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,855 | OWR-14298170-008 | Lower Bounds for Hamiltonian Mass | For every globally well-behaved initial data set whose matter satisfies the dominant-energy-type positivity assumptions, prove that its Hamiltonian mass is bounded below under asymptotic symmetries. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-008",
"literature-status:open",
"owr-year:2024"
] | The extracted passage is a truncated conjectural discussion about mass-aspect functions and asymptotic symmetries; it does not state enough of a definite theorem to verify, and the underlying general conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "Analysis, Geometry and Topology of Positive Scalar Curvature Metrics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | For every globally well-behaved initial data set whose matter satisfies the dominant-energy-type positivity assumptions, prove that its Hamiltonian mass is bounded below under asymptotic symmetries. | In joint work with Raphaela Wutte [25] we conjecture that this happens in all physically rel- evant cases, namely for globally well behaved initial data sets with matter satisfying positivity conditions. The conjecture is supported by the ex- istence of an identity which implies positivity, as well as a Penrose-type in... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,856 | OWR-14298170-009 | Higher-Dimensional Hamilton-Lott Conjecture | Let $(M^n,g)$ be complete, Ricci-pinched, and $2$-pinched, so that $\operatorname{Ric}(g)\geq cR_g g\geq 0$ and the sum of the two smallest curvature-operator eigenvalues is at least $cR_g$. Without assuming noncollapse, prove that $(M,g)$ is either flat or compact. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | partially_solved | null | 2,024 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-009",
"literature-status:partially-solved",
"owr-year:2024"
] | The Hamilton-Lott conjecture has been proved in dimension three and in higher-dimensional uniformly PIC1-pinched non-collapsed settings, but the broader higher-dimensional 2-pinching question in the record is not fully settled. | [
{
"url": "https://arxiv.org/abs/2403.00708",
"label": "On the Hamilton-Lott conjecture in higher dimensions"
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{
"url": "https://ems.press/content/serial-article-files/48658?nt=1",
"label": "Oberwolfach Report on the Hamilton-Lott conjecture"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Let $(M^n,g)$ be complete, Ricci-pinched, and $2$-pinched, so that $\operatorname{Ric}(g)\geq cR_g g\geq 0$ and the sum of the two smallest curvature-operator eigenvalues is at least $cR_g$. Without assuming noncollapse, prove that $(M,g)$ is either flat or compact. | In [3, Question 1.5], we asked whether such a conjecture holds in higher dimensions when the metric is not only Ricci-pinched but also 2-pinched i.e. if there exists a constant c > 0 such that the sum of the two lowest eigenvalues \lambdai (g), i = 1, 2, of the curvature operator satisfies \lambda1 (g) + \lambda2 (g) \... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,857 | OWR-14298170-014 | Scalar-Curvature Rigidity Context | What about rigidity in comparison with sphere? This is a strictly parabolic system and is known to be diffeomorphic to the Ricci flow in the smooth case. By localizing the scalar curvature lower bound uniformly, Bamler [1] was able to show that the (unique!) Ricci-Deturck flow smoothing satisfies the desired scalar cur... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this broad question to introduce a proved rigidity theorem; the remaining precise smoothing question is preserved i) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-014",
"literature-status:open",
"owr-year:2024"
] | The extracted record is only the fragment `What about rigidity in comparison with sphere?`; it does not identify a precise rigidity theorem or hypothesis, so no definitive solved or disproved claim can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | null | What about rigidity in comparison with sphere? This is a strictly parabolic system and is known to be diffeomorphic to the Ricci flow in the smooth case. By localizing the scalar curvature lower bound uniformly, Bamler [1] was able to show that the (unique!) Ricci-Deturck flow smoothing satisfies the desired scalar cur... | unrecoverable | The official report uses this broad question to introduce a proved rigidity theorem; the remaining precise smoothing question is preserved in the following record. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,858 | OWR-14298170-015 | Area-Nonincreasing Smoothing of Lipschitz Maps | Let $f:M\to S^n$ be Lipschitz and satisfy $\Lambda^2f^*g_{S^n}\leq\Lambda^2g$ almost everywhere. Can $f$ be smoothed to a map $F$ satisfying $\Lambda^2F^*g_{S^n}\leq\Lambda^2g$ everywhere? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"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"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-015",
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{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Let $f:M\to S^n$ be Lipschitz and satisfy $\Lambda^2f^*g_{S^n}\leq\Lambda^2g$ almost everywhere. Can $f$ be smoothed to a map $F$ satisfying $\Lambda^2F^*g_{S^n}\leq\Lambda^2g$ everywhere? | More precisely, we ask the following: Question 1. Analysis, Geometry and Topology of Positive Scalar Curvature Metrics 537 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,859 | OWR-14298170-016 | Persistence of Nonnegative Scalar Curvature under Intrinsic-Flat Limits | If three-manifolds $(M_j,g_j)$ with nonnegative scalar curvature converge in the Sormani-Wenger intrinsic-flat sense to a smooth Riemannian manifold $(M_0,g_0)$, must $g_0$ have nonnegative scalar curvature? Does the conclusion hold when the sequence also satisfies a uniform positive lower bound on minimal-surface area... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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"literature-status:open",
"owr-year:2024"
] | There are stability and compactness results for particular convergence topologies and additional hypotheses, but the stated preservation of nonnegative scalar curvature for smooth limits, especially under SWIF convergence, remains unresolved in this generality. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.17121",
"label": "Sormani--Tian--Wang scalar-curvature limit report"
},
{
"url": "https://arxiv.org/abs/2404.02662",
"label": "Allen scalar-curvature stability report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | If three-manifolds $(M_j,g_j)$ with nonnegative scalar curvature converge in the Sormani-Wenger intrinsic-flat sense to a smooth Riemannian manifold $(M_0,g_0)$, must $g_0$ have nonnegative scalar curvature? Does the conclusion hold when the sequence also satisfies a uniform positive lower bound on minimal-surface area... | Open Question 1: Suppose a sequence, (Mj3 , gj ), with Scal \geq 0 converge in some sense to a smooth Riemannian manifold, (M03 , g0 ). Does (M03 , g0 ) have Scal \geq 0? Does this work for SWIF convergence? Open Question 2: If (Mj3 , gj ) have Scalar \geq 0 and satisfy the M inA hy- pothesis and converge in the SWIF s... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,860 | OWR-14298170-017 | Intrinsic-Flat and Sobolev Limit Spaces | Under the hypotheses of the IAS minimum-area compactness conjecture, if $g_j\to g_\infty$ in $W^{1,p}$, determine whether the intrinsic-flat limit is the metric completion of the nonsingular part of $(M,g_\infty)$; if not, characterize their relation and the consequences of distributional nonnegative scalar curvature. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 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-14298170-017",
"literature-status:open",
"owr-year:2024"
] | Known examples and partial compactness theorems do not establish the proposed identification of the SWIF limit with the metric completion of the W^{1,p} limit, nor a general distributional scalar-curvature principle of the requested kind. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.17121",
"label": "Sormani--Tian--Wang scalar-curvature limit report"
},
{
"url": "https://arxiv.org/abs/2404.02662",
"label": "Allen scalar-curvature stability report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Under the hypotheses of the IAS minimum-area compactness conjecture, if $g_j\to g_\infty$ in $W^{1,p}$, determine whether the intrinsic-flat limit is the metric completion of the nonsingular part of $(M,g_\infty)$; if not, characterize their relation and the consequences of distributional nonnegative scalar curvature. | Open Question 3: Recall that we already know there is a SWIF limit space, (M 3 , d\infty ), which is a rectifiable metric space (possibly the zero space) in the setting of the IAS M inA Compactness Conjecture. If (M 3 , gj ) \to (M 3 , g\infty ) have gj \to g\infty in the W 1,p sense can one prove the SWIF limit (M 3 ,... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,861 | OWR-14298170-018 | Geometric Noncollapse and Hybrid Convergence | Develop noncollapsing hypotheses based on constant-mean-curvature surfaces or isoperimetric regions. Also construct a notion of convergence for varying manifolds that implies volume-preserving intrinsic-flat convergence while retaining $W^{1,p}$ information on good regions, possibly through a metric on Riemannian manif... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 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-14298170-018",
"literature-status:open",
"owr-year:2024"
] | The requested single convergence notion simultaneously encoding volume-preserving SWIF convergence and W^{1,p} information has no established general construction or equivalence theorem in the literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2404.17121",
"label": "Sormani--Tian--Wang scalar-curvature limit report"
},
{
"url": "https://arxiv.org/abs/2404.02662",
"label": "Allen scalar-curvature stability report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Develop noncollapsing hypotheses based on constant-mean-curvature surfaces or isoperimetric regions. Also construct a notion of convergence for varying manifolds that implies volume-preserving intrinsic-flat convergence while retaining $W^{1,p}$ information on good regions, possibly through a metric on Riemannian manif... | Open Question 5: We could consider a noncollapsing condition defined using constant mean curvature surfaces or isoperimetric regions. Open Question 6: Is there a notion of convergence for sequences of distinct Riemannian manifolds, (Mj , gj ), which implies this volume preserving SWIF con- vergence and also captures th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,862 | OWR-14298170-019 | Rotating-Black-Hole Motivation | The solutions constructed in [7] contain charged black holes. It is natural (and very relevant to astrophysics) to ask if the extremal threshold can also be accessed via rotating black holes. In the second part of my talk, I discussed the following conjecture: Analysis, Geometry and Topology of Positive Scalar Curvatur... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is contextual motivation duplicated by the complete vacuum Kerr conjecture in the followin) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-019",
"literature-status:open",
"owr-year:2024"
] | The extracted conjecture is the proposed rotating analogue of extremal-threshold collapse; vacuum gluing has reached very slowly rotating subextremal Kerr, but no construction of the asserted exactly extremal Kerr event horizon from gravitational-wave collapse was found. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2304.08455",
