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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,516 | OWR-14299587-005 | Automatic Action Reconstruction for Countably Categorical Structures | Can the action of $\operatorname{Aut}(A)$ or $\operatorname{EEmb}(A)$ on its underlying set be reconstructed up to conjugation, thereby recovering $A$ up to bi-definability? Does every $\omega$-categorical structure without algebraicity have automatic action reconstruction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Automatic action reconstruction is solved for elementary-embedding monoids under the stated no-algebraicity setting, while the corresponding general automorphism-group problem remains open. | [
{
"url": "https://arxiv.org/abs/2603.28419",
"label": "de la Nuez Gonzalez et al., Minimal and intrinsic topologies on monoids"
},
{
"url": "https://doi.org/10.4171/owr/2025/58",
"label": "Oberwolfach Report 2025/58"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | Can the action of $\operatorname{Aut}(A)$ or $\operatorname{EEmb}(A)$ on its underlying set be reconstructed up to conjugation, thereby recovering $A$ up to bi-definability? Does every $\omega$-categorical structure without algebraicity have automatic action reconstruction? | Can we also reconstruct the action of Aut(A) or EEmb(A) on Ω (up to conjugation by a bijection), thus recovering A up to bi-definability? However, it is currently an open problem whether \omega-categorical structures with no algebraicity always have automatic action reconstruction. Homogeneous Structures: Model Theory m... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,517 | OWR-14299587-006 | Smooth Classification and Outer Automorphisms of Oligomorphic Groups | Is topological isomorphism of oligomorphic groups smoothly classifiable? In particular, does there exist an oligomorphic group whose outer automorphism group is not profinite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-006",
"literature-status:partially-solved",
"owr-year:2025"
] | Topological-isomorphism smoothness is proved for important subclasses and their outer automorphism groups are profinite there, but the general smoothness question and a non-profinite example remain open. | [
{
"url": "https://arxiv.org/abs/2410.02248",
"label": "Paolini--Nies, Two classes of oligomorphic groups with smooth isomorphism relation"
},
{
"url": "https://arxiv.org/abs/1903.08436",
"label": "Nies--Schlicht--Tent, Coarse groups and oligomorphic groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | Is topological isomorphism of oligomorphic groups smoothly classifiable? In particular, does there exist an oligomorphic group whose outer automorphism group is not profinite? | Work of Nies, Schlicht, and Tent [9] showed that topological iso- morphism on oligomorphic groups is Borel reducible to a Borel equivalence relation with countable classes, but the question of whether this isomorphism relation is smooth (Borel reducible to equality on R) remains open. A key open question is whether the... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,518 | OWR-14299587-007 | Abstract-Group Reconstruction of Countably Categorical Structures | When can an $\omega$-categorical structure $M$ be reconstructed from $\operatorname{Aut}(M)$ or $\operatorname{EEmb}(M)$ as an abstract group or monoid, without using the topology of pointwise convergence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124](https://doi.org/10.4171/owr/2025/58)
## Literature review... | 3 | partially_solved | null | 2,025 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299587-007",
"literature-status:partially-solved",
"owr-year:2025"
] | Topological reconstruction is classical, and purely algebraic reconstruction is established under several additional hypotheses, but no general topology-free reconstruction theorem is known. | [
{
"url": "https://arxiv.org/abs/0907.2925",
"label": "Bodirsky--Pinsker, Aleph-zero-categorical structures"
},
{
"url": "https://doi.org/10.1007/S11225-017-9756-6",
"label": "Pech--Pech, Reconstructing topology of elementary self-embedding monoids"
},
{
"url": "https://doi.org/10.4171/OW... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/58 | null | null | null | When can an $\omega$-categorical structure $M$ be reconstructed from $\operatorname{Aut}(M)$ or $\operatorname{EEmb}(M)$ as an abstract group or monoid, without using the topology of pointwise convergence? | By a result attributed to Coquand by Ahlbrandt and Ziegler [1] and proved inde- pendently by Makkai [5], any ℵ0 -categorical structure M is reconstructed up to bi-interpretability by its automorphism group Aut(M) endowed with the topology of pointwise convergence. A natural question to ask is under which circumstances ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Homogeneous Structures: Model Theory meets Universal Algebra (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/58, pp. 3063--3124 |
30,006,519 | OWR-14299904-001 | Finiteness and Tail Decay of Infinite-Noodle Components | Writing $C(0)$ for the component of the origin in the infinite-noodle model, is $C(0)$ almost surely finite? Does its size satisfy $\mathbb{P}(|C(0)|\geq k)=k^{-(2\sqrt{2}-1)/7+o(1)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-001",
"literature-status:open",
"owr-year:2026"
] | The component of zero is not known to be finite almost surely, and the stated power-law tail conjecture consequently remains unresolved. | [
{
"url": "https://arxiv.org/abs/2201.11572",
"label": "Féray--Thévenin, Components in meandric systems and the infinite noodle"
},
{
"url": "https://arxiv.org/abs/1701.01083",
"label": "Curien et al., Uniqueness of the infinite noodle"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Writing $C(0)$ for the component of the origin in the infinite-noodle model, is $C(0)$ almost surely finite? Does its size satisfy $\mathbb{P}(|C(0)|\geq k)=k^{-(2\sqrt{2}-1)/7+o(1)}$? | We are interested in the component of 0. In particular, it is conjectured in [4] that it is finite almost surely and in [1, \sqrt{ } Conjecture 1.10] that the probability that it has size at least k decays as k −(2 2−1)/7+o(1) . The sums S(T ) come into the picture when computing the probability that the component of 0 ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,520 | OWR-14299904-002 | Upward Closure of Grothendieck Schubert Supports | Let $G_w$ be a Grothendieck polynomial. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $v\in\operatorname{Supp}_S(G_w)$ with $u<_L v$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299904-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-002",
"literature-status:partially-solved",
"owr-year:2026"
] | The general Grothendieck-support assertion remains open, although special cases including Grassmannian and fireworks families have been proved. | [
{
"url": "https://arxiv.org/abs/2201.09452",
"label": "Mészáros--Setiabrata--St. Dizier, On the support of Grothendieck polynomials"
},
{
"url": "https://arxiv.org/abs/2403.12186",
"label": "Chou--Yu, Grothendieck polynomials of inverse fireworks permutations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Let $G_w$ be a Grothendieck polynomial. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $v\in\operatorname{Supp}_S(G_w)$ with $u<_L v$? | Conjecture 1. If u \in SuppS (Gw ) and ℓ(u) < deg(Gw ), then there exists v \in SuppS (Gw ) such that u <L v. There is a stronger statement that implies Conjecture 1. support analogues of the Grothendieck monomial support conjectures of [3]. For our conjectures, we replace monomial support with Schubert support, degree... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,521 | OWR-14299904-003 | Upper Elements in Grothendieck Schubert Supports | Let $w\in S_n$. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $v\in\operatorname{Supp}_S(G_w)$ such that $u<_L v$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate extraction; the canonical question is OWR-14299904-002. | [
"OWR-14299904-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-003",
"literature-status:partially-solved",
"owr-year:2026"
] | Duplicate extraction; the canonical question is OWR-14299904-002. Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved.
