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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,016 | OWR-9790358-014 | Universal Four-Point Polynomial Interpolation Subspaces | What is the minimum size of a family of four-dimensional subspaces of $K[x,y]$ such that every set of four planar points admits arbitrary-data interpolation in at least one member of the family? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428](https://doi.org/10.4171/owr/2022/7)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790358-014",
"literature-status:open",
"owr-year:2022"
] | The extracted question asks for the minimum number of four-dimensional polynomial subspaces that collectively interpolate every four-point set; no general determination of that minimum was found. | [
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR interpolation report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | What is the minimum size of a family of four-dimensional subspaces of $K[x,y]$ such that every set of four planar points admits arbitrary-data interpolation in at least one member of the family? | What is the corresponding minimal number of four-dimensional subspaces of K[x, y] with the property that at least one of them will interpolate functions for any set of four points? Dimensions of Spline spaces. (Schenck) Let ∆ be a simplicial subdivision (triangulation) of a simply connected bounded domain in the plane ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,017 | OWR-9790358-015 | Equations of Three-Dimensional Wachspress Varieties | For a polytope $P\subset\mathbb R^3$, its Wachspress coordinates define a rational map to projective space with one coordinate for each vertex of $P$. What are the homogeneous equations of the Zariski closure of its image, and what are the higher-dimensional analogues? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428](https://doi.org/10.4171/owr/2022/7)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790358-015",
"literature-status:open",
"owr-year:2022"
] | For mean-value barycentric coordinates, the algebraicity and basic properties are known, but a general set of homogeneous equations for the Zariski closure requested in the record remains an open research problem. | [
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR barycentric-coordinate problem session"
},
{
"url": "https://doi.org/10.2140/ant.2014.8.369",
"label": "Irving--Schenck, related Wachspress surfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | For a polytope $P\subset\mathbb R^3$, its Wachspress coordinates define a rational map to projective space with one coordinate for each vertex of $P$. What are the homogeneous equations of the Zariski closure of its image, and what are the higher-dimensional analogues? | What are the homogeneous equations for the Zariski closure of the image? It is not hard to see that an upper bound is provided by the spans of monomials corresponding to the five partitions of 4, K\{1, x, x2 , x3 \} , K\{1, x, x2 , y\} , K\{1, x, y, xy\} , K\{1, x, y, y 2 \} , K\{1, y, y 2, y 3 \} . Also, at least thre... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,018 | OWR-9790358-016 | Mean-Value Coordinate Equations and Wachspress-Surface Moduli | For an $n$-gon, determine the homogeneous equations of the Zariski closure of the image of the mean-value barycentric-coordinate map to $\mathbb P^{n-1}$. For Wachspress surfaces arising from $n$-gons, describe flat limits under polygon degeneration and construct a natural compactified moduli space. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428](https://doi.org/10.4171/owr/2022/7)
## Literature review (checke... | 3 | partially_solved | null | 2,022 | 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 | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **Algebraic Relations Among Mean Value Coordinates: A Complete Answer for Quadrilaterals and Partial Results for Larger Polygons** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23064820) | [
"owr",
"oberwolfach-reports",
"OWR-9790358-016",
"literature-status:partially-solved",
"owr-year:2022"
] | Projective and adjoint theory now describes Wachspress maps and varieties in broad generality and gives substantial three-dimensional results, but equations and a complete description in arbitrary higher dimensions remain open. | [
{
"url": "https://arxiv.org/abs/1904.02123",
"label": "Kohn--Ranestad, projective geometry of Wachspress coordinates"
},
{
"url": "https://doi.org/10.1007/s10208-019-09441-z",
"label": "Kohn--Ranestad, Wachspress-coordinate map"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | For an $n$-gon, determine the homogeneous equations of the Zariski closure of the image of the mean-value barycentric-coordinate map to $\mathbb P^{n-1}$. For Wachspress surfaces arising from $n$-gons, describe flat limits under polygon degeneration and construct a natural compactified moduli space. | What about in higher dimensions? Mean-value coordinates. (Sottile, but inspired by Schafer’s talk) Given a polygon with n sides in the plane, there are mean-value barycentric co- ordinates \betav , one for each vertex v of the polygon. These define a map from the polygon to the affine plane in Rn where the sum of the c... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,019 | OWR-9790358-018 | Relations among Adjoint Curves from Cyclic Point Orders | Given $n$ points in $\mathbb P^2$, each cyclic ordering up to reversal defines an $n$-gon and hence an adjoint curve. How are the adjoint curves arising from the $(n-1)!/2$ orderings related? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428](https://doi.org/10.4171/owr/2022/7)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790358-018",
"literature-status:open",
"owr-year:2022"
] | The question compares adjoint curves arising from different cyclic orders on the same point set; the 2024 heptagon result resolves the generic degree of one adjoint map but not the general relations among these curves. | [
{
"url": "https://arxiv.org/abs/2408.15759",
"label": "Agostini--Plaumann--Sinn--Wesner, heptagon adjoints"
},
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR adjoints problem session"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Given $n$ points in $\mathbb P^2$, each cyclic ordering up to reversal defines an $n$-gon and hence an adjoint curve. How are the adjoint curves arising from the $(n-1)!/2$ orderings related? | How are their adjoint curves related? Mini-Workshop: Interpolation, Approximation, and Algebra 425 Aluffi’s adjoint of a toric variety. (Schenck) Toric varieties have well-understood Weil divisors (which are torus orbits). It would be good to understand Aluffi’s formula in this case, as presented in Kohn’s talk. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,020 | OWR-9790359-001 | LOCAL Coloring Complexity and Constant-Round Decidability on Trees | Determine the LOCAL complexity of $(\Delta+1)$-coloring. Also decide whether an arbitrary locally checkable labeling problem on trees admits a constant-round algorithm. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | partially_solved | null | 2,022 | 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-9790359-001",
"literature-status:partially-solved",
"owr-year:2022"
] | The LOCAL complexity of (\Delta+1)-coloring has improved substantially, but its optimal complexity is still open; constant-round decidability is known on paths and cycles, while the corresponding general tree question remains unresolved. | [
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.18",
"label": "Chang--Pettie--Suomela, LCL complexity on trees"
},
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol361-opodis2025/LIPIcs.OPODIS.2025.23/LIPIcs.OPODIS.2025.23.pdf",
"label": "2025 distrib... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Determine the LOCAL complexity of $(\Delta+1)$-coloring. Also decide whether an arbitrary locally checkable labeling problem on trees admits a constant-round algorithm. | on the lower bound side nothing better is known than the 30-year-old Ω(log∗ n) lower bound, leading us to one of the big open problems in the LOCAL model. Open Problem 1. What is the LOCAL complexity of (∆ + 1)-coloring? In particular, the following simple question is wide open. Open Problem 2. Is it decidable whether,... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,021 | OWR-9790359-002 | Six Problems in Borel Graph Combinatorics | Resolve the following questions for Borel graphs: (1) a Borel Lovász Local Lemma for graphs generated by amenable-group actions; (2) uniqueness of Lebesgue measure among finitely additive measures on Borel subsets of $S^n$ for $n\geq2$; (3) existence of unfriendly Borel colorings for every bounded-degree Borel graph; (... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | partially_solved | null | 2,022 | 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-9790359-002",
"literature-status:partially-solved",
"owr-year:2022"
] | Several listed questions have major partial or complete results, including measurable Lovász Local Lemma variants, measurable edge colorings, and the classical Banach--Ruziewicz problem; the full Borel and Bernoulli-shift questions in the list remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR descriptive-combinatorics report"
},
{
"url": "https://doi.org/10.1016/j.aam.2019.06.031",
"label": "Bernshteyn, measurable Lovász Local Lemma"
},
{
"url": "https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-s... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Resolve the following questions for Borel graphs: (1) a Borel Lovász Local Lemma for graphs generated by amenable-group actions; (2) uniqueness of Lebesgue measure among finitely additive measures on Borel subsets of $S^n$ for $n\geq2$; (3) existence of unfriendly Borel colorings for every bounded-degree Borel graph; (... | We also discuss some open problems: • Is there a Borel version of the Lovász Local Lemma for graphs generated by actions of amenable groups? • The Borel Ruziewicz problem: is Lebesgue measure the only finitely ad- ditive measure defined on the Borel subsets of the n-sphere for n \geq 2? • Does every bounded degree Borel... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,022 | OWR-9790359-003 | Open Problems in Local Graph Complexity | Classify finitary-factor-of-independent-and-identically-distributed complexity; characterize derandomization on graph classes; determine the limits of Borel and continuous Lovász Local Lemmas; construct finitary-factor-of-independent-and-identically-distributed perfect matchings on trees; decide when Borel unfriendly c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-003",
"literature-status:open",
"owr-year:2022"
] | The record is an intentionally broad list of open problems in finitary factors, Borel colorings, and general complexity theory; progress on individual instances does not settle the general questions stated. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR descriptive-combinatorics report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Classify finitary-factor-of-independent-and-identically-distributed complexity; characterize derandomization on graph classes; determine the limits of Borel and continuous Lovász Local Lemmas; construct finitary-factor-of-independent-and-identically-distributed perfect matchings on trees; decide when Borel unfriendly c... | Next, we collect the open problems, see also [1, 2, 3, 4, 5, 6, 7, 8]: Finitary fiid The finitary factor of iid formalism [8], or equivalently the model of uniform local algorithms [7], offers finer scale to measure complexity of local problems than the one provided by the LOCAL model of distributed computing. Is there a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,023 | OWR-9790359-004 | Constraint-Satisfaction Table Caption | Does a CSP have a well-behaved solution? 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:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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 the extraction is a table caption summarizing a taxonomy, not a standalone open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790359-004",
"literature-status:open",
"owr-year:2022"
] | The extracted question `Does a CSP have a well-behaved solution?' lacks the definitions and hypotheses needed for a specific theorem; no determinate resolution can be assigned, so it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR descriptive-combinatorics report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | null | Does a CSP have a well-behaved solution? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that the extraction is a table caption summarizing a taxonomy, not a standalone open mathematical problem. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,024 | OWR-9790359-005 | Finite-Mean Coding Radius for Finitely Dependent Processes | Does there exist a finitely dependent invariant process that is not a finitary factor of any i.i.d. process with finite expected coding radius? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-005",
"literature-status:open",
"owr-year:2022"
] | Every finitely dependent invariant process on a transitive amenable graph is known to be ffiid, and examples with finite-mean or exponential coding tails exist, but the existence of a finitely dependent process with no finite-expected-radius ffiid representation remains unresolved. | [
{
"url": "https://doi.org/10.1214/19-AOP1363",
"label": "Holroyd--Hutchcroft--Levy, finite-mean examples"
},
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR finitary-process report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Does there exist a finitely dependent invariant process that is not a finitary factor of any i.i.d. process with finite expected coding radius? | An interesting open problem is whether there exists a finitely dependent invariant process which cannot be expressed as an ffiid with finite expected coding radius. Markov random fields. Another class of processes of interest are Markov ran- dom fields (MRFs), which are the higher dimensional analogue of Markov chains. Thes... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,025 | OWR-9790359-006 | Finitary-Factor Characterization of Markov Random Fields | Characterize the invariant Markov random fields that are finitary factors of independent and identically distributed processes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-006",
"literature-status:open",
"owr-year:2022"
] | Ffiid characterizations are known for important classes such as spatially mixing models and selected Ising regimes, but no classification of all Markov random fields is available. | [
{
"url": "https://arxiv.org/abs/1803.10578",
"label": "Spinka, finitary codings for spatially mixing MRFs"
},
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR finitary-process report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Characterize the invariant Markov random fields that are finitary factors of independent and identically distributed processes. | An open problem is to determine which MRFs are ffiid. factors with bounded coding radius) of i.i.d. processes. More interesting examples, which are not block factors of i.i.d. processes, are the 1-dependent 4-coloring and 2-dependent 3-coloring of Z constructed by Holroyd and Liggett [5]. A result of Smorodinsky [8] show... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,026 | OWR-9790359-007 | Simultaneous Spatial and Informational Coding Efficiency | Let $X$ be a finitary factor of an independent and identically distributed process with exponentially decaying coding-radius tails. Must $X$ also be a finitary factor of a finite-valued independent process having entropy arbitrarily close to that of $X$ and exponentially decaying coding-radius tails? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-007",
"literature-status:open",
"owr-year:2022"
] | The extracted question asks whether two coding-efficiency properties can hold simultaneously; the report supplies examples and separate partial results but leaves this compatibility question open. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR finitary-process report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Let $X$ be a finitary factor of an independent and identically distributed process with exponentially decaying coding-radius tails. Must $X$ also be a finitary factor of a finite-valued independent process having entropy arbitrarily close to that of $X$ and exponentially decaying coding-radius tails? | Is it the case that both properties can be realized simultaneously? Descriptive Combinatorics, LOCAL Algorithms and Random Processes 449 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,027 | OWR-9790359-008 | Algebraic Complexity of Borel Constraint Problems | For a finite relational structure $D$, absence of a homomorphism $f:D^4\to D$ satisfying $f(a,r,e,a)=f(r,a,r,e)$ makes $\operatorname{CSP}_B(D)$ $\boldsymbol{\Sigma}^1_2$-complete. Is the converse true? Can Borel complexity, efficient local solvability for directed graphs, and extension to all locally checkable labelin... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-008",
"literature-status:open",
"owr-year:2022"
] | The listed converse, algebraic characterization, and extension from special LCLs to all LCLs are broad unresolved questions; existing decidability results cover restricted graph classes and do not settle the extracted list. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "OWR descriptive-combinatorics report"
},
{
"url": "https://doi.org/10.1007/s00446-022-00435-9",
