id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,916 | OWR-8415359-002 | The Erdős–Rado Sunflower Conjecture | For every integer $r\geq3$, does there exist a constant $c(r)$ such that every family $\mathcal{F}$ of sets of size at most $w$ contains an $r$-sunflower whenever $|\mathcal{F}|>c(r)^w$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,021 | 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-8415359-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The sunflower conjecture remains unsettled in its original constant-base form, although the sunflower lemma has seen major quantitative improvements. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
},
{
"url": "https://doi.org/10.4007/annals.2021.194.3.5",
"label": "Improved bounds for the sunflower lemma"
},
{
"url": "https://link.springer.com/article/10.1007/s00493-026-00222-1",
"label": "Cu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | For every integer $r\geq3$, does there exist a constant $c(r)$ such that every family $\mathcal{F}$ of sets of size at most $w$ contains an $r$-sunflower whenever $|\mathcal{F}|>c(r)^w$? | The sunflower conjecture is a famous conjecture in extremal combinatorics due to Erdös and Rado (1960). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The linked report was inspected and the precise Erdős–Rado sunflower conjecture was restored from the surrounding paragraph. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,917 | OWR-8415359-005 | Probabilistic Box Models | What if we consider probabilistic boxes? 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:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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 linked report was inspected: this is a rhetorical transition immediately followed by a definition of quantum functions, not a freestandi) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415359-005",
"literature-status:open",
"owr-year:2021"
] | The proposed probabilistic-box and noncommutative property-testing questions are broad research questions with no general resolution established in the literature. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | null | What if we consider probabilistic boxes? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The linked report was inspected: this is a rhetorical transition immediately followed by a definition of quantum functions, not a freestanding open problem. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,918 | OWR-8415359-006 | Property Testing for Noncommutative Quantum Functions | What kinds of noncommutative properties are there? How does one measure a quantum function’s distance to a noncommutative property? What properties of quantum functions can be tested using few queries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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-8415359-006",
"literature-status:open",
"owr-year:2021"
] | The questions asking for general noncommutative properties, distance notions, and few-query tests remain open at the stated level of generality. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | What kinds of noncommutative properties are there? How does one measure a quantum function’s distance to a noncommutative property? What properties of quantum functions can be tested using few queries? | What kinds of noncommutative properties are there? How does one measure a quantum function’s distance to a noncommutative property? What properties of quantum functions can be tested using few queries? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The linked report was inspected and the three explicit questions were retained after removal of extraction boilerplate. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,919 | OWR-8415359-007 | Dimension–Complexity Tradeoffs in Quantum-Function Testing | What about tests for larger dimensions? Are there tradeoffs between the di- mension guarantee, the complexity of the test, and the test’s robustness? Theorem 1.3 (Corollary of MIP* = RE). There exist finite sets X , A and a test T for quantum functions F : X \to A such that (1) the test T makes only two queries to F , ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,021 | 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 linked report was inspected: the apparent question is immediately answered by the stated corollary of $\mathrm{MIP}^*=\mathrm{RE}$, so t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415359-007",
"literature-status:partially-solved",
"owr-year:2021"
] | MIP star equals RE supplies robust infinite-dimensional separation and related tests, but the requested general dimension-versus-query-complexity tradeoffs remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
},
{
"url": "https://arxiv.org/abs/2001.04383",
"label": "MIP star equals RE"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | null | What about tests for larger dimensions? Are there tradeoffs between the di- mension guarantee, the complexity of the test, and the test’s robustness? Theorem 1.3 (Corollary of MIP* = RE). There exist finite sets X , A and a test T for quantum functions F : X \to A such that (1) the test T makes only two queries to F , ... | unrecoverable | The linked report was inspected: the apparent question is immediately answered by the stated corollary of $\mathrm{MIP}^*=\mathrm{RE}$, so the extraction is not an unresolved problem. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,920 | OWR-8415359-008 | Algebraic and Graph-Property Tests for Quantum Functions | Can one characterize when a test forces a quantum function to be commutative? What happens when graph properties are tested with quantum functions? Beyond dimension testing, can one design tests forcing the measurements of a quantum function to generate a specified algebra? Are there applications to algorithms, complex... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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-8415359-008",
"literature-status:open",
"owr-year:2021"
] | The requested characterization of tests forcing commutativity and their graph, algebraic, or application-specific instances remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | Can one characterize when a test forces a quantum function to be commutative? What happens when graph properties are tested with quantum functions? Beyond dimension testing, can one design tests forcing the measurements of a quantum function to generate a specified algebra? Are there applications to algorithms, complex... | For example, is there a characterization of when a test forces a quantum function to be commutative? What happens if we try to test graph properties with quantum functions? Beyond testing dimension, can one design tests that force a quantum function’s measure- ments to generate a specific algebra? Are there application... | corrected_verified | The linked report was inspected and all four explicit follow-up questions were retained after removing extraction boilerplate. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,921 | OWR-8415359-009 | Canonical Paths Versus Spectral Independence | Establish a general relationship between the canonical-path method and spectral independence, with applications to approximate counting and sampling such as sampling perfect matchings in nonbipartite graphs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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-8415359-009",
"literature-status:open",
"owr-year:2021"
] | The canonical-path and spectral-independence frameworks have not been related by a general theorem of the kind requested in the record. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
},
{
"url": "https://courses.cs.washington.edu/courses/cse599s/22wi/lecture-11.pdf",
"label": "Spectral independence lecture notes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | Establish a general relationship between the canonical-path method and spectral independence, with applications to approximate counting and sampling such as sampling perfect matchings in nonbipartite graphs. | Open Problem. It remains an open problem to relate the canonical path method to the spectral independence technique. Sampling Bases of Matroids: Given a matroid M of rank n, defined on the ground set of elements U , let \pin be the uniform distribution over the bases of M . In [3] it was shown that such a distribution ... | corrected_verified | The linked report was inspected and the explicit open problem, including its stated application, was isolated from preceding examples. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,922 | OWR-8415359-010 | Derandomizing Space-Bounded Computation | Prove that $\mathsf{L}=\mathsf{BPL}$; equivalently, show that randomness is unnecessary for space-efficient computation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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-8415359-010",
"literature-status:open",
"owr-year:2021"
] | The long-standing space-bounded derandomization question L equals BPL remains unresolved; recent work and barriers provide progress without a full derandomization. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
},
{
"url": "https://williamhoza.com/research/papers/H4/",
"label": "Space-bounded derandomization survey"
},
{
"url": "https://eccc.weizmann.ac.il/report/2024/173/",
"label": "ECCC derandomization ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | Prove that $\mathsf{L}=\mathsf{BPL}$; equivalently, show that randomness is unnecessary for space-efficient computation. | Recent progress on derandomizing space-bounded computation William Hoza It is a long-standing open problem to prove that L = BPL, i.e., randomness is unnecessary for space-efficient computation. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The linked report was inspected and the long-standing open problem was isolated from its talk title and author. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,923 | OWR-8415359-011 | Good Locally Testable Quantum Codes and Linear-Rate PCPs | Construct asymptotically good, locally testable quantum LDPC codes, and construct probabilistically checkable proofs of linear rate. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,021 | 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-8415359-011",
"literature-status:partially-solved",
"owr-year:2021"
] | Asymptotically good quantum LDPC codes and locally testable classical codes are now constructed, but PCPs of linear rate remain an explicit open component of the record. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "Oberwolfach Report 54/2021"
},
{
"url": "https://arxiv.org/abs/2111.03654",
"label": "Asymptotically good quantum and classical LDPC codes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | Construct asymptotically good, locally testable quantum LDPC codes, and construct probabilistically checkable proofs of linear rate. | Major obvious open questions that remain are to construct asymptotically good, locally testable quantum LDPC codes, and to construct PCPs of linear rate. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The linked report was inspected and both explicit construction problems were retained. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,924 | OWR-8415359-014 | Average-Case Metacomplexity Characterizations of One-Way Functions | “Meta-complexity” refers to the computational complexity of problems that are themselves about complexity, eg., the Minimum Circuit Size Problem MCSP and the problem Kpoly of computing the polynomial-time bounded Kolmogorov com- plexity of a string. In this plenary talk, I gave a brief overview of recent work on meta-c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** open
**... | 3 | open | null | 2,021 | 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 linked report was inspected: this passage surveys proved characterizations of one-way functions and contains no explicit unresolved prob) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415359-014",
"literature-status:open",
"owr-year:2021"
] | The record is a survey fragment rather than a single precise conjecture; known meta-complexity characterizations establish important special results, but the broader questions named in the fragment remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/54",
"label": "original Oberwolfach report"
},
{
"url": "https://eccc.weizmann.ac.il/report/2021/082/",
"label": "Ilango--Ren--Santhanam, meta-complexity characterization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | null | “Meta-complexity” refers to the computational complexity of problems that are themselves about complexity, eg., the Minimum Circuit Size Problem MCSP and the problem Kpoly of computing the polynomial-time bounded Kolmogorov com- plexity of a string. In this plenary talk, I gave a brief overview of recent work on meta-c... | unrecoverable | The linked report was inspected: this passage surveys proved characterizations of one-way functions and contains no explicit unresolved problem. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,925 | OWR-8415359-015 | Size-Efficient Circuits Resilient to Short-Circuit Errors | Given a Boolean circuit $C$, can one construct a circuit $C'$ of comparable size that computes the same function even when an adversary replaces the output of some gates by one of their inputs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005](https://doi.org/10.4171/owr/2021/54)
## Literature review (checked 2026-08-22)
**Status:** partiall... | 3 | partially_solved | null | 2,021 | 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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"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-8415359-015",
"literature-status:partially-solved",
"owr-year:2021"
] | The STOC paper constructs resilient circuits of quasi-polynomial size for general circuits and near-linear size for formulas; this answers the existence question in weaker regimes, but roughly comparable size for arbitrary circuits is not established. | [
{
"url": "https://par.nsf.gov/servlets/purl/10359538",
"label": "Efremenko et al., Circuits Resilient to Short-Circuit Errors"
},
{
"url": "https://doi.org/10.1145/3519935.3520007",
"label": "STOC 2022 publication"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/54 | null | null | null | Given a Boolean circuit $C$, can one construct a circuit $C'$ of comparable size that computes the same function even when an adversary replaces the output of some gates by one of their inputs? | Can we design such a resilient circuit C ′ whose size is roughly comparable to that of C? Circuits Resilient to Short-Circuit Errors Yael Kalai (joint work with Klim Efremenko, Bernhard Haeupler, Pritish Kamath, Gillat Kol, Nicolas Resch, and Raghuvansh Saxena) On the Complexity of Evaluating Highest Weight Vectors Mar... | corrected_verified | The linked report was inspected; the setup immediately preceding the question was restored and two following talk headings were removed. | null | null | null | null | null | Complexity Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/54, pp. 2955--3005 |
30,004,926 | OWR-8415360-004 | Rank Dependence of Sample Complexity in Matrix Sensing | Is the quadratic dependence of matrix-sensing sample complexity $m$ on the rank $r_\star$ necessary, or is it an artifact of the proof? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 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-8415360-004",
"literature-status:partially-solved",
"owr-year:2021"
] | Later matrix-sensing work breaks the quadratic rank dependence for factorized gradient descent in symmetric positive-semidefinite settings, and newer scaled methods report linear-rank sampling in broader settings; the exact 2021 algorithmic question is not fully settled. | [
{
"url": "https://arxiv.org/abs/2408.13276",
"label": "Stöger--Zhu, breaking the quadratic rank barrier"
},
{
"url": "https://arxiv.org/abs/2604.00060",
"label": "Li--Huang, optimal sampling for scaled gradient descent"
},
{
"url": "https://doi.org/10.4171/owr/2021/55",
"label": "ori... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | Is the quadratic dependence of matrix-sensing sample complexity $m$ on the rank $r_\star$ necessary, or is it an artifact of the proof? | At the end of the talk, we will discuss a number of open problems. It is also an interesting open question whether the quadratic dependence of the sample complexity m on r⋆ in our results is really necessary or rather an artefact of the proof. Ut+1 = Ut − µ∇f (Ut ) = Ut + µ (A∗ A) XX T − Ut UtT Ut . Here, our initializ... | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,927 | OWR-8415360-005 | Convergence and Effective Rates of Unwinding Series | What can be rigorously established about convergence of the unwinding series, and can one obtain effective convergence rates for sufficiently regular functions $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 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-8415360-005",
"literature-status:partially-solved",
"owr-year:2021"
] | Convergence of unwinding or Blaschke expansions has been proved in several Hardy, Sobolev, and reproducing-kernel settings, but general pointwise convergence and effective rates for the broad class of functions asked about remain open. | [
{
"url": "https://arxiv.org/abs/2310.01269",
"label": "nonlinear expansions in reproducing-kernel Hilbert spaces"
},
{
"url": "https://arxiv.org/abs/2404.13296",
"label": "almost-everywhere convergence for a wavelet-type series"
},
{
"url": "https://doi.org/10.4171/owr/2021/55",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | What can be rigorously established about convergence of the unwinding series, and can one obtain effective convergence rates for sufficiently regular functions $F$? | Perhaps the most pressing open question is as follows. What can be rigorously established about the conver- gence properties of the unwinding series? Is it possible to obtain an effective convergence rate for sufficiently nice functions F ? we have B(x) = ei\theta(x) where X x − Re ak \theta(x) = \sigma Im ak k\geq0 | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,928 | OWR-8415360-006 | Phase Retrieval from Gabor and Wavelet Magnitudes | What uniqueness and stability guarantees hold for recovering $f\in H$ from magnitude measurements $(|\langle f,\phi_\lambda\rangle|)_{\lambda\in\Lambda}$, particularly for Gabor or wavelet frames? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 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-8415360-006",
"literature-status:partially-solved",
"owr-year:2021"
] | There are substantial uniqueness and stability theorems for Gabor and wavelet measurements, including discrete stability estimates and recent counterexamples separating sampled uniqueness from continuous stability; no general uniqueness-and-stability characterization is known. | [
{
"url": "https://doi.org/10.1007/s43670-023-00079-1",
"label": "Alaifari et al., sampled versus continuous Gabor phase retrieval"
},
{
"url": "https://arxiv.org/abs/1901.05296",
"label": "stability from discrete Gabor measurements"
},
{