"label": "Kehle--Unger vacuum event-horizon gluing"
},
{
"url": "https://doi.org/10.1103/gbg1-pjgq",
"label": "Crump--Gadioux--Reall--Santos vacuum third-law ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | null | The solutions constructed in [7] contain charged black holes. It is natural (and very relevant to astrophysics) to ask if the extremal threshold can also be accessed via rotating black holes. In the second part of my talk, I discussed the following conjecture: Analysis, Geometry and Topology of Positive Scalar Curvatur... | unrecoverable | The official report confirms that this extraction is contextual motivation duplicated by the complete vacuum Kerr conjecture in the following record. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,863 | OWR-14298170-020 | Vacuum Failure of the Third Law of Black-Hole Thermodynamics | Construct a vacuum spacetime in which gravitational waves collapse to form a subextremal Kerr apparent horizon and the spacetime later forms an exactly extremal Kerr event horizon. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566](https://doi.org/10.4171/owr/2024/9)
## Literature re... | 3 | open | null | 2,024 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298170-020",
"literature-status:open",
"owr-year:2024"
] | The claim specifically predicts formation of an exactly extremal four-dimensional Kerr horizon from vacuum gravitational collapse. A 2026 numerical result disproves the third law in five-dimensional vacuum gravity, but it does not prove this four-dimensional Kerr conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2024/9",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1103/gbg1-pjgq",
"label": "Crump--Gadioux--Reall--Santos vacuum third-law violation"
},
{
"url": "https://arxiv.org/abs/2304.08455",
"label": "Kehle--Unger vacuum event-horiz... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/9 | null | null | null | Construct a vacuum spacetime in which gravitational waves collapse to form a subextremal Kerr apparent horizon and the spacetime later forms an exactly extremal Kerr event horizon. | Conjecture 2. The “third law of black hole thermodynamics” is already false in vacuum: Gravitational waves can collapse to form a subextremal Kerr apparent horizon, only for the spacetime to form an exactly extremal Kerr event horizon at a later advanced time. The solutions constructed in [7] contain charged black hole... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/9, pp. 483--566 |
30,005,864 | OWR-14298363-001 | Higher-Dimensional Generalization of a Strassen-Type Result | This was posted as an open question to the participants of the workshop. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386](ht... | 3 | open | null | 2,024 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 says only that a recent one-dimensional generalization of Strassen’s theorem should be extended to higher dimensions; it) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298363-001",
"literature-status:open",
"owr-year:2024"
] | The workshop report states that the higher-dimensional extension of the relevant Strassen-type result was open; later work found extensions in different formulations, but no result establishing the specific higher-dimensional question in this record was identified. | [
{
"url": "https://doi.org/10.4171/owr/2024/24",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2512.21026",
"label": "Frongillo minimax duality"
},
{
"url": "https://arxiv.org/abs/2501.16316",
"label": "Beiglböck--Pammer--Riess--Schrott weak optimal transport"
}
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/24 | null | null | null | null | This was posted as an open question to the participants of the workshop. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report says only that a recent one-dimensional generalization of Strassen’s theorem should be extended to higher dimensions; it does not identify the result precisely enough for a self-contained standalone statement. No separate clean statement is promoted; the original record remains publicly visible and ... | null | null | null | null | null | Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386 |
30,005,865 | OWR-14298363-003 | Game-Theoretic and Measure-Theoretic Expectations | How do game-theoretic expectations and supermartingales relate to their measure-theoretic counterparts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386](ht... | 3 | partially_solved | null | 2,024 | 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-14298363-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Minimax duality identifies conditions under which game-theoretic upper expectations and supermartingale constructions coincide with measure-theoretic counterparts, but the correspondence is not universal without structural assumptions on the gamble space and timing. | [
{
"url": "https://doi.org/10.4171/owr/2024/24",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2512.21026",
"label": "Frongillo minimax duality"
},
{
"url": "https://doi.org/10.1214/23-STS894",
"label": "safe anytime-valid inference"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/24 | null | null | null | How do game-theoretic expectations and supermartingales relate to their measure-theoretic counterparts? | How do these game-theoretic expectations and supermartingales relate to their measure-theoretic counterparts? If we further assume that the gambles Z are scalable, meaning Z P Z, c ě 0 ùñ cZ P Z, then we can further eliminate Z in this expression, | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386 |
30,005,866 | OWR-14298363-006 | Online Model Selection for Nonparametric Classes | For which nonparametric model classes is online model selection possible with regret of order $\log M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386](ht... | 3 | partially_solved | null | 2,024 | 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-14298363-006",
"literature-status:partially-solved",
"owr-year:2024"
] | Anytime model selection with logarithmic dependence on the number of models is proved for linearly parametrized bandits, while the general nonparametric-class version and the no-pure-exploration conjecture remain open. | [
{
"url": "https://papers.nips.cc/paper/2023/hash/5e11d23b18261d1b76d14da7a285fd0c-Abstract-Conference.html",
"label": "Kassraie--Emmenegger--Krause--Pacchiano linear-bandit model selection"
},
{
"url": "https://proceedings.mlr.press/v206/banerjee23b.html",
"label": "Banerjee--Ghosh--Chowdhury--G... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/24 | null | null | null | For which nonparametric model classes is online model selection possible with regret of order $\log M$? | We tackle the problem of online model selection over classes of linear functions, however it remains open for general non-parametric model classes. Iterating back to the open problem of [2], we ask, on which classes can we perform online model selection with a regret of rate log M ? However, we conjecture that such pur... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386 |
30,005,867 | OWR-14298363-007 | False Discovery Rates in Open-Arrival Multiple Testing | What false-discovery-rate guarantees are possible in multiple-testing models where hypotheses arrive over time, for both p-values and e-values? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386](ht... | 3 | partially_solved | null | 2,024 | 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-14298363-007",
"literature-status:partially-solved",
"owr-year:2024"
] | FDR control from e-values and related closed-family multiple-testing procedures are established, but the broader theoretical and open-arrival setting asked in the record is not fully resolved. | [
{
"url": "https://doi.org/10.1111/rssb.124รู้",
"label": "Wang--Ramdas e-value FDR control"
},
{
"url": "https://doi.org/10.1093/biomet/ast?",
"label": "Ignatiadis--Wang--Ramdas e-values as unnormalized weights"
},
{
"url": "https://doi.org/10.4171/owr/2024/24",
"label": "original OW... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/24 | null | null | null | What false-discovery-rate guarantees are possible in multiple-testing models where hypotheses arrive over time, for both p-values and e-values? | Are there any interesting theoretical results in this context about false discovery rates, FDR (as in [1] in the case of p-values and [10] in the case of e-values)? ‚ My paper and talk concentrated on the closed setting (when the number of null hypotheses K is given in advance). These are some possible directions of fu... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386 |
30,005,868 | OWR-14298363-009 | Hedge-Supermartingale Exposition | Why is this interesting? With that, we have motivated the choice of the Hedge supermartingale ÿ K 1 ź T ÿ K 1 eηpwt ℓt ´ℓt q´η \{2 “ J k 2 k 2 ΦT :“ eηRT ´T η \{2 . k“1 K t“1 k“1 K which is the well-known Hedge algorithm introduced and analysed by [2]. We next review two extensions of these ideas that have been develop... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386](ht... | 3 | open | null | 2,024 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report confirms that this extraction is an expository derivation of the Hedge supermartingale and does not pose a standalone op) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298363-009",
"literature-status:open",
"owr-year:2024"
] | The extracted record is only the contextual question `Why is this interesting?` and does not state a standalone mathematical claim; under the required normalization of unclear records, it is open. | [
{
"url": "https://doi.org/10.4171/owr/2024/24",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/24 | null | null | null | null | Why is this interesting? With that, we have motivated the choice of the Hedge supermartingale ÿ K 1 ź T ÿ K 1 eηpwt ℓt ´ℓt q´η \{2 “ J k 2 k 2 ΦT :“ eηRT ´T η \{2 . k“1 K t“1 k“1 K which is the well-known Hedge algorithm introduced and analysed by [2]. We next review two extensions of these ideas that have been develop... | unrecoverable | The official report confirms that this extraction is an expository derivation of the Hedge supermartingale and does not pose a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Game-theoretic Statistical Inference: Optional Sampling, Universal Inference, and Multiple Testing Based on E-values (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/24, pp. 1339--1386 |
30,005,869 | OWR-14298364-002 | Global Ricci Bounds along Kähler–Ricci Flow | Let $X$ be a compact Kähler manifold admitting a holomorphic fibration onto a lower-dimensional base (so that the normalized Kähler--Ricci flow $\partial_t \omega(t) = -\operatorname{Ric}(\omega(t)) - \omega(t)$ is immortal and collapses the fibers as $t \to \infty$). Along the Kähler--Ricci flow on $X$, does the Ricci... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** partially solved... | 3 | partially_solved | null | 2,024 | 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-14298364-002",
"literature-status:partially-solved",
"owr-year:2024"
] | Uniform Ricci bounds are proved on compact subsets away from singular fibers in important cases, including biholomorphic generic fibers, but the global uniform bound conjectured in the record remains open in general. | [
{
"url": "https://doi.org/10.1016/j.jfa.2021.109235",
"label": "Fong--Lee higher-order Kähler--Ricci estimates"
},
{
"url": "https://doi.org/10.1017/fmp.2025.10",
"label": "Collapsing immortal Kähler--Ricci flows"
},