"label": "LCLs in rooted trees"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | For a finite relational structure $D$, absence of a homomorphism $f:D^4\to D$ satisfying $f(a,r,e,a)=f(r,a,r,e)$ makes $\operatorname{CSP}_B(D)$ $\boldsymbol{\Sigma}^1_2$-complete. Is the converse true? Can Borel complexity, efficient local solvability for directed graphs, and extension to all locally checkable labelin... | There are many open questions in this directions. Is the converse to the above theorem true? Can we algebraically characterize Borel notions of complexity such effectiviability or the presence of a dichotomy theorem? Does the above theorem hold for all LCLs? The report passage is retained verbatim as the relevant contex... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,028 | OWR-9790359-009 | Complexity of Low-Chromatic Compact Free Subshifts | Is the collection of compact free subshifts of $2^{\mathbb Z_2*\mathbb Z_2*\mathbb Z_2}$ with Borel chromatic number at most $3$ $\boldsymbol{\Sigma}^1_2$-complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-009",
"literature-status:open",
"owr-year:2022"
] | The 2024 primary paper still treats the compact free subshift characterization as an open direction; no result found establishes the stronger completeness claim for this class. | [
{
"url": "https://doi.org/10.1017/fmp.2024.8",
"label": "On Homomorphism Graphs"
},
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Is the collection of compact free subshifts of $2^{\mathbb Z_2*\mathbb Z_2*\mathbb Z_2}$ with Borel chromatic number at most $3$ $\boldsymbol{\Sigma}^1_2$-complete? | Finally, let us list a couple of natural open problems related to the topic. Is the collection of compact free subshifts of 2Z2 ∗Z2 ∗Z2 with Borel chromatic number \leq 3 also Σ12 -complete? Descriptive Combinatorics, LOCAL Algorithms and Random Processes 453 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,029 | OWR-9790359-010 | Determinacy Methods in LOCAL and Borel Coloring | Can shift-graph and Galvin–Prikry methods be used in the LOCAL model? Can determinacy arguments construct functions of large Borel chromatic number, and does the Axiom of Determinacy imply that the shift graph $G_S$ has infinite chromatic number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455](https://doi.org/10.4171/owr/2022/8)
## Li... | 3 | open | null | 2,022 | 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-9790359-010",
"literature-status:open",
"owr-year:2022"
] | The workshop report explicitly records the determinacy question as open and links it to the unresolved issue of whether AD implies the Ramsey property for all subsets of the infinite subsets of the naturals. | [
{
"url": "https://doi.org/10.4171/owr/2022/8",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00222-021-01047-z",
"label": "A complexity problem for Borel graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/8 | null | null | null | Can shift-graph and Galvin–Prikry methods be used in the LOCAL model? Can determinacy arguments construct functions of large Borel chromatic number, and does the Axiom of Determinacy imply that the shift graph $G_S$ has infinite chromatic number? | Is there a way to utilize GS and Galvin-Prikry-like theorems in the LOCAL model? A natural question is, whether one can relate determinacy arguments to the shift graph. Is it possible to construct functions with large Borel chromatic num- ber using determinacy arguments? Does it follow from the Axiom of Determinacy ove... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Descriptive Combinatorics, LOCAL Algorithms and Random Processes (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/8, pp. 429--455 |
30,005,030 | OWR-9790360-001 | Spatial Regularity Versus Time Integrability for Fractional SDEs | For the stochastic differential equation $$dX_t=b(t,X_t)\,dt+dW_t^H$$ driven by fractional Brownian motion of Hurst parameter $H$, can higher time integrability $b\in L_t^qC_x^\alpha$ lower the spatial regularity threshold below $\alpha>1-1/(2H)$ in accordance with the scaling prediction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488](https://doi.org/10.417... | 3 | open | null | 2,022 | 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-9790360-001",
"literature-status:open",
"owr-year:2022"
] | The source states that lowering the spatial regularity threshold by replacing the time integrability exponent with higher values remains open; no later result located settles this exact threshold question. | [
{
"url": "https://doi.org/10.4171/owr/2022/9",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/9 | null | null | null | For the stochastic differential equation $$dX_t=b(t,X_t)\,dt+dW_t^H$$ driven by fractional Brownian motion of Hurst parameter $H$, can higher time integrability $b\in L_t^qC_x^\alpha$ lower the spatial regularity threshold below $\alpha>1-1/(2H)$ in accordance with the scaling prediction? | Thus the fundamental question of whether one can lower the value of ^{3}, by assuming b * Lqt Cx^{3} for higher values of q, in accordance to formula (2), remains open. The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488 |
30,005,031 | OWR-9790360-002 | Global Regularity of Three-Dimensional Navier–Stokes Flow | Do the three-dimensional incompressible Navier–Stokes equations admit a global-in-time smooth solution for every smooth divergence-free initial velocity field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488](https://doi.org/10.417... | 3 | open | null | 2,022 | 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-9790360-002",
"literature-status:open",
"owr-year:2022"
] | This is the global existence and smoothness problem for three dimensional incompressible Navier Stokes, which remains unresolved despite substantial conditional and partial regularity results. | [
{
"url": "https://www.claymath.org/millennium/Navier-Stokes-Equation/",
"label": "Clay problem statement"
},
{
"url": "https://doi.org/10.4171/owr/2022/9",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/9 | null | null | null | Do the three-dimensional incompressible Navier–Stokes equations admit a global-in-time smooth solution for every smooth divergence-free initial velocity field? | Well-posedness in the sense of existence of global-in-time smooth solu- tions to (1) is a largely open problem: though in the regime of small initial data or hyperdissipative variants there exist positive results exploiting symmetry and cancellation property of B, these, however, do not extend to the general case. with... | 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 | Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488 |
30,005,032 | OWR-9790360-003 | Solution Concepts for Stable SDEs with Distributional Drift | For linear and McKean–Vlasov stochastic differential equations driven by a symmetric stable process and having distributional drift, which notion of solution gives a well-defined and unique dynamics, including regimes below the Young threshold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488](https://doi.org/10.417... | 3 | open | null | 2,022 | 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-9790360-003",
"literature-status:open",
"owr-year:2022"
] | Martingale, virtual, Dirichlet, and related solution notions yield well posedness in restricted regularity regimes, but the general distributional drift dynamics asked for in the extract remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/9",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2205.11866",
"label": "Stable driven McKean Vlasov equations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/9 | null | null | null | For linear and McKean–Vlasov stochastic differential equations driven by a symmetric stable process and having distributional drift, which notion of solution gives a well-defined and unique dynamics, including regimes below the Young threshold? | What notion of solution can we consider to solve (L) and (NL) and how can we specify a dynamics? and Z s nZ o (NL) Xs = ¿ + b(r, Xr 2 y)µr (dy) dr + Ws , 0 Rd | 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 | Mini-Workshop: Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/9, pp. 457--488 |
30,005,033 | OWR-9790362-003 | Virtual Fibrations with Precisely Controlled Finiteness Properties | Is there a finite-index subgroup $\Lambda_0<\Lambda$ and a homomorphism $\phi:\Lambda_0\to\mathbb{Z}$ whose kernel is of type $F_{n-1}$ but not $F_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-003",
"literature-status:open",
"owr-year:2022"
] | The RFRS theory supplies homological FP n minus 1 but not FP n kernels in all dimensions, while the requested homotopical F n minus 1 but not F n result for lattices in SO(2n,1) remains a separate unresolved question. | [
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2112.00397",
"label": "Improved algebraic fibrings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Is there a finite-index subgroup $\Lambda_0<\Lambda$ and a homomorphism $\phi:\Lambda_0\to\mathbb{Z}$ whose kernel is of type $F_{n-1}$ but not $F_n$? | Is there a finite index subgroup Λ0 < Λ and a homomorphism \phi : Λ0 \to Z with kernel of type Fn−1 , but not Fn ? Evidence for this is provided by Fisher’s recent proof [2] of a conjecture of Kielak [7, 8] about finiteness properties of kernels of virtual algebraic fibrations of RFRS groups. The report passage is reta... | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,034 | OWR-9790362-005 | Equivalence Classes of Homological Filling Functions | Are there uncountably many equivalence classes of homological filling functions for groups; in particular, are the homological filling functions for $\operatorname{GL}(S)$ and $\operatorname{GL}(T)$ equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-005",
"literature-status:open",
"owr-year:2022"
] | The cited work proves only broad upper and lower comparisons and equality in special examples; equivalence for arbitrary proper subsets S and T remains posed as an open question. | [
{
"url": "https://arxiv.org/abs/2012.00730",
"label": "Homological Dehn functions of groups of type FP2"
},
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Are there uncountably many equivalence classes of homological filling functions for groups; in particular, are the homological filling functions for $\operatorname{GL}(S)$ and $\operatorname{GL}(T)$ equivalent? | Are there uncountably many equivalence classes of homological filling functions for groups? We pose the following as a first step towards this. Are the homological filling functions for GL (S) and GL (T ) equivalent? The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,035 | OWR-9790362-006 | Recursive Homological Filling and the Word Problem | Let $H$ be a finitely presented group whose homological filling function $\operatorname{FA}_H$ is bounded by a recursive function. Must $H$ have a solvable word problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 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-9790362-006",
"literature-status:open",
"owr-year:2022"
] | The extract does not identify H sufficiently to decide a single word problem, and the associated Leary group family has a criterion depending on the base group and on whether S is recursive; therefore the unqualified claim is unresolved. | [
{
"url": "https://arxiv.org/abs/2012.00730",
"label": "Homological Dehn functions of groups of type FP2"
},
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Let $H$ be a finitely presented group whose homological filling function $\operatorname{FA}_H$ is bounded by a recursive function. Must $H$ have a solvable word problem? | Does H have solvable word problem? The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,036 | OWR-9790362-007 | Kaplansky's Conjectures for Group Rings | Let $G$ be a group and $K$ a field. If $G$ is torsion-free, must $K[G]$ have no nontrivial units, no nonzero zero divisors, and no idempotents other than $0$ and $1$; and for arbitrary $G$, must $K[G]$ be directly finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-007",
"literature-status:partially-solved",
"owr-year:2022"
] | The unit conjecture is disproved by an explicit torsion free example, whereas the zero divisor, idempotent, and unrestricted direct finiteness conjectures remain open in full generality, although many classes are settled. | [
{
"url": "https://annals.math.princeton.edu/2021/194-3/p09",
"label": "A counterexample to the unit conjecture"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2004.06.023",
"label": "Sofic groups and direct finiteness"
},
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Obe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Let $G$ be a group and $K$ a field. If $G$ is torsion-free, must $K[G]$ have no nontrivial units, no nonzero zero divisors, and no idempotents other than $0$ and $1$; and for arbitrary $G$, must $K[G]$ be directly finite? | There is a series of four long-standing conjectures on group rings that are attrib- uted to Kaplansky, namely the unit, zero divisor, idempotent and direct finiteness conjectures. Conjecture. Let G be a group and K be a field. If G is torsion free, then the group ring K[G] has • no non-trivial units, • no non-zero zero... | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,037 | OWR-9790362-008 | Zero Divisors in a Seven-Generator Group Ring | Let $$\Delta=\langle a,b,c,d,e,f,g\mid acb,add,afg,bbf,cdg,cef,eeg\rangle,$$ a torsion-free group without the unique-product property. Does $\Delta$ satisfy Kaplansky's zero-divisor conjecture over every field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-008",
"literature-status:open",
"owr-year:2022"
] | For the specified torsion free non unique product group Delta, the source presents the zero divisor question as open; current literature still treats the general zero divisor conjecture as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2501.07646",
"label": "On zero divisors and units in group rings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Let $$\Delta=\langle a,b,c,d,e,f,g\mid acb,add,afg,bbf,cdg,cef,eeg\rangle,$$ a torsion-free group without the unique-product property. Does $\Delta$ satisfy Kaplansky's zero-divisor conjecture over every field? | While the unit conjecture remains open in characteristic zero, Murray subse- quently gave counterexamples with the same group P in every positive character- istic [6]. The zero divisor conjecture is known for many groups, such as residually torsion-free elementary amenable groups [5], whereas the unit conjecture is fal... | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,038 | OWR-9790362-009 | Bounded Conjugation-Invariant Metrics on Higher-Rank Lattices | Let $G$ be a lattice in a higher-rank simple Lie group with finite center, and let $d_S$ be the conjugation-invariant word metric induced by the union of all conjugates of a finite generating set. Is $d_S$ bounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-009",
"literature-status:open",
"owr-year:2022"
] | Boundedness of the conjugation invariant word metric for arbitrary lattices in higher rank simple Lie groups is still reported as an open problem; existing theorems cover important special groups only. | [
{
"url": "https://arxiv.org/abs/1102.0423",
"label": "On bi invariant word metrics"
},
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Let $G$ be a lattice in a higher-rank simple Lie group with finite center, and let $d_S$ be the conjugation-invariant word metric induced by the union of all conjugates of a finite generating set. Is $d_S$ bounded? | The following is a known open question: Question 2 ([1]). Is dS bounded? We conjecture that this coarse group is very far from being a coarsified group. Namely, we pose the following: Conjecture 3. The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,039 | OWR-9790362-010 | Coarse Automorphism Groups of Free Groups | For $n\geq 2$, what is the structure of the coarse automorphism group $\operatorname{Aut}_{\mathrm{Crs}}(F_n,d_S)$ and its subgroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790362-010",
"literature-status:open",
"owr-year:2022"
] | The record is an incomplete lead in to Problem 5, whose requested classification of coarse automorphism groups of free groups remains an active open direction. | [
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00209-025-03764-0",
"label": "Coarse invertibility spectrum"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | For $n\geq 2$, what is the structure of the coarse automorphism group $\operatorname{Aut}_{\mathrm{Crs}}(F_n,d_S)$ and its subgroups? | For concreteness, we propose the following: Problem 5. Gl(n, Z) \subset Gl(n, R). One can obtain a great deal of information on Gl(n, Z) by observing that the index two subgroup Sl(n, Z) < Gl(n, Z) is a lattice in the simple Lie group Sl(n, R) < Gl(n, R). In analogy, it is natural to wonder whether AutCrs (Fn , dS ) or... | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,040 | OWR-9790362-011 | Classification of Coarsifications of the Integers | Classify the coarsifications of $\mathbb{Z}$; in particular, determine when the word metric $d_S$ induced by an infinite generating set $S$ is bounded and whether two such sets induce the same coarse structure. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 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-9790362-011",
"literature-status:open",
"owr-year:2022"
] | The classification problem for coarsifications of the integers is still open; recent work distinguishes some examples but does not provide a complete classification. | [
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00209-025-03764-0",