"url": "https://doi.org/10.4171/owr/2021/55",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | What uniqueness and stability guarantees hold for recovering $f\in H$ from magnitude measurements $(|\langle f,\phi_\lambda\rangle|)_{\lambda\in\Lambda}$, particularly for Gabor or wavelet frames? | What can be said about uniqueness and stability of recovering functions f \in H from magnitude measurements (|hf, ϕ\lambda i|)\lambda\inΛ ? We have recently studied the question of uniqueness for phase retrieval when the measurement system is a Gabor or wavelet frame. (Non-)uniqueness of phase recovery from Gabor and w... | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,929 | OWR-8415360-008 | Computable Neural-Network Approximation from Noisy Samples | For a learning problem specified from point samples, is its ground-truth map computable; are the neural networks supplied by approximation theorems computable; and is there an algorithm that maps noisy samples to such a neural-network approximation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 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-8415360-008",
"literature-status:open",
"owr-year:2021"
] | The record explicitly poses computability, noisy-sample inversion, and algorithm-construction questions for neural-network approximation; the cited work gives a framework but not a general resolution of these questions. | [
{
"url": "https://doi.org/10.4171/owr/2021/55",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | For a learning problem specified from point samples, is its ground-truth map computable; are the neural networks supplied by approximation theorems computable; and is there an algorithm that maps noisy samples to such a neural-network approximation? | Moreover, we discuss the open questions which answers will allow us to give further insight into how to build stable and accurate networks. Given these insights, we ask three further questions which relate the results to their computability. (1) Is the ground truth a sensible problem? (2) Are the neural networks in the... | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,930 | OWR-8415360-009 | Computable Ground Truths for Learning Problems | When is the ground truth of a learning task a computable function, and how does that relate to approximation by computable neural networks? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415360-009",
"literature-status:open",
"owr-year:2021"
] | This is an underspecified foundational question about whether a learning task is a sensible computable ground truth; no general mathematical criterion resolving it is identified in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2021/55",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | When is the ground truth of a learning task a computable function, and how does that relate to approximation by computable neural networks? | The ground truth: We ask if the task, for example, a classification task, is a sensible problem. From a computer science perspective, we ask if the problem relates to a computable function. 3. Conclusion, Outlook and Open Questions We have seen that we can relate the computability from point samples to the existence of... | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,931 | OWR-8415360-010 | Optimal Neural-Network Depth for Sparse Recovery | For exact recovery of $s$-sparse vectors by ReLU networks, is the known depth bound $\lceil\log_2s+2\rceil$ optimal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 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-8415360-010",
"literature-status:open",
"owr-year:2021"
] | The cited theorem gives exact recovery with ceiling of log base 2 of s plus 2 hidden layers, but the optimal depth is explicitly unknown; the exact layer-minimization problem therefore remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46933",
"label": "Thesing--Hansen, exact sparse recovery with ReLU networks"
},
{
"url": "https://doi.org/10.4171/owr/2021/55",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | For exact recovery of $s$-sparse vectors by ReLU networks, is the known depth bound $\lceil\log_2s+2\rceil$ optimal? | any higher sparsity level, this is not an essential restriction in this direction. In all results, we assume that all networks have the commonly used ReLU activation function given by ReLU(x) = max(0, x) and use specific properties of it. Specifically, we show that no ReLU -neural network with only one hidden layer can... | 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,932 | OWR-8415360-011 | Stochasticity and Sample Complexity in Neural Networks | How does stochasticity affect neural-network performance, and how much data is needed to achieve small estimation error with high probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066](https://doi.org/10.4171/owr/2021/55)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 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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"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-8415360-011",
"literature-status:open",
"owr-year:2021"
] | The record asks broad statistical-learning questions about stochasticity and sample size for small estimation error; no single formal theorem or complete answer matching this formulation is available. | [
{
"url": "https://doi.org/10.4171/owr/2021/55",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/55 | null | null | null | How does stochasticity affect neural-network performance, and how much data is needed to achieve small estimation error with high probability? | How does stochasticity contribute in regard to this? • What is the amount of data needed for such a network to achieve a small estimation error with high probability? 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 | Applied Harmonic Analysis and Data Science (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/55, pp. 3007--3066 |
30,004,933 | OWR-8415361-001 | Unspecified Higher-Rank Dynamics Conjecture | conjecture. Two other aspects of Anosov actions were addressed in the talks: Thi Dang presented results on topological mixing of positive diagonal flows and Jialun Li presented new results about the counting and equidistribution of torus orbits for Weyl chamber flows on finite volume locally symmetric spaces of rank k ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099](https://doi.org/10.4171/owr/2021/56)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,021 | 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"
} | {
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"level": 3,
"name": "L3: Advanced",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this is introductory context pointing to the higher-rank rigidity conjecture retained in OWR-8415361-002. No ) | [
"OWR-8415361-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415361-001",
"literature-status:open",
"owr-year:2021"
] | The extracted statement is only the word conjecture followed by unrelated workshop context, so the mathematical claim is unclear; under the required normalization an unverified claim is open. | [
{
"url": "https://doi.org/10.4171/owr/2021/56",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/56 | null | null | null | null | conjecture. Two other aspects of Anosov actions were addressed in the talks: Thi Dang presented results on topological mixing of positive diagonal flows and Jialun Li presented new results about the counting and equidistribution of torus orbits for Weyl chamber flows on finite volume locally symmetric spaces of rank k ... | unrecoverable | The official report shows that this is introductory context pointing to the higher-rank rigidity conjecture retained in OWR-8415361-002. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099 |
30,004,934 | OWR-8415361-002 | Algebraic Rigidity of Higher-Rank Anosov Actions | Is every $C^\infty$ Anosov action of $\mathbb R^k$ or $\mathbb Z^k$, with $k\geq2$, on a compact manifold and without $C^\infty$ rank-one factors $C^\infty$-conjugate, after passage to finite covers, to an algebraic action? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099](https://doi.org/10.4171/owr/2021/56)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415361-001"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415361-002",
"literature-status:open",
"owr-year:2021"
] | The full Katok--Spatzier classification remains open for general higher-rank Anosov actions; major rigidity results verify important subclasses, including totally Cartan actions, but not the stated universal conjecture. | [
{
"url": "https://doi.org/10.1090/jams/1033",
"label": "Spatzier--Vinhage, Cartan actions and classification"
},
{
"url": "https://sites.lsa.umich.edu/spatzier/wp-content/uploads/sites/1081/2023/07/Katoks-work-Chapter4-final.pdf",
"label": "current survey of the conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/56 | null | null | null | Is every $C^\infty$ Anosov action of $\mathbb R^k$ or $\mathbb Z^k$, with $k\geq2$, on a compact manifold and without $C^\infty$ rank-one factors $C^\infty$-conjugate, after passage to finite covers, to an algebraic action? | Mini Course on Higher Rank Anosov Actions Ralf Spatzier Dynamical systems with extra symmetry turn out to be surprisingly rigid. For instance generically a diffeomorphism cannot have infinite index in its centralizer in the diffeomorphism group, as conjectured by Smale [10] and proved by Bonatti, Crovisier and Wilkinso... | 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: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099 |
30,004,935 | OWR-8415361-003 | Stable Hyperbolicity of Closed Geodesics for Riemannian Metrics | For a closed manifold $M$, let $\mathcal R_{\mathrm{hyp}}(M)$ be the set of Riemannian metrics for which every closed geodesic is hyperbolic. Is the $C^2$ interior of $\mathcal R_{\mathrm{hyp}}(M)$ exactly the set of metrics whose geodesic flows are Anosov, in every dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099](https://doi.org/10.4171/owr/2021/56)
## Literature review (checked 2026-08-22)
**Status... | 3 | open | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415361-003",
"literature-status:open",
"owr-year:2021"
] | The report proves the corresponding generic statement for Finsler metrics and for Riemannian surfaces but explicitly leaves the arbitrary-dimensional closed-Riemannian extension as a conjecture; no authoritative resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46934",
"label": "Mini-Workshop: Anosov cubed report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/56 | null | null | null | For a closed manifold $M$, let $\mathcal R_{\mathrm{hyp}}(M)$ be the set of Riemannian metrics for which every closed geodesic is hyperbolic. Is the $C^2$ interior of $\mathcal R_{\mathrm{hyp}}(M)$ exactly the set of metrics whose geodesic flows are Anosov, in every dimension? | We conjecture that Theorem A also holds for Riemannian metrics on closed manifolds of arbitrary dimensions. 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 | Mini-Workshop: \$(Anosov)^3\$ (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/56, pp. 3067--3099 |
30,004,936 | OWR-8415362-001 | Cluster Algebras Scattering Amplitudes and Positive Geometries | Abstract. Cluster algebras were developed by Fomin and Zelevinsky about twenty years ago. While the initial motivation came from within algebra (to- tal positivity, canonical bases), it quickly became clear that cluster algebras possess deep links to a host of other subjects in mathematics and physics. In a separate ve... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official source passage is the workshop abstract describing its themes, not a mathematical problem or conjecture. No separate clean stat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415362-001",
"literature-status:open",
"owr-year:2021"
] | The extracted record is an abstract describing workshop motivation, not a definite mathematical conjecture or theorem; the claim is therefore unresolved and cannot be upgraded beyond open. | [
{
"url": "https://doi.org/10.4171/owr/2021/57",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | null | Abstract. Cluster algebras were developed by Fomin and Zelevinsky about twenty years ago. While the initial motivation came from within algebra (to- tal positivity, canonical bases), it quickly became clear that cluster algebras possess deep links to a host of other subjects in mathematics and physics. In a separate ve... | unrecoverable | The official source passage is the workshop abstract describing its themes, not a mathematical problem or conjecture. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,937 | OWR-8415362-002 | Shift Maps Between Totally Nonnegative Grassmannians | Is the shift map a bijection $\operatorname{Gr}_{\geq 0}(k,n)\dashrightarrow\operatorname{Gr}_{\geq 0}(k-1,n)$ between the specified subsets of adjacent totally nonnegative Grassmannians, sending each positroid cell to its shifted cell? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 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-8415362-002",
"literature-status:open",
"owr-year:2021"
] | The proposed shift map between adjacent totally nonnegative Grassmannians remains conjectural; later work proves strong results for critical varieties but does not establish the full Grassmannian bijection stated here. | [
{
"url": "https://academic.oup.com/imrn/advance-article/doi/10.1093/imrn/rnad084/7146963",
"label": "Galashin, totally nonnegative critical varieties"
},
{
"url": "https://doi.org/10.4171/owr/2021/57",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | Is the shift map a bijection $\operatorname{Gr}_{\geq 0}(k,n)\dashrightarrow\operatorname{Gr}_{\geq 0}(k-1,n)$ between the specified subsets of adjacent totally nonnegative Grassmannians, sending each positroid cell to its shifted cell? | Shift maps, poset associahedra, and totally nonnegative critical varieties Pavel Galashin I will discuss some recent results on totally nonnegative parts of critical varieties and the associated polytopes [4, 5, 6]. Along the way, I will highlight a surprising relation between these results and the shift map (also know... | 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: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,938 | OWR-8415362-003 | Polyhedrality of Totally Nonnegative Critical Varieties | In the study of scattering amplitudes and positive geometries on the totally nonnegative Grassmannian $\mathrm{Gr}_{\geq 0}(k, n)$, let $\operatorname{Crit}^{\geq 0}_f$ denote a totally nonnegative critical variety (the closure of the critical locus of the master function $f$ on a positroid cell, as studied by Galashin... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 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-8415362-003",
"literature-status:open",
"owr-year:2021"
] | Primary work represents each totally nonnegative critical variety as an image of an affine poset cyclohedron and identifies the top-dimensional case with a polytope, but the assertion for every critical cell remains unproved. | [
{
"url": "https://arxiv.org/abs/2110.08548",
"label": "Galashin, totally nonnegative critical varieties"
},
{
"url": "https://doi.org/10.4171/owr/2021/57",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | In the study of scattering amplitudes and positive geometries on the totally nonnegative Grassmannian $\mathrm{Gr}_{\geq 0}(k, n)$, let $\operatorname{Crit}^{\geq 0}_f$ denote a totally nonnegative critical variety (the closure of the critical locus of the master function $f$ on a positroid cell, as studied by Galashin... | It remains an open problem to decide whether each Critf⩾0 is itself a polytope. Scattering Amplitudes, Cluster Algebras, and Positive Geometries 3107 | 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: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,939 | OWR-8415362-004 | Topology of Affine and Doubly Extended Associahedra | Is the affine generalized associahedron of rank $n+1$ homeomorphic to $S^n$; is the cluster complex of a doubly extended cluster algebra of rank $n+2$ homotopy equivalent to $S^{n-1}$; and does the stated product-of-spheres description hold for the associated doubly extended associahedron? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 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-8415362-004",
"literature-status:open",
"owr-year:2021"
] | The three topology assertions for affine and doubly extended associahedra are still stated as conjectures in subsequent research; no proof covering all listed types was located. | [
{
"url": "https://arxiv.org/abs/2107.10334",
"label": "cluster modular groups of affine and doubly extended cluster algebras"
},
{
"url": "https://api.drum.lib.umd.edu/server/api/core/bitstreams/b8a1780c-1d92-4a30-b06f-56ce0017d770/content",
"label": "current dissertation statement"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | Is the affine generalized associahedron of rank $n+1$ homeomorphic to $S^n$; is the cluster complex of a doubly extended cluster algebra of rank $n+2$ homotopy equivalent to $S^{n-1}$; and does the stated product-of-spheres description hold for the associated doubly extended associahedron? | We conjecture the following about the topology of these complexes: Conjecture 7. (1) The affine generalized associahedron of an affine cluster algebra of rank n + 1 is homeomorphic to a sphere of dimension n. (2) The cluster complex of a doubly extended cluster algebra of rank n + 2 is homotopy equivalent to S n−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 | Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,940 | OWR-8415362-005 | $u$-Equations for Arbitrary Hyperbolic Surfaces | In the positive-geometry and cluster-algebraic formulation of tree and loop string amplitudes (Arkani-Hamed et al.), the $u$-equations are a system of polynomial relations among cross-ratio variables $u_C$ associated to curves on a bordered surface. Do the proposed $u$-equations extend to arbitrary hyperbolic surfaces ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 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-8415362-005",
"literature-status:open",
"owr-year:2021"
] | Quiver-representation methods solve important finite-type and finite-representation cases of u-equations, but the conjectural formulation for arbitrary hyperbolic surfaces and its full string-integral consequences remain unverified. | [
{
"url": "https://doi.org/10.4171/owr/2021/57",
"label": "original Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/48645",
"label": "later Oberwolfach report on u-equations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | In the positive-geometry and cluster-algebraic formulation of tree and loop string amplitudes (Arkani-Hamed et al.), the $u$-equations are a system of polynomial relations among cross-ratio variables $u_C$ associated to curves on a bordered surface. Do the proposed $u$-equations extend to arbitrary hyperbolic surfaces ... | We conjecture the u equations for an arbitrary surface and show how these variables give new formulas for the functions that arise in string theory. The ‘u equations’ for hyperbolic surfaces, and string integrals Hadleigh Frost (joint work with Nima Arkani-Hamed, Pierre-Guy Plamondon, Giulio Salvatori, Hugh Thomas) 1. ... | 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: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,941 | OWR-8415362-007 | Gradient Flows and Ball Topology of Amplituhedra | Can one classify gradient flows preserving $A_{n,k,m}(Z)$, and does such a flow exist for every $Z$, implying that $A_{n,k,m}(Z)$ is homeomorphic to a closed ball? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133](https://doi.org/10.4171/owr/2021/57)