**What remains.** Consult the linked canonical record for the current question and review. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status updat... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Let $w\in S_n$. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $v\in\operatorname{Supp}_S(G_w)$ such that $u<_L v$? | There is a stronger statement that implies Conjecture 1. Conjecture 1. If u \in SuppS (Gw ) and ℓ(u) < deg(Gw ), then there exists v \in SuppS (Gw ) such that u <L v. Conjecture 2. Let w \in Sn . If u \in SuppS (Gw ) and ℓ(u) < deg(Gw ), then there exists k such that u < sk u and sk u \in SuppS (Gw ). | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,522 | OWR-14299904-004 | Weak-Order Growth of Grothendieck Schubert Supports | Let $w\in S_n$. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $k$ such that $u<_L s_k u$ and $s_k u\in\operatorname{Supp}_S(G_w)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 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-14299904-004",
"literature-status:partially-solved",
"owr-year:2026"
] | The support conjectures and their stronger variants are proved for several structured families, but the arbitrary-permutation statement remains unresolved. | [
{
"url": "https://arxiv.org/abs/2201.09452",
"label": "Mészáros--Setiabrata--St. Dizier, On the support of Grothendieck polynomials"
},
{
"url": "https://arxiv.org/abs/2403.12186",
"label": "Chou--Yu, Grothendieck polynomials of inverse fireworks permutations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Let $w\in S_n$. If $u\in\operatorname{Supp}_S(G_w)$ and $\ell(u)<\deg(G_w)$, must there exist $k$ such that $u<_L s_k u$ and $s_k u\in\operatorname{Supp}_S(G_w)$? | Conjecture 2. Let w \in Sn . If u \in SuppS (Gw ) and ℓ(u) < deg(Gw ), then there exists k such that u < sk u and sk u \in SuppS (Gw ). Proving Conjecture 1 and 2 would imply the analogous conjectures of [3], where one replaces Schubert support with monomial support and left weak order with divisibility. The next conje... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,523 | OWR-14299904-005 | Weak-Order Convexity of Grothendieck Schubert Supports | For every $w\in S_n$, is $\operatorname{Supp}_S(G_w)$ convex in left weak order? Equivalently, if $u,u^{\prime}\in\operatorname{Supp}_S(G_w)$, is every $v$ with $u\leq_L v\leq_L u^{\prime}$ also in the support? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 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-14299904-005",
"literature-status:partially-solved",
"owr-year:2026"
] | Convexity in left weak order is proved in the listed Grassmannian and dominant cases, with further partial results, but not for all permutations. | [
{
"url": "https://arxiv.org/abs/2201.09452",
"label": "Mészáros--Setiabrata--St. Dizier, On the support of Grothendieck polynomials"
},
{
"url": "https://arxiv.org/abs/2403.12186",
"label": "Chou--Yu, Grothendieck polynomials of inverse fireworks permutations"
},
{
"url": "https://arxiv.... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | For every $w\in S_n$, is $\operatorname{Supp}_S(G_w)$ convex in left weak order? Equivalently, if $u,u^{\prime}\in\operatorname{Supp}_S(G_w)$, is every $v$ with $u\leq_L v\leq_L u^{\prime}$ also in the support? | Conjecture 3. Let w \in Sn . The set SuppS (Gw ) is convex with respect to the left weak order. That is, if u, u′ \in SuppS (Gw ), then the interval [u, u′ ]L = \{v \in Sn : u \leqL v \leqL u′ \} is contained in SuppS (Gw ). We resolve these conjectures in the case of Grassmannian permutations and 1 \times u where u is... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,524 | OWR-14299904-006 | Triangle-Counting Figure Caption | How many triangles? Permutahedron Triangulations via Total Linear Stability and the Dual Braid Group Nathan Williams (joint work with Colin Defant and Melissa Sherman-Bennett) Figure 1. Left: How many triangles? Right: How many sim- plices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "miscellaneous",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a figure caption whose missing diagram and parameters prevent recovery of a standalone ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-006",
"literature-status:open",
"owr-year:2026"
] | The exact record is a figure-caption fragment asking only how many triangles, so it does not identify a definite claim that can be classified as solved. | [
{
"url": "https://arxiv.org/abs/2509.11497",
"label": "Defant--Sherman-Bennett--Williams, Permutahedron Triangulations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | null | How many triangles? Permutahedron Triangulations via Total Linear Stability and the Dual Braid Group Nathan Williams (joint work with Colin Defant and Melissa Sherman-Bennett) Figure 1. Left: How many triangles? Right: How many sim- plices? | unrecoverable | The official report confirms that this extraction is a figure caption whose missing diagram and parameters prevent recovery of a standalone counting problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,525 | OWR-14299904-007 | Duplicate Homotopy Question in Permutahedron-Triangulation Exposition | What would you have said if we had started with the Tamari lattice (or, more generally, a Cambrian lattice)? Objection: If we flip the noncrossing partition lattice onto its side, then cover relations would become horizontal. Good point. We actually cut the noncrossing partition lattice into pieces, and then move those ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"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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"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 confirms that this extraction is mostly expository discussion and repeats the explicit homotopy problem represented cano) | [
"OWR-14299904-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-007",
"literature-status:open",
"owr-year:2026"
] | The extracted question concerns the geometric meaning of the Cambrian or Tamari version of the construction and an explicit homotopy between the Salvetti and Bessis--Brady--Watt models; the current primary account still identifies this as open. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
},
{
"url": "https://personal.utdallas.edu/~nxw170830/docs/Bessalvetti/bessalvetti.html",
"label": "Williams, Permutahedron Triangulations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | null | What would you have said if we had started with the Tamari lattice (or, more generally, a Cambrian lattice)? Objection: If we flip the noncrossing partition lattice onto its side, then cover relations would become horizontal. Good point. We actually cut the noncrossing partition lattice into pieces, and then move those ... | unrecoverable | The official report confirms that this extraction is mostly expository discussion and repeats the explicit homotopy problem represented canonically by OWR-14299904-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,526 | OWR-14299904-008 | Homotopy Between Salvetti and Bessis–Brady–Watt Complexes | Construct an explicit homotopy between the Salvetti complex and the Bessis–Brady–Watt complex. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299904-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-008",
"literature-status:open",
"owr-year:2026"
] | The report explicitly states that an explicit homotopy between the Salvetti and Bessis--Brady--Watt complexes remains open; later triangulation work provides a framework but not the requested completed homotopy. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
},
{
"url": "https://personal.utdallas.edu/~nxw170830/docs/Bessalvetti/bessalvetti.html",
"label": "Williams, Permutahedron Triangulations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Construct an explicit homotopy between the Salvetti complex and the Bessis–Brady–Watt complex. | Does this have any geometric meaning? Ultimately, our triangulation is motivated by the question of giving an explicit homotopy between the Salvetti complex and the Bessis–Brady–Watt complex; this problem remains open. Objection: How do you cover all n! vertices of weak order with the Cat(n) vertices of the noncrossing... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,527 | OWR-14299904-009 | Monotonicity of Hook Counts in Symmetric Partitions | For each fixed positive integer $t$, let $\operatorname{sc}^{\star}_t(n)$ and $\operatorname{dd}^{\star}_t(n)$ count the $t$-hooks in self-conjugate and doubled-distinct partitions of $n$. Is $\operatorname{sc}^{\star}_t(n)\geq\operatorname{sc}^{\star}_{t+1}(n)$ and $\operatorname{dd}^{\star}_t(n)\geq\operatorname{dd}^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-009",