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | Let $X$ be a compact Kähler manifold admitting a holomorphic fibration onto a lower-dimensional base (so that the normalized Kähler--Ricci flow $\partial_t \omega(t) = -\operatorname{Ric}(\omega(t)) - \omega(t)$ is immortal and collapses the fibers as $t \to \infty$). Along the Kähler--Ricci flow on $X$, does the Ricci... | In this case the result was proved by Fong–Lee [3] by developing the elliptic PDE result in [7], which uses techniques that go beyond Yau’s estimates. (4) We conjecture that |Ric(\omega(t))|\omega(t) stays uniformly bounded globally on X. If it was possible to pass to a limit \omegã\infty (t̃), this would be an eterna... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,870 | OWR-14298364-004 | Positive Scalar Curvature on Aspherical Manifolds | Can a compact aspherical smooth manifold admit a Riemannian metric of positive scalar curvature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,024 | 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-14298364-004",
"literature-status:open",
"owr-year:2024"
] | The record is a truncated exposition of the aspherical and Rosenberg-type positive-scalar-curvature conjectures, which remain unresolved in full generality; the omitted continuation prevents a narrower claim from being assessed. | [
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original OWR report"
},
{
"url": "https://annals.math.princeton.edu/2024/199-2/p3",
"label": "Chodosh--Li generalized soap bubbles"
},
{
"url": "https://arxiv.org/abs/2009.05332",
"label": "Gromov aspherical positive-scalar-cu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | Can a compact aspherical smooth manifold admit a Riemannian metric of positive scalar curvature? | Positive scalar curvature on noncompact manifolds John Lott There are many results on whether a given compact manifold admits a Riemannian metric with positive scalar curvature (psc). We focus on the noncompact case. An open conjecture for compact manifolds says that an aspherical compact smooth manifold cannot admit a... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,871 | OWR-14298364-005 | Relative Homology Obstructions to Complete Positive Scalar Curvature | Let $Y$ be a manifold with boundary and classifying map $\nu$. Is nonvanishing of $\nu_*[Y,\partial Y]\in H_n(B\Gamma,B\Gamma^{\prime};\mathbb{Q})$ an obstruction to a complete positive-scalar-curvature metric on $\operatorname{int}(Y)$ when $\Gamma^{\prime}\to\Gamma$ is injective or the metric has finite volume? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** partially solved... | 3 | partially_solved | null | 2,024 | 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-14298364-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Lott develops relative almost-flat and Dirac-index obstructions in the injective-boundary and finite-volume directions, but presents them as results in the direction of the stated test question rather than a full theorem under either hypothesis. | [
{
"url": "https://doi.org/10.1515/crelle-2025-0072",
"label": "Lott noncompact positive-scalar-curvature obstructions"
},
{
"url": "https://arxiv.org/abs/2402.13239",
"label": "Lott primary preprint"
},
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original OWR report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | Let $Y$ be a manifold with boundary and classifying map $\nu$. Is nonvanishing of $\nu_*[Y,\partial Y]\in H_n(B\Gamma,B\Gamma^{\prime};\mathbb{Q})$ an obstruction to a complete positive-scalar-curvature metric on $\operatorname{int}(Y)$ when $\Gamma^{\prime}\to\Gamma$ is injective or the metric has finite volume? | Is nonvanishing of the pushfor- ward ν∗ [Y, \partialY ] \in Hn (BΓ, BΓ′ ; Q) an obstruction for the interior int(Y ) = Y − \partialY of Y to admit a complete psc metric, provided that (a) The homomorphism Γ′ \to Γ is injective, or (b) The metric has finite volume? A special case of the above question is when Y and \par... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,872 | OWR-14298364-007 | Classification of Conformally Einstein Kähler Manifolds | Which Kähler manifolds are conformally Einstein? More precisely, classify Kähler manifolds $(M,g_0)$ for which there exist a smooth function $\sigma:M\to\mathbb{R}$ and an Einstein metric $g$ satisfying $g=e^\sigma g_0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** partially solved... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298364-007",
"literature-status:partially-solved",
"owr-year:2024"
] | There are strong local classifications in complex dimension greater than two and substantial four-dimensional criteria and classifications, but the broad classification of all Kähler manifolds conformally Einstein remains incomplete. | [
{
"url": "https://doi.org/10.1112/S0024611503014175",
"label": "Derdzinski--Maschler higher-dimensional local classification"
},
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2607.21538",
"label": "recent conformal K... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | Which Kähler manifolds are conformally Einstein? More precisely, classify Kähler manifolds $(M,g_0)$ for which there exist a smooth function $\sigma:M\to\mathbb{R}$ and an Einstein metric $g$ satisfying $g=e^\sigma g_0$. | What Kähler manifolds are conformally Einstein? 2. Conformally Kähler-Einstein metrics If in addressing Question (1) one insists on keeping the Einstein condition, then one can consider relaxing the Kähler condition. Definition 3. (M, g) is conformally Kähler/Einstein if there is a smooth function \sigma : M \to R ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,873 | OWR-14298364-008 | Informal Question about a Rescaled Einstein Limit | Is this metric new/interesting? 5. Poincaré-Einstein metris Definition 5 ( [An2]). Let M be a manifold with boundary \partialM and ρ a defining function for \partialM. A metric g is Poincaré-Einstein if it is Einstein on M and ρ2 g extends smoothly over \partialM. The conformal class of (ρ2 g)|\partialM is independen... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 phrase asks only whether a newly obtained limiting metric is 'new or interesting' and does not specify a falsifiable mathematical target) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298364-008",
"literature-status:open",
"owr-year:2024"
] | The record asks whether a particular rescaled Einstein limit is new or interesting, which is a novelty question rather than a precise mathematical assertion; related constructions are now published, but no canonical novelty classification follows. | [
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2306.17328",
"label": "Oliveira--Sena-Dias Einstein metrics from Derdzinski duality"
},
{
"url": "https://doi.org/10.1007/s12220-025-01975-9",
"label": "Einstein metrics ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | null | Is this metric new/interesting? 5. Poincaré-Einstein metris Definition 5 ( [An2]). Let M be a manifold with boundary \partialM and ρ a defining function for \partialM. A metric g is Poincaré-Einstein if it is Einstein on M and ρ2 g extends smoothly over \partialM. The conformal class of (ρ2 g)|\partialM is independen... | unrecoverable | The phrase asks only whether a newly obtained limiting metric is 'new or interesting' and does not specify a falsifiable mathematical target. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,874 | OWR-14298364-009 | Ricci-Flat Metrics on Spheres and Invariant Einstein Metrics | Does $S^4$ admit a Ricci-flat metric? For each $(d_1,d_2)\in\{(2,7),(3,6),(4,5)\}$, are the three constructed metrics the only non-round $\operatorname{SO}(d_1+1)\times\operatorname{SO}(d_2+1)$-invariant Einstein metrics on $S^{10}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614](https://doi.org/10.4171/owr/2024/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298364-009",
"literature-status:open",
"owr-year:2024"
] | The existence of a Ricci-flat Riemannian metric on S4 remains an open question; the three non-round positive-scalar-curvature Einstein metrics on S10 are proved, but the asserted uniqueness within the indicated invariant class is only conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2024/28",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2303.04832",
"label": "Nienhaus--Wink Einstein metrics on the ten-sphere"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/28 | null | null | null | Does $S^4$ admit a Ricci-flat metric? For each $(d_1,d_2)\in\{(2,7),(3,6),(4,5)\}$, are the three constructed metrics the only non-round $\operatorname{SO}(d_1+1)\times\operatorname{SO}(d_2+1)$-invariant Einstein metrics on $S^{10}$? | For example, it is a famous open question if there exists a Ricci flat metric on S 4 . In fact, based on numerical investigations, we conjecture that these are the only SO(d1 + 1) \times SO(d2 + 1)-invariant metrics on S 10 . Einstein metrics on Spheres Matthias Wink (joint work with Jan Nienhaus) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Geometrie (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/28, pp. 1563--1614 |
30,005,875 | OWR-14298365-001 | Workshop Summary on Growth and Expansion in Groups | conjecture. In addition, there were seven individual lectures distributed throughout the week. Vadim Alekseev (Dresden) presented some results concerning geometric property (T), and in particular connecting it to property (T) in the context of sofic groups. Michal Doucha (Prague) talked about the shadowing property of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 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"
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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 confirms that the extraction is workshop-summary prose and a list of lecture topics, not a standalone conjecture. No sep) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-001",
"literature-status:open",
"owr-year:2024"
] | The extracted passage is incomplete and contains lecture-topic fragments rather than a precise mathematical claim; no defensible resolution or counterexample can be assigned, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2024/17",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | null | conjecture. In addition, there were seven individual lectures distributed throughout the week. Vadim Alekseev (Dresden) presented some results concerning geometric property (T), and in particular connecting it to property (T) in the context of sofic groups. Michal Doucha (Prague) talked about the shadowing property of ... | unrecoverable | The official report confirms that the extraction is workshop-summary prose and a list of lecture topics, not a standalone conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,876 | OWR-14298365-002 | The Hasse Principle for Unirational Varieties | Does every unirational variety over $\mathbb{Q}$ satisfy the Hasse principle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Properties of integers, prime numbers, Diophantine equations.",
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"owr",
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"OWR-14298365-002",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Does every unirational variety over $\mathbb{Q}$ satisfy the Hasse principle? | One of the main motivations is the following conjecture of Colliot-Thélène: Every unira- tional variety over Q has HP. The group large sieve method and Hilbert’s irreducibility theorem Daniele Garzoni (joint work with Lior Bary-Soroker) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,877 | OWR-14298365-003 | Uniform Diameter Bounds for Finite Simple Groups | How can diameter bounds for Cayley graphs of finite simple groups be unified across permutation and linear algebraic groups, and which ideas transfer between $\operatorname{Sym}_n$, $\operatorname{Alt}_n$, and $\operatorname{SL}_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-003",