#... | 3 | open | null | 2,021 | 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-8415362-007",
"literature-status:open",
"owr-year:2021"
] | Gradient-flow methods prove closed-ball topology for several important amplituhedron families, but the requested classification and existence of a suitable flow for every positive Z remain open. | [
{
"url": "https://doi.org/10.1007/s00220-022-04540-5",
"label": "Karp--Williams, Gradient Flows and Adjoint Orbits"
},
{
"url": "https://doi.org/10.4171/owr/2021/57",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/57 | null | null | null | Can one classify gradient flows preserving $A_{n,k,m}(Z)$, and does such a flow exist for every $Z$, implying that $A_{n,k,m}(Z)$ is homeomorphic to a closed ball? | Open problems. Can we classify gradient flows preserving An,k,m (Z)? Does there ex- ist such a flow for every Z, allowing one to show that An,k,m (Z) is homeomorphic to a closed ball? Scattering Amplitudes, Cluster Algebras, and Positive Geometries 3127 | 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: Scattering Amplitudes, Cluster Algebras, and Positive Geometries (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/57, pp. 3101--3133 |
30,004,942 | OWR-8415363-001 | Nonsymmetric Extensions of Dirichlet-Form Trace Constructions | Determine whether the trace construction for symmetric Dirichlet forms extends to nonsymmetric forms. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/58, pp. 3135--3186](https://doi.org/10.4171/owr/2021/58... | 3 | open | null | 2,021 | 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-8415363-001",
"literature-status:open",
"owr-year:2021"
] | The source explicitly leaves extension of the trace and curvature method from symmetric to nonsymmetric Dirichlet forms as an open problem; later literature does not supply a general resolution. | [
{
"url": "https://ems.press/content/serial-article-files/46936",
"label": "Mini-Workshop: Variable Curvature Bounds report"
},
{
"url": "https://doi.org/10.1016/j.matpur.2022.02.002",
"label": "Erbar--Rigoni--Sturm--Tamanini, tamed spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/58 | null | null | null | Determine whether the trace construction for symmetric Dirichlet forms extends to nonsymmetric forms. | It is an open problem whether this method still applies for nonsymmetric forms. 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: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/58, pp. 3135--3186 |
30,004,943 | OWR-8415364-001 | Kannan-Lovasz-Simonovits Spectral Gap Conjecture | The topic is at the heart of the Brunn–Minkowski theory, and offers many challenging open questions. Yuansi Chen presented an improved bound on the spectral gap of convex sets and log-concave probability measures, which almost matches the famous conjecture of Kannan–Lovász–Simonovits (Chen’s bound still involves a cons... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,021 | 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 | Duplicate/merged OWR extraction (The official report shows that this workshop-level introduction merely mentions the Kannan–Lovász–Simonovits conjecture, which is retained i) | [
"OWR-8415364-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Chen proved the subpolynomial-dimensional lower bound highlighted in the record, a major partial advance, but the dimension-free KLS conjecture itself remains unresolved as of the check date. | [
{
"url": "https://doi.org/10.1007/s00039-021-00558-4",
"label": "Chen, almost constant KLS lower bound"
},
{
"url": "https://arxiv.org/abs/2011.13661",
"label": "Chen primary preprint"
},
{
"url": "https://www.solveall.org/problem/kls-conjecture",
"label": "current KLS status"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | The topic is at the heart of the Brunn–Minkowski theory, and offers many challenging open questions. Yuansi Chen presented an improved bound on the spectral gap of convex sets and log-concave probability measures, which almost matches the famous conjecture of Kannan–Lovász–Simonovits (Chen’s bound still involves a cons... | unrecoverable | The official report shows that this workshop-level introduction merely mentions the Kannan–Lovász–Simonovits conjecture, which is retained in complete form in OWR-8415364-006. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,944 | OWR-8415364-002 | Unspecified Convex Geometry Conjecture | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3222 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:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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 extract is an incomplete contents fragment and does not state a standalone mathematical problem. No sepa) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-002",
"literature-status:open",
"owr-year:2021"
] | The extracted record is only a table-of-contents fragment ending with the word Conjecture and contains no checkable mathematical claim; it is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3222 The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report shows that this extract is an incomplete contents fragment and does not state a standalone mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,945 | OWR-8415364-003 | Unspecified Convex Geometry Conjecture | conjecture. 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:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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 extract contains only a conjecture label and no recoverable mathematical statement. No separate clean st) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-003",
"literature-status:open",
"owr-year:2021"
] | The extracted record is only the word conjecture and does not identify a mathematical proposition; it is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report shows that this extract contains only a conjecture label and no recoverable mathematical statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,946 | OWR-8415364-004 | Foundations of Convex Algebraic Geometry | What is convex algebraic geometry? 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:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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 immediately answers this expository heading by defining convex algebraic geometry; it is not posed as an open mathematic) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-004",
"literature-status:open",
"owr-year:2021"
] | This is a broad subject-level question with no precise claim or success criterion in the extracted record, so its status is open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | What is convex algebraic geometry? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report immediately answers this expository heading by defining convex algebraic geometry; it is not posed as an open mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,947 | OWR-8415364-005 | KLS Isoperimetric Coefficient Bound for Log-Concave Measures | conjecture (2003). The previous best bound with dimension dependency d1/4 was established by Lee and Vempala in 2017, which also matches the best dimension dependency Klartag obtained in 2006 for Bourgain’s slicing conjecture. In recent work, we improve the Eldan’s stochastic localization proof technique deployed in Le... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the Kannan–Lovász–Simonovits conjecture retained in OWR-8415364-006. No ) | [
"OWR-8415364-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-005",
"literature-status:open",
"owr-year:2021"
] | The record concerns the KLS conjecture. Primary work gives dimension-dependent and polylogarithmic bounds, but no dimension-free constant bound; the conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2203.15551",
"label": "Klartag--Lehec KLS bounds"
},
{
"url": "https://arxiv.org/abs/2406.01324",
"label": "current KLS lecture notes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | conjecture (2003). The previous best bound with dimension dependency d1/4 was established by Lee and Vempala in 2017, which also matches the best dimension dependency Klartag obtained in 2006 for Bourgain’s slicing conjecture. In recent work, we improve the Eldan’s stochastic localization proof technique deployed in Le... | unrecoverable | The official report confirms that this is a duplicate extraction of the Kannan–Lovász–Simonovits conjecture retained in OWR-8415364-006. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,948 | OWR-8415364-006 | Kannan–Lovász–Simonovits Isoperimetric Conjecture | Is there a universal constant $c>0$ such that every isotropic log-concave probability density $p$ satisfies $\psi(p)\geq c/\sqrt{\rho(p)}$, and hence has an isoperimetric coefficient bounded below by a universal positive constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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... | [
"OWR-8415364-001",
"OWR-8415364-005",
"OWR-8415364-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-006",
"literature-status:open",
"owr-year:2021"
] | The stated half-space formulation is the KLS hyperplane formulation. Its universal-constant lower bound is still unresolved; known results retain dimension dependence. | [
{
"url": "https://arxiv.org/abs/2203.15551",
"label": "Klartag--Lehec KLS bounds"
},
{
"url": "https://arxiv.org/abs/2406.01324",
"label": "current KLS lecture notes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | Is there a universal constant $c>0$ such that every isotropic log-concave probability density $p$ satisfies $\psi(p)\geq c/\sqrt{\rho(p)}$, and hence has an isoperimetric coefficient bounded below by a universal positive constant? | If the conjecture is true, the Cheeger isoperimetric coefficient can be determined by going through all the half- spaces instead of all subsets. For this reason, the KLS conjecture is also called the KLS hyperplane conjecture. p (\{x : d(x, S) \leq ǫ\}) − p(S) p+ (\partialS) := lim inf , ǫ\to0+ ǫ where d(x, S) is the Euc... | 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 | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,949 | OWR-8415364-007 | KLS Isoperimetric Coefficient Bound for Log-Concave Measures | The KLS conjecture is stated by Kannan, Lovász and Simonovits [1] as follows. Main text: Given a distribution, the isoperimetric coefficient of a subset is the ratio of the measure of the subset boundary to the minimum of the measures of the subset and its complement. Taking the minimum of such ratios over all subsets d... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the Kannan–Lovász–Simonovits conjecture retained in OWR-8415364-006. No ) | [
"OWR-8415364-006"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-007",
"literature-status:open",
"owr-year:2021"
] | This is the standard KLS isoperimetric conjecture for log-concave measures. The best primary results are approximate up to dimension-dependent or polylogarithmic factors, so the full claim remains open. | [
{
"url": "https://arxiv.org/abs/2203.15551",
"label": "Klartag--Lehec KLS bounds"
},
{
"url": "https://arxiv.org/abs/2406.01324",
"label": "current KLS lecture notes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | The KLS conjecture is stated by Kannan, Lovász and Simonovits [1] as follows. Main text: Given a distribution, the isoperimetric coefficient of a subset is the ratio of the measure of the subset boundary to the minimum of the measures of the subset and its complement. Taking the minimum of such ratios over all subsets d... | unrecoverable | The official report confirms that this is a duplicate extraction of the Kannan–Lovász–Simonovits conjecture retained in OWR-8415364-006. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,950 | OWR-8415364-008 | Unspecified Log-Concave Measure Conjecture | conjecture. Before this work we did not have many examples of measures which satisfy either (B) or (GZ) except \gamma. For (GZ) one can trivially take the Lebesgue measure restricted to a convex body T , but no other examples were known. In [12] Livshyts did show that (GZ) holds for every even log-concave measure, but ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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 places this fragment inside proved results on log-concave measures and does not state an open problem. No separate clean) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415364-008",
"literature-status:open",
"owr-year:2021"
] | The extracted record is fragmentary: it gives only the word conjecture and a definition of a measure class, without a complete proposition to verify; it is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | null | conjecture. Before this work we did not have many examples of measures which satisfy either (B) or (GZ) except \gamma. For (GZ) one can trivially take the Lebesgue measure restricted to a convex body T , but no other examples were known. In [12] Livshyts did show that (GZ) holds for every even log-concave measure, but ... | unrecoverable | The official report places this fragment inside proved results on log-concave measures and does not state an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,951 | OWR-8415364-009 | Uniform Bounds for Volume-Decomposition Functionals | Let $P\subset\mathbb R^n$ be a polytope whose centroid is the origin. For $1\leq k\leq n-1$, does a constant $c(n,k)$ exist such that
$$
\frac{X_k(P)}{V_n(P)}\leq c(n,k)
$$
for every such $P$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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-8415364-009",
"literature-status:open",
"owr-year:2021"
] | The volume-decomposition question is solved in dimension three and sharp inequalities are known for X sub 2 and X sub 3, but the extracted all-k boundedness question is not settled in general. | [
{
"url": "https://arxiv.org/abs/2404.09152",
"label": "Liu--Sun--Xiong on X sub 2 and X sub 3"
},
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | Let $P\subset\mathbb R^n$ be a polytope whose centroid is the origin. For $1\leq k\leq n-1$, does a constant $c(n,k)$ exist such that
$$
\frac{X_k(P)}{V_n(P)}\leq c(n,k)
$$
for every such $P$? | Does there exist a constant c(n, k) depending on n and k, k \in \{1, 2, . . . , n − 1\}, such that Xk (P ) \leq c(n, k)? to the Lutwak-Yang-Zhang U functional. So, in some sense, we trace the origin of LYZ’s U functional for the first time. In 2001, LYZ [4] conjectured that if P is a polytope in Rn with its centroid at ... | 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 | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,952 | OWR-8415364-010 | The $L_p$ Aleksandrov Problem for Integral Curvature Measures | For each real $p$, characterize the finite Borel measures on $S^{n-1}$ that occur as $L_p$ integral curvature measures of convex bodies. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,021 | 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-8415364-010",
"literature-status:partially-solved",
"owr-year:2021"
] | The Lp Aleksandrov problem has a complete existence characterization for positive p and substantial even-measure results for negative p, including discrete polytopes, but the unrestricted negative-p problem and uniqueness are not fully solved. | [
{
"url": "https://doi.org/10.4310/jdg/1536285625",
"label": "Huang--Lutwak--Yang--Zhang"
},
{
"url": "https://doi.org/10.1090/proc/14568",
"label": "Zhao on origin-symmetric polytopes"
},
{
"url": "https://www.yimingzhao.net/files/LpAleksandrov.pdf",
"label": "Zhao current negative-p... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | For each real $p$, characterize the finite Borel measures on $S^{n-1}$ that occur as $L_p$ integral curvature measures of convex bodies. | What are the necessary and sufficient conditions on a given Borel measure µ on S n−1 so that there exists a convex body K \in Kon with µ = Jp (K, \cdot)? dJp (K, \cdot) = ρpK dJ(K, \cdot). Observe that when p = 0, J0 (K, \cdot) = J(K, \cdot), the classical case. The Lp Aleksandrov problem asks about the existence of a co... | 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 | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,953 | OWR-8415364-011 | Optimal Great-Subsphere Concentration for the Negative-$p$ Aleksandrov Problem | For $p\leq-1$, what is the optimal upper bound on $\mu(\xi)/\mu(S^{n-1})$, over great subspheres $\xi\subset S^{n-1}$, that guarantees a convex body whose $L_p$ integral curvature measure is $\mu$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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-8415364-011",
"literature-status:open",
"owr-year:2021"
] | The record explicitly asks whether the cited concentration bound is optimal, and no primary source located by the cutoff establishes optimality; the problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | For $p\leq-1$, what is the optimal upper bound on $\mu(\xi)/\mu(S^{n-1})$, over great subspheres $\xi\subset S^{n-1}$, that guarantees a convex body whose $L_p$ integral curvature measure is $\mu$? | Whether the measure concentration bound in Theorem 2 is opti- mal is an open problem. 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 | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,954 | OWR-8415364-014 | Maximum-Volume Sections of $ell_p$ Balls | For $2<p<\infty$, which linear sections of an $\ell_p$ ball have maximum volume? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266](https://doi.org/10.4171/owr/2021/59)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,021 | 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-8415364-014",
"literature-status:open",
"owr-year:2021"
] | Maximal hyperplane sections of the lp ball remain unknown for 2 less than p less than infinity. Recent primary work proves restricted regimes and supports, rather than settles, the proposed phase-transition conjecture. | [
{
"url": "https://arxiv.org/abs/2409.06432",
"label": "Konig on maximal lp sections"
},
{
"url": "https://doi.org/10.4171/owr/2021/59",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/59 | null | null | null | For $2<p<\infty$, which linear sections of an $\ell_p$ ball have maximum volume? | What remains open is the case of the maximum-volume section when 2 < p < \infty. Such sharp inequalities for q \geq 1 were established by Latala and Oleszkiewicz in [9]. Out main result from [2] closes the picture by addressing the case 0 < q < 1: for every n \geq 2 and every unit vector a in Rn , we have q q n X Xm 1 ... | 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 | Convex Geometry and its Applications (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/59, pp. 3187--3266 |
30,004,955 | OWR-9790352-001 | Unspecified Structural Graph Theory Problem | Abstract. Graph theory is a quickly developing area of mathematics, with an increasing number of connections to various parts of mathematics and computer science. The workshop aimed at bringing together a broad range of researchers at various career stages to discuss recent exciting developments, in particular, the Pro... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this is workshop-level introductory prose rather than a standalone mathematical problem. No separate clean st) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-001",