"literature-status:partially-solved",
"owr-year:2026"
] | The July 2026 primary paper proves the self-conjugate odd-to-even inequalities and the stated doubled-distinct cases, including the exceptional values, but it does not prove the full fixed-t monotonicity conjecture. | [
{
"url": "https://doi.org/10.1016/j.ejc.2026.104390",
"label": "Cho--Kim--Kim--Yee, European Journal of Combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | For each fixed positive integer $t$, let $\operatorname{sc}^{\star}_t(n)$ and $\operatorname{dd}^{\star}_t(n)$ count the $t$-hooks in self-conjugate and doubled-distinct partitions of $n$. Is $\operatorname{sc}^{\star}_t(n)\geq\operatorname{sc}^{\star}_{t+1}(n)$ and $\operatorname{dd}^{\star}_t(n)\geq\operatorname{dd}^... | Motivated by the result of Singh and Barman, I with Cho, Kim, Kim inves- tigated further and proposed the following conjecture in [3]. Let sc⋆t (n) (resp. dd⋆t (n)) be the number of t-hooks in self-conjugate (resp. doubled distinct) parti- tions of n. Conjecture 3. For a fixed positive integer t, sc⋆t (n) \geq sc⋆t+1 (n... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,528 | OWR-14299904-010 | Cyclic Labelings and Full-Twist Braid Words | Do cyclic labelings correspond exactly to reduced words for the full twist in the squares of the Birman–Ko–Lee generators of the braid group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-010",
"literature-status:open",
"owr-year:2026"
] | The cyclic-labeling correspondence with reduced words for the full twist in squared Birman--Ko--Lee generators is presented as a conjecture; the cited report gives local moves but no proof of the global correspondence. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Do cyclic labelings correspond exactly to reduced words for the full twist in the squares of the Birman–Ko–Lee generators of the braid group? | (iii) I conjecture that cyclic labelings correspond to reduced words for the full twist in the squares of the Birman-Ko-Lee generators of the braid group. (iv) There are local moves that preserve the property of being a cyclic labeling: (a) disjoint edges with consecutive labels commute (as edge lists, we have the sequ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,529 | OWR-14299904-011 | Exact Enumeration and Distribution of Word Trees | Can $w$-trees be enumerated exactly by a formula, recurrence, or functional equation? For two words $W$ and $W^{\prime}$, under what conditions does the total-variation distance between their associated random functions tend to $0$, tend to $1$, or do neither? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-011",
"literature-status:partially-solved",
"owr-year:2026"
] | The exact enumeration of general w-trees and the total-variation comparison remain unresolved, while the primary random-automata literature gives structural results and records only partial enumeration and statistics results. | [
{
"url": "https://doi.org/10.1145/3736722",
"label": "Chapuy--Perarnau, ACM Transactions on Algorithms"
},
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Can $w$-trees be enumerated exactly by a formula, recurrence, or functional equation? For two words $W$ and $W^{\prime}$, under what conditions does the total-variation distance between their associated random functions tend to $0$, tend to $1$, or do neither? | My main question is: Question: Can one do exact enumeration of w-trees? Can you conjecture, or prove, an exact formula, or even a recurrence formula or functional equation, to produce the number of w-trees of size n? A related question is to ask, for two different words W and W ′ , whether the associated random function... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,530 | OWR-14299904-012 | Cycle Limits for Words in Random Permutations | Let $\sigma$ and $\tau$ be independent uniform random permutations and set $\pi=\sigma\tau\sigma^2\tau^2$. Does the normalized length $L_1/n$ of the cycle containing $1$ converge to the uniform distribution on $[0,1]$, and do the normalized ordered cycle lengths converge to the Poisson–Dirichlet distribution with param... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** parti... | 3 | partially_solved | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299904-012",
"literature-status:partially-solved",
"owr-year:2026"
] | For words in independent uniform permutations, primary work proves the universal Poisson limits for short cycles and the report proves several low-occurrence cases, but the asserted uniform and Poisson--Dirichlet limits for all primitive words remain unproved. | [
{
"url": "https://doi.org/10.1002/rsa.21203",
"label": "Kammoun--Maida, Random Structures and Algorithms"
},
{
"url": "https://doi.org/10.1214/20-ECP334",
"label": "Kammoun--Maida, Electronic Communications in Probability"
},
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "O... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Let $\sigma$ and $\tau$ be independent uniform random permutations and set $\pi=\sigma\tau\sigma^2\tau^2$. Does the normalized length $L_1/n$ of the cycle containing $1$ converge to the uniform distribution on $[0,1]$, and do the normalized ordered cycle lengths converge to the Poisson–Dirichlet distribution with param... | Conjecture 1. The random variable L1 /n converges in distribution to a uniform random variable in [0, 1]. We can also ask about the length Mk of the k-th largest cycle in \pi. Conjecture 2. The random variable (M1 /n, M2 /n, . . . ) converges in distribution to a the Poisson Dirichlet process of parameter 1. Informally... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,531 | OWR-14299904-013 | Forest Analogues of Schubert-Polynomial Properties | Find forest counterparts of the structural and positivity properties of Schubert polynomials. In particular, for an indexed forest $F$, give explicit coefficients $a^G_{i,F}$ in $(x_1+\cdots+x_i)P_F=\sum_Ga^G_{i,F}P_G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 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-14299904-013",
"literature-status:open",
"owr-year:2026"
] | The forest-counterpart question and the requested explicit coefficient description are not settled; forest-polynomial theory supplies positive bases and expansions but does not provide the general Schubert-property counterpart asked for here. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.109834",
"label": "Nadeau--Tewari, Advances in Mathematics"
},
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | Find forest counterparts of the structural and positivity properties of Schubert polynomials. In particular, for an indexed forest $F$, give explicit coefficients $a^G_{i,F}$ in $(x_1+\cdots+x_i)P_F=\sum_Ga^G_{i,F}P_G$. | A natural question is to find forest counterparts of various Schubert properties. Words with few occurrences of \sigma. • If one of the letter, say \sigma, appears only once, then, by conjugacy invariance, w has the same distribution as \sigma\tau k , which is uniformly distributed. Thus Conjectures 1 and 2 hold. • If o... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,532 | OWR-14299904-014 | Nonnegative Coefficients for Cylindric Order Polynomials | For every cylindric shape $\lambda/\mu/d$, is $\operatorname{CPP}_{\lambda/\mu/d}(n)$ a polynomial in $n$ with nonnegative coefficients? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 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-14299904-014",
"literature-status:open",
"owr-year:2026"
] | The nonnegative-coefficient conjecture for cylindric-shape order-polynomial expressions is still open in the report; the literature settles special circular-fence cases but not the full cylindric statement. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
},
{
"url": "https://doi.org/10.1016/j.disc.2022.113218",