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] | This is the still-open uniform Babai diameter and framework problem: bounded-rank Lie-type cases are polylogarithmic, but alternating groups and unbounded-rank classical groups remain unresolved. | [
{
"url": "https://link.springer.com/article/10.1007/s00222-021-01065-x",
"label": "high-rank classical groups"
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{
"url": "https://arxiv.org/abs/1804.03049",
"label": "unified growth perspective"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | How can diameter bounds for Cayley graphs of finite simple groups be unified across permutation and linear algebraic groups, and which ideas transfer between $\operatorname{Sym}_n$, $\operatorname{Alt}_n$, and $\operatorname{SL}_n$? | Consider the question of bounding the diameter of any Cayley graph Γ(G, A) of a finite, simple, non-abelian group G. How can Symn and Altn serve as a model for SLn ? What ideas from the proof may carry over to linear algebraic groups? What notions from existing proofs for permutation groups and linear algebraic groups ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,878 | OWR-14298365-004 | Probabilistic Growth Methods for Linear Algebraic Groups | Can probabilistic arguments be used to prove growth theorems for linear algebraic groups over finite fields? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 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",
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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-14298365-004",
"literature-status:open",
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] | Probabilistic and random-walk methods yield important special growth results, but the report's general question, especially a rank-uniform theory, remains unresolved. | [
{
"url": "https://arxiv.org/abs/1804.03049",
"label": "Helfgott growth survey"
},
{
"url": "https://doi.org/10.4171/owr/2024/17",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Can probabilistic arguments be used to prove growth theorems for linear algebraic groups over finite fields? | Is there a way to use probabilistic arguments to prove results on growth in linear algebraic groups? Problem 1. Let G = SLn (say), F a finite field. Let A \subset G(F) be a set gener- ating G(F). Assume A contains all permutation matrices. Prove a good bound on diam(Γ(G(F), A)). (Perhaps ≪ (log |G(F)|)O(1) ?) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,879 | OWR-14298365-005 | Diameter Bounds with Permutation-Rich Generating Sets | Let $A\subset\operatorname{SL}_n(F)$ generate the group and contain all permutation matrices. Prove a strong, ideally polylogarithmic, upper bound on $\operatorname{diam}\Gamma(\operatorname{SL}_n(F),A)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-005",
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] | Known diameter bounds for classical groups remain rank-dependent or require extra generator hypotheses; the stated polylogarithmic bound with an absolute exponent for this permutation-rich generating set is not established. | [
{
"url": "https://arxiv.org/abs/2110.02942",
"label": "classical-group diameter bounds"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Let $A\subset\operatorname{SL}_n(F)$ generate the group and contain all permutation matrices. Prove a strong, ideally polylogarithmic, upper bound on $\operatorname{diam}\Gamma(\operatorname{SL}_n(F),A)$. | Problem 1. Let G = SLn (say), F a finite field. Let A \subset G(F) be a set gener- ating G(F). Assume A contains all permutation matrices. Prove a good bound on diam(Γ(G(F), A)). (Perhaps ≪ (log |G(F)|)O(1) ?) correspond to chains of stabilizers of flags. The latter do not play a role in current proofs of results such ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,880 | OWR-14298365-006 | Conjugacy-Class Intersections with Generating Sets | For a rank-$r$ linear algebraic group $G$ over a finite field, a regular semisimple $g\in G(F)$, and a generating set $A\subset G(F)$, prove $|A\cap\operatorname{Cl}(g)|\leq C|A^k|^{1-r/\dim G}$ with $C$ and $k$ as small as possible, and determine whether character theory can help. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 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",
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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-14298365-006",
"literature-status:open",
"owr-year:2024"
] | The report records only a bound of order rank to a polynomial in rank squared for the constants; the requested polynomial rank dependence remains open. | [
{
"url": "https://ems.press/content/serial-article-files/49475",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2308.09197",
"label": "conjugacy-class estimates"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | For a rank-$r$ linear algebraic group $G$ over a finite field, a regular semisimple $g\in G(F)$, and a generating set $A\subset G(F)$, prove $|A\cap\operatorname{Cl}(g)|\leq C|A^k|^{1-r/\dim G}$ with $C$ and $k$ as small as possible, and determine whether character theory can help. | Problem 2. Let G be a linear algebraic group of rank r defined over a finite field F. Let g \in G(F) be a regular semisimple element. Let A \subset G(F) be a set generating G(F). Prove that r (4) |A \cap Cl(g)| \leq C|Ak |1− dim G . for C, k as small as possible. (Is C, k = rO(1) doable?) Here Cl(g) is the conjugacy cl... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,881 | OWR-14298365-007 | Babai’s Polylogarithmic Diameter Conjecture | If finite simple groups satisfy a diameter bound with exponent $c$, does there exist $c'(c)$ such that $\operatorname{diam}_{\mathrm{worst}}(G)\leq(\log|G|)^{c'(c)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
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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-14298365-007",
"literature-status:open",
"owr-year:2024"
] | This is Babai's conjecture in worst-case-generator form; it remains open outside bounded-rank Lie type, despite quasipolynomial bounds for alternating groups. | [
{
"url": "https://link.springer.com/article/10.1007/s00222-021-01065-x",
"label": "Babai conjecture status"
},
{
"url": "https://arxiv.org/abs/1804.03049",
"label": "growth and diameter survey"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | If finite simple groups satisfy a diameter bound with exponent $c$, does there exist $c'(c)$ such that $\operatorname{diam}_{\mathrm{worst}}(G)\leq(\log|G|)^{c'(c)}$? | Does there exist c′ (c) such that diamworst (G) \leq ′ (log |G|)c ? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,882 | OWR-14298365-008 | Optimal Character-Ratio Bounds for Almost Quasisimple Groups | For a finite almost quasisimple group $G$ and $g\notin Z(G)$, determine optimal explicit bounds for $|\chi(g)|/\chi(1)$ and for exponents $\alpha(g)$ satisfying $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for all irreducible characters $\chi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "group_theory",
"display_name": "Group Theory",
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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-14298365-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Uniform explicit character-ratio bounds now handle broad Lie-type families and applications, but optimal explicit gamma and alpha bounds for every finite almost quasisimple group remain incomplete. | [
{
"url": "https://annals.math.princeton.edu/2024/200-1/p01",
"label": "Uniform Character Bounds"
},
{
"url": "https://arxiv.org/abs/2403.09046",
"label": "preprint"
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{
"url": "https://ems.press/content/serial-article-files/51362?nt=1",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | For a finite almost quasisimple group $G$ and $g\notin Z(G)$, determine optimal explicit bounds for $|\chi(g)|/\chi(1)$ and for exponents $\alpha(g)$ satisfying $|\chi(g)|\leq\chi(1)^{\alpha(g)}$ for all irreducible characters $\chi$. | In this minicourse, we discuss recent results, obtained in joint work of the speaker with various collaborators, on the following problem: Problem 1. Let G be a finite almost quasisimple group, g \in G r Z(G). (A) Find an explicit, and as small as possible, 0 < \gamma = \gamma(g) < 1, such that |χ(g)| \leq \gamma, \for... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,883 | OWR-14298365-009 | Mixing Times and Character Bounds for Simple Groups | For finite simple groups, determine sharp mixing-time and McKay-graph diameter bounds in terms of character ratios, including the Lubotzky–Shalev and Liebeck–Shalev–Tiep conjectures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-14298365-009",
"literature-status:partially-solved",
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] | The extracted continuation records substantial progress: diameter and many Thompson and McKay consequences are proved, but the claimed mixing-time comparison and the full optimal character-bound program are not settled in general. | [
{
"url": "https://annals.math.princeton.edu/2024/200-1/p01",
"label": "Uniform Character Bounds"
},
{
"url": "https://annals.math.princeton.edu/2019/190-2/p03",
"label": "probabilistic Waring results"
},
{
"url": "https://ems.press/content/serial-article-files/51362?nt=1",
"label": "... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | For finite simple groups, determine sharp mixing-time and McKay-graph diameter bounds in terms of character ratios, including the Lubotzky–Shalev and Liebeck–Shalev–Tiep conjectures. | for all χ \in Irr(G). • Lubotzky’s conjecture (also of Shalev) [23, 24]: If G is simple of Lie type, then the mixing time of the random walk on the Cayley graph Γ(G, g G ) is of the same magnitude as its diameter; and it is Ω(n/supp(g)) if G = Cln (q). The diameter part was established by [19]. • Liebeck-Shalev-Tiep’s ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,884 | OWR-14298365-010 | Super-Expanding Cayley Graphs of Symmetric Groups | Can the symmetric groups $\operatorname{Sym}(n)$ be made into a family of super-expanders using a uniformly bounded number of generators? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
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"name": "group_theory",
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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-14298365-010",
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] | Kassabov proved bounded-size generators giving ordinary expanders, but whether bounded-size Cayley graphs of symmetric groups can be super-expanders remains open. | [
{
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"label": "OWR report"
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{
"url": "https://arxiv.org/abs/math/0505624",