"label": "Coarse invertibility spectrum"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Classify the coarsifications of $\mathbb{Z}$; in particular, determine when the word metric $d_S$ induced by an infinite generating set $S$ is bounded and whether two such sets induce the same coarse structure. | Problem 7. Classify the coarsifications of Z. If S is an infinite generating set of Z, the induced word metric dS defines a coarsification of Z. For a given set S, it is natural to ask whether dS is bounded. For instance, if S is the set of all primes, boundedness of dS is a non-effective version of the Goldbach conjec... | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,041 | OWR-9790362-012 | Interval Structure of Cohomology-Vanishing Exponents | Given a continuous homomorphism $$\sigma:G\longrightarrow\operatorname{Aut}(X,[\mu])\ltimes L^0(X,\mu;\{-1,1\}),$$ let $\pi_{p,\sigma}$ be the induced isometric representation on $L^p(X,\mu)$. Is the set $$\{p>0:H^1(G,\pi_{p,\sigma})=0\}$$ always an interval? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576](https://doi.org/10.4171/owr/2022/11)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,022 | 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-9790362-012",
"literature-status:open",
"owr-year:2022"
] | The refined fixed representation question asks whether vanishing of first cohomology is an interval in the exponent, and the cited work explicitly says that the general question remains unsettled. | [
{
"url": "https://arxiv.org/abs/2001.02490",
"label": "Isometric actions on Lp spaces"
},
{
"url": "https://doi.org/10.4171/owr/2022/11",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/11 | null | null | null | Given a continuous homomorphism $$\sigma:G\longrightarrow\operatorname{Aut}(X,[\mu])\ltimes L^0(X,\mu;\{-1,1\}),$$ let $\pi_{p,\sigma}$ be the induced isometric representation on $L^p(X,\mu)$. Is the set $$\{p>0:H^1(G,\pi_{p,\sigma})=0\}$$ always an interval? | The following question is therefore a refined form of Druţu’s conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Geometric Structures in Group Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/11, pp. 517--576 |
30,005,042 | OWR-9790363-001 | Weak Moment Conditions and Branching-Process Limit Laws | For the coupled branching process driven by a nondecreasing integer-valued offspring process $X(\lambda)$, determine whether convergence to its martingale limit persists under an $X\log X$ condition, and characterize the law of the limiting process $W$ from its distributional fixed-point equation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656](https://doi.org/10.4171/owr/2022/12)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790363-001",
"literature-status:open",
"owr-year:2022"
] | The report lists both weakening the moment and increment assumptions to an X log X condition and characterizing the limiting process distribution as open; general branching results do not settle this coupled process question. | [
{
"url": "https://doi.org/10.4171/owr/2022/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2106.01426",
"label": "Parametrised branching processes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/12 | null | null | null | For the coupled branching process driven by a nondecreasing integer-valued offspring process $X(\lambda)$, determine whether convergence to its martingale limit persists under an $X\log X$ condition, and characterize the law of the limiting process $W$ from its distributional fixed-point equation. | Open problems This work raises several open problems: (i) Can we relax assumption (H) to, e.g., an X log X condition, and still get Theorem 1? (ii) Can we describe the distribution of the limiting process W ? Can this fixed-point equation help characterising the distribution of W ? 3. A motivational example This projec... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656 |
30,005,043 | OWR-9790363-002 | Consensus Times on Erdős–Rényi Random Graphs | For the voter model started from distinct opinions on $G(n,p_n/n)$, determine the asymptotic consensus time as a function of $p_n$, in both discrete and continuous time. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656](https://doi.org/10.4171/owr/2022/12)
## Literature review (checke... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790363-002",
"literature-status:open",
"owr-year:2022"
] | Consensus time is known in several dense and random graph regimes, but the extract specifies neither the graph density nor the initial condition, and no single general asymptotic answer covers the stated question. | [
{
"url": "https://doi.org/10.4171/owr/2022/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2607.13183",
"label": "Meeting and coalescence times on Erdos Renyi components"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/12 | null | null | null | For the voter model started from distinct opinions on $G(n,p_n/n)$, determine the asymptotic consensus time as a function of $p_n$, in both discrete and continuous time. | How long does it take the voter model to reach consensus? \taucons := inf\{t \geq 0 : \existsi \in S : Vi (t) = V \}. Consensus time in the voter model on the Erdős-Rény random graph: A spectral approach Anton Klimovsky (joint work with Thomas van Belle) Population Dynamics and Statistical Physics in Synergy 617 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656 |
30,005,044 | OWR-9790363-003 | Explosion with Infinite-Mean Offspring | Can the contact process with fitness on a Galton–Watson tree explode when the offspring variable $\xi$ satisfies $\mathbb E[\xi]=\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656](https://doi.org/10.4171/owr/2022/12)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790363-003",
"literature-status:open",
"owr-year:2022"
] | The source leaves explosion with infinite mean offspring as an explicit open question for the contact process on Galton Watson trees; explosive branching examples do not resolve that model. | [
{
"url": "https://doi.org/10.4171/owr/2022/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1502.07538",
"label": "A special family of Galton Watson processes with explosions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/12 | null | null | null | Can the contact process with fitness on a Galton–Watson tree explode when the offspring variable $\xi$ satisfies $\mathbb E[\xi]=\infty$? | So a natural question is: can we close the gap? Can we get an explosion if E[ξ] = \infty? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656 |
30,005,045 | OWR-9790363-004 | Lamperti Limits of Multitype-Forest Profiles | For uniform multitype forests with a prescribed degree sequence, prove convergence of the profile and characterize its limit as a solution of the Lamperti transform. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656](https://doi.org/10.4171/owr/2022/12)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790363-004",
"literature-status:open",
"owr-year:2022"
] | The extracted conjecture asserts convergence and Lamperti characterization of profiles for uniform multitype forests with prescribed degree sequence; available work gives coding and partial convergence results but not this full profile theorem. | [
{
"url": "https://doi.org/10.4171/owr/2022/12",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2003.03036",
"label": "Multitype random forests with a given degree sequence"
},
{
"url": "https://arxiv.org/abs/1410.0250",
"label": "Breadth first search coding of multi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/12 | null | null | null | For uniform multitype forests with a prescribed degree sequence, prove convergence of the profile and characterize its limit as a solution of the Lamperti transform. | Finally, using our results, we conjecture the following. Population Dynamics and Statistical Physics in Synergy 631 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656 |
30,005,046 | OWR-9790363-005 | Contact Processes on Exponential-Growth Dynamic Graphs | Establish survival and criticality for contact processes on dynamical percolation throughout the untreated parameter regime on exponential-growth graphs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656](https://doi.org/10.4171/owr/2022/12)
## Literature review (checke... | 3 | open | null | 2,022 | 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-9790363-005",
"literature-status:open",
"owr-year:2022"
] | The extract records conjectural extension of the results to an untreated parameter regime on exponential growth graphs and further work beyond the supercritical regime; these directions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/12",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/12 | null | null | null | Establish survival and criticality for contact processes on dynamical percolation throughout the untreated parameter regime on exponential-growth graphs. | Finally we discuss some open problems, conjectures and further research directions, which we now briefly outline. • On exponential growth graphs there is a certain parameter regime for which our techniques are not applicable. We conjecture that our results should also extend to this regime. • We mainly focus on the sup... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Population Dynamics and Statistical Physics in Synergy (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/12, pp. 577--656 |
30,005,047 | OWR-9790364-001 | Unspecified Hypergeometric Positivity Problem | Dmitry Karp Results and conjectures on log-concavity and zeros of hypergeometric and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676 Bao-Xuan Zhu Some recent developments on positivity of combinatorial polynomials and matrices . . . . . . . . . . . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681](https://doi.org/10.4171/owr/2022/13)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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 shows that this is a contents fragment without a recoverable standalone hypergeometric-positivity problem. No separate c) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790364-001",
"literature-status:open",
"owr-year:2022"
] | The exact record is a table of contents fragment rather than a complete mathematical assertion, so its triage claim is unclear and is conservatively classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/13",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/13 | null | null | null | null | Dmitry Karp Results and conjectures on log-concavity and zeros of hypergeometric and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676 Bao-Xuan Zhu Some recent developments on positivity of combinatorial polynomials and matrices . . . . . . . . . . . . . . . . . ... | unrecoverable | The official report shows that this is a contents fragment without a recoverable standalone hypergeometric-positivity problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681 |
30,005,048 | OWR-9790364-002 | Elementary Proofs of Laguerre–Pólya Total Positivity | Can the complex-analytic proof of the total-positivity characterization of the Laguerre–Pólya class be replaced by an elementary argument? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681](https://doi.org/10.4171/owr/2022/13)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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-9790364-002",
"literature-status:open",
"owr-year:2022"
] | The primary source explicitly labels replacing the complex analytic proofs, including comparison with Okounkov's proof, as an intriguing open question; no later resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2022/13",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/13 | null | null | null | Can the complex-analytic proof of the total-positivity characterization of the Laguerre–Pólya class be replaced by an elementary argument? | The basic result of this type is the Aissen–Edrei–Whitney–Schoenberg theorem [1, 3]: An infinite Toeplitz matrix is totally positive if and only if the corresponding gen- f (t) erating function has the form , where both f (t) and g(t) are in LP + . g(−t) (An intriguing open question: may the complex analytic techniques... | 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 | The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681 |
30,005,049 | OWR-9790364-003 | Unspecified Laguerre-Polya Density Criterion Problem | The Laguerre-Pólya class via density criteria Dimitar Dimitrov We survey some recent progress towards long-standing open questions concerning the Laguerre-Pólya class. 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:** [The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681](https://doi.org/10.4171/owr/2022/13)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents survey context about a density criterion but does not state a complete standalone open problem. No separate cle) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790364-003",
"literature-status:open",
"owr-year:2022"
] | The extracted passage is a survey or talk description rather than a definite mathematical assertion, so there is no precise claim whose truth can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2022/13",
"label": "Oberwolfach Report 13/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/13 | null | null | null | null | The Laguerre-Pólya class via density criteria Dimitar Dimitrov We survey some recent progress towards long-standing open questions concerning the Laguerre-Pólya class. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report presents survey context about a density criterion but does not state a complete standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681 |
30,005,050 | OWR-9790364-004 | Extreme Normalized Gaps between Riemann-Zeta Zeros | If $0<\gamma_1\leq\gamma_2\leq\cdots$ are the ordinates of the nontrivial zeros of the Riemann zeta function, are
$$
\liminf_{n\to\infty}\frac{(\gamma_{n+1}-\gamma_n)\log\gamma_n}{2\pi}=0
\quad\text{and}\quad
\limsup_{n\to\infty}\frac{(\gamma_{n+1}-\gamma_n)\log\gamma_n}{2\pi}=\infty
$$
? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681](https://doi.org/10.4171/owr/2022/13)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790364-004",
"literature-status:open",
"owr-year:2022"
] | The normalized consecutive-zero gap limits are still conjectural: primary work gives finite unconditional or conditional bounds, not the asserted liminf zero and limsup infinity. | [
{
"url": "https://doi.org/10.4171/owr/2022/13",
"label": "Oberwolfach Report 13/2022"
},
{
"url": "https://arxiv.org/abs/1003.0752",
"label": "Conrey--Ghosh--Gonek on zeta gaps"
},
{
"url": "https://arxiv.org/abs/0910.2052",
"label": "Bui--Milinovich--Ng on zeta gaps"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/13 | null | null | null | If $0<\gamma_1\leq\gamma_2\leq\cdots$ are the ordinates of the nontrivial zeros of the Riemann zeta function, are
$$
\liminf_{n\to\infty}\frac{(\gamma_{n+1}-\gamma_n)\log\gamma_n}{2\pi}=0
\quad\text{and}\quad
\limsup_{n\to\infty}\frac{(\gamma_{n+1}-\gamma_n)\log\gamma_n}{2\pi}=\infty
$$
? | Conjecture. log \gamman lim inf (\gamman+1 − \gamman ) = 0; n\to\infty 2\pi log \gamman lim sup (\gamman+1 − \gamman ) = \infty; n\to\infty 2\pi We recall that we have T T T N (T ) = log − + O(log T ) 2\pi 2\pi 2\pi where N (T ) is the number of zeros of ζ(s) in 0 < Im s < T . Thus, the average gap of zeros of the Riem... | 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 | The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681 |
30,005,051 | OWR-9790364-005 | Spectral-Deformation Methods for the Riemann Hypothesis | Can the spectral-deformation method based on $H_\lambda(t)$ prove the Riemann hypothesis despite the failure of the analogous assertion for $H_0(t)$ in general? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681](https://doi.org/10.4171/owr/2022/13)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
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"level": 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-9790364-005",
"literature-status:open",
"owr-year:2022"
] | This is a method-level question about proving the Riemann hypothesis; the report records an obstruction for the lambda-zero analogue, but neither that obstruction nor later literature resolves the Riemann hypothesis. | [
{
"url": "https://doi.org/10.4171/owr/2022/13",
"label": "Oberwolfach Report 13/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/13 | null | null | null | Can the spectral-deformation method based on $H_\lambda(t)$ prove the Riemann hypothesis despite the failure of the analogous assertion for $H_0(t)$ in general? | Can we resolve the Riemann hypothesis by the method in this talk, although we already observed a negative sign for that? Assume that for some \delta \in \{0, 1\} \delta 1 (−1) ϕ(x) = ϕ (Re x > 0). x Put ! Z \infty N X dx h(s) = xs cn xn \psi (n) (x) . 0 n=0 x Then, for some polynomial P (s), h(s) = (−1)\delta h(k − s);... | 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 | The Laguerre-Pólya Class and Combinatorics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/13, pp. 657--681 |
30,005,052 | OWR-9790365-001 | Local-to-Global Tensorization of Information Functionals | For which families of information functionals does local tensorization imply global tensorization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"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-9790365-001",
"literature-status:open",
"owr-year:2022"
] | The report poses local-to-global tensorization as a general criterion for single-letterization; special tensorization results exist, but no theorem or counterexample settles the stated general implication. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://ems.press/content/serial-article-files/46950?nt=1",
"label": "Nair, local and global tensorization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | For which families of information functionals does local tensorization imply global tensorization? | Open problem: An open problem that is of considerable interest is the following: Does local ten- sorization imply global tensorzation for a family of information functionals. The motivation of this open problem is to see if a locally-testable criteria can determine whether functionals have the magical “single-letteriza... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,053 | OWR-9790365-002 | Reduction of Guessing Problems to Source Compression | Can every optimal guessing problem be reduced to its corresponding optimal source-compression problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"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-9790365-002",