"label": "Kantarci Oguz--Ravichandran, Discrete Mathematics"
},
{
"url": "https://arxiv.org/abs/2503.16403",
"label": "Skew shapes, Ehrhart po... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | For every cylindric shape $\lambda/\mu/d$, is $\operatorname{CPP}_{\lambda/\mu/d}(n)$ a polynomial in $n$ with nonnegative coefficients? | sum of determinants. The following conjecture in [5], states that CPP\lambda/µ/d (n) is also a polynomial with non-negative coefficients: Conjecture 4. For a cylindric shape \lambda/µ/d, we have that CPP\lambda/µ/d (n) is also a polynomial with non-negative coefficients. The case of circular fence posets was settled in [5,... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,533 | OWR-14299904-015 | Optimization over Nonzero Littlewood–Richardson Coefficients | For a partition $\lambda$ of $n$ with length $d$, define $\eta(\lambda)=n^2+\frac{d(d-1)(2d-1)}6-\sum_{i=1}^d(\lambda_i-(i-1))^2$ and $\Delta(\lambda,\mu,\nu)=\eta(\lambda)-\eta(\mu)-\eta(\nu)$. Given $n,k,d$ with $k\leq n/2$, maximize $\Delta(\lambda,\mu,\nu)$ over triples with $|\lambda|=n$, $|\mu|=k$, $|\nu|=n-k$, a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156](https://doi.org/10.4171/owr/2026/2)
## Literature review (checked 2026-08-22)
**Status:** open
... | 3 | open | null | 2,026 | 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 | {
"source_url": "https://zenodo.org/records/23392319",
"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, **Optimizing over Nonzero Littlewood–Richardson Coefficients: The Quantum Max d-Cut of Complete Bipartite Graphs** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23392319) | [
"owr",
"oberwolfach-reports",
"OWR-14299904-015",
"literature-status:open",
"owr-year:2026"
] | The extracted optimization problem asks for an exact maximum over all nonzero Littlewood--Richardson triples; existing work gives criteria and bounds for nonvanishing but no exact solution to this optimization. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
},
{
"url": "https://arxiv.org/abs/2208.06541",
"label": "Taskin--Gumus--Isik--Ulvi, Lower and Upper Bounds for Nonzero Littlewood--Richardson Coefficients"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/2 | null | null | null | For a partition $\lambda$ of $n$ with length $d$, define $\eta(\lambda)=n^2+\frac{d(d-1)(2d-1)}6-\sum_{i=1}^d(\lambda_i-(i-1))^2$ and $\Delta(\lambda,\mu,\nu)=\eta(\lambda)-\eta(\mu)-\eta(\nu)$. Given $n,k,d$ with $k\leq n/2$, maximize $\Delta(\lambda,\mu,\nu)$ over triples with $|\lambda|=n$, $|\mu|=k$, $|\nu|=n-k$, a... | Letting (Nℓ )ℓ denote the number of lattice paths using only east and north steps (of arbitrary lengths) from (2, 1) to (d − 1, d) or (d, d − 1) that have ℓ steps, also the following conjecture is open. 10. Optimizing over nonzero LR coefficients (problem of Matjaž Konvalinka) (Problem communicated by Igor Klep at Uni... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Enumerative Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/2, pp. 81--156 |
30,006,534 | OWR-14299905-001 | Workshop-Highlights Fragment | for some c > 0, a major breakthrough! Further, their methods are sufficiently robust to yield analogous bounds not only on permanents of random matrices with independent entries but can also to recover the known estimates on the anti- concentration properties of the determinant. The only assumption that is required on th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction splices conclusions about permanent anticoncentration and Rota’s basis conjecture without ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299905-001",
"literature-status:open",
"owr-year:2026"
] | The exact record is a truncated workshop-overview fragment combining permanent anticoncentration with an asymptotic Rota Basis Conjecture statement; it does not contain a complete mathematical problem or a verifiable resolution target. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | null | for some c > 0, a major breakthrough! Further, their methods are sufficiently robust to yield analogous bounds not only on permanents of random matrices with independent entries but can also to recover the known estimates on the anti- concentration properties of the determinant. The only assumption that is required on th... | unrecoverable | The official report confirms that this extraction splices conclusions about permanent anticoncentration and Rota’s basis conjecture without stating a new open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,535 | OWR-14299905-002 | Spectral-Graph-Theory Highlight Fragment | conjecture. The third highlight of the workshop was presented by Aleksa Milojević and Istvan Tomon in two consecutive talks, which covered their joint work with Zhihan Jin and Shengtong Zhang on spectral graph theory and its applications to the maximum cut problem in graphs and to Chowla’s cosine problem in harmonic a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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 confirms that this extraction summarizes proved workshop highlights and begins with a stray word from an earlier conject) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299905-002",
"literature-status:open",
"owr-year:2026"
] | The exact record is a fragment ending at the word conjecture and reports results without stating a complete claim to verify; under the triage rule the unresolved or unclear extracted claim is open. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | null | conjecture. The third highlight of the workshop was presented by Aleksa Milojević and Istvan Tomon in two consecutive talks, which covered their joint work with Zhihan Jin and Shengtong Zhang on spectral graph theory and its applications to the maximum cut problem in graphs and to Chowla’s cosine problem in harmonic a... | unrecoverable | The official report confirms that this extraction summarizes proved workshop highlights and begins with a stray word from an earlier conjecture; it is not a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,536 | OWR-14299905-003 | Combinatorics Contents Fragment | problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Michael Krivelevich (joint with Sahar Diskin, Itay Markbreit, Maksim Zhukovskii) A large hole in pseudo-random graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Matija Bucić (joint with K. Hendrey, B. Mohar... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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 confirms that this extraction is a table-of-contents fragment spanning unrelated talks and does not state a problem. No ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299905-003",
"literature-status:open",
"owr-year:2026"
] | The exact record is a table-of-contents fragment rather than a mathematical problem statement, so no specific proposition can be assessed as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | null | problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Michael Krivelevich (joint with Sahar Diskin, Itay Markbreit, Maksim Zhukovskii) A large hole in pseudo-random graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Matija Bucić (joint with K. Hendrey, B. Mohar... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment spanning unrelated talks and does not state a problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,537 | OWR-14299905-004 | Extremal-Combinatorics Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Jacques Verstraete (joint with Jiaxi Nie, Jeroen Schillewaert, Chase Wilson) Independent sets in Hypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Alexey Pokrovskiy Bounded ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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 confirms that this extraction is another table-of-contents fragment and does not state a problem. No separate clean stat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299905-004",
"literature-status:open",
"owr-year:2026"