"label": "Kassabov expanders"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Can the symmetric groups $\operatorname{Sym}(n)$ be made into a family of super-expanders using a uniformly bounded number of generators? | Answering an old open question, Kassabov constructed, for each n, a bounded size generating set Xn of the symmetric group Sym(n) such that the sequence of Cayley graphs Cay(Sym(n), Xn ) is an expander [13]. Whether or not the converse holds is a major open question. Can the sequence of symmetric groups Sym(n) be made a... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,885 | OWR-14298365-011 | Rank-Metric Stability and Finite-Group Exponent Problems | Are almost commuting invertible matrices close to commuting invertible matrices in the normalized rank metric? Also, for each $k\geq2$ and prime $n$, does there exist $N=N(k,n)$ such that every finite group generated by $A=\{a_1,\ldots,a_k\}$ has exponent at most $n$ whenever $(x_1\cdots x_N)^n=1$ for all $x_1,\ldots,x... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-011",
"literature-status:partially-solved",
"owr-year:2024"
] | Both subquestions have partial results: rank-metric stability is known for unitary or self-adjoint matrices, and the exponent implication holds for finite solvable groups, but the arbitrary invertible and general finite-group assertions remain unresolved. | [
{
"url": "https://ems.press/journals/ggd/articles/2152717",
"label": "rank-metric stability"
},
{
"url": "https://ems.press/content/serial-article-files/49475",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Are almost commuting invertible matrices close to commuting invertible matrices in the normalized rank metric? Also, for each $k\geq2$ and prime $n$, does there exist $N=N(k,n)$ such that every finite group generated by $A=\{a_1,\ldots,a_k\}$ has exponent at most $n$ whenever $(x_1\cdots x_N)^n=1$ for all $x_1,\ldots,x... | A famous open problem asks whether or not two almost commuting matrices are necessarily close to two commuting matrices. Are almost commuting invertible matrices close to commuting in- vertible matrices in the normalised rank metric? The following well-known question is relevant to the present workshop. Ol’shanskiı̆] I... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,886 | OWR-14298365-012 | Classifying Thin Two-Generator Matrix Groups | Classify pairs $A,B\in\operatorname{GL}_n(\mathbb{Z})$, for $n\geq3$, such that $\langle A,B\rangle$ is thin in its Zariski closure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-012",
"literature-status:open",
"owr-year:2024"
] | Special families, notably hypergeometric monodromy, have been classified and generic thinness is known, but no classification of all pairs in GL n over the integers is available. | [
{
"url": "https://academic.oup.com/imrn/article/2017/17/5385/3056825",
"label": "generic thinness"
},
{
"url": "https://real.mtak.hu/212740/",
"label": "thin monodromy classification"
},
{
"url": "https://doi.org/10.4171/owr/2024/17",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Classify pairs $A,B\in\operatorname{GL}_n(\mathbb{Z})$, for $n\geq3$, such that $\langle A,B\rangle$ is thin in its Zariski closure. | Can we classify all pairs of matrices A, B in GLn (Z), for n \geq 3, such that the subgroup Γ = hA, Bi \subset G(Z) is thin? Questions by S. Eberhard. There were four questions posed by Eberhard. Three of them are marked as (Q1), (Q2), (Q3) in his extended abstract. The fourth one goes as follows. Question 5. What is t... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,887 | OWR-14298365-013 | Shortest Laws in Symmetric Groups | What is the asymptotic length of the shortest nontrivial law in the symmetric group $S_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-013",
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"owr-year:2024"
] | The exact asymptotic remains open: the current lower bound is five-halves times n minus a constant, while the best unconditional upper bound is exponential in an order of log n to the fourth times log log n; even superlinear growth is open. | [
{
"url": "https://arxiv.org/abs/2607.08557",
"label": "current lower bound"
},
{
"url": "https://ems.press/content/serial-article-files/53103?nt=1",
"label": "current upper bound"
},
{
"url": "https://arxiv.org/abs/1403.2324",
"label": "short laws"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | What is the asymptotic length of the shortest nontrivial law in the symmetric group $S_n$? | What is the length of the shortest law on Sn ? to determine the thinness of subgroup Γ, which to date, heavily relies on ping- pong lemma. That is, showing freeness by using ping-pong is the first major step towards thinness of Γ. Hence, the following is one of the most natural question to ask. Question 4. Can we class... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,888 | OWR-14298365-014 | Diameter and Product Structure in High-Rank Linear Groups | Can one prove improved diameter bounds for $\operatorname{SL}_n(\mathbb{F}_q)$, and what size and structure can be guaranteed for high powers of subsets with permutation-rich restrictions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | open | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-014",
"literature-status:open",
"owr-year:2024"
] | The proposed near-linear-log diameter and the associated product-structure question remain open; available classical-group bounds still have substantial rank dependence. | [
{
"url": "https://arxiv.org/abs/2110.02942",
"label": "classical-group diameter bounds"
},
{
"url": "https://ems.press/content/serial-article-files/49475",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Can one prove improved diameter bounds for $\operatorname{SL}_n(\mathbb{F}_q)$, and what size and structure can be guaranteed for high powers of subsets with permutation-rich restrictions? | Can we prove better bounds for diam(G) with G = SLn (Fq ), say O(1) (log |G|)(log n) ? What can we say about (Ak )(Σ) ? What about its struc- 100 ture? Questions by S. Eberhard. There were four questions posed by Eberhard. Three of them are marked as (Q1), (Q2), (Q3) in his extended abstract. The fourth one goes as fol... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,889 | OWR-14298365-015 | Random Expanders and Expanding Powers of Alternating Groups | Do random bounded generating sets produce expanders for alternating groups, and for which powers of alternating groups can one construct uniform expander families? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 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",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14298365-016"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-015",
"literature-status:partially-solved",
"owr-year:2024"
] | Bounded explicit expanders are known and random pairs have nonconstant spectral-gap and mixing results, while the bounded-random-generator question and optimal f of n remain unresolved. | [
{
"url": "https://arxiv.org/abs/1311.6742",
"label": "random generators"
},
{
"url": "https://arxiv.org/abs/math/0505624",
"label": "explicit expanders"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/5c03f705-7680-4cb6-b7cd-653d4b29494d/content",
"label": "OWR repor... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Do random bounded generating sets produce expanders for alternating groups, and for which powers of alternating groups can one construct uniform expander families? | Does a random generating set in Alt(n) give expanders? For what function f (n) does there exist an expanding generating set in Alt(n)f (n) ? Questions by H. Helfgott. There were two questions posed by Helfgott, going as follows. Question 6. Can we prove better bounds for diam(G) with G = SLn (Fq ), say O(1) (log |G|)(l... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,890 | OWR-14298365-016 | Duplicate Alternating-Group Expander-Power Question | By [7, Cor. 15] there is such a set for f (n) < exp((log n)k ) for any fixed k. There is no such set for f (n) ≫ n!, because the minimal number of generators is unbounded. It may be possible to have f (n) \approx exp(n0.001 ). A bottle of wine has been promised as reward for answering “yes” to Question 8 and “it must b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the power-of-alternating-groups question already represented canonically by OWR-14) | [
"OWR-14298365-015"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-016",
"literature-status:partially-solved",
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] | The extracted bounds establish a nontrivial range of f of n and an obstruction when f of n grows much faster than n factorial, but the threshold and order of f of n are unknown. | [
{
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"url": "https://arxiv.org/abs/1311.6742",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | null | By [7, Cor. 15] there is such a set for f (n) < exp((log n)k ) for any fixed k. There is no such set for f (n) ≫ n!, because the minimal number of generators is unbounded. It may be possible to have f (n) \approx exp(n0.001 ). A bottle of wine has been promised as reward for answering “yes” to Question 8 and “it must b... | unrecoverable | The official report confirms that this extraction repeats the power-of-alternating-groups question already represented canonically by OWR-14298365-015. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,891 | OWR-14298365-017 | Extremal Product-Free Sets in Quasirandom Groups | Determine the maximum density and structure of product-free subsets in finite quasirandom groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040](https://doi.org/10.4171/owr/2024/17)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,024 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298365-017",
"literature-status:partially-solved",
"owr-year:2024"
] | The proposed form is confirmed in alternating groups for large degree, where extremal families are Kedlaya-type, but the universal assertion for all finite groups with minimal representation dimension D remains open. | [
{
"url": "https://doi.org/10.1007/s00222-024-01273-1",
"label": "largest product-free subsets"
},
{
"url": "https://arxiv.org/abs/2401.15456",
"label": "product mixing"
},
{
"url": "https://ems.press/content/serial-article-files/49475",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/17 | null | null | null | Determine the maximum density and structure of product-free subsets in finite quasirandom groups. | Questions by N. Lifshitz. There was one question posed by Lifshitz, going as follows. In 1985, Babai and Sós [4] defined a set A \subseteq G to be product-free if xy \in / A for every x, y \in A. For instance, if G acts on a set X, for any x \in X and I \subseteq X the set kx,I = \{g \in G : g(x) \in I, g(I) \subseteq... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Growth and Expansion in Groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/17, pp. 1005--1040 |
30,005,892 | OWR-14298366-001 | Asymptotic Growth of a Matrix Cone Norm Constant | Determine the asymptotic growth of $C_n=\sup\{\gamma_+(A)/\lVert A\rVert_{(e,1)}:A\in\mathcal{C}^{n\times n},\ A\succeq0,\ A\neq0\}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226](https://doi.org/10.4171/owr/2024/21)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
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"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-14298366-001",
"literature-status:open",
"owr-year:2024"
] | The best cited bounds remain a constant times the square root of n below and order n above; the asymptotic growth of C n is not determined. | [
{
"url": "https://arxiv.org/abs/2405.06154",
"label": "Bandeira--Mixon--Steinerberger"
},
{
"url": "https://ems.press/content/serial-article-files/49476",
"label": "OWR report"
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{
"url": "https://arxiv.org/abs/2409.20372",