"literature-status:open",
"owr-year:2022"
] | The cited guessing papers establish important special relations to compression, but the proposed reduction of every guessing problem to a corresponding compression problem remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2106.13341",
"label": "Graczyk--Lapidoth--Yan, guessing a tuple"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Can every optimal guessing problem be reduced to its corresponding optimal source-compression problem? | Open problem: As demonstrated in [1, 2] below, there is an intimate relation between guessing a chance variable X using the least number of guesses in expectation, and com- pressing X using the least number of bits. We propose verifying this conjecture as a key open problem in guessing. Takeaways from the Guessing Prob... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,054 | OWR-9790365-003 | Universal Compression with Large Unknown Alphabets | For block size $k>\delta\sqrt{\log n}$, can one construct a universal compressor for the large or unknown alphabets arising from the submatrix decomposition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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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"id": 3,
"level": 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-9790365-003",
"literature-status:open",
"owr-year:2022"
] | The published universal graph-compression scheme covers a wide class of stochastic block models, but the specific large-unknown-alphabet regime beyond logarithmic block size remains an open compressor-design problem. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2006.02643",
"label": "Bhatt--Wang--Wang--Wang, universal graph compression"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | For block size $k>\delta\sqrt{\log n}$, can one construct a universal compressor for the large or unknown alphabets arising from the submatrix decomposition? | Open problem: In our work, the submatrix decomposition is asymptotically i.i.d. for block \sqrt{ } size k with \omega(1) \leq k \leq o(n), and the compression algorithm is\sqrt{ }universal for k \leq \delta log n, with n being the size of the adjacency matrix. For k > \delta log n, finding a universal compressor for la... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,055 | OWR-9790365-004 | Optimal Distributed Hypothesis Testing beyond Conditional Independence | Determine the optimal distributed hypothesis-testing scheme beyond testing against conditional independence. In particular, is the Shimokawa–Han–Amari scheme optimal when both hypotheses are binary symmetric double sources? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790365-004",
"literature-status:partially-solved",
"owr-year:2022"
] | For product binary-symmetric double sources, a sequential scheme strictly improves the Shimokawa--Han--Amari scheme, so its optimality is disproved there; the optimal scheme in the general setting remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2201.13005",
"label": "Watanabe, suboptimality of random binning"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Determine the optimal distributed hypothesis-testing scheme beyond testing against conditional independence. In particular, is the Shimokawa–Han–Amari scheme optimal when both hypotheses are binary symmetric double sources? | Open problem: Determine the optimal distributed hypothesis testing scheme for cases other than testing against (conditional) independence. Is the Shimokawa-Han-Amari testing scheme optimal when both the null hypothesis and the alternative hypothesis are binary symmetric double sources? On the Suboptimality of Random Bi... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,056 | OWR-9790365-005 | Capacity Criteria for Arbitrarily Varying Channels with Causal State Information | For arbitrarily varying channels with causal state information at the encoder, when do deterministic-code and random-code capacities coincide, and does the criterion necessarily require a multiletter characterization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"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-9790365-005",
"literature-status:open",
"owr-year:2022"
] | The report asks whether the deterministic-code capacity criterion for arbitrarily varying channels with causal side information must be multiletter; existing primary work supplies bounds and special cases, not a general characterization. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/1701.03342",
"label": "Pereg--Steinberg, arbitrarily varying channels"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | For arbitrarily varying channels with causal state information at the encoder, when do deterministic-code and random-code capacities coincide, and does the criterion necessarily require a multiletter characterization? | This talk will provide an overview of the state-of-the-art in network communication systems with uncertainty, and introduce open problems in these topics. Open problems: 1. Is it necessarily a multiletter condition? 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,057 | OWR-9790365-007 | Mutual-Information Bounds and Dimension-Free Dual Sudakov Minoration | Prove the proposed mutual-information inequality for log-concave random vectors and derive a dimension-free dual Sudakov minoration for general log-concave measures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"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-9790365-007",
"literature-status:open",
"owr-year:2022"
] | The report contains two unresolved questions: the stated mutual-information inequality and a dimension-independent dual-Sudakov-type minoration for general log-concave measures; the cited program has only partial cases and reductions. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/1610.09287",
"label": "Mendelson--Milman--Paouris, generalized dual Sudakov program"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Prove the proposed mutual-information inequality for log-concave random vectors and derive a dimension-free dual Sudakov minoration for general log-concave measures. | Open problems: 1. An information inequality: Motivated by problems in multiuser information theory and analogous results in empirical processes, we conjecture the following inequality: there is a constant c > 0 such that for any distribution PX on Rn , we have the following bound relating the mutual information and the... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,058 | OWR-9790365-008 | Unified Gaussian Comparison Framework for Entropic Inequalities | Can a unified Gaussian-comparison framework prove the entropic and geometric inequalities that do not follow from the available Gaussian extremality principle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790365-008",
"literature-status:partially-solved",
"owr-year:2022"
] | Aras and Courtade established a broad Gaussian-comparison framework unifying many entropy and geometric inequalities, but the report asks for coverage of additional inequalities and that broader coverage is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2206.14182",
"label": "Aras--Courtade, entropy inequalities and Gaussian comparisons"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Can a unified Gaussian-comparison framework prove the entropic and geometric inequalities that do not follow from the available Gaussian extremality principle? | Open problem: While (1) gives a concise unification of many entropic and geometric inequalities found in the literature, there remain several that are not obviously implied. Is there a common framework that does? non-negative scalars (dj )m m j=1 and linear maps (Bj )j=1 with suitably dimensioned domains, it can be sho... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,059 | OWR-9790365-009 | Decidability of Linear Information Inequalities | Is the validity of linear information inequalities decidable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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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"id": 3,
"level": 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-9790365-009",
"literature-status:open",
"owr-year:2022"
] | The decidability of validity for arbitrary linear information inequalities is still explicitly identified as open in the primary decision-problems literature; only restricted arithmetical-hierarchy results are known. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://doi.org/10.4230/LIPIcs.ICALP.2020.106",
"label": "Abo Khamis--Kolaitis--Ngo--Suciu, decision problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Is the validity of linear information inequalities decidable? | Open problem: An open problem in this area is the decidability of the linear information inequality, i.e., whether there exists an algorithm that can determine whether a given linear information inequality holds for all sequences of random variables. New Mathematical Techniques in Information Theory 697 | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,060 | OWR-9790365-010 | Tight Bounds for Many-User Multiple-Access Coding | Determine tight achievable and converse bounds for Gaussian many-user multiple-access coding, including the random-access setting. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"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-9790365-010",
"literature-status:open",
"owr-year:2022"
] | The many-user Gaussian multiple-access literature provides achievable regions and converse bounds, but the cited gap and practical-random-access extensions are not closed in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Determine tight achievable and converse bounds for Gaussian many-user multiple-access coding, including the random-access setting. | We propose efficient coding schemes based on random linear models with approximate message passing (AMP) decoding, and study the tradeoff between energy-per-bit and achievable user density for a fixed target error rate. Open problems: This work discussed achievable regions and converse bounds for the Gaussian multiple-... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,061 | OWR-9790365-011 | Type-II Error Exponents in Distributed Hypothesis Testing | Determine the optimal type-II error exponent for rate-limited distributed hypothesis testing and for its interactive two-sensor variant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790365-011",
"literature-status:open",
"owr-year:2022"
] | Known distributed-testing results characterize important testing-against-independence and variable-length cases, but the general single-sensor exponent and the interactive two-sensor optimum posed here remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2005.08610",
"label": "Salehkalaibar--Wigger, variable-length distributed testing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Determine the optimal type-II error exponent for rate-limited distributed hypothesis testing and for its interactive two-sensor variant. | Open problems: The most prominent open problem in distributed hypothesis testing is the char- acterization of the maximum type-II error exponent of the simple single-sensor, single decision center problem where the sensor communicates with the decision center over a rate-limited noise-free link. Another interesting ope... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,062 | OWR-9790365-012 | Capacity and Reliability of Mismatched Decoding | Find a single-letter characterization of mismatched decoding capacity, and determine the exact reliability function for mismatched decoding. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 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-9790365-012",
"literature-status:partially-solved",
"owr-year:2022"
] | Single-letter converse bounds and tightness for special channel-metric classes are known, but a general single-letter mismatch-capacity formula and the exact reliability function remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://doi.org/10.1109/TIT.2022.3146308",
"label": "Somekh-Baruch, single-letter upper bound"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Find a single-letter characterization of mismatched decoding capacity, and determine the exact reliability function for mismatched decoding. | The question of characterizing the fundamental limits of channel coding when the receiver uses a suboptimal decoding rule, also known as “mismatched decoding”, has been a longstanding open problem. Open problems: The work presented relates to the following two open problems. The Multicast Transmission Approach to Conve... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,063 | OWR-9790365-013 | Convex Relaxations for Planted Graph Matching | Let $\pi$ be a uniformly random permutation, and let $A$ and $B$ be correlated symmetric random matrices under the planted correspondence $\pi$. For which correlations does the minimizer of
$$
\min_{X\ \mathrm{doubly\ stochastic}}\|AX-XB\|_F^2
$$
round to $\pi$ with high probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 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,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790365-013",
"literature-status:partially-solved",
"owr-year:2022"
] | Results prove that a common convex relaxation can fail for broad graph families and that other relaxations succeed under restricted models, but no general theory justifies the practical success of the natural relaxation. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/1405.3133",
"label": "Lyzinski--Fishkind--Fiori--Vogelstein--Priebe--Sapiro, graph matching"
},
{
"url": "https://arxiv.org/abs/2310.20609",
"label": "Araya Valdiv... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Let $\pi$ be a uniformly random permutation, and let $A$ and $B$ be correlated symmetric random matrices under the planted correspondence $\pi$. For which correlations does the minimizer of
$$
\min_{X\ \mathrm{doubly\ stochastic}}\|AX-XB\|_F^2
$$
round to $\pi$ with high probability? | Open problem: The most significant open problem in the area of graph matching at large is to theoretically justify the success of a natural and commonly used convex relaxation. Impossibility Results for Planted Matching Problems Yihong Wu (joint work with Jian Ding, Jiaming Xu, Dana Yang, Haoyu Wang and Israel Yolou) | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,064 | OWR-9790365-014 | Belief-Propagation Uniqueness Boundary for Randomly Colored Ising Models | In the randomly colored stochastic block model with parameters $(q,a,b)$, what is the exact boundary separating the parameter values for which belief propagation has a unique fixed point from those for which it does not? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 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-9790365-014",
"literature-status:partially-solved",
"owr-year:2022"
] | The two-community Ising case is settled by a uniqueness theorem and Potts-model work gives broad parameter regimes, but the precise good--bad boundary for all q, a, and b remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://arxiv.org/abs/2211.15242",
"label": "Yu--Polyanskiy, Ising cavity-equation uniqueness"
},
{
"url": "https://proceedings.mlr.press/v195/gu23a.html",
"label": "Gu--Polyanskiy, Pot... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | In the randomly colored stochastic block model with parameters $(q,a,b)$, what is the exact boundary separating the parameter values for which belief propagation has a unique fixed point from those for which it does not? | Open problem: Suppose that n vertices are randomly colored using q colors. An open problem is to find the precise boundary of bad values of (q, a, b) from good ones. Uniqueness of BP fixed point for Ising models Yury Polyanskiy (joint work with Qian Yu) | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,065 | OWR-9790365-015 | Sharp Min-Entropy Power Inequalities | For sums of $N$ independent random vectors in $\mathbb R^d$, determine the sharp constant and all extremizers in the Rényi entropy-power inequality for orders other than $0$, $1$, and $\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | open | null | 2,022 | 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-9790365-015",
"literature-status:open",
"owr-year:2022"
] | The universal-constant min-entropy inequality is established, but the sharper dimension-and-summand-dependent constant and the broader Renyi entropy-power extremizer questions stated in the record remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://doi.org/10.1109/ISIT.2017.8006613",
"label": "Xu--Melbourne--Madiman, min-entropy power inequality for groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | For sums of $N$ independent random vectors in $\mathbb R^d$, determine the sharp constant and all extremizers in the Rényi entropy-power inequality for orders other than $0$, $1$, and $\infty$. | Open problems: We presented a min-entropy power inequality for sums of N independent random vectors in Rd , with a constant that is independent of N but sharp for any fixed dimension d. Min-Entropy Inequalities on Algebraic Structures Mokshay Madiman (joint work with James Melbourne, Cyril Roberto, Peng Xu) | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,066 | OWR-9790365-016 | Gaussian Mean Testing under Information Constraints | Determine optimal tests and matching lower bounds for Gaussian mean testing under communication or information constraints. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707](https://doi.org/10.4171/owr/2022/14)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 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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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790365-016",