] | The exact record is a table-of-contents fragment ending in a generic conjecture entry and contains no complete mathematical claim for literature verification. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Jacques Verstraete (joint with Jiaxi Nie, Jeroen Schillewaert, Chase Wilson) Independent sets in Hypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Alexey Pokrovskiy Bounded ... | unrecoverable | The official report confirms that this extraction is another table-of-contents fragment and does not state a problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,538 | OWR-14299905-005 | Radon Numbers for Unions of Convex Sets | What is the least integer $f(d,s,t)$ such that every set $P$ of $f(d,s,t)$ points in $\mathbb R^d$ admits a partition $P=A\sqcup B$ for which every $s$-convex set containing $A$ intersects every $t$-convex set containing $B$? Is $f(d,s,t)$ polynomial in its parameters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-005",
"literature-status:partially-solved",
"owr-year:2026"
] | Alon and Smorodinsky prove the first near-optimal polynomial upper bound for the Radon-type function f(d,s,t), resolving the long-standing polynomial-growth question, but the exact least value remains unknown. | [
{
"url": "https://arxiv.org/abs/2506.17777",
"label": "Alon--Smorodinsky, Extended VC-dimension and Radon and Tverberg type theorems"
},
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | What is the least integer $f(d,s,t)$ such that every set $P$ of $f(d,s,t)$ points in $\mathbb R^d$ admits a partition $P=A\sqcup B$ for which every $s$-convex set containing $A$ intersects every $t$-convex set containing $B$? Is $f(d,s,t)$ polynomial in its parameters? | In our recent paper [1] described here we settle an open problem posed by Kalai in the 70s and reiterated in later surveys (e.g., [2]) that asks for a generalization of Radon’s Theorem (and Tverberg’s Theorem) to sets which are not necessarily convex nor even connected, but are the union of a bounded number of convex s... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,539 | OWR-14299905-006 | Tverberg Numbers for Unions of Convex Sets | What is the least integer $f_r(d,s_1,\ldots,s_r)$ such that every set $P$ of that many points in $\mathbb R^d$ has a partition $P=P_1\sqcup\cdots\sqcup P_r$ with the following property: whenever each $C_i$ is $s_i$-convex and contains $P_i$, the intersection $\bigcap_{i=1}^r C_i$ is nonempty? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-006",
"literature-status:partially-solved",
"owr-year:2026"
] | The primary paper proves polynomial upper bounds and near-matching lower bounds for the generalized Tverberg function, but the exact least integer requested in the record is not determined in general. | [
{
"url": "https://arxiv.org/abs/2506.17777",
"label": "Alon--Smorodinsky, Extended VC-dimension and Radon and Tverberg type theorems"
},
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | What is the least integer $f_r(d,s_1,\ldots,s_r)$ such that every set $P$ of that many points in $\mathbb R^d$ has a partition $P=P_1\sqcup\cdots\sqcup P_r$ with the following property: whenever each $C_i$ is $s_i$-convex and contains $P_i$, the intersection $\bigcap_{i=1}^r C_i$ is nonempty? | Problem 4. What is the least integer f = fr (d, s1 , . . . , sr ) such that for S any set r P of f points in Rd there is a partition into r pairwise disjoint sets P = i=1 Pi T C1 , . . . , Cr with Pi \subset Ci where Ci is an si -convex such that for any family of sets set for every i \in [r] we have ri=1 Ci 6= \varnot... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,540 | OWR-14299905-007 | Maximum-Cut Surplus in Clique-Free Graphs | For each $r\geq3$, determine the largest guaranteed surplus over $m/2$ in the maximum cut of an $m$-edge $K_r$-free graph. In particular, does there exist an absolute $\varepsilon>0$ such that every such graph has surplus $\Omega_r(m^{1/2+\varepsilon})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-007",
"literature-status:partially-solved",
"owr-year:2026"
] | The absolute-epsilon surplus problem for K_r-free graphs has been solved by Zhang and strengthened by Jin--Milojevic--Tomon, while the stronger Alon--Bollobas--Krivelevich--Sudakov exponent conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2507.13298",
"label": "Jin--Milojevic--Tomon, Beyond the MaxCut problem in H-free graphs"
},
{
"url": "https://arxiv.org/abs/2509.03490",
"label": "Jin--Milojevic--Tomon--Zhang, From small eigenvalues to large cuts"
},
{
"url": "https://doi.org/10.4171/owr... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For each $r\geq3$, determine the largest guaranteed surplus over $m/2$ in the maximum cut of an $m$-edge $K_r$-free graph. In particular, does there exist an absolute $\varepsilon>0$ such that every such graph has surplus $\Omega_r(m^{1/2+\varepsilon})$? | This naturally raises the question: can one improve this bound if G is far from being a disjoint union of cliques? Neverthe- less, the conjecture of Alon, Bollobás, Krivelevich and Sudakov remains wide open. For many years, it was a tantalizing open problem to find any absolute constant \varepsilon > 0, independent of ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,541 | OWR-14299905-011 | Solved Sparse-Graph Conjecture Fragment | conjecture. Theorem 3. For every c > 0 and every graph H, there exists a constant C such that if G is a (c, t)-sparse graph with average degree at least Ct, then G contains an induced subdivision of H. In particular, this theorem immediately follows from the following strengthening of Theorem 2, after recalling that C4... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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 confirms that the extraction attaches a stray word to two theorems proving the formerly conjectured sparse-graph stateme) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299905-011",
"literature-status:open",
"owr-year:2026"
] | The exact record is a truncated fragment beginning with conjecture and then listing theorems, without a complete standalone problem claim; the extracted assertion is therefore unresolved or unclear. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | null | conjecture. Theorem 3. For every c > 0 and every graph H, there exists a constant C such that if G is a (c, t)-sparse graph with average degree at least Ct, then G contains an induced subdivision of H. In particular, this theorem immediately follows from the following strengthening of Theorem 2, after recalling that C4... | unrecoverable | The official report confirms that the extraction attaches a stray word to two theorems proving the formerly conjectured sparse-graph statement; it contains no remaining open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,542 | OWR-14299905-012 | Product-Free Sets in Symmetric and Alternating Groups | For a permutation group $G$ and an integer $k$, determine the maximum density $m_k(G)$ of a $k$-product-free subset. In particular, determine $m_k(\operatorname{Sym}(n))$ and $m_k(\operatorname{Alt}(n))$ in the unresolved ranges of $k$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-012",
"literature-status:partially-solved",
"owr-year:2026"
] | The record reports sharp order results for k-product-free subsets in several ranges and stability for k=3, but it does not determine the general mk(G) problem for all permutation groups or all k. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
},
{
"url": "https://www.maths.ox.ac.uk/node/71359",
"label": "Ghosal--Keevash primary-work abstract"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For a permutation group $G$ and an integer $k$, determine the maximum density $m_k(G)$ of a $k$-product-free subset. In particular, determine $m_k(\operatorname{Sym}(n))$ and $m_k(\operatorname{Alt}(n))$ in the unresolved ranges of $k$. | Problem 7.1] also raised the more general problem of determining mk (G) for permutation groups G. We provide the follow- ing construction of a k-product-free set of permutations, which is analogous to the Calkin–Erdős construction in the integers. Consider the set of permutations \{\sigma \in Sym(n) : \sigma(i) = i + ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,543 | OWR-14299905-013 | Linear-Extension Wins and Poset Variance | Let $P$ be an $n$-element poset and let $\operatorname{win}(x)$ and $\sigma^2(x)$ denote the win statistic and rank variance of an element $x$. Is $\operatorname{win}(x)=\Omega(\sigma^2(x)/n)$ for every $P$ and $x$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-013",