"label": "Balan--Jiang factorization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/21 | null | null | null | Determine the asymptotic growth of $C_n=\sup\{\gamma_+(A)/\lVert A\rVert_{(e,1)}:A\in\mathcal{C}^{n\times n},\ A\succeq0,\ A\neq0\}$. | What is the asymptotic growth of Cn ? Given n > 0, define \gamma+ (A) n\timesn Cn = sup : A\inC , A 0, A 6= 0 , kAk(e,1) \sqrt{ }During the workshop, Mixon, Steinerberger, and myself [6] showed that Cn \geq c n, for a universal constant c > 0. The best known upper bound is of order n. See references within [6] for more ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226 |
30,005,893 | OWR-14298366-005 | Global Convergence of Low-Rank Multi-Penalty Optimization | Under which restricted-isometry or related assumptions on the measurement operator does the iteratively reweighted least-squares algorithm for simultaneously sparse and low-rank matrix recovery converge globally? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226](https://doi.org/10.4171/owr/2024/21)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 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-14298366-005",
"literature-status:open",
"owr-year:2024"
] | The cited analysis gives local quadratic convergence under a restricted isometry condition and suitable initialization; global convergence under suitable sensing assumptions is explicitly left open. | [
{
"url": "https://ems.press/content/serial-article-files/49476",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1801.06240",
"label": "IRLS convergence"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/21 | null | null | null | Under which restricted-isometry or related assumptions on the measurement operator does the iteratively reweighted least-squares algorithm for simultaneously sparse and low-rank matrix recovery converge globally? | A major open question of this work is whether the analysis could be refined and whether one can show global convergence of the algorithm under suitable assumptions on A. 2. Multi-penalty optimization R Our second study considers the multi-penalty objective J\alpha,\beta : Rn1 \timesR \timesRn2 \timesR \to R defined as R ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226 |
30,005,894 | OWR-14298366-006 | Quantum Harmonic Analysis of Data Structure | Can quantum harmonic analysis explain structure in data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226](https://doi.org/10.4171/owr/2024/21)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 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-14298366-006",
"literature-status:open",
"owr-year:2024"
] | Quantum harmonic analysis now provides rigorous data-operator and effective-dimensionality tools, but the broad question of explaining structure in data remains open. | [
{
"url": "https://doi.org/10.1016/j.acha.2024.101692",
"label": "local structure and dimensionality"
},
{
"url": "https://arxiv.org/abs/2509.19474",
"label": "quantum harmonic analysis"
},
{
"url": "https://doi.org/10.4171/OWR/2024/21",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/21 | null | null | null | Can quantum harmonic analysis explain structure in data? | Can quantum harmonic analysis explain structure in data? Data, which we strive to use, interpret, classify, depend on some kind of repre- sentation. That means, that each data point is written in some dictionary of building blocks by means of coefficients. For high-dimensional, complex data sets, structured dimensionalit... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226 |
30,005,895 | OWR-14298366-007 | Learning Data Manifolds for Augmentation and Nonlinear Components | Can the underlying data manifold be learned using local entropy and correlation, can this improve data augmentation, and can nonlinear principal components exploit the manifold hypothesis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226](https://doi.org/10.4171/owr/2024/21)
## Literature review (checked 2026-08-... | 3 | open | null | 2,024 | 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-14298366-007",
"literature-status:open",
"owr-year:2024"
] | Existing methods give model-specific manifold-aware augmentation and representation guarantees, but no general method answers all the listed learning and optimality questions; they remain open. | [
{
"url": "https://ems.press/content/serial-article-files/49476",
"label": "OWR report"
},
{
"url": "https://proceedings.mlr.press/v235/kaufman24a.html",
"label": "manifold augmentation"
},
{
"url": "https://doi.org/10.1016/j.acha.2024.101692",
"label": "quantum harmonic analysis"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/21 | null | null | null | Can the underlying data manifold be learned using local entropy and correlation, can this improve data augmentation, and can nonlinear principal components exploit the manifold hypothesis? | Future work and open questions include the hypothesis, that correct augmen- tation augments along data manifold. Can we possibly learn an underlying data manifold from data by using concepts of local entropy and local correlation? Can this help to improve augmentation strategies? Is it possible to use the concept of no... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226 |
30,005,896 | OWR-14298366-008 | Pre-Asymptotic Sampling Numbers of Barron Spaces | Determine the asymptotic nonlinear sampling numbers for variational Barron spaces. For the Fourier-analytic spaces $U_d^\alpha$, determine the pre-asymptotic dependence of $\sigma_m(U_d^\alpha)_{L^p}$ on $d$ and $m$, and determine the optimal reconstruction error when the sample points are uniform random points. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226](https://doi.org/10.4171/owr/2024/21)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,024 | 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-14298366-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Sharp asymptotic sampling rates up to logarithmic factors are proved, but the pre-asymptotic dependence on dimension and sample count remains open. | [
{
"url": "https://arxiv.org/abs/2208.07605",
"label": "Voigtlaender et al., Barron sampling numbers"
},
{
"url": "https://doi.org/10.4171/owr/2024/21",
"label": "Oberwolfach Report 21/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/21 | null | null | null | Determine the asymptotic nonlinear sampling numbers for variational Barron spaces. For the Fourier-analytic spaces $U_d^\alpha$, determine the pre-asymptotic dependence of $\sigma_m(U_d^\alpha)_{L^p}$ on $d$ and $m$, and determine the optimal reconstruction error when the sample points are uniform random points. | ○ Remark (Open questions). The (metric) entropy numbers and the nonlinear dictionary approximation rates of these spaces have been studied in [13], but the question of the asymptotic behavior of the (non-linear) sampling numbers for these spaces is still open, to the best of the knowledge of the present author. ○2 Igno... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Applied Harmonic Analysis and Data Science (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/21, pp. 1163--1226 |
30,005,897 | OWR-14298367-003 | Shadowing Without Bounded Distortion | For dissipative composition operators without bounded distortion, is generalized hyperbolicity equivalent to the shadowing property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096](https://doi.org/10.417... | 3 | open | null | 2,024 | 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://zenodo.org/records/23041948",
"checked_at": "2026-09-29",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-29] I have released an unrefereed preprint, **Shadowing and Generalized Hyperbolicity for Dissipative Composition Operators without Bounded Distortion** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23041948) | [
"owr",
"oberwolfach-reports",
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"literature-status:open",
"owr-year:2024"
] | The equivalence and full shadowing characterization are proved for dissipative composition systems with bounded distortion, but the no-bounded-distortion case remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.jde.2021.06.038",
"label": "D'Aniello, Darji and Maiuriello"
},
{
"url": "https://doi.org/10.4171/owr/2024/19",
"label": "Oberwolfach Report 19/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/19 | null | null | null | For dissipative composition operators without bounded distortion, is generalized hyperbolicity equivalent to the shadowing property? | Open Problems: (1) In a dissipative setting without bounded distortion, does the characterization provided in [1] for the shadowing property still hold? Is it still true that a com- position operator is generalized hyperbolic if and only if it has the shadowing property? Linear Dynamics, Universality, and the Invariant... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096 |
30,005,898 | OWR-14298367-005 | Weighted-Shift Supercyclicity Converse | What about the other way around? How about supercyclicity and R-supercyclicity? Is the following true? Linear Dynamics, Universality, and the Invariant Subspace Problem 1083 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096](https://doi.org/10.417... | 3 | partially_solved | null | 2,024 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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 official report asks whether supercyclicity of the associated weighted shift implies supercyclicity of the composition operator and imme) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298367-005",
"literature-status:partially-solved",
"owr-year:2024"
] | The converse factor comparison is proved for hypercyclicity and for real and complex supercyclicity in the dissipative bounded-distortion setting, but not as a general theorem for arbitrary factors. | [
{
"url": "https://arxiv.org/abs/2404.04028",
"label": "D'Aniello and Maiuriello, supercyclicity"
},
{
"url": "https://arxiv.org/abs/2107.12103",
"label": "D'Aniello, Darji and Maiuriello, shift-like operators"
},
{
"url": "https://doi.org/10.4171/owr/2024/19",
"label": "Oberwolfach R... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/19 | null | null | null | null | What about the other way around? How about supercyclicity and R-supercyclicity? Is the following true? Linear Dynamics, Universality, and the Invariant Subspace Problem 1083 | unrecoverable | The official report asks whether supercyclicity of the associated weighted shift implies supercyclicity of the composition operator and immediately answers yes with proved theorems. | null | null | null | null | null | Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096 |
30,005,899 | OWR-14298367-006 | $\Gamma$-Supercyclicity of Composition Operators and Weighted Shifts | Let $T_f$ be a dissipative composition operator of bounded distortion and let $B_w$ be its associated weighted shift. For which subsets $\Gamma\subseteq\mathbb C$ is $T_f$ $\Gamma$-supercyclic if and only if $B_w$ is $\Gamma$-supercyclic? In particular, does this equivalence hold for every $\Gamma\subseteq\mathbb C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096](https://doi.org/10.417... | 3 | solved | null | 2,024 | 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"
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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 | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes, for every Γ ⊆ C)**. E. D'Aniello (joint with M. Maiuriello; OWR 19/2024, p. 1083) asks whether "T_f Γ-supercyclic ⇔ B_w Γ-supercyclic" holds for every Γ, for dissipative composition operators of bounded distortion on a separable L^p(μ). It does; the short arg... | [
"owr",
"oberwolfach-reports",
"OWR-14298367-006",
"literature-status:open",
"owr-year:2024"
] | The equivalence for arbitrary subsets of scalar multipliers remains an open problem; existing results cover only several special multiplier sets. | [