"literature-status:partially-solved",
"owr-year:2022"
] | Earlier work supplied bounds and conjectures for distributed Gaussian mean testing; a 2026 paper resolves substantially broader communication allocations, but optimal testing under the full information-constraint formulation remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/14",
"label": "Oberwolfach Report 14/2022"
},
{
"url": "https://proceedings.mlr.press/v125/acharya20b.html",
"label": "Acharya--Canonne--Tyagi, distributed signal detection"
},
{
"url": "https://arxiv.org/abs/2605.29426",
"label": "Canonne--... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/14 | null | null | null | Determine optimal tests and matching lower bounds for Gaussian mean testing under communication or information constraints. | How difficult is it to solve statistical inference prob- lems under such constraints? This is work in progress and raises several interesting open problems. Open problem: Optimal Gaussian mean testing under information constraints: We need new al- gorithms as well as a new approach for lower bounds. Lower Bounds for In... | 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 | New Mathematical Techniques in Information Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/14, pp. 683--707 |
30,005,067 | OWR-9790366-001 | Classification of Singular Radial Fractional-Laplacian Solutions | Classify the radial solutions of $(-\Delta)^\gamma u=A u^p$ on $\mathbb R^n\setminus\{0\}$ with an isolated singularity, equivalently the solutions of the autonomous nonlocal equation obtained by the cylindrical change of variables. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715](https://doi.org/10.4171/owr/2022/15)
## Li... | 3 | partially_solved | null | 2,022 | 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-9790366-001",
"literature-status:partially-solved",
"owr-year:2022"
] | The cited primary work develops the infinite-ODE method and proves nondegeneracy and related structural results for fast-decay singular solutions, but the full classification of the nonlocal ODE remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2022/15",
"label": "Oberwolfach Report 15/2022"
},
{
"url": "https://arxiv.org/abs/1910.14512",
"label": "Ao--Chan--DelaTorre--Fontelos--Gonzalez--Wei, ODE methods"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/15 | null | null | null | Classify the radial solutions of $(-\Delta)^\gamma u=A u^p$ on $\mathbb R^n\setminus\{0\}$ with an isolated singularity, equivalently the solutions of the autonomous nonlocal equation obtained by the cylindrical change of variables. | But up to today, the classiûcation result for nonlocal ODE (3) is still unknown and it is an open question. n n+2^{3} For p subcritical, p * ( n22^{3} , n22^{3} ), we study the existence of radial fast decay- ing solution u7 and the mapping property of the linearized problem around u7 . Basically there are two key prob... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715 |
30,005,068 | OWR-9790366-002 | Boundary Curvature and Stickiness of Nonlocal Minimal Surfaces | For nonlocal minimal surfaces beyond planar graphs, determine whether the nonlocal mean-curvature equation holds up to the boundary and characterize how generally boundary stickiness occurs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715](https://doi.org/10.4171/owr/2022/15)
## Li... | 3 | partially_solved | null | 2,022 | 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-9790366-002",
"literature-status:partially-solved",
"owr-year:2022"
] | Boundary continuity and stickiness have been rigorously classified in several smooth and singular geometries, but the general boundary equation and typicality question in the extracted form remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/15",
"label": "Oberwolfach Report 15/2022"
},
{
"url": "https://arxiv.org/abs/2305.15271",
"label": "Dipierro--Savin--Valdinoci, boundary continuity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/15 | null | null | null | For nonlocal minimal surfaces beyond planar graphs, determine whether the nonlocal mean-curvature equation holds up to the boundary and characterize how generally boundary stickiness occurs. | Is the nonlocal mean curvature equation satisûed up to the boundary? How typical is the stickiness phenomenon? Nonlocal minimal surfaces Serena Dipierro (joint work with Ovidiu Savin, Enrico Valdinoci) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715 |
30,005,069 | OWR-9790366-003 | Continuous Minimizers for a Regional Fractional-Laplacian Functional | For the Rayleigh–Faber–Krahn variational problem associated with the regional fractional Laplacian, does there exist a minimizer continuous on all of $\mathbb R^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715](https://doi.org/10.4171/owr/2022/15)
## Li... | 3 | open | null | 2,022 | 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-9790366-003",
"literature-status:open",
"owr-year:2022"
] | The variational problem has an attained minimizer, but whether some minimizer is continuous on all of Euclidean space remains an explicitly open regularity question. | [
{
"url": "https://doi.org/10.4171/owr/2022/15",
"label": "Oberwolfach Report 15/2022"
},
{
"url": "https://arxiv.org/abs/2108.07967",
"label": "Jin--Kriventsov--Xiong, regional fractional Laplacian"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/15 | null | null | null | For the Rayleigh–Faber–Krahn variational problem associated with the regional fractional Laplacian, does there exist a minimizer continuous on all of $\mathbb R^n$? | Open Question: Is there a minimizer that is continuous in Rn ? Nonlocality in Analysis, Probability and Statistics 747 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715 |
30,005,070 | OWR-9790366-004 | Analytic Proofs of Dimension-Free Nonlocal Regularity | Give a purely analytic proof that solutions $w$ of the perturbed Kolmogorov equation satisfy $\|D_x^2w\|_{L^p((0,T)\times\mathbb R^2)}\leq M_p\|f\|_{L^p((0,T)\times\mathbb R^2)}$, ideally with the sharp constant $M_p=C_p$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715](https://doi.org/10.4171/owr/2022/15)
## Li... | 3 | open | null | 2,022 | 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-9790366-004",
"literature-status:open",
"owr-year:2022"
] | The probabilistic representation proves the stated regularity estimates, but the requested purely analytic proof is still described as unavailable and no later primary proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2022/15",
"label": "Oberwolfach Report 15/2022"
},
{
"url": "https://doi.org/10.1016/j.spa.2021.06.009",
"label": "Marino--Menozzi--Priola, Poisson process and sharp constants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/15 | null | null | null | Give a purely analytic proof that solutions $w$ of the perturbed Kolmogorov equation satisfy $\|D_x^2w\|_{L^p((0,T)\times\mathbb R^2)}\leq M_p\|f\|_{L^p((0,T)\times\mathbb R^2)}$, ideally with the sharp constant $M_p=C_p$. | Thus it remains a challenging open problem to have a purely analytic proof of our regularity results. Remark 1. In [12] to show the previous stability result for (3) we use a probabilis- tic approach based on the Poisson process. This approach has been introduced in [9]. There, it was established in particular that Lp ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Nonlocality in Analysis, Probability and Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/15, pp. 709--715 |
30,005,071 | OWR-9790367-001 | Module Categories of Affine Vertex Algebras | For affine vertex algebras at admissible level, classify simple modules and their projective covers and injective hulls, prove projectives have finite length, and construct rigid braided tensor-category structures with explicit fusion rules. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | open | null | 2,022 | 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-9790367-001",
"literature-status:open",
"owr-year:2022"
] | The extracted fragment is meeting prose about progress and open questions, not a mathematically identifiable claim that can be verified or refuted. | [
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | For affine vertex algebras at admissible level, classify simple modules and their projective covers and injective hulls, prove projectives have finite length, and construct rigid braided tensor-category structures with explicit fusion rules. | Here, I will summarize recent progress, highlighting difficulties and open questions. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,072 | OWR-9790367-002 | Unified Construction of Deformed W-Algebras | Determine the structure of the deformed $W$-algebras of exceptional and higher-rank types and decide whether they arise from one uniform construction. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | open | null | 2,022 | 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-9790367-002",
"literature-status:open",
"owr-year:2022"
] | The report leaves the general structure and unification of the exhibited deformed W-algebras as a main question; the cited constructions provide examples, not a classification or common construction. | [
{
"url": "https://arxiv.org/abs/2112.14631",
"label": "Feigin--Jimbo--Mukhin"
},
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | Determine the structure of the deformed $W$-algebras of exceptional and higher-rank types and decide whether they arise from one uniform construction. | The main question is: what is the nature of these algebras? Are these examples a part of one construction? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,073 | OWR-9790367-003 | Habiro-Ring Refinements of Three-Manifold Quantum Invariants | For every rational homology sphere $Y$, construct elements $I_s(Y)$ of the Habiro ring, indexed by $s\in\operatorname{Spin}^c(Y)$, such that $\widetilde N_r(Y,\omega)=\sum_s C_s(Y,\omega)I_s(Y)|_{q=e^{2\pi i/r}}$ for all admissible $r$ and $\omega$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | partially_solved | null | 2,022 | 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-9790367-003",
"literature-status:partially-solved",
"owr-year:2022"
] | Costantino--Gukov--Putrov prove the q-series/root-of-unity relation under technical hypotheses and for several families, but the general existence and uniqueness conjecture for all rational homology spheres remains unproved. | [
{
"url": "https://doi.org/10.3842/SIGMA.2023.010",
"label": "Costantino--Gukov--Putrov, SIGMA"
},
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | For every rational homology sphere $Y$, construct elements $I_s(Y)$ of the Habiro ring, indexed by $s\in\operatorname{Spin}^c(Y)$, such that $\widetilde N_r(Y,\omega)=\sum_s C_s(Y,\omega)I_s(Y)|_{q=e^{2\pi i/r}}$ for all admissible $r$ and $\omega$. | where Cs (Y, \omega) are universal coefficients depending on r and certain simple homo- topy-type invariants of Y (see [2] for details). The conjecture was verified for a certain family of manifolds in [2], where it was also shown that the conjecture holds if its certain analog for links in a 3- sphere holds. An analog... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,074 | OWR-9790367-004 | Strength of Semisimple TQFT Invariants | How strong are these invariants? Recent Developments in Representation Theory and Mathematical Physics 833 Theorem A ([3] in 4 dimensions, [4] in arbitrary even dimensions). Even-dimen- sional semisimple TQFTs lead to stable diffeomorphism invariants. An upshot of this theorem is that stable diffeomorphism is a much co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. D. Reutter (joint with C. Schommer-Pries; OWR 16/2022, pp. 833–834) asks how strong the closed-manifold invariants of TQFTs are, and answers it for even-dimensional semisimple TQFTs, which, the authors note, include all functorial exampl... | [
"owr",
"oberwolfach-reports",
"OWR-9790367-004",
"literature-status:open",
"owr-year:2022"
] | The extracted question asks broadly about the strength of the invariants and supplies no precise theorem or criterion; the report does not resolve it. | [
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | null | How strong are these invariants? Recent Developments in Representation Theory and Mathematical Physics 833 Theorem A ([3] in 4 dimensions, [4] in arbitrary even dimensions). Even-dimen- sional semisimple TQFTs lead to stable diffeomorphism invariants. An upshot of this theorem is that stable diffeomorphism is a much co... | unrecoverable | The official report answers this rhetorical heading with a theorem characterizing the stable-diffeomorphism sensitivity of the invariants; it does not state an open problem. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,075 | OWR-9790367-005 | Affine–Virasoro Derivation of Nekrasov Blow-Up Identities | Derive Nekrasov's blow-up identity for the $N_f=4$, $\operatorname{SU}(2)$ instanton partition function from the affine–Virasoro vertex-operator-algebra identity under $\frac{\epsilon_1-\epsilon_2}{\epsilon_2}=b^2=-\frac{k+3}{k+2}$, including the required normalization of conformal blocks. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | open | null | 2,022 | 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-9790367-005",
"literature-status:open",
"owr-year:2022"
] | The report explicitly labels the proposed derivation of (2) from (3) a conjecture and says that the required normalisation relations still have to be determined. | [
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | Derive Nekrasov's blow-up identity for the $N_f=4$, $\operatorname{SU}(2)$ instanton partition function from the affine–Virasoro vertex-operator-algebra identity under $\frac{\epsilon_1-\epsilon_2}{\epsilon_2}=b^2=-\frac{k+3}{k+2}$, including the required normalization of conformal blocks. | We conjecture that it should be possible to derive (2) from (3) if one assumes the relations ǫ1ǫ−ǫ 2 2 k+3 = b2 = − k+2 . We are using the following notations (similar to [BFL]): b 2,k with level k and highest weight h. • Vh,k : Representation of affine sl • WP,b : Representation of the Virasoro algebra with central ch... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,076 | OWR-9790367-007 | Fivebrane Filtrations and Holomorphic Field Theories | Let $F^\bullet E(5|10)$ be the conjectural filtration of the exceptional Lie superalgebra. Identify its $N$th level with the holomorphic field theory $\chi_{\mathrm{hol}}(\mathfrak{sl}(N))$ for every $N>1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848](https://doi.org/10.4171/owr/2022/16)... | 3 | partially_solved | null | 2,022 | 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-9790367-007",
"literature-status:partially-solved",
"owr-year:2022"
] | The N=2 case has character and localization evidence identifying the associated graded piece with E(3|6), but the general filtration-to-\chi_{\mathrm{hol}}(\mathfrak{sl}(N)) identification remains conjectural. | [
{
"url": "https://arxiv.org/abs/2210.07910",
"label": "A holographic approach to the six-dimensional superconformal index"
},
{
"url": "https://doi.org/10.4171/owr/2022/16",
"label": "Oberwolfach Report 2022/16"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/16 | null | null | null | Let $F^\bullet E(5|10)$ be the conjectural filtration of the exceptional Lie superalgebra. Identify its $N$th level with the holomorphic field theory $\chi_{\mathrm{hol}}(\mathfrak{sl}(N))$ for every $N>1$. | There is a filtration F • this Lie algebra whose N th term we conjecture is related to the theory χhol (sl(N )). Infinitesimally, a translation invariant QFT is one which has a symmetry by the abelian Lie algebra of constant vector fields \{\partial/\partialxi \}. A theory on Rn is (infinites- imally) topological if th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Recent Developments in Representation Theory and Mathematical Physics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/16, pp. 817--848 |
30,005,077 | OWR-10252925-001 | Minimal Resolutions from Virtual Multigraded Resolutions | Prove that the Fourier–Mukai complex $G^\bullet$ associated with a multigraded module $M$ is the minimal free resolution of its truncation $M_{\geq d}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,022 | 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-10252925-001",
"literature-status:open",
"owr-year:2022"
] | The report leaves the assertion that the virtual complex G is the minimal free resolution as Conjecture 2.5; later work characterizes regularity and virtual resolutions but does not establish this exact claim in full generality. | [
{
"url": "https://doi.org/10.1016/j.aim.2026.111049",
"label": "Bruce--Cranton Heller--Sayrafi"
},
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/17"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | Prove that the Fourier–Mukai complex $G^\bullet$ associated with a multigraded module $M$ is the minimal free resolution of its truncation $M_{\geq d}$. | (2) Making use of a spectral sequence argument we show that even though G• is not a priori a resolution of M\geqd we have that: \betai,a (M\geqd ) = \betai,a (G• ) . (3) Finally, we characterize M being d-regular in terms of the vanishing of the cohomology in (1) above. Note the complex G• constructed in part (1) of th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,078 | OWR-10252925-002 | Algorithms for Multigraded Castelnuovo–Mumford Regularity | Develop an effective algorithm computing all minimal elements of the multigraded Castelnuovo–Mumford regularity of a coherent sheaf or module on a product of projective spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,022 | 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-10252925-002",