"literature-status:open",
"owr-year:2022"
] | The extracted record is only a workshop abstract and contains no specific mathematical problem or claim to verify; it is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Abstract. Graph theory is a quickly developing area of mathematics, with an increasing number of connections to various parts of mathematics and computer science. The workshop aimed at bringing together a broad range of researchers at various career stages to discuss recent exciting developments, in particular, the Pro... | unrecoverable | The official report shows that this is workshop-level introductory prose rather than a standalone mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,956 | OWR-9790352-002 | Unspecified Structural Graph Theory Conjecture | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Matija Bucić (joint with Jacob Fox and Benny Sudakov) Clique minors in graphs with a forbidden subgraph . . . . . . . . . . . . . . . . . . . 12 Johannes Carmesin Local Separators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this extract is a table-of-contents fragment without a recoverable standalone statement. No separate clean st) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-002",
"literature-status:open",
"owr-year:2022"
] | The extracted record is a table-of-contents fragment rather than a mathematical statement, so no resolution can be assigned and it is open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Matija Bucić (joint with Jacob Fox and Benny Sudakov) Clique minors in graphs with a forbidden subgraph . . . . . . . . . . . . . . . . . . . 12 Johannes Carmesin Local Separators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | unrecoverable | The official report shows that this extract is a table-of-contents fragment without a recoverable standalone statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,957 | OWR-9790352-003 | Unspecified Structural Graph Theory Conjecture | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Nicolas Trotignon (joint with Pegah Pournajafi) Burling graphs revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Benny Sudakov (joint with David Munhá Correia and Alexey Pokrovskiy) Short proofs of rainbow ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this extract is a second table-of-contents fragment without a recoverable standalone statement. No separate c) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-003",
"literature-status:open",
"owr-year:2022"
] | The extracted record is a table-of-contents fragment ending with the word Conjecture and does not identify a checkable claim; it is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Nicolas Trotignon (joint with Pegah Pournajafi) Burling graphs revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Benny Sudakov (joint with David Munhá Correia and Alexey Pokrovskiy) Short proofs of rainbow ... | unrecoverable | The official report shows that this extract is a second table-of-contents fragment without a recoverable standalone statement. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,958 | OWR-9790352-004 | Gallai’s Path-Decomposition Conjecture | Can the edge set of every connected graph on $n$ vertices be decomposed into at most $\lceil n/2\rceil$ paths? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-004",
"literature-status:open",
"owr-year:2022"
] | Gallai's general path-decomposition conjecture remains unresolved. Primary work proves important restricted cases, including planar and block graphs, but not the general statement. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.3934/math.2025066",
"label": "Chen--Wu block-graph result"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Can the edge set of every connected graph on $n$ vertices be decomposed into at most $\lceil n/2\rceil$ paths? | Gallai’s conjecture is still unsolved as of today, and has only been confirmed on very specific classes of graphs. Gallai’s path-decomposition conjecture Marthe Bonamy (joint work with Alexandre Blanché and Nicolas Bonichon) | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,959 | OWR-9790352-005 | Local Separators in Large Networks | What are local separators of large networks? 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:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report immediately answers the rhetorical heading by defining local separators, so it is not an open problem. No separate clean) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-005",
"literature-status:open",
"owr-year:2022"
] | The question is a broad research prompt about local separators, and the extracted record does not specify a unique theorem whose truth would constitute a resolution; it is open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | What are local separators of large networks? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report immediately answers the rhetorical heading by defining local separators, so it is not an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,960 | OWR-9790352-006 | Unspecified Graph Structure Problem | What is the structure of the graph in 1? 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:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report answers this figure-specific question in the following sentence; the extract is contextual exposition rather than an ope) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-006",
"literature-status:open",
"owr-year:2022"
] | The phrase refers to an unspecified graph in an omitted item numbered 1, so the mathematical claim is not identifiable and is open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | What is the structure of the graph in 1? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report answers this figure-specific question in the following sentence; the extract is contextual exposition rather than an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,961 | OWR-9790352-008 | Report-Proved Logarithmic Treewidth Bound | Additionally the authors of [7] observed that the number of vertices of the graphs Gℓ from Theorem 3 is exponential in their treewidth, while for walls and their line graphs, the number of vertices is polynomial in the treewidth. This radical difference lead to the following conjecture. Theorem 5. [2] For every subdivi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report states this logarithmic-treewidth conjecture and then proves it as a theorem in the same contribution, so it must not be) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-008",
"literature-status:open",
"owr-year:2022"
] | The extracted record is only a fragment ending with the word conjecture and does not state the proposed treewidth claim; its exact status is therefore open under the stated uncertainty rule. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Additionally the authors of [7] observed that the number of vertices of the graphs Gℓ from Theorem 3 is exponential in their treewidth, while for walls and their line graphs, the number of vertices is polynomial in the treewidth. This radical difference lead to the following conjecture. Theorem 5. [2] For every subdivi... | unrecoverable | The official report states this logarithmic-treewidth conjecture and then proves it as a theorem in the same contribution, so it must not be published as open. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,962 | OWR-9790352-010 | Polynomial $chi$-Bounds for Pivot-Minor-Closed Classes | For every fixed graph $H$, are graphs with no pivot-minor isomorphic to $H$ polynomially $\chi$-bounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-010",
"literature-status:open",
"owr-year:2022"
] | The ordinary chi-boundedness theorem for proper pivot-minor-closed classes is proved, but the extracted polynomial chi-bounded strengthening remains a conjecture in the current literature. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.dam.2024.03.011",
"label": "Kim--Oum vertex-minor survey"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For every fixed graph $H$, are graphs with no pivot-minor isomorphic to $H$ polynomially $\chi$-bounded? | conjecture. Conjecture 2. Every proper pivot-minor-closed class of graphs is polynomially χ-bounded. The discussed natural classes closed under pivot-minors are all polynomially χ-bounded. For circle graphs this was proved by Davies and McCarty [5], and furthermore it is now know that they have a χ-bounding function 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,963 | OWR-9790352-011 | Optimal Product Structure for Planar Graphs | What is the smallest integer $k$ such that every planar graph is a subgraph of $H\boxtimes P$ for some path $P$ and some graph $H$ of treewidth at most $k$? Is the optimum between $3$ and $6$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-011",
"literature-status:open",
"owr-year:2022"
] | The product-structure gap between the upper bound six and lower bound three is not closed. Recent work improves related product representations but does not settle this exact single-path product question. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2411.00343",
"label": "2025 related product-structure result"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | What is the smallest integer $k$ such that every planar graph is a subgraph of $H\boxtimes P$ for some path $P$ and some graph $H$ of treewidth at most $k$? Is the optimum between $3$ and $6$? | Closing the gap between the upper bound 6 in Theorem 3 and the lower bound 3 is an interesting open problem. Since their discovery, Theorem 1 and Theorem 2 have been used to solve a number of long standing open problems, including: queue number of planar graphs [5], non-repetitive chromatic number of planar graphs [3] ... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,964 | OWR-9790352-012 | Sketchability and Bounded Expansion of Graph Classes | If a monotone graph class is $(C,s)$-sketchable for some $C>1$ and some $s$, must it have bounded expansion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-012",
"literature-status:open",
"owr-year:2022"
] | The extracted statement is Conjecture 5 about sketchability and bounded expansion. The report presents it as unresolved and relates it to Thomassen's still-open large-girth subgraph conjecture. | [
{
"url": "https://doi.org/10.4171/OWR/2022/1",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/0095-8956(83)90067-9",
"label": "Thomassen Girth in graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | If a monotone graph class is $(C,s)$-sketchable for some $C>1$ and some $s$, must it have bounded expansion? | We conjecture that the following stronger result holds. As alluded to above, Conjecture 5 would be implied by a conjecture of Thomassen [3], stating that every graph of large average degree contains a subgraph of large girth and average degree. The report passage is retained verbatim as the relevant context for this ex... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,965 | OWR-9790352-013 | Small Induced-Universal Graphs for Planar Graphs | What is the minimum order of a graph that contains every planar graph on $n$ vertices as an induced subgraph? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-013",
"literature-status:open",
"owr-year:2022"
] | Sparse universal constructions now give n^{1+o(1)} vertices for induced universality of n-vertex planar graphs, but the asymptotically exact minimum remains open. | [
{
"url": "https://arxiv.org/abs/2010.05779",
"label": "Esperet, Joret, and Morin, Sparse universal graphs for planarity"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | What is the minimum order of a graph that contains every planar graph on $n$ vertices as an induced subgraph? | The best known bound is O(n3/2 ), due to Babai, Chung, Erdös, Graham, and Spencer [2]. (2) What is the minimum number of vertices in a graph containing all n- vertex planar graphs as induced subgraphs? Further applications of the product structure theorem Gwenaël Joret (joint work with Vida Dujmović, Louis Esperet, ... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,966 | OWR-9790352-014 | Extremal Subgraph Counts in Sparse Graph Classes | For a graph class $\mathcal G$ and a graph $H$, determine $\operatorname{ex}(H,\mathcal G,n)$, the maximum number of subgraphs isomorphic to $H$ in an $n$-vertex member of $\mathcal G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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-9790352-014",
"literature-status:open",
"owr-year:2022"
] | The extracted record does not define the graph class G or the pattern H, so no determinate extremal claim can be verified; under the required rule the claim is open. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For a graph class $\mathcal G$ and a graph $H$, determine $\operatorname{ex}(H,\mathcal G,n)$, the maximum number of subgraphs isomorphic to $H$ in an $n$-vertex member of $\mathcal G$. | What is the maximum number ex(H, G, n) of H-subgraphs contained in an n-vertex graph in G? Homomorphism counts in robustly sparse graphs Chun-Hung Liu | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,967 | OWR-9790352-015 | Unspecified Colin de Verdiere Graph Parameter Problem | Theorem 3 solves a number of open questions. For example, proper minor- closed families are known to have bounded expansion, so Theorem 3 implies the following result, solving a question of Eppstein [1]. The following corollary of Theorem 3 disproves a conjecture of Huynh and Wood [4]. Theorem 3 also implies the follow... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that the extract states a theorem and corollary about the Colin de Verdière parameter, not an open problem. No sep) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-015",
"literature-status:open",
"owr-year:2022"
] | This record is only a meta-level statement that an unnamed Theorem 3 resolves and refutes earlier questions; it does not identify a mathematical claim whose final status can be checked. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Theorem 3 solves a number of open questions. For example, proper minor- closed families are known to have bounded expansion, so Theorem 3 implies the following result, solving a question of Eppstein [1]. The following corollary of Theorem 3 disproves a conjecture of Huynh and Wood [4]. Theorem 3 also implies the follow... | unrecoverable | The official report shows that the extract states a theorem and corollary about the Colin de Verdière parameter, not an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,968 | OWR-9790352-016 | Unspecified Nonrepetitive Graph Coloring Problem | This was a central open problem in a very lively area of research. \pi(G) ⩽ \pi(H ⊠ P ⊠ K3 ) ⩽ \pi ∗ (H ⊠ P ⊠ K3 ) ⩽ \pi ∗ (H ⊠ P ) \cdot 3 ⩽ \pi ∗ (H) \cdot 4 \cdot 3 ⩽ 43 \cdot 4 \cdot 3 = 768. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses the extracted formula to record a proved nonrepetitive-coloring bound rather than a standalone open problem. No sep) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-016",
"literature-status:open",
"owr-year:2022"
] | The extracted statement only says that an unnamed problem was central and open, while the surrounding bound is not tied to a complete question; the target is therefore unresolved and unidentifiable. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | This was a central open problem in a very lively area of research. \pi(G) ⩽ \pi(H ⊠ P ⊠ K3 ) ⩽ \pi ∗ (H ⊠ P ⊠ K3 ) ⩽ \pi ∗ (H ⊠ P ) \cdot 3 ⩽ \pi ∗ (H) \cdot 4 \cdot 3 ⩽ 43 \cdot 4 \cdot 3 = 768. | unrecoverable | The official report uses the extracted formula to record a proved nonrepetitive-coloring bound rather than a standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,969 | OWR-9790352-018 | Hadwiger’s Graph-Coloring Conjecture | Does every graph $G$ with chromatic number $\chi(G)=t$ contain $K_t$ as a minor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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-9790352-018",
"literature-status:partially-solved",
"owr-year:2022"
] | Hadwiger's conjecture is proved in the known low-order cases and many special graph classes, but the general conjecture for larger clique minors remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
},
{
"url": "https://mathworld.wolfram.com/HadwigerConjecture.html",
"label": "Wolfram MathWorld, current status"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Does every graph $G$ with chromatic number $\chi(G)=t$ contain $K_t$ as a minor? | Hadwiger’s Conjecture is widely considered among the most important problems in graph theory and has motivated numerous developments in graph coloring and graph minor theory. Recent Progress on Hadwiger’s Conjecture Luke Postle (joint work with Michelle Delcourt) | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,970 | OWR-9790352-019 | Structural and Algorithmic Properties of Burling Graphs | For a fixed Burling graph $H$, are graphs with no subdivision of $H$ $\chi$-bounded, and do Burling graphs with no induced copy of $H$ have bounded chromatic number? Can Burling graphs be characterized or recognized in polynomial time? Is maximum stable set polynomial-time solvable on Burling graphs? Can the Burling co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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... | [
"OWR-9790352-020"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-019",
"literature-status:open",
"owr-year:2022"
] | The record is an introductory sentence followed by several Burling-graph questions, but it does not isolate one proposition; the extracted target is therefore unclear and classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
},
{
"url": "https://arxiv.org/abs/2510.19650",
"label": "Abrishami et al., Burling graphs in graphs with large chromatic number"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For a fixed Burling graph $H$, are graphs with no subdivision of $H$ $\chi$-bounded, and do Burling graphs with no induced copy of $H$ have bounded chromatic number? Can Burling graphs be characterized or recognized in polynomial time? Is maximum stable set polynomial-time solvable on Burling graphs? Can the Burling co... | Therefore, the focus is on open questions that we explain now and that were not advertised previously. • Could it be that for all Burling graph H, graphs with no subdivisions of H are χ-bounded? This is probably far too much, but disproving it would be interesting. • Let H be a Burling graph. Is the chromatic number 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,971 | OWR-9790352-020 | Chi-Bounds and Stable Sets in Burling Graphs | Is the chromatic number of Burling graphs that do not contain H as an induced subgraph bounded? Or maybe just recognize them in polytime which seem to be possible. • Is there a polytime algorithm to compute a maximum stable set in an input Burling graph? they have geometric representations and because they provide coun... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a partial duplicate of the Burling-graph questions retained in OWR-9790352-019. No separate clean ) | [
"OWR-9790352-019"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-020",
"literature-status:open",
"owr-year:2022"
] | Recent structural work on Burling graphs does not settle the recorded induced-subgraph chi-boundedness or polynomial maximum-stable-set questions, so both remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