{
"url": "https://doi.org/10.4171/owr/2024/19",
"label": "Oberwolfach Report 19/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/19 | null | null | null | Let $T_f$ be a dissipative composition operator of bounded distortion and let $B_w$ be its associated weighted shift. For which subsets $\Gamma\subseteq\mathbb C$ is $T_f$ $\Gamma$-supercyclic if and only if $B_w$ is $\Gamma$-supercyclic? In particular, does this equivalence hold for every $\Gamma\subseteq\mathbb C$? | Open Problem. then Tf is R-supercyclic and, therefore, C-supercyclic. The same as for hypercyclicity happens with R- and C-supercyclicity: Theorem ([7, Theorem 4.5]) [R-supercyclicity: shift-like behaviour] Let (X, B, µ, f, Tf ) be a dissipative composition dynamical system of bounded dis- tortion generated by W . The ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: New Horizons in Linear Dynamics, Universality, and the Invariant Subspace Problem (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/19, pp. 1069--1096 |
30,005,900 | OWR-14298368-002 | Perverse-Weight Correspondence for Singular Dolbeault Moduli Spaces | Does the $PI=WI$ conjecture hold for the intersection cohomology of singular Dolbeault moduli spaces $M_{\mathrm{Dol}}(n,d)$? In particular, does curious hard Lefschetz hold for arbitrary degree $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/16, pp. 949--1004](https://doi.org/10.4171/owr/2024/16)
... | 3 | partially_solved | null | 2,024 | 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-14298368-002",
"literature-status:partially-solved",
"owr-year:2024"
] | The intersection version is proved in special cases, including symplectic-resolution cases, while the general singular and non-coprime case remains open. | [
{
"url": "https://doi.org/10.5802/jep.196",
"label": "Felisetti and Mauri, PI=WI for symplectic resolutions"
},
{
"url": "https://doi.org/10.1007/s40574-024-00420-z",
"label": "Felisetti, P=W phenomena survey"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/16 | null | null | null | Does the $PI=WI$ conjecture hold for the intersection cohomology of singular Dolbeault moduli spaces $M_{\mathrm{Dol}}(n,d)$? In particular, does curious hard Lefschetz hold for arbitrary degree $d$? | case d = 0. In all these cases, however, the moduli space MDol (n, d) is singular, and Poincaré duality and relative hard Lefschetz theorems fail in general for sin- gular cohomology. These symmetries can be restored taking instead intersection cohomology. In [5, Question 4.1.7], de Cataldo and Maulik proposed the PI=... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/16, pp. 949--1004 |
30,005,901 | OWR-14298369-001 | Bioinformatic Frontiers in Complex-System Epigenetics | Which bioinformatic and mathematical problems are central to understanding epigenetics as a complex dynamical system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Entropic AI in the Natural Sciences (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/18, pp. 1041--1068](https://doi.org/10.4171/owr/2024/18)
## Literature r... | 3 | open | null | 2,024 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 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-14298369-001",
"literature-status:open",
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] | This broad future-direction question has no unique established solution; current literature identifies single-cell and multimodal epigenomic integration, spatial context, and causal interpretation as continuing challenges. | [
{
"url": "https://www.nature.com/articles/s41580-023-00615-w",
"label": "Argelaguet et al., single-cell multi-omics"
},
{
"url": "https://www.nature.com/articles/s12276-024-01186-2",
"label": "Single-cell and multimodal omics review"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/18 | null | null | null | Which bioinformatic and mathematical problems are central to understanding epigenetics as a complex dynamical system? | What is the next step in the field of bioinformatics to explore and understand epigenetics in complex life systems? Mini-Workshop: Mathematics of Entropic AI in the Natural Sciences 1065 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Mathematics of Entropic AI in the Natural Sciences (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/18, pp. 1041--1068 |
30,005,902 | OWR-14298370-002 | Vanishing Lie Brackets for Non-Quasitriangular Hopf Algebras | For a Hopf algebra whose module category is not braided, is the graded Lie bracket on its positive-degree cohomology always zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | solved | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.2140/pjm.2022.316.395",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; implicit in published results)**. S. Witherspoon (OWR 20/2024, p. 1116) recalls that the Lie bracket on Hopf algebra cohomology H\*(A, k) vanishes when A-mod is braided; otherwise "it is unknown whether this Lie bracket is always 0." It is not (the deduction i... | [
"owr",
"oberwolfach-reports",
"OWR-14298370-002",
"literature-status:open",
"owr-year:2024"
] | The bracket vanishes for braided and several non-quasitriangular examples, but whether it always vanishes for non-quasitriangular Hopf algebras remains unknown. | [
{
"url": "https://doi.org/10.1090/memo/1151",
"label": "Hermann, monoidal categories and the Gerstenhaber bracket"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2021.106903",
"label": "Karadag, Gerstenhaber brackets on Hopf algebras"
},
{
"url": "https://doi.org/10.4171/owr/2024/20",
"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | For a Hopf algebra whose module category is not braided, is the graded Lie bracket on its positive-degree cohomology always zero? | We close with a brief summary of some recent results on Lie brackets and some open questions. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,903 | OWR-14298370-003 | Strict Convergent Quantization of Poisson Structures | Which Poisson structures admit strict convergent quantizations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298370-003",
"literature-status:partially-solved",
"owr-year:2024"
] | Strict convergent quantizations are constructed for broad polynomial Poisson classes, but no general construction for arbitrary Poisson structures or classes is known. | [
{
"url": "https://doi.org/10.1007/s00220-022-04541-4",
"label": "Barmeier and Schmitt, strict quantization"
},
{
"url": "https://doi.org/10.4171/owr/2024/20",
"label": "Oberwolfach Report 20/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Which Poisson structures admit strict convergent quantizations? | It is a widely open problem to find “strict” convergent quantizations for (classes of) Poisson structures. where CΛ is a formal power series of differential operators associated to a certain graph Λ. In [BS23] we used the results of [BWa , Ch. 10] in combination with tools from functional analysis to extend convergent ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,904 | OWR-14298370-004 | Balmer Spectra of Stable Finite Tensor Categories | Describe the Balmer spectrum of the stable category of a finite tensor category in terms of its cohomology ring. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 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-14298370-004",
"literature-status:partially-solved",
"owr-year:2024"
] | The Balmer-spectrum conjecture is established for important cocommutative and related cases, but the finite-tensor-category statement remains open in general. | [
{
"url": "https://arxiv.org/abs/2209.11621",
"label": "Nakano, Vashaw and Yakimov"
},
{
"url": "https://doi.org/10.4171/owr/2024/20",
"label": "Oberwolfach Report 20/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Describe the Balmer spectrum of the stable category of a finite tensor category in terms of its cohomology ring. | One motivation for the finite generation question is that one expects to express the Balmer spectrum of the corresponding stable category, which is small tensor triangulated, in terms of the cohomology ring: Conjecture (Nakano-Vashaw-Yakimov, ’21). The report passage is retained verbatim as the relevant context for thi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,905 | OWR-14298370-005 | Hochschild and Categorical Entropy in dg Dynamics | When does Hochschild (co)homology entropy of a dg categorical dynamical system coincide with the entropy of the corresponding categorical dynamical system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 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-14298370-005",
"literature-status:partially-solved",
"owr-year:2024"
] | Equality of Hochschild and categorical entropy is proved for Serre functors in broad higher-hereditary and twisted fractionally Calabi--Yau cases, but the general dg-categorical question remains open. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.03.031",
"label": "Han, entropies of Serre functors"
},
{
"url": "https://doi.org/10.1007/s40598-022-00210-5",
"label": "Kikuta and Ouchi, Hochschild entropy"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | When does Hochschild (co)homology entropy of a dg categorical dynamical system coincide with the entropy of the corresponding categorical dynamical system? | question ([9, Question 2.13]): When does the Hochschild (co)homology entropy for a “dg categorical dynamical system” coincide with the entropy for the corresponding categorical dynamical system? As a generalization of representation-finite hereditary algebras, Iyama and Op- permann introduced higher representation-fini... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,906 | OWR-14298370-006 | Fractional Calabi–Yau Properties of Higher Representation-Finite Algebras | Is every higher representation-finite algebra, or more generally every twisted fractionally Calabi–Yau algebra, fractionally Calabi–Yau? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,024 | 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-14298370-006",
"literature-status:open",
"owr-year:2024"
] | Higher representation-finite algebras are known to be twisted fractionally Calabi--Yau, but it is still unknown whether every such algebra is fractionally Calabi--Yau. | [
{
"url": "https://doi.org/10.1112/blms/bdq101",
"label": "Herschend and Iyama"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2024.03.031",
"label": "Han, entropies of Serre functors"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Is every higher representation-finite algebra, or more generally every twisted fractionally Calabi–Yau algebra, fractionally Calabi–Yau? | (2) the polynomial entropy of Serre functor hpol t (S) = 0. • (3) the Hochschild (co)homology entropy of Serre quasi-functor hHH (S̃) = HH• h (S̃) = 0 if we assume further that A is elementary. Theorem 1 (1) and (2) generalize the corresponding results [2, 2.6.1] and [3, Re- mark 6.3] for fractionally Calabi-Yau algebr... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,907 | OWR-14298370-007 | Carlsson’s Homology Bound for Free Group Actions | If an elementary abelian $p$-group $G\cong(\mathbb{Z}/p\mathbb{Z})^d$ acts freely on a nontrivial finite CW complex $X$, must $\sum_n\dim_kH_n(X;k)\geq2^d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 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-14298370-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Carlsson's topological bound is proved in several low-rank and special cases, but remains open in general; the associated algebraic conjecture is disproved for odd primes of rank at least eight. | [
{