"literature-status:open",
"owr-year:2022"
] | Recent work gives effective characterizations and bounds on products of projective spaces, but no general finite algorithm for computing every minimal multigraded-regularity element has been established. | [
{
"url": "https://doi.org/10.1016/j.aim.2026.111049",
"label": "Bruce--Cranton Heller--Sayrafi"
},
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/17"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | Develop an effective algorithm computing all minimal elements of the multigraded Castelnuovo–Mumford regularity of a coherent sheaf or module on a product of projective spaces. | Is there an effective algorithm for computing the multigraded Castelnuovo–Mumford regularity of a coherent sheaf or module on Pn ? (2) Making use of a spectral sequence argument we show that even though G• is not a priori a resolution of M\geqd we have that: \betai,a (M\geqd ) = \betai,a (G• ) . (3) Finally, we characte... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,079 | OWR-10252925-004 | Nondivisorial Valuations in Explicit Fano Degenerations | Construct an explicit nontrivial canonical degeneration of a Fano variety whose entropy-minimizing valuation is nondivisorial. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,022 | 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-10252925-004",
"literature-status:partially-solved",
"owr-year:2022"
] | Explicit non-trivial Kähler--Ricci-soliton Fano examples are now available, including families with non-trivial moduli, but the stronger request for an explicitly computed non-divisorial minimizing valuation remains unresolved. | [
{
"url": "https://doi.org/10.1007/s00208-025-03202-w",
"label": "Miao--Wang, Mathematische Zeitschrift"
},
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/17"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | Construct an explicit nontrivial canonical degeneration of a Fano variety whose entropy-minimizing valuation is nondivisorial. | An important problem is to explicitly describe non-trivial examples and, hopefully, find one where the valuation v is not divisorial. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,080 | OWR-10252925-006 | Białynicki–Birula Cell Construction | conjecture. For every Y \in Y we consider the Bialynicki-Birula cells of the action (cf. [2]): X + (Y ) := \{x \in X | lim tx \in Y \}, X − (Y ) := \{x \in X | lim tx \in Y \}. t\to0 t\to\infty Following Mumford’s Geometric Invariant Theory (GIT), given a reductive group G acting on a variety X, one may consider the pr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report passage contains definitions and a proved construction but no open mathematical claim.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252925-006",
"literature-status:open",
"owr-year:2022"
] | The extracted fragment is a definition of Bialynicki--Birula cells inside a broader C^*--action discussion and contains no complete conjecture or verifiable problem statement. | [
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/17"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | null | conjecture. For every Y \in Y we consider the Bialynicki-Birula cells of the action (cf. [2]): X + (Y ) := \{x \in X | lim tx \in Y \}, X − (Y ) := \{x \in X | lim tx \in Y \}. t\to0 t\to\infty Following Mumford’s Geometric Invariant Theory (GIT), given a reductive group G acting on a variety X, one may consider the pr... | unrecoverable | The official report passage contains definitions and a proved construction but no open mathematical claim. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,081 | OWR-10252925-007 | Computation and Comparison of Toric Degenerations | Develop general methods to compute toric degenerations of a projective variety $X$ and characterize the relationships among distinct toric degenerations of $X$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,022 | 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-10252925-007",
"literature-status:partially-solved",
"owr-year:2022"
] | Gröbner, tropical, and matching-field methods compute many toric degenerations and relate important families, but no general method or classification of all degenerations and their relationships is known. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.09.026",
"label": "Clarke--Mohammadi--Zaffalon"
},
{
"url": "https://doi.org/10.3842/SIGMA.2021.059",
"label": "Bossinger--Mohammadi--Nájera Chávez"
},
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | Develop general methods to compute toric degenerations of a projective variety $X$ and characterize the relationships among distinct toric degenerations of $X$. | The study of toric degenerations is motivated by two natural questions: (1) How do we compute toric degenerations of X? (2) What is the relationship between two different toric degenerations of a fixed algebraic variety X? Computing toric degenerations of varieties Fatemeh Mohammadi (joint work with Oliver Clarke, France... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,082 | OWR-10252925-008 | Mutations of Higher Grassmannian Degenerations | Characterize the combinatorial mutations relating toric degenerations arising from distinct maximal cones in tropical Grassmannians $\operatorname{Gr}(k,n)$ for $k>2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** open
**Asses... | 3 | open | null | 2,022 | 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-10252925-008",
"literature-status:open",
"owr-year:2022"
] | Combinatorial mutations are understood for several matching-field families and low-dimensional cases, but the corresponding general problem for higher Grassmannians remains open. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.09.026",
"label": "Clarke--Mohammadi--Zaffalon"
},
{
"url": "https://doi.org/10.4171/owr/2022/17",
"label": "Oberwolfach Report 2022/17"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | Characterize the combinatorial mutations relating toric degenerations arising from distinct maximal cones in tropical Grassmannians $\operatorname{Gr}(k,n)$ for $k>2$. | The natural question is to understand such mutations for higher Grassmannians. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,083 | OWR-10252925-009 | Nondegeneracy in the Spectral Edges Conjecture | For a sufficiently general periodic discrete Schrödinger operator $L$, prove that every extremum of the dispersion function $\lambda$ on the real Bloch variety is nondegenerate. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927](https://doi.org/10.4171/owr/2022/17)
## Literature review (checked 2026-08-22)
**Status:** partially sol... | 3 | partially_solved | null | 2,022 | 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-10252925-009",
"literature-status:partially-solved",
"owr-year:2022"
] | Critical-point bounds and effective criteria are proved, and the spectral-edges conjecture is established for broad families of periodic graphs, but the general conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/JST/503",
"label": "Faust--Sottile, Journal of Spectral Theory"
},
{
"url": "https://arxiv.org/abs/2512.01226",
"label": "Faust--Robinson--Sottile"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/17 | null | null | null | For a sufficiently general periodic discrete Schrödinger operator $L$, prove that every extremum of the dispersion function $\lambda$ on the real Bloch variety is nondegenerate. | A first step towards the spectral edges conjecture is to understand the critical points of \lambda. Figure 2. Bloch varieties with edge parameters 6,3,2 and 1,1,1 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Toric Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/17, pp. 861--927 |
30,005,084 | OWR-10252926-001 | Unspecified Geometric Representation Theory Conjecture | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950 Shane Kelly Combinatorial Origins of Geometric Satake . . . . . . . . . . . . . . . . . . . . . . . . . 953 Leonardo Patimo Geometric Satake and Finkelberg–Mirković . . . . . . . . . . . . . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Geometric Representation Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/18, pp. 929--978](https://doi.org/10.4171/owr/2022/18)
## Literature review (checked ... | 3 | open | null | 2,022 | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this is a table-of-contents fragment without a recoverable standalone conjecture. No separate clean statement) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252926-001",
"literature-status:open",
"owr-year:2022"
] | The extracted fragment is only a table-of-contents fragment and does not identify a mathematical conjecture or claim that can be assessed. | [
{
"url": "https://doi.org/10.4171/owr/2022/18",
"label": "Oberwolfach Report 2022/18"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/18 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950 Shane Kelly Combinatorial Origins of Geometric Satake . . . . . . . . . . . . . . . . . . . . . . . . . 953 Leonardo Patimo Geometric Satake and Finkelberg–Mirković . . . . . . . . . . . . . . . . . . . . . . . . .... | unrecoverable | The official report shows that this is a table-of-contents fragment without a recoverable standalone conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Geometric Representation Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/18, pp. 929--978 |
30,005,085 | OWR-10252926-004 | Finkelberg–Mirković Equivalence in Modular Geometric Satake | Let $k$ have characteristic $p$, let $G$ be reductive with Weyl group $W$, and let $\operatorname{Rep}^{\mathrm{ext}}_0(G_k^\vee)$ be the Serre subcategory generated by the modules $L(\lambda)$ for $\lambda\in W\mathbin{\cdot}0\cap X^+$. Does an equivalence
$$
Q:\operatorname{Perv}_{\mathrm{Iw}}(\operatorname{Gr}_G,k)\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Geometric Representation Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/18, pp. 929--978](https://doi.org/10.4171/owr/2022/18)
## Literature review (checked ... | 3 | open | null | 2,022 | 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-10252926-004",
"literature-status:open",
"owr-year:2022"
] | The Finkelberg--Mirkovic equivalence remains open in general; geometric Satake and modular affine-Hecke advances provide substantial partial progress but not a proof of the stated equivalence. | [
{
"url": "https://doi.org/10.1007/s10240-022-00134-y",
"label": "Riche--Williamson, Smith--Treumann theory"
},
{
"url": "https://doi.org/10.4171/owr/2022/18",
"label": "Oberwolfach Report 2022/18"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/18 | null | null | null | Let $k$ have characteristic $p$, let $G$ be reductive with Weyl group $W$, and let $\operatorname{Rep}^{\mathrm{ext}}_0(G_k^\vee)$ be the Serre subcategory generated by the modules $L(\lambda)$ for $\lambda\in W\mathbin{\cdot}0\cap X^+$. Does an equivalence
$$
Q:\operatorname{Perv}_{\mathrm{Iw}}(\operatorname{Gr}_G,k)\... | The Finkelberg–Mirković conjecture. Assume now that k is a field of char- acteristic p. There are several properties of the category Rep(G∨k ) which have no known counterpart on the geometric side. The Finkelberg–Mirković conjecture would explain how to construct the Frobenius twist functor geometrically. Let W be th... | 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: Geometric Representation Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/18, pp. 929--978 |
30,005,086 | OWR-10252928-001 | Unspecified Conic Optimization Research Problem | Abstract. From a mathematical perspective, optimization is the science of proving inequalities. In this sense, computational optimization is a method for computer-assisted proofs. Conic (linear) optimization is the problem of minimizing a linear func- tional over the intersection of a convex cone with an affine subspac... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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 shows that this is workshop-level introductory prose rather than a standalone conic-optimization problem. No separate cl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252928-001",
"literature-status:open",
"owr-year:2022"
] | The extracted fragment is a workshop abstract describing a research program, not a specific mathematical claim with a determined truth status. | [
{
"url": "https://doi.org/10.4171/owr/2022/20",
"label": "Oberwolfach Report 2022/20"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | null | Abstract. From a mathematical perspective, optimization is the science of proving inequalities. In this sense, computational optimization is a method for computer-assisted proofs. Conic (linear) optimization is the problem of minimizing a linear func- tional over the intersection of a convex cone with an affine subspac... | unrecoverable | The official report shows that this is workshop-level introductory prose rather than a standalone conic-optimization problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,087 | OWR-10252928-002 | Vizing’s Cartesian-Product Domination Conjecture | For all finite graphs $G$ and $H$, is $\gamma(G\square H)\geq\gamma(G)\gamma(H)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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-10252928-002",
"literature-status:open",
"owr-year:2022"
] | Vizing's conjecture remains open in general; the report's certificates concern only classes already known to satisfy the inequality, while 2026 work improves constant-factor bounds without proving the conjecture. | [
{
"url": "https://doi.org/10.1016/j.jsc.2023.102236",
"label": "Gaar--Siebenhofer, Journal of Symbolic Computation"
},
{
"url": "https://arxiv.org/abs/2606.14414",
"label": "Steiner, A constant-factor step towards Vizing's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2022/20",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | For all finite graphs $G$ and $H$, is $\gamma(G\square H)\geq\gamma(G)\gamma(H)$? | Finally, it should be mentioned that for all specifically considered graph classes it is already known in the literature that the inequality in Vizing’s conjecture is true. As a result, we do not gain new knowledge on whether Vizing’s conjecture is true or not for any graph classes. The report passage is retained verba... | 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 | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,088 | OWR-10252928-003 | Unspecified Flag Algebra Extremal Problem | of convex sets Φk , each containing Φ. Moreover, with appropriate control, opti- mization over the relaxations Φk can be carried out efficiently, for instance via semidefinite programming. This allows us to compute upper bounds for ex(C, H). Many significant results in extremal combinatorics have been obtained via the ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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 gives a descriptive account of flag-algebra methods but does not formulate a standalone open extremal problem. No separa) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252928-003",
"literature-status:open",
"owr-year:2022"
] | The extracted text is a descriptive flag-algebra passage rather than a determinate conjecture; no standalone claim can be resolved, so it remains open under the queue rule. | [
{
"url": "https://doi.org/10.4171/owr/2022/20",
"label": "Oberwolfach Report 20/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | null | of convex sets Φk , each containing Φ. Moreover, with appropriate control, opti- mization over the relaxations Φk can be carried out efficiently, for instance via semidefinite programming. This allows us to compute upper bounds for ex(C, H). Many significant results in extremal combinatorics have been obtained via the ... | unrecoverable | The official report gives a descriptive account of flag-algebra methods but does not formulate a standalone open extremal problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,089 | OWR-10252928-004 | Closed Forms for Multivariate Polynomial Approximation Kernels | Can the coefficients of the optimal multivariate polynomial-approximation kernel be expressed in closed form? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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-10252928-004",
"literature-status:open",
"owr-year:2022"
] | The multivariate closed-form question for optimal polynomial-approximation kernels remains explicitly open; subsequent work gives constructions but no closed-form resolution. | [
{
"url": "https://doi.org/10.4171/owr/2022/20",
"label": "Oberwolfach Report 20/2022"
},
{
"url": "https://arxiv.org/abs/2203.05892",
"label": "Kirschner--de Klerk, multivariate approximation kernels"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | Can the coefficients of the optimal multivariate polynomial-approximation kernel be expressed in closed form? | It is a open question whether it is possible to find a closed form for the multivariate case as well. 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 | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,090 | OWR-10252928-005 | Kissing Number of Regular Tetrahedra | What is the maximum number of pairwise interior-disjoint regular tetrahedra in three-dimensional Euclidean space that can share a common vertex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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-10252928-005",
"literature-status:open",
"owr-year:2022"
] | The icosahedral construction gives 20 tetrahedra and the report improves the elementary upper bound 22, but the exact value and optimality of 20 are not proved. | [
{
"url": "https://doi.org/10.4171/owr/2022/20",