"literature-status:open",
"owr-year:2026"
] | Conjecture 10 remains explicitly open; available results establish implications among width, window, and variance parameters but do not prove the pointwise lower bound win(x)=Omega(sigma^2(x)/n). | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 2026/1"
},
{
"url": "https://arxiv.org/abs/2509.11549",
"label": "Aires--Kahn, Balancing Extensions in Posets of Large Width"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Let $P$ be an $n$-element poset and let $\operatorname{win}(x)$ and $\sigma^2(x)$ denote the win statistic and rank variance of an element $x$. Is $\operatorname{win}(x)=\Omega(\sigma^2(x)/n)$ for every $P$ and $x$? | Conjecture 10. For every P and x, win(x) = Ω(\sigma 2 (x)/n). We don’t even know that one can’t have \sigma 2 (x) = Ω(n2 ) while win(x) = O(1) (respectively the largest and smallest possible values). The implications w win \sigma \pi are again “local,” the first in the sense that a large antichain must contain an elemen... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,544 | OWR-14299905-014 | Height Bounds for Ideals in Finite Posets | For every ideal $A$ of a finite poset, is
$$\max_{x\in A}h(x)\geq |A|-|\max(A)|+1?$$
More generally, is $|A|-\max_{x\in A}h(x)$ bounded by a function of $|\max(A)|$ alone? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-014",
"literature-status:open",
"owr-year:2026"
] | The stated cylindric-shape nonnegative-coefficient conjecture is not proved in general; known work proves special fence and circular-fence cases and leaves the full cylindric family unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/2",
"label": "Oberwolfach Report 2026/2"
},
{
"url": "https://doi.org/10.1016/j.disc.2022.113218",
"label": "Kantarci Oguz--Ravichandran, Discrete Mathematics"
},
{
"url": "https://arxiv.org/abs/2503.16403",
"label": "Skew shapes, Ehrhart po... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every ideal $A$ of a finite poset, is
$$\max_{x\in A}h(x)\geq |A|-|\max(A)|+1?$$
More generally, is $|A|-\max_{x\in A}h(x)$ bounded by a function of $|\max(A)|$ alone? | Conjecture 12. For any ideal A, max\{h(x) : x \in A\} \geq |A| − | max(A)| + 1. This is true (mainly because of [14]) and tight when A = P , but in general we don’t know that |A| − max\{h(x) : x \in A\} is bounded by any function of | max(A)|. Regarding Theorem 8, we mention two possible strengthenings, the first of whi... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,545 | OWR-14299905-018 | Polylogarithmic Treewidth in Induced-Subgraph-Free Graph Classes | For every positive integer $t$, does there exist an integer $d(t)$ such that every $n$-vertex graph in the hereditary class $\mathcal C_t^*$ has treewidth at most $(\log n)^{d(t)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-018",
"literature-status:open",
"owr-year:2026"
] | The conjectured polylogarithmic treewidth bound remains open; current work proves only a subpolynomial bound for the same induced-minor-free classes. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2512.18835",
"label": "Chudnovsky et al., Induced minors and subpolynomial treewidth"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every positive integer $t$, does there exist an integer $d(t)$ such that every $n$-vertex graph in the hereditary class $\mathcal C_t^*$ has treewidth at most $(\log n)^{d(t)}$? | Conjecture 3. For every t \in N there is an integer d = d(t) such that every n-vertex graph G \in Ct∗ with n > 2 satisfies tw(G) \leq logd n. This is still open, but a weaker result where the poly-logarithmic bound on treewidth is replaced by a subpolynomial one was proved in [1]. Theorem 4. For every t \in N, there exi... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,546 | OWR-14299905-020 | Optimal Covering Density of Euclidean Balls | Determine the optimal asymptotic covering density of Euclidean space by congruent balls. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-020",
"literature-status:open",
"owr-year:2026"
] | For Euclidean balls the best upper and lower covering-density asymptotics still differ by a factor of about two, and the report explicitly identifies closing this gap as open. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2510.25685",
"label": "Bukh et al., Covering large-dimensional Euclidean spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Determine the optimal asymptotic covering density of Euclidean space by congruent balls. | Closing this gap for ball covering is a major open problem. The K-covering density of P over Rn is defined by ϑK (P ) := lim sup ϑK P, [−r, r]n . r\to\infty | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,547 | OWR-14299905-021 | Sharp Constants for Multicolor Rainbow Triangles | For an integer $r$ such that no affine plane of order $r-1$ exists, determine the sharp constant in the maximum possible number of rainbow triangles in a simple $r$-edge-colored graph with $m$ edges. In particular, determine it for $r=7$ and $r=11$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-021",
"literature-status:open",
"owr-year:2026"
] | The exact rainbow-triangle constant when no affine plane of the required order exists is posed as an open problem; the general upper bound and prime-power constructions do not determine it. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2407.14084",
"label": "Chao--Yu, A purely entropic approach"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For an integer $r$ such that no affine plane of order $r-1$ exists, determine the sharp constant in the maximum possible number of rainbow triangles in a simple $r$-edge-colored graph with $m$ edges. In particular, determine it for $r=7$ and $r=11$. | Let us end with an open problem. simpler than the earlier proofs. However, the proof that I will present today is a new proof using the mixture bound that is due to Maya Sankar. Using the idea in the proof, we can generalize the rainbow triangle theorem to more q colors and show that a simple r-edge-colored graph with ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,548 | OWR-14299905-022 | Independent Sets in Uniform Hypergraphs | Determine the largest possible independence number of a uniform hypergraph with prescribed numbers of vertices and edges. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-022",
"literature-status:open",
"owr-year:2026"
] | Determining the extremal independence number from only the number of vertices and edges is the hypergraph Turan problem and remains unresolved in general. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.1017/9781009585835.024",
"label": "Verstraete--Wilson, Independent Sets in Hypergraphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Determine the largest possible independence number of a uniform hypergraph with prescribed numbers of vertices and edges. | The fundamental question is to determine the largest size of an independent set in a uniform hypergraph with a prescribed number of vertices and edges. This question arises naturally in many applications and contains some of the main open problems in Extremal Hypergraph Theory, Ramsey Theory and Algorithms. Independent... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,549 | OWR-14299905-023 | Efficient Algorithms for Large Hypergraph Independent Sets | For some absolute $c>0$, give a polynomial-time algorithm that finds an independent set of size at least $c\,\mathbb E|I|$ in every large-girth, $d$-regular, $r$-uniform hypergraph, where $I$ is the independent set produced by the random-ordering construction. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-023",
"literature-status:open",
"owr-year:2026"
] | Known randomized-greedy results quantify the expected independent set in high-girth regular hypergraphs, but no efficient algorithm achieving a fixed positive fraction of that expectation is known in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.1002/rsa.70047",