},
{
"url": "https://doi.org/10.1016/j.ejc.2023.103849",
"label": "Burling graphs revisited, part II"
},
{
"url": "https://arxiv.org/abs/2510.19650",
"label": "Abrishami et al., Burling graphs in grap... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Is the chromatic number of Burling graphs that do not contain H as an induced subgraph bounded? Or maybe just recognize them in polytime which seem to be possible. • Is there a polytime algorithm to compute a maximum stable set in an input Burling graph? they have geometric representations and because they provide coun... | unrecoverable | The official report confirms that this is a partial duplicate of the Burling-graph questions retained in OWR-9790352-019. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,972 | OWR-9790352-021 | Ryser–Brualdi–Stein Near-Transversal Conjecture | Does every Latin square of order $n$ contain a partial transversal of length $n-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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-9790352-021",
"literature-status:partially-solved",
"owr-year:2022"
] | The near-transversal part is proved for all sufficiently large orders, including large even n, but the full-transversal assertion for odd orders and the finite residual cases remain open. | [
{
"url": "https://arxiv.org/abs/2310.19779",
"label": "Montgomery, large-even-order Ryser--Brualdi--Stein"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Does every Latin square of order $n$ contain a partial transversal of length $n-1$? | Indeed, the celebrated conjecture of Ryser, Brualdi and Stein [10, 5, 11] states that every Latin square contains a transversal which uses all but at most one symbol. The Ryser-Brualdi-Stein conjecture is just one thread of the research on rainbow matchings and rainbow subgraphs more broadly. As an example, consider 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,973 | OWR-9790352-022 | Unspecified Alspach Rainbow Matching Conjecture | The motivation for this conjecture is the Ryser-Brualdi-Stein conjecture which it strengthens (to see this, consider a properly coloured Kn,n as in Conjecture 2; delete one colour to obtain a graph satisfying the Aharoni-Berger conjecture). Furthermore, we ob- tain a new asymptotically tight bound for Grinblat’s proble... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this fragment reports the asymptotic resolution of Alspach's conjecture and does not state a complete open pr) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-022",
"literature-status:open",
"owr-year:2022"
] | The record is a fragment reporting an asymptotic proof of an unnamed Alspach conjecture and gives no complete target statement; the extracted claim is therefore unclear and classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
},
{
"url": "https://arxiv.org/abs/2108.07734",
"label": "Munha Correia, Pokrovskiy, and Sudakov, rainbow matching results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | The motivation for this conjecture is the Ryser-Brualdi-Stein conjecture which it strengthens (to see this, consider a properly coloured Kn,n as in Conjecture 2; delete one colour to obtain a graph satisfying the Aharoni-Berger conjecture). Furthermore, we ob- tain a new asymptotically tight bound for Grinblat’s proble... | unrecoverable | The official report shows that this fragment reports the asymptotic resolution of Alspach's conjecture and does not state a complete open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,974 | OWR-9790352-023 | Aharoni-Berger Rainbow Matching Conjecture | The motivation for this conjecture is the Ryser-Brualdi-Stein conjecture which it strengthens (to see this, consider a properly coloured Kn,n as in Conjecture 2; delete one colour to obtain a graph satisfying the Aharoni-Berger conjecture). Conjecture 2. Let G be a properly edge-coloured bipartite multigraph with n col... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This is a later cross-report duplicate of the Aharoni–Berger rainbow-matching conjecture canonically retained in OWR-16763-030. No separate ) | [
"OWR-16763-030"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-023",
"literature-status:partially-solved",
"owr-year:2022"
] | The Aharoni--Berger rainbow-matching conjecture has asymptotic and several structured-case proofs, but the exact n+1-edge statement for arbitrary properly colored bipartite multigraphs remains open. | [
{
"url": "https://arxiv.org/abs/2108.07734",
"label": "Munha Correia, Pokrovskiy, and Sudakov, short rainbow-matching proofs"
},
{
"url": "https://arxiv.org/abs/1609.06346",
"label": "Pokrovskiy, approximate Aharoni--Berger conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | The motivation for this conjecture is the Ryser-Brualdi-Stein conjecture which it strengthens (to see this, consider a properly coloured Kn,n as in Conjecture 2; delete one colour to obtain a graph satisfying the Aharoni-Berger conjecture). Conjecture 2. Let G be a properly edge-coloured bipartite multigraph with n col... | unrecoverable | This is a later cross-report duplicate of the Aharoni–Berger rainbow-matching conjecture canonically retained in OWR-16763-030. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,975 | OWR-9790352-024 | Unspecified Alspach Rainbow Matching Conjecture | Furthermore, we ob- tain a new asymptotically tight bound for Grinblat’s problem as a function of edge multiplicity of the corresponding multigraph. • We give the first asymptotic proof of a 30 year old conjecture of Alspach. 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:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this is another fragment reporting the asymptotic resolution of Alspach's conjecture, not a standalone open p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-024",
"literature-status:open",
"owr-year:2022"
] | This is only a context fragment saying that an asymptotic Alspach result was obtained; the underlying conjecture is not stated sufficiently to assess as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | Furthermore, we ob- tain a new asymptotically tight bound for Grinblat’s problem as a function of edge multiplicity of the corresponding multigraph. • We give the first asymptotic proof of a 30 year old conjecture of Alspach. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report shows that this is another fragment reporting the asymptotic resolution of Alspach's conjecture, not a standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,976 | OWR-9790352-026 | Rainbow Turán Number of Cycles | For the family $\mathcal C$ of all cycles, is the rainbow Turán number $\operatorname{ex}^*(n,\mathcal C)$ bounded by $O(n\log n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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-9790352-026",
"literature-status:partially-solved",
"owr-year:2022"
] | The n^{1+o(1)} rainbow-cycle bound and the polylogarithmic upper bound are proved, but the sharp O(n log n) upper bound matching the hypercube lower bound remains open. | [
{
"url": "https://arxiv.org/abs/2006.01062",
"label": "Janzer, rainbow Turán number of cycles"
},
{
"url": "https://doi.org/10.1112/plms.70044",
"label": "Alon et al., essentially tight rainbow-cycle bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For the family $\mathcal C$ of all cycles, is the rainbow Turán number $\operatorname{ex}^*(n,\mathcal C)$ bounded by $O(n\log n)$? | conjecture. Regarding the rainbow Turán number of the family C of all cycles, Keevash, Mubayi, Sudakov and Verstraëte [8] showed that ex∗ (n, C) = Ω(n log n), by con- sidering a naturally defined proper edge-colouring of the hypercube Qk , where k = ⌊log n⌋. The vertices of Qk are binary vectors of length k and for a... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,977 | OWR-9790352-027 | Density Threshold for Rainbow Clique Subdivisions | For fixed $m\geq2$, what is the smallest $c$ such that every sufficiently large properly edge-colored graph on $n$ vertices with $\Omega(n(\log n)^c)$ edges contains a rainbow subdivision of $K_m$? In particular, does $c=1$ suffice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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... | [
"OWR-9790352-028"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-027",
"literature-status:partially-solved",
"owr-year:2022"
] | The threshold for rainbow clique subdivisions is now n times a logarithmic factor with exponent 1 plus a term tending to zero, while the lower bound is n log n; the exact smallest exponent and c=1 remain unresolved. | [
{
"url": "https://arxiv.org/abs/2602.08390",
"label": "Kuang and Wang, nearly tight rainbow clique subdivisions"
},
{
"url": "https://doi.org/10.1016/j.ejc.2022.103675",
"label": "Jiang, Methuku, and Yepremyan, rainbow Turán number of clique subdivisions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For fixed $m\geq2$, what is the smallest $c$ such that every sufficiently large properly edge-colored graph on $n$ vertices with $\Omega(n(\log n)^c)$ edges contains a rainbow subdivision of $K_m$? In particular, does $c=1$ suffice? | Open questions To conclude, by our results it follows that there is a constant c ⩽ 60 such that any n-vertex properly edge-coloured graph G with at least n(log n)c edges contains a rainbow subdivision of Km . We pose the following question. that no colour is used on too many of these paths P (v) and Q(v). It easily fol... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,978 | OWR-9790352-028 | Density Threshold for Rainbow Clique Subdivisions | What is the smallest c such that for all sufficiently large n the following holds: if G is a properly edge-coloured graph on n vertices with at least Ω(n(log n)c ) edges, then it contains a rainbow subdivision of Km ? We pose the following question, which strengthens Question 6.2 in [4]. 3. Open questions To conclude, ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a corrupted duplicate of the rainbow clique-subdivision question retained in OWR-9790352-027. No s) | [
"OWR-9790352-027"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-028",
"literature-status:partially-solved",
"owr-year:2022"
] | The same rainbow-subdivision threshold has been reduced to n(log n)^{1+o(1)} up to constants depending on the clique size, but the exact exponent-one assertion in the question is not proved. | [
{
"url": "https://arxiv.org/abs/2602.08390",
"label": "Kuang and Wang, nearly tight rainbow clique subdivisions"
},
{
"url": "https://doi.org/10.1016/j.ejc.2022.103675",
"label": "Jiang, Methuku, and Yepremyan, rainbow Turán number of clique subdivisions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | null | What is the smallest c such that for all sufficiently large n the following holds: if G is a properly edge-coloured graph on n vertices with at least Ω(n(log n)c ) edges, then it contains a rainbow subdivision of Km ? We pose the following question, which strengthens Question 6.2 in [4]. 3. Open questions To conclude, ... | unrecoverable | The official report confirms that this is a corrupted duplicate of the rainbow clique-subdivision question retained in OWR-9790352-027. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,979 | OWR-9790352-029 | Blow-Ups of Clique Subdivisions in Dense Graphs | For fixed integers $m,r\geq2$, does every $n$-vertex graph with $\Omega(n^{2-1/r})$ edges contain the $r$-blow-up of a subdivision of $K_m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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-9790352-029",
"literature-status:partially-solved",
"owr-year:2022"
] | The log-free density exponent is known up to a polylogarithmic factor: the current theorem requires (log n)^{60/r}, and the proposed threshold without that factor remains open. | [
{
"url": "https://arxiv.org/abs/2108.08814",
"label": "Jiang, Letzter, Methuku, and Yepremyan, rainbow clique subdivisions and blow-ups"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For fixed integers $m,r\geq2$, does every $n$-vertex graph with $\Omega(n^{2-1/r})$ edges contain the $r$-blow-up of a subdivision of $K_m$? | Is it true that if G is an n-vertex graph with at least 1 Ω(n2− r ) edges then it contains an r-blow-up of a subdivision of Km ? Question 6. Fix m ⩾ 2. What is the smallest c such that for all sufficiently large n the following holds: if G is a properly edge-coloured graph on n vertices with at least Ω(n(log n)c ) edge... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,980 | OWR-9790352-030 | Maximum Twin-Width of $n$-Vertex Graphs | What is the maximum twin-width among graphs on $n$ vertices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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-9790352-030",
"literature-status:partially-solved",
"owr-year:2022"
] | General n-vertex graphs have twin-width at most n/2 plus a lower-order term, and conference graphs attain (n-1)/2; the conjectured exact maximum (n-1)/2 remains open. | [
{
"url": "https://arxiv.org/abs/2110.03957",
"label": "Ahn, Hendrey, Kim, and Oum, bounds for twin-width"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | What is the maximum twin-width among graphs on $n$ vertices? | What is the maximum twin-width of an n-vertex graphs? 4. Treewidth of hereditary classes (Nicolas Trotignon) The following conjecture was made by several people: Conjecture: For every integer ℓ, there exists Cℓ > 0 such that if a graph G contains none of the following as an induced subgraph: • subdivision of an ℓ \time... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,981 | OWR-9790352-031 | Bollobás–Erdős–Tuza Independent-Set Hitting Conjecture | If a sequence of graphs $G$ satisfies $\alpha(G)=\Omega(|V(G)|)$, must the minimum order $h(G)$ of a vertex set meeting every maximum independent set satisfy $h(G)=o(|V(G)|)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-031",
"literature-status:partially-solved",
"owr-year:2022"
] | The Bollobás--Erdős--Tuza conjecture remains open, although substantial bounds and structural cases are known, including recent reductions and results for dense or restricted graph classes. | [
{
"url": "https://arxiv.org/abs/2608.18963",
"label": "Bai, Chang, and Yan, hitting maximum independent sets"
},
{
"url": "https://doi.org/10.1002/jgt.23246",
"label": "Cheng and Xu, Bollobás--Erdős--Tuza for forbidden subgraphs"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | If a sequence of graphs $G$ satisfies $\alpha(G)=\Omega(|V(G)|)$, must the minimum order $h(G)$ of a vertex set meeting every maximum independent set satisfy $h(G)=o(|V(G)|)$? | Conjecture (Bollobás, Erdős and Tuza, 1991): If \alpha(G) = Ω(n) then h(G) = o(n). A relaxed conjecture: If χ(G) = O(1) then h(G) = o(n). (Open even for χ(G) = 3.) Remarks: • Hajnal (1965): If \alpha(G) > n/2 then h(G) = 1. • There are graphs \sqrt{ } G = Gn on n vertices with \alpha(G) > n/4, χ(G) ⩽ 8 and h(G) > n/2... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,982 | OWR-9790352-032 | Hitting Maximum Independent Sets in Bounded-Chromatic Graphs | If a sequence of graphs $G$ has $\chi(G)=O(1)$, must the minimum order $h(G)$ of a vertex set meeting every maximum independent set satisfy $h(G)=o(|V(G)|)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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"
} | {
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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-9790352-032",
"literature-status:partially-solved",
"owr-year:2022"
] | The constant-chromatic-number relaxation is still open even for 3-colorable graphs, while recent work proves only restricted dense, regular, or highly connected cases. | [
{
"url": "https://arxiv.org/abs/2608.18963",
"label": "Bai, Chang, and Yan, hitting maximum independent sets"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | If a sequence of graphs $G$ has $\chi(G)=O(1)$, must the minimum order $h(G)$ of a vertex set meeting every maximum independent set satisfy $h(G)=o(|V(G)|)$? | A relaxed conjecture: If χ(G) = O(1) then h(G) = o(n). (Open even for χ(G) = 3.) Conjecture (Bollobás, Erdős and Tuza, 1991): If \alpha(G) = Ω(n) then h(G) = o(n). Remarks: • Hajnal (1965): If \alpha(G) > n/2 then h(G) = 1. • There are graphs \sqrt{ } G = Gn on n vertices with \alpha(G) > n/4, χ(G) ⩽ 8 and h(G) > n/2... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,983 | OWR-9790352-033 | Clique Minors in Graphs Excluding a Fixed Subgraph | For which graphs $F$ does there exist $c(F)>0$ such that every graph $G$ with no subgraph isomorphic to $F$ contains a clique minor of order at least $\chi(G)^{1+c(F)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-033",
"literature-status:partially-solved",
"owr-year:2022"
] | Polynomially larger clique minors are proved for important forbidden-subgraph classes and the Hall-ratio variant holds generally, but the requested classification in terms of chromatic number is not complete. | [
{
"url": "https://arxiv.org/abs/2002.11100",
"label": "Bucic, Fox, and Sudakov, clique minors with a forbidden subgraph"
},
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | For which graphs $F$ does there exist $c(F)>0$ such that every graph $G$ with no subgraph isomorphic to $F$ contains a clique minor of order at least $\chi(G)^{1+c(F)}$? | 6. Beyond Hadwiger in F -free graphs (Matija Bucić) Question (B., Fox and Sudakov). For which graphs F does the following hold: G does not contain F as a subgraph =\Rightarrow \exists a clique minor of size (χ(G))1+c for c = c(F ) > 0? • Kuhn-Osthus, 2005: true if F is bipartite and ask the question for F = Ks . • Dvo... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,984 | OWR-9790352-034 | Planar Connectivity Models for Cross-Free Societies | Which cross-free societies admit a planar connectivity model, and how can such societies be characterized? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 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,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-034",
"literature-status:open",
"owr-year:2022"
] | The cross-free-society question asks for an exact planar connectivity-preserving replacement and is presented without a resolving theorem; no authoritative resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Which cross-free societies admit a planar connectivity model, and how can such societies be characterized? | If (G, Ω) is a cross-free society, then is it true that there always is a planar digraph H with Ω(G) \subseteq V (H) such that H has an embedding into the plane with the vertices of Ω(H) appearing in the outer face in the order specified by Ω such that H allows for exactly the same connectivity between vertices of Ω(G)... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,985 | OWR-9790352-036 | Reconstruction of Point Sets from $k$-Decks | Does a universal integer $k$ exist such that every finite subset of $\mathbb R^3$ is determined up to isometry by the multiset of its $k$-point subsets, each considered up to isometry? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-036",
"literature-status:partially-solved",
"owr-year:2022"
] | The original extracted text included an adjacent, unrelated source item. The source report confirms the existing clean statement; the original_statement field is now restricted to this problem. No theorem about the neighbouring item is treated as a solution here.