"label": "Spomer et al., regular-tetrahedron kissing number"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/c99d51a5-c8ce-41bf-afb1-b59e6547c379/download",
"label": "Oberwolfach primary abstract"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | What is the maximum number of pairwise interior-disjoint regular tetrahedra in three-dimensional Euclidean space that can share a common vertex? | What is the maximum number \tau3 of pairwise nonoverlapping regular tetrahedra in R3 that share a vertex? The kissing number problem for regular tetrahedra Andreas Spomer (joint work with Frank Vallentin, Fernando Mário de Oliveira Filho, Stefan Krupp and Fabrı́cio C. Machado) Conic Linear Optimization for Computer-As... | 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 | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,091 | OWR-10252928-006 | Sharp Linear-Programming Bounds for Sphere Packing | Does the Cohn–Elkies linear-programming method yield an asymptotic sphere-packing upper bound
$$
2^{-(\lambda+o(1))n}
$$
for some $0.604<\lambda<0.605$? Is the strengthened three-point lattice bound sharp in dimension $4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089](https://doi.org/10.4171/owr/2022/20)
## Literature review (chec... | 3 | open | null | 2,022 | 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-10252928-006",
"literature-status:open",
"owr-year:2022"
] | The asymptotic lambda bound and sharpness of the strengthened lattice bound in dimension 4 remain conjectural; the cited computations support but do not prove them. | [
{
"url": "https://doi.org/10.4171/owr/2022/20",
"label": "Oberwolfach Report 20/2022"
},
{
"url": "https://doi.org/10.1007/JHEP12(2020)066",
"label": "Afkhami-Jeddi et al., high-dimensional sphere packing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/20 | null | null | null | Does the Cohn–Elkies linear-programming method yield an asymptotic sphere-packing upper bound
$$
2^{-(\lambda+o(1))n}
$$
for some $0.604<\lambda<0.605$? Is the strengthened three-point lattice bound sharp in dimension $4$? | based on this we conjecture it can be used to get the asymptotic upper bound 2−(\lambda+o(1))n with 0.604 < \lambda < 0.605. Based on the computational results we conjecture this new bound is sharp for the lattice sphere packing problem in dimension 4. The report passage is retained verbatim as the relevant context 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 | Conic Linear Optimization for Computer-Assisted Proofs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/20, pp. 1039--1089 |
30,005,092 | OWR-10252929-001 | Zilber-Pink Unlikely Intersection Conjecture | The conjecture of Zilber-Pink on unlikely intersections encompasses many classi- cal results and conjectures from Diophantine geometry including the Mordell and André–Oort Conjectures. 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:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report contains only workshop-level context mentioning the Zilber–Pink conjecture; the complete modular formulation is retained) | [
"OWR-10252929-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252929-001",
"literature-status:open",
"owr-year:2022"
] | Zilber--Pink contains the stated classical conjectures, but current primary literature still describes the general conjecture as widely open; only substantial special cases are known. | [
{
"url": "https://doi.org/10.4171/RLM/1086",
"label": "Pila, combining Schanuel and Zilber--Pink"
},
{
"url": "https://arxiv.org/abs/2402.09487",
"label": "Daw--Orr, Zilber--Pink in products of modular curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | null | The conjecture of Zilber-Pink on unlikely intersections encompasses many classi- cal results and conjectures from Diophantine geometry including the Mordell and André–Oort Conjectures. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report contains only workshop-level context mentioning the Zilber–Pink conjecture; the complete modular formulation is retained separately in OWR-10252929-008. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,093 | OWR-10252929-004 | Irrationality of Catalan’s Constant | Is Catalan's constant $G=\sum_{n\geq0}(-1)^n/(2n+1)^2$ irrational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252929-004",
"literature-status:open",
"owr-year:2022"
] | The irrationality of Catalan's constant remains unproved; effective rational-approximation results improve bounds but do not establish irrationality. | [
{
"url": "https://doi.org/10.4171/owr/2022/21",
"label": "Viola, rational approximations to Catalan's constant"
},
{
"url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v10i1r14",
"label": "Zudilin, Apéry-like equation for Catalan's constant"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | Is Catalan's constant $G=\sum_{n\geq0}(-1)^n/(2n+1)^2$ irrational? | Catalan considered the constant \infty X (−1)n G = . n=0 (2n + 1)2 G is supposed to be transcendental, but even the irrationality of G is a famous open problem. Rational approximations to Catalan’s constant Carlo Viola (joint work with Raffaele Marcovecchio) for positive integer parameters a1 , a2 , a3 , b1 , b2 satisf... | 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,094 | OWR-10252929-006 | Counting Integer Matrices with Fixed Characteristic Polynomial | Let $R_n(H;f)$ count the integer $n\times n$ matrices of height at most $H$ with characteristic polynomial $f$. Uniformly over $f$, is $R_n(H;f)\leq H^{n(n-1)/2+o(1)}$ as $H\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252929-006",
"literature-status:open",
"owr-year:2022"
] | The uniform characteristic-polynomial matrix-counting conjecture remains unresolved; the primary report proves only n equal to 2 and weaker uniform bounds in higher dimensions. | [
{
"url": "https://doi.org/10.4171/owr/2022/21",
"label": "Oberwolfach Report 21/2022"
},
{
"url": "https://doi.org/10.48550/arXiv.2203.03880",
"label": "Ostafe--Shparlinski, integer matrices"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | Let $R_n(H;f)$ count the integer $n\times n$ matrices of height at most $H$ with characteristic polynomial $f$. Uniformly over $f$, is $R_n(H;f)\leq H^{n(n-1)/2+o(1)}$ as $H\to\infty$? | conjecture. Conjecture 1. Uniformly over polynomials f we have Rn (H; f ) \leq H n(n−1)/2+o(1) , as H \to \infty. Unconditionally, only counting matrices with a given determinant and apply- ing [8, Theorem 4], we instantly obtain 2 (13) Rn (H; f ) \leq H n −n+o(1) . Furthermore, we also show that Conjecture 1 holds 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,095 | OWR-10252929-007 | Relative Bogomolov Conjecture for Abelian Schemes | Let $\pi:A\to S$ be an abelian scheme and let $X\subset A$ be irreducible with $\pi(X)=S$. Must either the points of arbitrarily small canonical height fail to be Zariski dense in $X$, or $X$ have codimension at most $\dim S$ in a horizontal torsion coset? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | partially_solved | null | 2,022 | 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-10252929-007",
"literature-status:partially-solved",
"owr-year:2022"
] | The relative Bogomolov conjecture is proved for arbitrary subvarieties in fiber products of elliptic families, while the general abelian-scheme formulation remains open. | [
{
"url": "https://doi.org/10.1515/crelle-2022-0082",
"label": "Kühne, relative Bogomolov for elliptic curves"
},
{
"url": "https://doi.org/10.1016/j.jnt.2021.03.028",
"label": "Dimitrov--Gao--Habegger, relative Bogomolov"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | Let $\pi:A\to S$ be an abelian scheme and let $X\subset A$ be irreducible with $\pi(X)=S$. Must either the points of arbitrarily small canonical height fail to be Zariski dense in $X$, or $X$ have codimension at most $\dim S$ in a horizontal torsion coset? | In this form, the conjecture is a theorem due to Ullmo [11] and Zhang [12], later reproven by David and Philippon [3]. The setting of the relative Bogomolov conjecture is a straightforward generalization: Instead of a single abelian variety we consider a family \pi : A \to S of abelian varieties over an irreducible Q-v... | 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,096 | OWR-10252929-008 | Zilber–Pink for Powers of the Modular Curve | For an irreducible Hodge-generic subvariety $V\subset Y(1)^n$, is the union of the atypical components of intersections of $V$ with proper special subvarieties non-Zariski-dense in $V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-10252929-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252929-008",
"literature-status:partially-solved",
"owr-year:2022"
] | Zilber--Pink for asymmetric curves is a theorem, and later work adds boundary cases, but the general problem in powers of the modular curve remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/21",
"label": "Daw, Zilber--Pink in Y(1) powers"
},
{
"url": "https://arxiv.org/abs/2402.09487",
"label": "Daw--Orr, beyond multiplicative degeneration"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | For an irreducible Hodge-generic subvariety $V\subset Y(1)^n$, is the union of the atypical components of intersections of $V$ with proper special subvarieties non-Zariski-dense in $V$? | By Y (1) we denote the modular curve SL2 (Z)\H and (by abuse of notation) the underlying algebraic variety, the affine line over Q. As such, Y (1) (and, therefore, Y (1)n ) is a Shimura variety and, hence, the subject of the Zilber–Pink conjecture. In 2012, Habegger and Pila obtained a major result in the direction of ... | 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,097 | OWR-10252929-010 | Hermite and GL2 Equivalence Classes of Number Fields | Does $\operatorname{PI}(K)$ contain only finitely many Hermite-equivalence classes that split into more than one $\operatorname{GL}_2(\mathbb{Z})$-equivalence class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.2422/2036-2145.201107_005",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] keep **partially_solved**, but **restate it**. J.-H. Evertse (joint with M. Bhargava, K. Győry, L. Remete and A. Swaminathan; OWR 21/2022, p. 1154) asks whether, for a number field K, only finitely many Hermite equivalence classes in PI(K) split into more than one GL₂(Z)-cl... | [
"owr",
"oberwolfach-reports",
"OWR-10252929-010",
"literature-status:partially-solved",
"owr-year:2022"
] | There are finite-class results for suitable symmetric Galois closures and infinitely many split Hermite classes, but the exact finiteness question for arbitrary number fields remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/21",
"label": "Evertse et al., Hermite equivalence"
},
{
"url": "https://arxiv.org/abs/2109.02932",
"label": "Bhargava et al., Hermite equivalence of polynomials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | Does $\operatorname{PI}(K)$ contain only finitely many Hermite-equivalence classes that split into more than one $\operatorname{GL}_2(\mathbb{Z})$-equivalence class? | Is it true that PI(K) has only finitely many Hermite equivalence classes that fall apart into more than one GL2 (Z)-equivalence class? Theorem 2 ([4]). Let n \geq 4. Then PI(n) contains infinitely many Hermite equivalence classes that are the union of at least two GL2 (Z)-equivalence classes. Theorem 3. Let K be a numb... | 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,098 | OWR-10252929-011 | Vojta's Diophantine Approximation Conjecture | Let $X$ be a smooth projective variety over a number field $k$, let $D$ be a reduced normal-crossings divisor, let $K_X$ be a canonical divisor, and let $A$ be ample. For every $\varepsilon>0$, does there exist a proper Zariski-closed set $Z_\varepsilon\subsetneq X$ such that $\sum_{v\in S}\lambda_v(D,P)+h_{K_X}(P)<\va... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164](https://doi.org/10.4171/owr/2022/21)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252929-011",
"literature-status:open",
"owr-year:2022"
] | Vojta's conjecture in the stated number-field generality remains open; recent primary work proves only function-field or other special cases. | [
{
"url": "https://doi.org/10.4171/owr/2022/21",
"label": "Oberwolfach Report 21/2022"
},
{
"url": "https://doi.org/10.1016/j.aim.2025.110358",
"label": "Guo et al., Vojta's abc conjecture over function fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/21 | null | null | null | Let $X$ be a smooth projective variety over a number field $k$, let $D$ be a reduced normal-crossings divisor, let $K_X$ be a canonical divisor, and let $A$ be ample. For every $\varepsilon>0$, does there exist a proper Zariski-closed set $Z_\varepsilon\subsetneq X$ such that $\sum_{v\in S}\lambda_v(D,P)+h_{K_X}(P)<\va... | conjecture. Conjecture 2. (Vojta) Let X be a smooth projective variety, D be a reduced normal-crossing (NC) divisor, K be a canonical divisor, and A be an ample divisor, all def. over k. Then for all ǫ > 0, there exists a Zariski-closed Zǫ 6= X such that for all P \in X(k)\Zǫ , X \lambdav (D, P ) + h(K, P ) < ǫh(A, P )... | 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 | Diophantische Approximationen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/21, pp. 1091--1164 |
30,005,099 | OWR-10252930-001 | Matching Thresholds for Pseudorandom Clique Factors | For clique factors larger than triangles in sparse pseudorandom graphs, do matching constructions attain the known threshold bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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-10252930-001",
"literature-status:open",
"owr-year:2022"
] | For pseudorandom K-subscript-r factors, Morris proves a sufficient condition for every fixed r and tightness for r equal to 3, but matching obstructions for larger cliques remain unresolved. | [
{
"url": "https://doi.org/10.4171/JEMS/1388",
"label": "Morris, clique factors in pseudorandom graphs"
},
{
"url": "https://doi.org/10.4171/owr/2022/22",
"label": "Oberwolfach Report 22/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For clique factors larger than triangles in sparse pseudorandom graphs, do matching constructions attain the known threshold bounds? | Pham presented the proof of a related conjecture of Talagrand, which also follows from their method. Patrick Morris presented his recent proof of a beautiful conjecture of Krivele- vich, Sudakov and Szabó, on the threshold for the existence of a triangle-factor in a sparse pseudorandom graph. He also obtained bounds f... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,100 | OWR-10252930-002 | Talagrand's Conjecture on Selector Processes | 1197 Huy Tuan Pham (joint with Jinyoung Park) On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Workshop: Combinatorics, Probability and Computing Table of Contents | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (a title line, not a question)) | null | null | [Discussion #4 literature review, 2026-09-29] **solved (a title line, not a question)**. The record is the table-of-contents line of H. T. Pham's talk (joint with J. Park; OWR 22/2022, pp. 1199–1201; "1197" is the previous entry's page). The talk proves the conjecture its title names, Talagrand's selector-process conje... | [
"owr",
"oberwolfach-reports",
"OWR-10252930-002",
"literature-status:open",
"owr-year:2022"
] | This is only a table-of-contents fragment identifying a talk, not a mathematical claim; no resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2022/22",
"label": "Oberwolfach Report 22/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | null | 1197 Huy Tuan Pham (joint with Jinyoung Park) On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Workshop: Combinatorics, Probability and Computing Table of Contents | unrecoverable | The official source passage is a table-of-contents entry identifying a talk, not a mathematical claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,101 | OWR-10252930-004 | Erdős–Gallai Cycle-Decomposition Conjecture | Can every $n$-vertex graph be decomposed into $O(n)$ cycles and edges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 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-10252930-004",
"literature-status:partially-solved",
"owr-year:2022"
] | Bucic and Montgomery improve the decomposition to order n times log-star n cycles and edges, but the conjectured order n bound is not proved. | [
{
"url": "https://arxiv.org/abs/2211.07689",
"label": "Bucic--Montgomery, Erdős--Gallai cycle decomposition"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870823005777",
"label": "published primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Can every $n$-vertex graph be decomposed into $O(n)$ cycles and edges? | That Opnq cycles might be sufficient is easily seen to be equivalent to the following conjecture of Erdős and Gallai [4] dating back to 1966, which is one of the major open problems on graph decompositions. New bounds on the Erdős-Gallai Cycle Decomposition Conjecture Matija Bucić (joint work with Richard Montgomery... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,102 | OWR-10252930-007 | Largest Product-Free Subsets of Alternating Groups | What is the maximum size of a product-free subset of the alternating group $A_n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-007",
"literature-status:partially-solved",
"owr-year:2022"
] | Keevash, Lifshitz, and Minzer determine the maximum and all extremizers in A-subscript-n for sufficiently large n, while the unrestricted finite-n formulation is not fully covered. | [
{
"url": "https://doi.org/10.1007/s00222-024-01273-1",
"label": "Keevash--Lifshitz--Minzer, product-free alternating groups"
},
{
"url": "https://arxiv.org/abs/2205.15191",