"label": "Verstraete--Wilson, Independent Sets in Hypergraphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For some absolute $c>0$, give a polynomial-time algorithm that finds an independent set of size at least $c\,\mathbb E|I|$ in every large-girth, $d$-regular, $r$-uniform hypergraph, where $I$ is the independent set produced by the random-ordering construction. | It is a notorious open problem to give an efficient algorithm to find, for some c > 0, independent sets of size c \cdot E[|I|] in a d-regular r-uniform hypergraph of large girth, including in random d-regular graphs, where an independent set of size (2 − o(1))E[|I|] is known to exist. Define the quantities g−3 d(d − 1)⌊ 2 ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,550 | OWR-14299905-024 | Independent Sets in Steiner Triple Systems | Does every Steiner triple system on $n$ vertices contain an independent set of size at least $(1+o(1))\sqrt{3n\log n}$ as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-024",
"literature-status:open",
"owr-year:2026"
] | The proposed sharp asymptotic lower bound for independent sets in Steiner triple systems, and the associated shadow-moment estimate, remain conjectural beyond the known constant-factor bounds. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/1106.3098",
"label": "Kostochka--Mubayi--Verstraete, On independent sets in hypergraphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Does every Steiner triple system on $n$ vertices contain an independent set of size at least $(1+o(1))\sqrt{3n\log n}$ as $n\to\infty$? | We ask [17] whether this expected value is at most roughly dn1−r E(|I|r ). The following conjecture is raised in [10] in the specific case of Steiner triple systems: Every n-vertex \sqrt{ } Steiner triple system contains an independent set of size at least (1 + on (1)) 3n log n as n \to \infty. The method of the proof a... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,551 | OWR-14299905-025 | Small Maximal Partial Ovoids in Polar Spaces | For odd $q$, do the hyperbolic quadrics $Q^+(2n+1,q)$, parabolic quadrics $Q(2n,q)$, and elliptic quadrics $Q^-(2n+1,q)$ have no maximal partial ovoids of size $O(q)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-025",
"literature-status:open",
"owr-year:2026"
] | The O(q) lower-scale conjecture for maximal partial ovoids in the listed polar spaces is not proved; existing constructions give O(q log q) or comparable polylogarithmic bounds. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/1308.1899",
"label": "Schillewaert--Verstraete, Small maximal partial ovoids"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For odd $q$, do the hyperbolic quadrics $Q^+(2n+1,q)$, parabolic quadrics $Q(2n,q)$, and elliptic quadrics $Q^-(2n+1,q)$ have no maximal partial ovoids of size $O(q)$? | We conjecture [13] these polar spaces have no maximal partial ovoids of size O(q). Acknowledgments. Joint work in parts with Chase Wilson, Jiaxi Nie and Jeroen Schillewaert. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,552 | OWR-14299905-026 | Bounded-Diameter Monochromatic Covers | For every integer $r\geq2$, does there exist $D(r)$ such that every $r$-edge-colored complete graph can be covered by $r-1$ monochromatic connected subgraphs, each of diameter at most $D(r)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-026",
"literature-status:open",
"owr-year:2026"
] | The bounded-diameter monochromatic-cover conjecture is proved only in several parameter cases and via reductions to Ryser's conjecture; the all-parameter statement remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2009.07239",
"label": "DeBiasio et al., Generalizations and strengthenings of Ryser's conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every integer $r\geq2$, does there exist $D(r)$ such that every $r$-edge-colored complete graph can be covered by $r-1$ monochromatic connected subgraphs, each of diameter at most $D(r)$? | This conjecture is a variant of an earlier conjecture of Milićević, which said that there a constant D(r) such that every r-edge-coloured complete graph can be covered by r − 1 monochromatic components of diameter \leq D(r). This conjecture is known for (\alpha, r) = (1, 2), (1, 3), (1, 4) (where it was proved by Mil... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,553 | OWR-14299905-027 | Graph Removal in the $L_infty$ Metric | Does graph removal remain valid when distance from being $H$-free is measured by the $L_\infty$ norm of removed-edge degrees rather than by total edit distance? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-027",
"literature-status:partially-solved",
"owr-year:2026"
] | The L-infinity removal question is settled for cliques and several other families, including bipartite and odd-cycle cases, but the general graph statement remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Does graph removal remain valid when distance from being $H$-free is measured by the $L_\infty$ norm of removed-edge degrees rather than by total edit distance? | Does a variant of the graph removal lemma hold under the L\infty distance? Local Removal Lemmas Fan Wei (joint work with Jacob Fox, Hung Le, Ruilin Shi) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,554 | OWR-14299905-028 | The Correct Parameter for Local Graph Removal | For every graph $H$, is there an integer $a(H)$ such that an $n$-vertex graph is $o(1)$-close to being $H$-free in $L_\infty$ if and only if every set of $a(H)$ vertices extends to $o(n^{v(H)-a(H)})$ copies of $H$? Is the proposed local-cover parameter the correct value of $a(H)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-028",
"literature-status:partially-solved",
"owr-year:2026"
] | The proposed parameter a(H) is verified for cliques, connected bipartite graphs, and further special cases, while the general characterization using a(H) is still a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every graph $H$, is there an integer $a(H)$ such that an $n$-vertex graph is $o(1)$-close to being $H$-free in $L_\infty$ if and only if every set of $a(H)$ vertices extends to $o(n^{v(H)-a(H)})$ copies of $H$? Is the proposed local-cover parameter the correct value of $a(H)$? | The following definition gives what we conjecture is the correct function a(H) for such a local graph removal lemma. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,555 | OWR-14299905-030 | Efficient Recognition of Graph Metrizability | Find a polynomial-time algorithm with practical complexity for deciding whether a finite graph is metrizable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
*... | 3 | partially_solved | null | 2,026 | 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-14299905-030",
"literature-status:partially-solved",
"owr-year:2026"
] | Metrizability is decidable in polynomial time and Delta can now be computed efficiently with strong lower-bound constructions, but a truly efficient practical metrizability algorithm and the extremal order of Delta remain open. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2601.21982",
"label": "Cizma--Linial, Metric Approximations of Consistent Path Systems"
},
{
"url": "https://doi.org/10.1007/s00454-024-00685-3",
"label": "Chudnovsk... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Find a polynomial-time algorithm with practical complexity for deciding whether a finite graph is metrizable. | Open Problem: Find a truly efficient algorithm to decide graph metrizability. Specifics: • All outerplanar graphs are metrizable. • Every 2-connected metrizable graph on 11 or more vertices can be made outerplanar by removing at most one vertex. • We conjecture that a graph is not strictly metrizable iff it has a minor tha... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,556 | OWR-14299905-031 | Two Low-Multiplicity Distances in Planar Point Sets | Given $n>4$ distinct points in the plane, must there be two distinct distances that each occur among at most $n$ pairs of points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-031",
"literature-status:open",
"owr-year:2026"
] | The recent distance-multiplicity paper proves the claim for convex or not-too-convex sets, but the universal two-distance assertion for arbitrary planar point sets remains open. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2505.04283",