**What remains.** The clean problem retains its existin... | [
{
"url": "https://doi.org/10.4171/owr/2022/1",
"label": "Oberwolfach Report 1/2022"
},
{
"url": "https://digitalcommons.unl.edu/mathfacpub/142/",
"label": "Pebody, Radcliffe, and Scott, finite planar subsets"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4"... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Does a universal integer $k$ exist such that every finite subset of $\mathbb R^3$ is determined up to isometry by the multiset of its $k$-point subsets, each considered up to isometry? | How large does k need to be so that every set of n points is reconstructible from its k-deck? | corrected_verified | Removed material belonging to a neighbouring source item after checking the original report. The clean mathematical statement is unchanged. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,986 | OWR-9790352-037 | Chromatic Number of Almost-Linear Graph Unions | Let $G_1,\ldots,G_n$ be graphs with $\chi(G_i)\leq n-1$ such that every two have at most one vertex in common. How large can $\chi(G_1\cup\cdots\cup G_n)$ be? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 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"
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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-9790352-037",
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] | The Erdős--Faber--Lovász bound is proved for all sufficiently large n, but the question asks for the exact maximum for every n and the finite exceptional range is not completely resolved. | [
{
"url": "https://doi.org/10.4007/annals.2023.198.2.2",
"label": "Kang et al., proof of the Erdős--Faber--Lovász conjecture"
},
{
"url": "https://arxiv.org/abs/2110.06181",
"label": "Kang et al., bounded-codegree extension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Let $G_1,\ldots,G_n$ be graphs with $\chi(G_i)\leq n-1$ such that every two have at most one vertex in common. How large can $\chi(G_1\cup\cdots\cup G_n)$ be? | A variant of the Erdős–Faber–Lovász conjecture (Tom Kelly) The Erdős–Faber–Lovász conjecture is the following: If G1 , . . . , Gn are complete graphs, S each on at most n vertices, such that every pair shares at most one vertex, n then χ( i=1 Gi ) ⩽ n. There are still several variations and possible generalizations... | 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 | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,987 | OWR-9790352-039 | Subgraph Query Complexity for Fixed Pattern Graphs | Let $f(H,p)$ be the minimum number of adaptive adjacency queries needed to reveal a copy of a fixed graph $H$ in a hidden countably infinite Erdős–Rényi graph $G(\mathbb N,p)$ with probability at least $1/2$. What is the growth of $f(H,p)$ as $p\to0$, and for which $H$ is it of order $p^{-c}$ for some constant $c$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78](https://doi.org/10.4171/owr/2022/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
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"name": "graph_theory",
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"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790352-039",
"literature-status:open",
"owr-year:2022"
] | The original extracted text included an adjacent, unrelated source item. The source report confirms the existing clean statement; the original_statement field is now restricted to this problem. No theorem about the neighbouring item is treated as a solution here.
**What remains.** The clean problem retains its existin... | [
{
"url": "https://arxiv.org/abs/1911.04413",
"label": "Alweiss--Ben Hamida--He--Moreira, On the subgraph query problem"
},
{
"url": "https://arxiv.org/abs/1806.09726",
"label": "Conlon--Fox--Grinshpun--He, Online Ramsey Numbers and the Subgraph Query Problem"
},
{
"url": "https://doi.org... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2022/1 | null | null | null | Let $f(H,p)$ be the minimum number of adaptive adjacency queries needed to reveal a copy of a fixed graph $H$ in a hidden countably infinite Erdős–Rényi graph $G(\mathbb N,p)$ with probability at least $1/2$. What is the growth of $f(H,p)$ as $p\to0$, and for which $H$ is it of order $p^{-c}$ for some constant $c$? | What is the growth rate of f (H, p) as p \to 0+ ? | corrected_verified | Removed material belonging to a neighbouring source item after checking the original report. The clean mathematical statement is unchanged. | null | null | null | null | null | Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78 |
30,004,988 | OWR-9790353-002 | Topological Triviality of Borel Quotient Isomorphisms | Under what assumptions is every isomorphism between the Borel quotient structures $M/E$ and $N/F$ topologically trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/2, pp. 79--106](https://doi.org/10.4171/owr/2022/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,022 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"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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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790353-002",
"literature-status:open",
"owr-year:2022"
] | Results under forcing axioms and in important Boolean and C-star quotient classes establish instances, but no general assumption-free characterization for arbitrary Borel quotient structures is known. | [
{
"url": "https://arxiv.org/abs/2201.11618",
"label": "Farah--Ghasemi--Vaccaro--Vignati, Corona Rigidity"
},
{
"url": "https://arxiv.org/abs/1112.3571",
"label": "Farah--Shelah, Trivial automorphisms"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/2 | null | null | null | Under what assumptions is every isomorphism between the Borel quotient structures $M/E$ and $N/F$ topologically trivial? | Under what assumptions is it true that every isomorphism between M/E and N /F is topologically trivial? 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 | Set Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/2, pp. 79--106 |
30,004,989 | OWR-9790353-003 | Set-Theoretic Dichotomy for Borel-Quotient Automorphisms | Does CH imply that $M/E$ has $2^{\mathfrak c}$ automorphisms, while forcing axioms imply that every isomorphism between $M/E$ and $N/F$ is topologically trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/2, pp. 79--106](https://doi.org/10.4171/owr/2022/2)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,022 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
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"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790353-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The stated CH and forcing-axiom pattern is verified for broad families of Boolean, C-star, and corona quotients, while the full Borel-quotient conjecture remains a survey-level open problem. | [
{
"url": "https://arxiv.org/abs/2201.11618",
"label": "Farah--Ghasemi--Vaccaro--Vignati, Corona Rigidity"
},
{
"url": "https://doi.org/10.1017/bsl.2025.10084",
"label": "2025 Bulletin of Symbolic Logic version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/2 | null | null | null | Does CH imply that $M/E$ has $2^{\mathfrak c}$ automorphisms, while forcing axioms imply that every isomorphism between $M/E$ and $N/F$ is topologically trivial? | Conjecture 3. For Borel quotient structures M/E and N /F , consider the fol- lowing statements. (1) The Continuum Hypothesis (CH) implies that M/E has 2c automorphisms (and therefore 2c topologically nontrivial automorphisms). (2) Forcing Axioms imply that every isomorphism between M/E and N /F is topologically trivial... | 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 | Set Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/2, pp. 79--106 |
30,004,990 | OWR-9790354-001 | Dynamical Comparison for Amenable Minimal Nonamenable-Group Actions | Conjecture that every amenable minimal action of a nonamenable group on a compact metric space has dynamical comparison. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 3 | partially_solved | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 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-9790354-001",
"literature-status:partially-solved",
"owr-year:2022"
] | Dynamical comparison is proved for amenable minimal actions of a large class of non-amenable groups, including non-amenable hyperbolic groups and several products, but not for all such groups. | [
{
"url": "https://arxiv.org/abs/2201.03409",
"label": "Gardella--Geffen--Kranz--Naryshkin, Classifiability of crossed products by nonamenable groups"
},
{
"url": "https://doi.org/10.1515/crelle-2023-0012",
"label": "Journal version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Conjecture that every amenable minimal action of a nonamenable group on a compact metric space has dynamical comparison. | We conjecture that all minimal (amenable) actions of non-amenable groups on compact metric spaces have dynamical comparison. Purely infinite crossed products by non-amenable groups Shirly Geffen (joint work with Eusebio Gardella, Julian Kranz, Petr Naryshkin) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,991 | OWR-9790354-002 | Type-I Conjecture Section Heading | A type I conjecture Let G be a second countable locally compact group. Hyperbolic groups of type I Pierre-Emmanuel Caprace (joint work with Mehrdad Kalantar and Nicolas Monod) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is only a section heading and an incomplete setup duplicated by the following complete conj) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790354-002",
"literature-status:open",
"owr-year:2022"
] | The extracted record is an incomplete formulation of the type-I conjecture; known results cover substantial hyperbolic and tree cases, but the general locally compact-group statement is unresolved. | [
{
"url": "https://arxiv.org/abs/2110.00190",
"label": "Caprace--Kalantar--Monod, A type I conjecture and boundary representations"
},
{
"url": "https://doi.org/10.1112/plms.70100",
"label": "Glasner, Boundary representations of locally compact hyperbolic groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | null | A type I conjecture Let G be a second countable locally compact group. Hyperbolic groups of type I Pierre-Emmanuel Caprace (joint work with Mehrdad Kalantar and Nicolas Monod) | unrecoverable | The official report confirms that the extraction is only a section heading and an incomplete setup duplicated by the following complete conjecture. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,992 | OWR-9790354-003 | Cocompact Amenable Subgroups of Type-I Groups | Let $G$ be a second-countable locally compact group. If $G$ is type I, must $G$ have a cocompact amenable subgroup? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 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"
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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-9790354-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The conjecture that every second-countable locally compact type-I group has a cocompact amenable subgroup is proved in important hyperbolic and unimodular cases, but remains open in general. | [
{
"url": "https://arxiv.org/abs/2110.00190",
"label": "Caprace--Kalantar--Monod, A type I conjecture and boundary representations"
},
{
"url": "https://doi.org/10.1112/plms.70100",
"label": "Glasner, Boundary representations of locally compact hyperbolic groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Let $G$ be a second-countable locally compact group. If $G$ is type I, must $G$ have a cocompact amenable subgroup? | Conjecture 1. Let G be a second countable locally compact group. If G is type I, then G has a cocompact amenable subgroup. This statement is of course meaningless if G is amenable. The existence of amenable groups that are not type I shows that the converse to Conjecture 1 need not hold. However, it might potentially h... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,993 | OWR-9790354-004 | Quadratic Schreier Growth for Torsion-Free Solvable Groups | Let $G$ be a finitely generated torsion-free solvable group. Prove that either $G$ is virtually abelian or every faithful $G$-set $X$ satisfies $\operatorname{vol}_{G,X}(n)\succeq n^2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 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"
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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-9790354-004",
"literature-status:partially-solved",
"owr-year:2022"
] | The quadratic Schreier-growth conclusion is proved for metabelian and broad finite-rank or linear classes and for faithful actions with finitely many orbits, while the arbitrary torsion-free solvable case remains open. | [
{
"url": "https://arxiv.org/abs/2205.11924",
"label": "Le Boudec--Matte Bon, Growth of actions of solvable groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Let $G$ be a finitely generated torsion-free solvable group. Prove that either $G$ is virtually abelian or every faithful $G$-set $X$ satisfies $\operatorname{vol}_{G,X}(n)\succeq n^2$. | We conjecture that the previous result should hold for arbitrary torsion-free solvable groups. We show that the conjecture is true if we restrict to transitive actions, and more generally to actions with finitely many orbits. 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 | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,994 | OWR-9790354-005 | Entropy and Nondiagonal Asymptotic Pairs | Let an amenable countably infinite discrete group $\Gamma$ act expansively and algebraically on a compact metrizable space $X$. Is $h(\Gamma\curvearrowright X)>0$ equivalent to the existence of a nondiagonal asymptotic pair? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 3 | partially_solved | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 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-9790354-005",
"literature-status:partially-solved",
"owr-year:2022"
] | The equivalence is established for polycyclic-by-finite algebraic actions and related classes, while counterexamples and unresolved cases show that the general amenable expansive algebraic-action question is not settled. | [
{
"url": "https://arxiv.org/abs/1103.1567",
"label": "Chung--Li, Homoclinic groups, IE groups, and expansive algebraic actions"
},
{
"url": "https://arxiv.org/abs/1701.01318",
"label": "Meyerovitch, Pseudo-Orbit Tracing and Algebraic actions"
},
{
"url": "https://arxiv.org/abs/1911.00785... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Let an amenable countably infinite discrete group $\Gamma$ act expansively and algebraically on a compact metrizable space $X$. Is $h(\Gamma\curvearrowright X)>0$ equivalent to the existence of a nondiagonal asymptotic pair? | Is is true that h(Γ y X) > 0 if and only if there are non-diagonal asymptotic pairs? The new tool we use to study Question is the following notion. Groups and Dynamics: Topology, Measure, and Borel Structure 141 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,995 | OWR-9790354-006 | Borel Extensions of Hyper-Aperiodic Coloring Theorems | Let $S\subseteq q^\Gamma$ be a subshift of finite type and let $f:\operatorname{Free}(k^\Gamma)\to q$ be an $S$-coloring whose coding map has no nonidentity element of $\Gamma$ fixing its entire image. Determine additional hypotheses ensuring that, when $f$ is Borel rather than continuous, every free Borel $\Gamma$-act... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 3 | open | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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"literature-status:open",
"owr-year:2022"
] | The continuous theorem has a Borel analogue only under additional hypotheses; the source explicitly leaves the unrestricted Borel replacement as an open problem. | [
{
"url": "https://arxiv.org/abs/2106.09673",
"label": "Bernshteyn, Equivariant maps to subshifts whose points have small stabilizers"
},
{
"url": "https://doi.org/10.4171/owr/2022/3",