"label": "primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | What is the maximum size of a product-free subset of the alternating group $A_n$? | By contrast, it is a long-standing open problem to find the largest product-free subset of An . The largest product-free subsets of the alternating groups Peter Keevash (joint work with Noam Lifshitz, Dor Minzer) | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,103 | OWR-10252930-008 | Structure of Extremal Product-Free Subsets | For a product-free subset $A$ of the alternating group $A_n$, characterize the structure of extremal and near-extremal choices of $A$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-008",
"literature-status:partially-solved",
"owr-year:2022"
] | The same theorem gives extremal structure and stability for sufficiently large n, but the vague unrestricted structure question is not fully resolved for every n. | [
{
"url": "https://doi.org/10.1007/s00222-024-01273-1",
"label": "Keevash--Lifshitz--Minzer, product-free alternating groups"
},
{
"url": "https://arxiv.org/abs/2205.15191",
"label": "primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For a product-free subset $A$ of the alternating group $A_n$, characterize the structure of extremal and near-extremal choices of $A$. | What can be said about the structure of A? The report passage is retained verbatim as the relevant context for this extracted problem. | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,104 | OWR-10252930-010 | Ryser–Brualdi–Stein Transversal Conjecture | The following combined form of these conjectures, known as the Ryser-Brualdi-Stein conjecture, has become the most widely known open problem on transversals in Latin squares. A proof of the Ryser-Brualdi-Stein conjecture for large even n Richard Montgomery | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report states the Ryser–Brualdi–Stein conjecture, but the identical conjecture is already represented by the earlier canonical ) | [
"OWR-16763-027"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-010",
"literature-status:partially-solved",
"owr-year:2022"
] | Montgomery proves the Ryser--Brualdi--Stein conclusion for all sufficiently large even n, but the all-orders conjecture remains unresolved. | [
{
"url": "https://arxiv.org/abs/2310.19779",
"label": "Montgomery, Ryser--Brualdi--Stein for large even n"
},
{
"url": "https://doi.org/10.4171/owr/2022/22",
"label": "Oberwolfach Report 22/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | null | The following combined form of these conjectures, known as the Ryser-Brualdi-Stein conjecture, has become the most widely known open problem on transversals in Latin squares. A proof of the Ryser-Brualdi-Stein conjecture for large even n Richard Montgomery | unrecoverable | The official report states the Ryser–Brualdi–Stein conjecture, but the identical conjecture is already represented by the earlier canonical record OWR-16763-027. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,105 | OWR-10252930-013 | Induced Structures in Highly Chromatic Graphs | Which induced subgraphs must occur in graphs of sufficiently large chromatic number? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"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-10252930-013",
"literature-status:open",
"owr-year:2022"
] | This is a broad methodological question rather than a definite theorem or conjecture; the record supplies no uniquely testable claim, so its resolution is unclear and is classified as open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Which induced subgraphs must occur in graphs of sufficiently large chromatic number? | It is a fundamental problem of graph theory to understand what structures must appear in graphs of large chromatic number. Induced subgraphs of induced subgraphs of large chromatic number Alex Scott (joint work with António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Youri Tamitegama and Jane Tan) | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,106 | OWR-10252930-015 | Existence of the Diagonal Ramsey Growth Limit | If $R(n)=R(n,n)$ denotes the diagonal Ramsey number, does the limit $$\lim_{n\to\infty}R(n)^{1/n}$$ exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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-10252930-015",
"literature-status:open",
"owr-year:2022"
] | The statement concerns the still-unresolved existence of the exponential growth limit for diagonal Ramsey numbers; the cited primary literature continues to describe this as a famous open problem. | [
{
"url": "https://arxiv.org/abs/2111.02373",
"label": "Shapira and Tyomkyn, weak saturation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | If $R(n)=R(n,n)$ denotes the diagonal Ramsey number, does the limit $$\lim_{n\to\infty}R(n)^{1/n}$$ exist? | While it is easy to see that the first quantity indeed tends to a limit [18], it is a famous open problem of Erdős [9, 10, 12] to prove that the second one does so as well. Weakly Saturated Hypergraphs and a Conjecture of Tuza Asaf Shapira (joint work with M. Tyomkyn) | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,107 | OWR-10252930-017 | Gyárfás Tree-Packing Conjecture | Can $K_n$ be decomposed into any family of trees $T_1,\ldots,T_n$ in which $T_i$ has $i$ vertices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-017",
"literature-status:open",
"owr-year:2022"
] | Gyarfás's tree-packing conjecture for an arbitrary sequence of trees of orders one through n remains open; only bounded-degree and other substantial special cases are known. | [
{
"url": "https://doi.org/10.1016/j.jctb.2016.03.003",
"label": "Bottcher et al., Journal of Combinatorial Theory B"
},
{
"url": "https://doi.org/10.1007/s00039-021-00576-2",
"label": "Montgomery, Pokrovskiy, and Sudakov"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Can $K_n$ be decomposed into any family of trees $T_1,\ldots,T_n$ in which $T_i$ has $i$ vertices? | Ringel’s conjecture was well-known as one of the major open problems in the area of graph packing. Besides Ringel’s conjecture, the other major open problem of this type is a conjecture of Gyárfás [6], saying that Kn should have a decom- position into any family of trees T1 , . . . , Tn where each Ti has i vertices. ... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,108 | OWR-10252930-018 | Enumeration and Typical Structure of $k$-SAT Functions | How many $k$-SAT functions on $n$ Boolean variables are there, and what does a typical such function look like? In particular, for fixed $k\geq 2$, is a $1-o(1)$ fraction of all such functions unate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | solved | null | 2,022 | 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 | {
"source_url": "https://doi.org/10.1145/3564246.3585123",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved**. Y. Zhao (joint with D. Dong and N. Mani; OWR 22/2022, pp. 1222–1224) states the Bollobás–Brightwell–Leader conjecture, then known for k ≤ 5: for fixed k ≥ 2 there are (1+o(1))2^{n+C(n,k)} k-SAT functions on n variables, i.e. almost all are unate. Balogh–Dong–Lid... | [
"owr",
"oberwolfach-reports",
"OWR-10252930-018",
"literature-status:partially-solved",
"owr-year:2022"
] | The Bollobas--Brightwell--Leader enumeration conjecture is proved for k equal to 2, 3, 4, and 5, but remains open for general fixed k; the record's broad counting question therefore has only a partial answer. | [
{
"url": "https://arxiv.org/abs/2107.09233",
"label": "Dong, Mani, and Zhao, Enumerating k-SAT functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | How many $k$-SAT functions on $n$ Boolean variables are there, and what does a typical such function look like? In particular, for fixed $k\geq 2$, is a $1-o(1)$ fraction of all such functions unate? | How many k-SAT functions on n boolean variables are there? What does a typical such function look like? Enumerating k-SAT functions Yufei Zhao (joint work with Dingding Dong and Nitya Mani) Conjecture 1 (Bollobás, Brightwell, and Leader [3]). Fix k ě 2. The number of n k-SAT functions on n boolean variables is p1 ` op... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,109 | OWR-10252930-019 | Asymptotic Counts of Growing-Width $k$-SAT Functions | If $k=k(n)\leq(1/2-c)n$ for some constant $c>0$, what is the asymptotic number of $k$-SAT functions on $n$ Boolean variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 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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"id": 3,
"level": 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-10252930-019",
"literature-status:partially-solved",
"owr-year:2022"
] | The conjectured asymptotic formula is known for k equal to 2 and 3, proved for k equal to 4, and verified computationally for k equal to 5, while the all-k statement remains unresolved. | [
{
"url": "https://arxiv.org/abs/2107.09233",
"label": "Dong, Mani, and Zhao, Enumerating k-SAT functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | If $k=k(n)\leq(1/2-c)n$ for some constant $c>0$, what is the asymptotic number of $k$-SAT functions on $n$ Boolean variables? | conjecture for k “ 2 was proved by Allen [1] and k “ 3 by Ilinca and Kahn [6]. Bollobás and Brightwell [2] conjectured that if k “ kpnq is allowed to increase with n, as long as k ď p1\{2 ´ cqn for some constant c ą 0, the number of k-SAT n functions on n-variables is 2p1`op1qqpk q . The situation is different for k ě... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,110 | OWR-10252930-020 | Extremal Conjecture for Partially Directed Uniform Hypergraphs | For fixed $k\geq 2$ and all sufficiently large $n$, does every $n$-vertex $k$-PDG without $\widetilde T_k$ as a subgraph satisfy $\alpha+(\log_2 3)\beta\leq 1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 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"
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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-10252930-020",
"literature-status:partially-solved",
"owr-year:2022"
] | The proposed partially directed hypergraph extremal conjecture is established in the k equal to 4 case and checked computationally for k equal to 5, but no proof for every fixed k is known. | [
{
"url": "https://arxiv.org/abs/2107.09233",
"label": "Dong, Mani, and Zhao, Enumerating k-SAT functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For fixed $k\geq 2$ and all sufficiently large $n$, does every $n$-vertex $k$-PDG without $\widetilde T_k$ as a subgraph satisfy $\alpha+(\log_2 3)\beta\leq 1$? | Conjecture 4. Fix k ě 2. For all sufficiently large n (depending on k), every n-vertex k-PDG without T\textasciitilde{}k as a subgraph satisfies \alpha ` plog2 3q\beta ď 1. One of the our main results is the following. Theorem 5. For each fixed k ě 2, Conjecture 4 implies Conjecture 1. Furthermore, we prove Conjecture ... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,111 | OWR-10252930-021 | Elementary Proof of the Closed Walk Stacking Criterion | Find an elementary proof that a closed walk $W$ has a stacking in a graph $G$ if and only if $W\neq kW'$ for every walk $W'$ and every integer $k\geq 2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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-10252930-021",
"literature-status:open",
"owr-year:2022"
] | The underlying stacking characterization is a theorem of Louder and Witten, but the extracted problem asks for an elementary proof and no such resolution was identified; the proof request remains open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Find an elementary proof that a closed walk $W$ has a stacking in a graph $G$ if and only if $W\neq kW'$ for every walk $W'$ and every integer $k\geq 2$. | Problem 3. Find an elementary proof of Theorem 2. 1226 Oberwolfach Report 22/2022 Proposed by Ashwin Sah Problem 4. Let tp pF, Gq “ p´epF q |G|´|F | hompF, Gq, the p-normalized homomorphism count of F within graph G. Is it possible to con- struct a sequence of graphs Gn with |Gn | Ñ 8‘ with edge densities pn “ |Gn |´op... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,112 | OWR-10252930-022 | Sparse Graph Sequences with Prescribed Homomorphism Limits | For a graph $F$ and a graph $G$ of edge density $p$, define $$t_p(F,G)=p^{-e(F)}|G|^{-|F|}\operatorname{hom}(F,G).$$ Can one construct graphs $G_n$ with $|G_n|\to\infty$ and edge densities $p_n=|G_n|^{-o(1)}$ such that $a_F=\lim_{n\to\infty}t_{p_n}(F,G_n)$ exists for every $F$, while $$a_{C_4}=a_{K_3}=1,\qquad \sup_F a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-022",
"literature-status:open",
"owr-year:2022"
] | The graph-sequence existence question in the extracted Problem 4 is still posed as an open extremal-density problem; no primary result resolving all five stated conditions was found. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For a graph $F$ and a graph $G$ of edge density $p$, define $$t_p(F,G)=p^{-e(F)}|G|^{-|F|}\operatorname{hom}(F,G).$$ Can one construct graphs $G_n$ with $|G_n|\to\infty$ and edge densities $p_n=|G_n|^{-o(1)}$ such that $a_F=\lim_{n\to\infty}t_{p_n}(F,G_n)$ exists for every $F$, while $$a_{C_4}=a_{K_3}=1,\qquad \sup_F a... | Proposed by Ashwin Sah Problem 4. Let tp pF, Gq “ p´epF q |G|´|F | hompF, Gq, the p-normalized homomorphism count of F within graph G. Is it possible to con- struct a sequence of graphs Gn with |Gn | Ñ 8‘ with edge densities pn “ |Gn |´op1q such that: (1) aF “ limnÑ8 tpn pF, Gn q exists for every graph F (2) aC4 “ 1 (3... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,113 | OWR-10252930-023 | Polynomial-Density Hales–Jewett Problem for Graph Families | If $\mathcal{F}$ is a family of graphs on $[n]$ such that $F_1\triangle F_2$ is not a clique for any distinct $F_1,F_2\in\mathcal{F}$, must $|\mathcal{F}|=o(2^{\binom n2})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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-10252930-023",
"literature-status:open",
"owr-year:2022"
] | Alon's family-size assertion is explicitly identified as the first open case of polynomial-density Hales--Jewett, and current primary discussion still describes the corresponding density problem as wide open. | [
{
"url": "https://web.math.princeton.edu/~nalon/PDFS/gcs4.pdf",
"label": "Alon, Graph-Codes"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | If $\mathcal{F}$ is a family of graphs on $[n]$ such that $F_1\triangle F_2$ is not a clique for any distinct $F_1,F_2\in\mathcal{F}$, must $|\mathcal{F}|=o(2^{\binom n2})$? | Noga Alon Problem 5. Given graphs G1 and G2 on the vertex set rns define G1 ‘ G2 “ prns, E1 ‘ E2 q. Let F be a family of graphs on the vertex set rns such that for any distinct pair of graph F1 and F2 we have that F1 ‘ F2 is not a clique. Prove (or disprove) that ˆ ˙ n |F | “ o 2 p 2 q . Proposed by Ashwin Sah Problem ... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,114 | OWR-10252930-024 | Spread Bounds for the Random Triangle-Removal Process | For the random triangle-removal process on $K_n$, run for $n^2/6-n^{1.99}$ steps with output triangle set $\mathcal{T}_n$, do there exist events $E_n$ of probability $1-o(1)$ and a constant $C$ such that $\Pr(T_1,\ldots,T_k\in\mathcal{T}_n\mid E_n)\leq(C/n)^k$ for every collection of distinct triangles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 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-10252930-024",
"literature-status:open",
"owr-year:2022"
] | The random triangle-removal process has a settled final-edge exponent, but the much stronger conditional spread estimate for the stopped output and large k in this record remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.aim.2015.04.015",
"label": "Bohman, Frieze, and Lubetzky, Random triangle removal"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For the random triangle-removal process on $K_n$, run for $n^2/6-n^{1.99}$ steps with output triangle set $\mathcal{T}_n$, do there exist events $E_n$ of probability $1-o(1)$ and a constant $C$ such that $\Pr(T_1,\ldots,T_k\in\mathcal{T}_n\mid E_n)\leq(C/n)^k$ for every collection of distinct triangles? | Does there exist a constant C and a sequence of events En which occur with probability 1 ´ op1q such that for any k distinct triangles T1 , . . . , Tk of Kn we have PrT1 , . . . , Tk P Tn |En s ď pC\{nqk ?} Remark. This can be thought of as the first open case of polynomial density Hales–Jewett. David Conlon Problem 7.... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,115 | OWR-10252930-025 | Sharp Triangle Threshold in Pseudorandom Graphs | Is there a sharp constant $c_0$ such that, for every $\varepsilon>0$, each sufficiently large $(n,d,\lambda)$-graph satisfying $$\lambda<(c_0-\varepsilon)d^2/n$$ contains a triangle, while arbitrarily large triangle-free examples exist with $$\lambda<(c_0+\varepsilon)d^2/n?$$ If so, does the first inequality force many... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 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-10252930-025",
"literature-status:partially-solved",
"owr-year:2022"
] | For the sharp pseudorandom triangle threshold, the existence and triangle-free sides are known with different constants, while identifying a common sharp constant c0 remains open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Is there a sharp constant $c_0$ such that, for every $\varepsilon>0$, each sufficiently large $(n,d,\lambda)$-graph satisfying $$\lambda<(c_0-\varepsilon)d^2/n$$ contains a triangle, while arbitrarily large triangle-free examples exist with $$\lambda<(c_0+\varepsilon)d^2/n?$$ If so, does the first inequality force many... | Does there exist a constant c “ c0 such that: ‚ Fix \varepsilon ą 0. Mehtaab Sawhney Problem 6. Consider the random triangle removal process in Kn run for n2 \{6 ´ n1.99 steps, and let the output set be Tn . Does there exist a constant C and a sequence of events En which occur with probability 1 ´ op1q such that for an... | 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 | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
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