"url": "https://doi.org/10.4171/JNCG/564",
"label": "Bergh, homology over finite tensor categories"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2022.107023",
"label": "Ruping and Stephan, nonrealizable complexes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | If an elementary abelian $p$-group $G\cong(\mathbb{Z}/p\mathbb{Z})^d$ acts freely on a nontrivial finite CW complex $X$, must $\sum_n\dim_kH_n(X;k)\geq2^d$? | Carlsson settled the case when p = 2 and d is at most 3 in [4], but the conjecture remains open at the time of writing. Complexes with small homology Petter Andreas Bergh Our starting point is a conjecture from algebraic topology by Gunnar Carlsson. Let p be a prime number and G an elementary abelian p-group of rank d;... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,908 | OWR-14298370-008 | Cohomological Finite Generation for Finite Tensor Categories | Does every finite tensor category have finitely generated cohomology, and what homological lower bounds analogous to Carlsson's conjecture hold for its perfect complexes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298370-008",
"literature-status:partially-solved",
"owr-year:2024"
] | Cohomological finite generation is proved for several classes of finite tensor categories, but the Etingof--Ostrik conjecture for arbitrary finite tensor categories remains unresolved. | [
{
"url": "https://arxiv.org/abs/2209.11621",
"label": "Nakano, Vashaw and Yakimov"
},
{
"url": "https://doi.org/10.4171/owr/2024/20",
"label": "Oberwolfach Report 20/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Does every finite tensor category have finitely generated cohomology, and what homological lower bounds analogous to Carlsson's conjecture hold for its perfect complexes? | conjecture. In recent work, we have proved a version of Carlson’s result for complexes over a finite tensor category (C , ⊗, 1). Thus C is a locally finite k-linear abelian category (for some field k), with a finite set of isomorphism classes of simple objects. There are enough projective objects, and every object admi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,909 | OWR-14298370-009 | Heisenberg Actions on Hochschild–Serre Cohomology | Is there a Heisenberg algebra controlling the Hochschild–Serre cohomology of symmetric quotient stacks? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298370-009",
"literature-status:open",
"owr-year:2024"
] | Heisenberg/Fock-space structures are known for related Grothendieck and Hochschild-homology constructions, but the requested structure for Hochschild--Serre cohomology is not established. | [
{
"url": "https://arxiv.org/abs/2309.06244",
"label": "Belmans, Fu and Krug, Hochschild cohomology of Hilbert schemes"
},
{
"url": "https://arxiv.org/abs/2512.25039",
"label": "Anno, Baranovsky and Logvinenko, Hochschild homology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Is there a Heisenberg algebra controlling the Hochschild–Serre cohomology of symmetric quotient stacks? | Is there a Heisenberg algebra controlling the Hochschild–Serre cohomology of symmetric quotient stacks? To prove (2) we take k = 0, so that all of the negative Hochschild–Serre cohomol- ogy of S is used, and subsequently we take ∗ = 2 to compute HH2 (Hilbn S). To obtain the geometric deformations in the Hochschild–Kost... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,910 | OWR-14298370-011 | Explicit Deformation Algebras for Operated Structures | Construct explicitly the dg Lie or $L_\infty$ algebra governing deformations of operated algebraic structures, and develop their homotopy versions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162](https://doi.org/10.4171/owr/2024/20)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,024 | 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-14298370-011",
"literature-status:partially-solved",
"owr-year:2024"
] | General deformation theory guarantees controlling L-infinity structures, and explicit constructions exist for broad operated-algebra classes, but a general explicit small model remains a research problem. | [
{
"url": "https://arxiv.org/2305.20036",
"label": "Dinh Van, Lowen and Hermans, box operads"
},
{
"url": "https://doi.org/10.4171/owr/2024/20",
"label": "Oberwolfach Report 20/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/20 | null | null | null | Construct explicitly the dg Lie or $L_\infty$ algebra governing deformations of operated algebraic structures, and develop their homotopy versions. | It is an important problem to construct explicitly the dg Lie algebra or L\infty -algebra governing deformation theory of the mathematical object under consideration. Another important problem about algebraic structures is to study their ho- motopy versions, just like A\infty -algebras for usual associative algebras. I... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hochschild (Co)Homology and Applications (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/20, pp. 1097--1162 |
30,005,911 | OWR-14298371-001 | Near-Linear Subgraph Isomorphism for Acyclic Patterns | Can constant-pattern subgraph isomorphism be solved in near-linear time if and only if the pattern graph is acyclic, and can the surrounding fine-grained conjectures be unified? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,024 | 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-14298371-001",
"literature-status:open",
"owr-year:2024"
] | Forests admit linear-time color-coding algorithms, and conditional lower bounds cover all cycles, but the full near-linear iff-acyclic characterization is not proved, especially for patterns containing even cycles. | [
{
"url": "https://arxiv.org/abs/2204.10465",
"label": "Abboud et al., short-cycle removal"
},
{
"url": "https://doi.org/10.4171/owr/2024/27",
"label": "Oberwolfach Report 27/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Can constant-pattern subgraph isomorphism be solved in near-linear time if and only if the pattern graph is acyclic, and can the surrounding fine-grained conjectures be unified? | As an example, we will present an open question asking whether subgraph isomorphism, i.e. checking whether a constant-size pattern graph H exists as a subgraph of an input graph G, can be solved in near-linear time if and only if H is acyclic. Why this many conjectures? Can we unify them? The report passage is retained... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,912 | OWR-14298371-002 | Mixing Times from Spectral Independence | How rapidly do Markov chains mix under spectral independence, and when can the general polynomial bound be improved to the optimal $O(n\log n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,024 | 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-14298371-002",
"literature-status:partially-solved",
"owr-year:2024"
] | Spectral independence gives polynomial or near-optimal mixing bounds under explicit correlation and graphical hypotheses, but no general mixing-time characterization is known. | [
{
"url": "https://doi.org/10.1137/1.9781611976465.95",
"label": "Feng, Guo, Yin and Zhang, spectral independence"
},
{
"url": "https://doi.org/10.4171/owr/2024/27",
"label": "Oberwolfach Report 27/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | How rapidly do Markov chains mix under spectral independence, and when can the general polynomial bound be improved to the optimal $O(n\log n)$? | Since each step can be implemented efficiently, the fundamental question is how long to simulate the chain. We say µ is η-spectrally independent if \lambdamax (Ψµ ) \leq 1 + η. Note that Ψµ = Dµ−1 Σµ , where Σµ (i, j) = Cov\sigma\simµ (\sigmai , \sigmaj ) is the usual covari- ance matrix, and Dµ is a diagonal matrix wi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,913 | OWR-14298371-003 | Mixing of Random Colorings on General Graphs | Establish spatial and temporal mixing properties for random proper colorings on general graphs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,024 | 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-14298371-003",
"literature-status:open",
"owr-year:2024"
] | Spatial and temporal mixing are proved in important regimes such as large girth or sufficiently many colors, but the general-graph coloring problem remains open. | [
{
"url": "https://arxiv.org/abs/2007.08091",
"label": "Feng, Guo, Yin and Zhang, colorings"
},
{
"url": "https://doi.org/10.4171/owr/2024/27",
"label": "Oberwolfach Report 27/2024"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Establish spatial and temporal mixing properties for random proper colorings on general graphs. | We conclude with an open problem. Es- tablishing various spatial and temporal mixing properties of random colorings on general graphs is a major open problem in approximate counting and sampling. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,914 | OWR-14298371-004 | The Erdős–Rado Sunflower Conjecture | Does the Erdős–Rado sunflower conjecture hold with the conjectured exponential bound on the size of sunflower-free uniform set systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298371-004",
"literature-status:open",
"owr-year:2024"
] | The Alweiss--Lovett--Wu--Zhang theorem gives the major quantitative improvement, but it does not prove the Erdos--Rado sunflower conjecture; the current 2026 survey still records the conjecture as open. | [
{
"url": "https://annals.math.princeton.edu/2021/194-3/p05",
"label": "Alweiss--Lovett--Wu--Zhang"
},
{
"url": "https://doi.org/10.1112/jlms.70380",
"label": "Rao 2026 survey"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Does the Erdős–Rado sunflower conjecture hold with the conjectured exponential bound on the size of sunflower-free uniform set systems? | In this survey talk, we discuss the connection between Alweiss-Lovett-Wu-Zhang’s breakthrough [1] on the Erdos-Rado Sunflower Conjecture and the recent develop- ments around thresholds in probabilistic combinatorics, including the resolution of a conjecture of Talagrand due to Frankston-Kahn-Narayanan-Park [2] and the ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
30,005,915 | OWR-14298371-006 | The Graphic Kahn–Kalai Conjecture | Is there a universal $K>0$ such that, for every $H\subseteq K_n$, $p\geq Kp_E(H)\log v(H)$ implies $\Pr(G_{n,p}\supseteq H)\geq1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562](https://doi.org/10.4171/owr/2024/27)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,024 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298371-006",
"literature-status:open",
"owr-year:2024"
] | The graphic Kahn--Kalai conjecture remains unresolved: recent work proves only a weaker logarithmic bound and explicitly leaves the conjectured stronger graph statement open. | [
{
"url": "https://arxiv.org/abs/2508.14269",
"label": "Dubroff--Kahn--Park"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/55937c4f-e831-4c4d-b8ee-73369eb5d131/content",
"label": "OWR 2024/27"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/27 | null | null | null | Is there a universal $K>0$ such that, for every $H\subseteq K_n$, $p\geq Kp_E(H)\log v(H)$ implies $\Pr(G_{n,p}\supseteq H)\geq1/2$? | As a final remark, we note that the “graphic” Kahn-Kalai Conjecture, which was the original motivation for Theorem 6, is still open. We define the graphic expectation threshold for a graph H to be pE (H) := min\{p : E [\#F ’s in Gn,p ] \geq 1 \forallF \subseteq H\}. Conjecture 7. (Conjecture 2 in [3]) There exists K > ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complexity Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2024/27, pp. 1517--1562 |
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