"label": "Oberwolfach Report 3/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Let $S\subseteq q^\Gamma$ be a subshift of finite type and let $f:\operatorname{Free}(k^\Gamma)\to q$ be an $S$-coloring whose coding map has no nonidentity element of $\Gamma$ fixing its entire image. Determine additional hypotheses ensuring that, when $f$ is Borel rather than continuous, every free Borel $\Gamma$-act... | Is there a version of Theorem 3 that only needs f to be Borel (rather than continuous)? The proofs of our results rely on combinatorial methods, in particular on the continuous version of the Lovász Local Lemma developed in [1]. We conclude with a couple of open problems. The difficulty with Problem 1 is that it is no... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,996 | OWR-9790354-007 | Hyper-Aperiodic Colorings from Aperiodic SFT Colorings | Let $S\subseteq q^\Gamma$ be a subshift of finite type and let $f:\operatorname{Free}(k^\Gamma)\to q$ be a Borel aperiodic $S$-coloring. Must $\operatorname{Free}(k^\Gamma)$ also admit a Borel hyper-aperiodic $S$-coloring? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 3 | open | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 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-9790354-007",
"literature-status:open",
"owr-year:2022"
] | The concrete Borel aperiodic-to-hyper-aperiodic SFT-coloring question is still presented as unresolved; existing theorems require continuity or extra structural assumptions. | [
{
"url": "https://arxiv.org/abs/2106.09673",
"label": "Bernshteyn, Equivariant maps to subshifts whose points have small stabilizers"
},
{
"url": "https://doi.org/10.4171/owr/2022/3",
"label": "Oberwolfach Report 3/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Let $S\subseteq q^\Gamma$ be a subshift of finite type and let $f:\operatorname{Free}(k^\Gamma)\to q$ be a Borel aperiodic $S$-coloring. Must $\operatorname{Free}(k^\Gamma)$ also admit a Borel hyper-aperiodic $S$-coloring? | Problem 2. Let S \subseteq q Γ be an SFT and let f : Free(k Γ ) \to q be a Borel aperiodic S-coloring. Must exist a Borel hyper-aperiodic S-coloring of Free(k Γ ) as well? The difficulty with Problem 1 is that it is not even clear what the right statement of the desired result should be. It is certainly not enough to s... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,997 | OWR-9790354-008 | Definable Analogues of Finite Combinatorial Theorems | Which results of finite combinatorics admit counterparts for Borel graphs that are Borel, $\mu$-measurable, or $\tau$-Baire measurable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169](https://doi.org/10.4171/owr/2022/3)
## Literature review (che... | 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-9790354-008",
"literature-status:open",
"owr-year:2022"
] | This is a broad research program rather than a single theorem; many Borel, measurable, and Baire analogues are known, but no general transfer principle from finite combinatorics is established. | [
{
"url": "https://arxiv.org/abs/2004.04905",
"label": "Bernshteyn, Distributed algorithms, the Lovasz Local Lemma, and descriptive combinatorics"
},
{
"url": "https://arxiv.org/abs/1611.02204",
"label": "Conley--Jackson--Marks--Seward--Tucker-Drob, Hyperfiniteness and Borel combinatorics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/3 | null | null | null | Which results of finite combinatorics admit counterparts for Borel graphs that are Borel, $\mu$-measurable, or $\tau$-Baire measurable? | A natural question is which results from finite combinatorics have analogues ’definable’ (i.e., Borel, µ-measurable, \tau -Baire measurable) counterparts for Borel graphs. Measurable combinatorics in hyperfinite graphs Matt Bowen (joint work with Gabor Kun and Marcin Sabok; Felix Weilacher; Antoine Poulin and Jenna Zom... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Groups and Dynamics: Topology, Measure, and Borel Structure (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/3, pp. 107--169 |
30,004,998 | OWR-9790355-001 | Unspecified Multiscale Complex Media Modeling Problem | Here there are still a lot of open questions concerning the analysis and also the modelling for such kind of problems. 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:** [Multiscale Coupled Models for Complex Media: From Analysis to Simulation in Geophysics and Medicine (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/4, pp. 171--229](https://doi.org/10.417... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report shows that this is broad workshop context mentioning many questions without stating a recoverable standalone target. No ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790355-001",
"literature-status:open",
"owr-year:2022"
] | The extracted record is a non-specific statement that many analytical and modeling questions remain; it does not formulate a resolved mathematical claim. | [
{
"url": "https://doi.org/10.4171/owr/2022/4",
"label": "Oberwolfach Report 4/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/4 | null | null | null | null | Here there are still a lot of open questions concerning the analysis and also the modelling for such kind of problems. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report shows that this is broad workshop context mentioning many questions without stating a recoverable standalone target. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Multiscale Coupled Models for Complex Media: From Analysis to Simulation in Geophysics and Medicine (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/4, pp. 171--229 |
30,004,999 | OWR-9790355-002 | Optimization and Multiscale Simulation in Additive Manufacturing | Develop methods for variable-density structural optimization in a fixed design domain, for optimizing deposition paths in fiber-oriented additive manufacturing, and for immersed two-level space-time simulation of strongly nonlinear local problems. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiscale Coupled Models for Complex Media: From Analysis to Simulation in Geophysics and Medicine (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/4, pp. 171--229](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-9790355-002",
"literature-status:open",
"owr-year:2022"
] | The record lists broad structural-optimization and additive-manufacturing research problems without a single precise theorem or conjecture; no general resolution can be asserted. | [
{
"url": "https://doi.org/10.4171/owr/2022/4",
"label": "Oberwolfach Report 4/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/4 | null | null | null | Develop methods for variable-density structural optimization in a fixed design domain, for optimizing deposition paths in fiber-oriented additive manufacturing, and for immersed two-level space-time simulation of strongly nonlinear local problems. | After a short introduction to the technology and possible applications, the pre- sentation has focused on open problems of interest for the audience community and in particular on the following problems: " structural optimization problem allowing the possibility of distributing material with different density in a spec... | 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 | Multiscale Coupled Models for Complex Media: From Analysis to Simulation in Geophysics and Medicine (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/4, pp. 171--229 |
30,005,000 | OWR-9790356-001 | Higgs Bundles Arising from p-Adic Representations | Characterize the Higgs bundles that correspond to genuine representations under the $p$-adic Simpson correspondence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302](https://doi.org/10.4171/owr/2022/5)
## Literature review (checked 2026-08-22)
... | 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-9790356-001",
"literature-status:partially-solved",
"owr-year:2022"
] | The essential image of genuine representations is characterized in rank one and important geometric cases, but the general p-adic Simpson correspondence question remains open. | [
{
"url": "https://arxiv.org/abs/2207.13657",
"label": "Heuer, A geometric p-adic Simpson correspondence in rank one"
},
{
"url": "https://doi.org/10.1007/s00208-022-02371-2",
"label": "Heuer--Mann, The p-adic Corlette--Simpson correspondence for abeloids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/5 | null | null | null | Characterize the Higgs bundles that correspond to genuine representations under the $p$-adic Simpson correspondence. | Since this condition can be checked in interesting cases, these results are an important step towards the fundamental open question which Higgs bun- dles correspond to genuine representations in a p-adic Simpson correspondence. 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 | Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302 |
30,005,001 | OWR-9790356-002 | Riemann–Hilbert Correspondence for Étale and v-Sheaves | Extend the $p$-torsion Riemann–Hilbert correspondence from overconvergent étale $\mathbb F_p$-sheaves to all étale $\mathbb F_p$-sheaves, and ultimately to $v$-sheaves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302](https://doi.org/10.4171/owr/2022/5)
## Literature review (checked 2026-08-22)
... | 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-9790356-002",
"literature-status:partially-solved",
"owr-year:2022"
] | A p-torsion Riemann--Hilbert correspondence is established for overconvergent sheaves and small v-stacks, but the conjectural extension to all etale sheaves and v-sheaves is not complete. | [
{
"url": "https://arxiv.org/abs/2206.02022",
"label": "Mann, A p-Adic 6-Functor Formalism in Rigid-Analytic Geometry"
},
{
"url": "https://arxiv.org/abs/1711.04148",
"label": "Bhatt--Lurie, A Riemann-Hilbert correspondence in positive characteristic"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/5 | null | null | null | Extend the $p$-torsion Riemann–Hilbert correspondence from overconvergent étale $\mathbb F_p$-sheaves to all étale $\mathbb F_p$-sheaves, and ultimately to $v$-sheaves. | Another interesting question is whether the above Riemann-Hilbert correspondence can be extended to all étale Fp -sheaves (not just the overconvergent ones) – in fact we conjecture that it can even be extended to v-sheaves. 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 | Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302 |
30,005,002 | OWR-9790356-003 | Integral Geometrization with Nilpotent Singular Support | For quasi-split $G$, let $W_\psi$ be the Whittaker sheaf associated with a nondegenerate character $\psi$. Prove that the spectral-action functor $F\mapsto F*W_\psi$ extends to an equivalence from $\operatorname{Coh}_{\mathrm{Nilp}}(\operatorname{LocSys}_{\widehat G}/\mathbb Z_\ell)$ to $D_{\mathrm{lis}}(\operatorname{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302](https://doi.org/10.4171/owr/2022/5)
## Literature review (checked 2026-08-22)
... | 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-9790356-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The Fargues--Scholze program proves major foundational and spectral-action results, but the stated categorical equivalence with nilpotent singular support is still a conjecture in this generality. | [
{
"url": "https://arxiv.org/abs/2102.13459",
"label": "Fargues--Scholze, Geometrization of the local Langlands correspondence"
},
{
"url": "https://doi.org/10.4171/owr/2022/5",
"label": "Oberwolfach Report 5/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/5 | null | null | null | For quasi-split $G$, let $W_\psi$ be the Whittaker sheaf associated with a nondegenerate character $\psi$. Prove that the spectral-action functor $F\mapsto F*W_\psi$ extends to an equivalence from $\operatorname{Coh}_{\mathrm{Nilp}}(\operatorname{LocSys}_{\widehat G}/\mathbb Z_\ell)$ to $D_{\mathrm{lis}}(\operatorname{... | 6. The geometrization conjecture We finally state the categorical form of the geometrization conjecture. For this we suppose that G is quasi-split. Let U be the unipotent radical of a Borel subgroup \times and \psi : U (E) \to Zℓ be a non-degenerate character. We note G(E) W\psi = (i1 )! c-indU(E) \psi , the so-called W... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/5, pp. 231--302 |
30,005,003 | OWR-9790357-001 | Convolutional Reconstruction in Many Interface Field Models | Conclusions and open questions. However, there remain several open questions that we would like to address. Remark that in order to find the densities \lambda\varepsilonapp,k (t), we need to solve the system of N convolutional equations. Next, knowing the densities \lambda\varepsilonk , the approximated field u\varepsi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Space-Time Methods for Time-Dependent Partial Differential Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/6, pp. 303--381](https://doi.org/10.4171/owr/2022/6)
## Literature re... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official source says only that several questions remain and then describes a reconstruction procedure; it does not state an independentl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790357-001",
"literature-status:open",
"owr-year:2022"
] | The extracted record is an unspecified conclusion that several open questions remain and does not identify a precise proposition that can be classified as solved. | [
{
"url": "https://doi.org/10.4171/owr/2022/6",
"label": "Oberwolfach Report 6/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/6 | null | null | null | null | Conclusions and open questions. However, there remain several open questions that we would like to address. Remark that in order to find the densities \lambda\varepsilonapp,k (t), we need to solve the system of N convolutional equations. Next, knowing the densities \lambda\varepsilonk , the approximated field u\varepsi... | unrecoverable | The official source says only that several questions remain and then describes a reconstruction procedure; it does not state an independently identifiable unresolved claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Space-Time Methods for Time-Dependent Partial Differential Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/6, pp. 303--381 |
30,005,004 | OWR-9790358-001 | Gasca–Maeztu Maximal-Line Conjecture | Does every planar $GC_n$ set contain a maximal line? | 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 | 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... | [
"OWR-9790358-006",
"OWR-9790358-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-001",
"literature-status:partially-solved",
"owr-year:2022"
] | The Gasca--Maeztu conjecture is proved for degrees n at most 5 and has partial progress for n equal to 6, but remains open in general. | [
{
"url": "https://arxiv.org/abs/2208.06784",
"label": "Hakopian--Vardanyan--Vardanyan, On the Gasca-Maeztu conjecture for n=6"
},
{
"url": "https://arxiv.org/abs/2108.12799",
"label": "Vardanyan, A new proof of the Gasca-Maeztu conjecture for n=5"
},
{
"url": "https://doi.org/10.4171/owr... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Does every planar $GC_n$ set contain a maximal line? | of linear forms lk such that Qi (pj ) = \deltaij . In 1982, Gasca and Maeztu made the following Conjecture 1.2. [[21]] For a GCn set, there is a line V (l) with l | Qi for some Qi , such that V (l) contains n + 1 points of X. The Gasca-Maeztu conjecture traces its origin back to the last century, in partic- ular to 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 | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,005 | OWR-9790358-002 | Combinatorial Approaches to the Gasca–Maeztu Conjecture | Can combinatorial properties of maximal lines be used to prove or generalize the Gasca–Maeztu conjecture? | 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 | {
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"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-9790358-002",
"literature-status:open",
"owr-year:2022"
] | The Gasca--Maeztu conjecture is proved through degree n=5, but no proof or counterexample is known in the general planar case; the extracted goal concerns extending this unresolved program. | [
{
"url": "https://arxiv.org/abs/2108.12799",
"label": "Vardanyan, second proof for n=5"
},
{
"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 | Can combinatorial properties of maximal lines be used to prove or generalize the Gasca–Maeztu conjecture? | Conjecture 1.2 is easily seen to hold for n = 1, 2. For n = 3, 4, it was first proved by Busch in [8]. Additional proofs for n = 4, using different techniques, appear in [9] and [25]. Last year, Hakopian-Jetter-Zimmerman showed in [26] that the conjecture holds for n = 5. For more on the problem and related work, see [... | 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 |
30,005,006 | OWR-9790358-003 | Unspecified Polynomial Interpolation Conjecture | conjecture . . . . . . . . . . . . . . . . . . . . 393 Tomas Sauer (joint with Jesus Carnicer, Carmen Godés) Berzolari, Radon, H-bases, syzygies and maximal lines . . . . . . . . . . . . . . . 396 Evelyne Hubert, Michael Singer Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials . . 397 Thomas Fink Ana... | 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 | false | {
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"name": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 shows that this extract is a contents fragment and does not state a recoverable standalone problem. No separate clean st) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-003",
"literature-status:open",
"owr-year:2022"
] | The extracted record is only a truncated table-of-contents fragment ending in `conjecture' and does not identify a mathematical claim; under the stated rule the unresolved record is classified as open. | [
{
"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 | null | conjecture . . . . . . . . . . . . . . . . . . . . 393 Tomas Sauer (joint with Jesus Carnicer, Carmen Godés) Berzolari, Radon, H-bases, syzygies and maximal lines . . . . . . . . . . . . . . . 396 Evelyne Hubert, Michael Singer Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials . . 397 Thomas Fink Ana... | unrecoverable | The official report shows that this extract is a contents fragment and does not state a recoverable standalone problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,007 | OWR-9790358-005 | Higher-Dimensional GC Set Counterexamples | conjecture. The counterex- ample for d = 3 in [3] is obtained by choosing a triple Ai = \{ai , aj , ak \} and replacing bjk by some b′jk in ♭\{bij , bik \}\\{bij , bik \}, thus depriving hi of its maxi- mality while all other hj are still maximal. The resulting X ′ is still GC2 as one sees by verifying that |X ′ is sti... | 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 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report recounts known higher-dimensional counterexamples and unsuccessful approaches rather than posing a new standalone open p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-005",
"literature-status:open",
"owr-year:2022"
] | The extracted passage is an incomplete discussion of a proposed higher-dimensional GC-set counterexample and does not state a complete proposition; no definite truth value can be assigned, so it is classified as open. | [
{
"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 | null | conjecture. The counterex- ample for d = 3 in [3] is obtained by choosing a triple Ai = \{ai , aj , ak \} and replacing bjk by some b′jk in ♭\{bij , bik \}\\{bij , bik \}, thus depriving hi of its maxi- mality while all other hj are still maximal. The resulting X ′ is still GC2 as one sees by verifying that |X ′ is sti... | unrecoverable | The official report recounts known higher-dimensional counterexamples and unsuccessful approaches rather than posing a new standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,008 | OWR-9790358-006 | Gasca-Maeztu Maximal Line Conjecture | conjecture. Conjecture 1 (Gasca-Maeztu conjecture). Each planar GCn set has a maximal line. Different authors have contributed to the conjecture showing that it holds for all GCn sets up to degree n \leq 5 (see [2, 4, 12]). Theorem 1. If X is a GCn set with n \leq 5, there exists a maximal line. A hope for solving the ... | 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 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the Gasca–Maeztu conjecture retained in OWR-9790358-001. No separate cle) | [
"OWR-9790358-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-006",
"literature-status:open",
"owr-year:2022"
] | This is a review passage about the Gasca--Maeztu conjecture and classifications conditional on it; the conjecture remains unresolved beyond the known low-degree cases. | [
{
"url": "https://arxiv.org/abs/2108.12799",
"label": "Vardanyan, current low-degree status"
},
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR interpolation report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | null | conjecture. Conjecture 1 (Gasca-Maeztu conjecture). Each planar GCn set has a maximal line. Different authors have contributed to the conjecture showing that it holds for all GCn sets up to degree n \leq 5 (see [2, 4, 12]). Theorem 1. If X is a GCn set with n \leq 5, there exists a maximal line. A hope for solving the ... | unrecoverable | The official report confirms that this is a duplicate extraction of the Gasca–Maeztu conjecture retained in OWR-9790358-001. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,009 | OWR-9790358-007 | Structure of n-Independent and GCn Interpolation Sets | This talk considers some of the recent results on n-independent, n-correct, and GCn sets, concerning the Gasca-Maeztu conjecture. Along with the maximal line we consider also line passing through exactly n- nodes, as well as the subset of the nodes in an n-correct set that use a given line. Next, the space of curves of... | 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 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
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"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Unrecoverable OWR statement (The official report presents descriptive background about interpolation sets but does not formulate a standalone open mathematical target. N) | [
"OWR-9790358-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-007",
"literature-status:open",
"owr-year:2022"
] | Abstract introduction without an open question; the Gasca–Maeztu conjecture is retained separately.
**What remains.** The source extraction is retained for provenance and excluded from published problem counts. | [
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428"
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"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion ... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | null | This talk considers some of the recent results on n-independent, n-correct, and GCn sets, concerning the Gasca-Maeztu conjecture. Along with the maximal line we consider also line passing through exactly n- nodes, as well as the subset of the nodes in an n-correct set that use a given line. Next, the space of curves of... | unrecoverable | The official report presents descriptive background about interpolation sets but does not formulate a standalone open mathematical target. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,010 | OWR-9790358-008 | Higher-Order Vanishing Ideals in Polynomial Interpolation | Given a finite point set $X$, determine the least degree of a nonzero polynomial in the symbolic power $I_X^{(m)}$, determine the dimension of each graded component $(I_X^{(m)})_\delta$, and characterize when polynomials vanishing to order $m$ on $X$ factor into products of polynomials vanishing on $X$. | 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 | {
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"name": "algebra",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-008",
"literature-status:open",
"owr-year:2022"
] | The minimum-degree and dimension problems for higher-order vanishing ideals are broad interpolation questions; existing work gives substantial special cases and bounds, but no general solution to the extracted questions. | [
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR higher-order interpolation report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Given a finite point set $X$, determine the least degree of a nonzero polynomial in the symbolic power $I_X^{(m)}$, determine the dimension of each graded component $(I_X^{(m)})_\delta$, and characterize when polynomials vanishing to order $m$ on $X$ factor into products of polynomials vanishing on $X$. | Two fundamental open problems in higher order interpolation are: (m) (1) Given X, find the smallest degree of a polynomial in IX . (2) Given X, \delta, find the dimension of the space of degree \delta polynomials in (m) IX . How can polynomials vanishing to order m at X be expressed in terms of products of polynomials ... | 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 |
30,005,011 | OWR-9790358-009 | Compatible Polynomial Interpolation on Algebraic Varieties | Given algebraic varieties $V_1,\ldots,V_m\subseteq\mathbb C^d$ and polynomials $p_1,\ldots,p_m$, when does a polynomial $f\in\mathbb C[x_1,\ldots,x_d]$ exist such that $f|_{V_j}=p_j|_{V_j}$ for every $j$? | 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 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebra",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-009",
"literature-status:partially-solved",
"owr-year:2022"
] | Hilbert-Nullstellensatz and ideal-theoretic criteria solve disjoint varieties and give exact criteria under radicality hypotheses, while the fully general data-dependent interpolation problem remains only partially characterized. | [
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "McKinley--Shekhtman--Tuesink report results"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Given algebraic varieties $V_1,\ldots,V_m\subseteq\mathbb C^d$ and polynomials $p_1,\ldots,p_m$, when does a polynomial $f\in\mathbb C[x_1,\ldots,x_d]$ exist such that $f|_{V_j}=p_j|_{V_j}$ for every $j$? | When does there exist a polynomial f \in C [x1 , . . . , xd ] such that the restriction f onto Vj coincides with pj on Vj ? 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 | Mini-Workshop: Interpolation, Approximation, and Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/7, pp. 383--428 |
30,005,012 | OWR-9790358-010 | Nonsingularity of Bernstein-Basis Collocation Matrices | Let $T$ be a triangle, let $D_{d,T}$ be the degree-$d$ domain points, and let $\Gamma\subseteq D_{d,T}$. Is the collocation matrix
$$
\bigl(B_\eta^d(\xi)\bigr)_{\xi,\eta\in\Gamma}
$$
always nonsingular? | 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 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-9790358-010",
"literature-status:partially-solved",
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] | Schumaker's arbitrary-subset Bernstein collocation conjecture is proved for degrees through 17 and several infinite families, and 3-by-3 cases were later proved, but the all-degree conjecture remains open. | [
{
"url": "https://doi.org/10.1016/j.amc.2013.11.034",
"label": "Jaklič--Kanduč, degrees through 17"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021904523000588",
"label": "2023 principal-minor result"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Let $T$ be a triangle, let $D_{d,T}$ be the degree-$d$ domain points, and let $\Gamma\subseteq D_{d,T}$. Is the collocation matrix
$$
\bigl(B_\eta^d(\xi)\bigr)_{\xi,\eta\in\Gamma}
$$
always nonsingular? | A Conjecture on Bernstein Basis Polynomials Larry L. Schumaker I made the following conjecture in 2003. It has not yet been completely proved mathematically. However, there has been some progress to report on. Conjecture 1. Given d and a triangle T := hv1 , v2 , v3 i, let Γ be an arbitrary subset of the set Dd,△ of dom... | 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 |
30,005,013 | OWR-9790358-011 | Gaussian Cubature for Three-Variable Product Chebyshev Weights | Does a Gaussian cubature rule of the prescribed degree exist for the product Chebyshev weight in three variables? | 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 | 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 | {
"source_url": "https://zenodo.org/records/23399617",
"checked_at": "2026-10-15",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-15] I have released an unrefereed preprint, **Gaussian Cubature of Even Degree for the Product Chebyshev Weight in Three Variables: An Explicit Ten-Node Rule and No Twenty-Node Rule with a Sign Symmetry** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/233996... | [
"owr",
"oberwolfach-reports",
"OWR-9790358-011",
"literature-status:open",
"owr-year:2022"
] | Three-dimensional product-Chebyshev cubature formulas with the required exactness and near-minimal node counts are known, but a minimal or Gaussian rule of the type asked for was still not established. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0898122107007493",
"label": "De Marchi--Vianello--Xu, cube hyperinterpolation"
},
{
"url": "https://www.global-sci.com/nmtma/article/view/13901",
"label": "Li--Sun--Xu, cubic-domain cubature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Does a Gaussian cubature rule of the prescribed degree exist for the product Chebyshev weight in three variables? | An open question of considerable interest is if such a rule exists for the product Chebyshev weight function in three variables. polynomials of degree n with respect to w. For m = 2n − 2, the nodes need to be common zeros of a basis of quasi-orthogonal polynomials of degree n. Whenever a Gauss cubature rule exists, its... | 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 |
30,005,014 | OWR-9790358-012 | Dimensions of Planar Spline Spaces in Intermediate Degrees | For a triangulated planar polygonal subdivision $\Delta \subset \mathbb{R}^2$, let $S_d^r(\Delta)$ denote the vector space of piecewise polynomial splines on $\Delta$ of degree at most $d$ and global smoothness $C^r$. Determine the exact dimension $\dim S_d^r(\Delta)$ throughout the intermediate degree range $r + 1 \le... | 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 | 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-9790358-012",
"literature-status:partially-solved",
"owr-year:2022"
] | Dimension formulas and sharp bounds are known in several degree ranges, including sufficiently large degree, but the exact planar dimension in the range r+1\leq d\leq3r is not determined in general. | [
{
"url": "https://arxiv.org/abs/math/0608449",
"label": "Tohaneanu, smooth planar r-splines"
},
{
"url": "https://arxiv.org/abs/1909.13399",
"label": "Schenck--Stillman--Yuan, new spline bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | For a triangulated planar polygonal subdivision $\Delta \subset \mathbb{R}^2$, let $S_d^r(\Delta)$ denote the vector space of piecewise polynomial splines on $\Delta$ of degree at most $d$ and global smoothness $C^r$. Determine the exact dimension $\dim S_d^r(\Delta)$ throughout the intermediate degree range $r + 1 \le... | The computation of dim Sdr (∆) for planar ∆ when r + 1 \leq d \leq 3r remains an open problem. On the dimension of trivariate spline spaces Nelly Villamizar (joint work with Michael DiPasquale) | 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 |
30,005,015 | OWR-9790358-013 | Geometry and Combinatorics of Planar Spline Dimensions | Can the dimension of a planar spline space be determined from the geometry and combinatorics of its underlying subdivision? | 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-9790358-013",
"literature-status:open",
"owr-year:2022"
] | The general dimension of planar spline spaces still depends on subtle local and global geometry; known formulas and homological bounds do not give the requested combinatorial-geometric characterization in full generality. | [
{
"url": "https://arxiv.org/abs/1909.13399",
"label": "Schenck--Stillman--Yuan, spline bounds"
},
{
"url": "https://doi.org/10.4171/owr/2022/7",
"label": "OWR spline report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/7 | null | null | null | Can the dimension of a planar spline space be determined from the geometry and combinatorics of its underlying subdivision? | This is a spline space and its elements are called splines. r The open question is to determine the dimension of Sm (∆) in terms of the combinatorics of ∆, the local geometry of ∆, and the global geometry of ∆. Interpolation spaces. (Shekhtman) Let K be a field of characteristic zero. A subspace V of K[x, y] interpolat... | 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 |
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