"label": "Clemen--Dumitrescu--Liu, On the multiplicities of interpoint distances"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Given $n>4$ distinct points in the plane, must there be two distinct distances that each occur among at most $n$ pairs of points? | Given a set P of n > 4 distinct points in the plane, can one always find two distances that each occur as distances between pairs of points in P at most n times? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,557 | OWR-14299905-032 | Comparing Monotone and Ordinary Crossing Numbers | Is there an absolute constant $C$ such that $\operatorname{mon-cr}(G)\leq C\operatorname{cr}(G)$ for every graph $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-032",
"literature-status:open",
"owr-year:2026"
] | The best general comparison currently gives a quadratic-type upper bound for monotone crossing number in terms of crossing number, and no universal linear constant is known. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.1007/978-3-642-25878-7_27",
"label": "Pach--Toth, Monotone Crossing Number"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Is there an absolute constant $C$ such that $\operatorname{mon-cr}(G)\leq C\operatorname{cr}(G)$ for every graph $G$? | Does there exist an absolute constant C such that, for every graph G, the inequality mon-cr(G) \leq C \cdot cr(G) holds? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,558 | OWR-14299905-033 | Hamiltonicity of Highly Connected Induced-Star-Free Graphs | Does there exist a function $f$ such that every $f(k)$-vertex-connected graph with no induced $K_{1,k}$ is Hamiltonian? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-033",
"literature-status:open",
"owr-year:2026"
] | The Matthews--Sumner conjecture, the k=3 case requiring four-connectivity, remains unresolved; known results establish it only under stronger connectivity or extra structural hypotheses. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.1016/j.disc.2021.112522",
"label": "Carraher et al., Forbidden subgraphs and Hamiltonicity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Does there exist a function $f$ such that every $f(k)$-vertex-connected graph with no induced $K_{1,k}$ is Hamiltonian? | Alexey Pokrovskiy A graph is claw-free if it has no claw (i.e., K1,3 ) as an induced subgraph, and Hamiltonian if it possesses a cycle which passes through all of its vertices. The Matthews–Sumner conjecture [1] posits that every 4-vertex-connected claw-free graph is Hamiltonian. This inspires the following conjecture.... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,559 | OWR-14299905-034 | Equilateral Sets in Finite-$p$ Metric Tori | For each finite $p\geq1$, is there a constant $C_p$ such that the largest equilateral subset of the metric torus $T_p^n$ has size at most $C_p n$? If $2n+1$ is prime, is this maximum exactly $2n+1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-034",
"literature-status:open",
"owr-year:2026"
] | For finite p the current bounds on equilateral subsets of the Lp torus are polynomial but far from linear, while the prime lower bound does not establish the proposed equality. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://web.math.princeton.edu/~nalon/PDFS/equitor.pdf",
"label": "Alon, Equilateral sets in the torus"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For each finite $p\geq1$, is there a constant $C_p$ such that the largest equilateral subset of the metric torus $T_p^n$ has size at most $C_p n$? If $2n+1$ is prime, is this maximum exactly $2n+1$? | Is it true that, for every finite p \geq 1, we have e(Tpn ) \leq Cp n? Can it be true that moreover, if 2n + 1 is a prime, then e(Tpn ) = 2n + 1? Hans Yu The following question is motivated by incidence geometry. What is the maximum number of vertex sets S of size r such that H[S] contains at least one edge of each colo... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,560 | OWR-14299905-035 | Vertex Sets Meeting Every Edge Color | Let $r\geq3$, and let $H$ be a three-colored $(r-1)$-uniform hypergraph with $R$, $G$, and $B$ edges of the three colors. What is the maximum number of $r$-vertex sets $S$ for which $H[S]$ contains an edge of every color? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-035",
"literature-status:open",
"owr-year:2026"
] | The extremal count of r-sets meeting all three edge colors is bounded by 6 square root of RGB, with a sharp 2 square root of RGB result for r=3, but the conjectured bound for all r is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Let $r\geq3$, and let $H$ be a three-colored $(r-1)$-uniform hypergraph with $R$, $G$, and $B$ edges of the three colors. What is the maximum number of $r$-vertex sets $S$ for which $H[S]$ contains an edge of every color? | Hans Yu The following question is motivated by incidence geometry. What is the maximum number of vertex sets S of size r such that H[S] contains at least one edge of each color? The answer to this question is monotonically non-decreasing in r. \sqrt{ } Theorem 9. One always has e(Tpn ) \geq 2n; this is given by the set... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,561 | OWR-14299905-036 | Periodic Constructions for Colored-Lattice Packing Constants | For every dimension $d$ and word $w$, is the extremal word-occurrence constant $C_d(w)$ attained asymptotically by a periodic grid? What are $C_d(ABB)$ for $d>2$ and $C_2(ABBB)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23282536",
"checked_at": "2026-10-10",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **The Word-Search Constants C_2(ABBB) = 8/5 and C_3(ABB) = 6: On Two Questions of Schildkraut and of Halberstam and Schildkraut** (Alper Ferudun, Mercury Software GmbH). It determines the two concrete constants asked for in the record,... | [
"owr",
"oberwolfach-reports",
"OWR-14299905-036",
"literature-status:open",
"owr-year:2026"
] | Only selected word and dimension cases are known; periodic attainment in general and the constants C_d(ABB) and C_2(ABBB) remain open. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://arxiv.org/abs/2511.19678",
"label": "Halberstam--Schildkraut, Words with repeated letters in a grid"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every dimension $d$ and word $w$, is the extremal word-occurrence constant $C_d(w)$ attained asymptotically by a periodic grid? What are $C_d(ABB)$ for $d>2$ and $C_2(ABBB)$? | Is it true for all d and w that Cd (w) is always attained in the limit by some periodic construction? What is Cd (ABB) for d > 2? What is C2 (ABBB)? Figure 1. A blowup of the proper 3-coloring of K4 . \sqrt{ } For r = 3, the bound 2RGB is asymptotically tight when R = G = B. This is attained by a blowup of a proper 3-c... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,562 | OWR-14299905-037 | Independence-Number Degeneracy in Induced-Subdivision-Free Graphs | For every positive integer $t$, does there exist $C>0$ such that every graph with no induced $K_{t,t}$ and no induced subdivision of $K_t$ in which every edge is subdivided at least once has a vertex $v$ satisfying $\alpha(N(v))\leq C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-037",
"literature-status:open",
"owr-year:2026"
] | The proposed independence-number degeneracy analogue is not implied by the known induced-subdivision theorem, and no proof of a uniform C for all t is currently available. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.1007/s00493-004-0017-8",
"label": "Kuehn--Osthus, Induced subdivisions in K-free graphs"
},
{
"url": "https://doi.org/10.1016/j.jctb.2025.04.002",
"label": "Du et al., ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | For every positive integer $t$, does there exist $C>0$ such that every graph with no induced $K_{t,t}$ and no induced subdivision of $K_t$ in which every edge is subdivided at least once has a vertex $v$ satisfying $\alpha(N(v))\leq C$? | For every positive integer t, does there exist C > 0 such that the following holds? Figure 3. The conjectured optimal construction for C2 (ABBB). | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,563 | OWR-14299905-038 | Colorings Without Disjoint Color-Isomorphic Triangles | Let $g(n)$ be the fewest colors needed to edge-color $K_n$ with no two vertex-disjoint color-isomorphic triangles. Determine the order of growth of $g(n)$; in particular, is $g(n)=\Theta(n)$, or even $g(n)=n-O(1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-038",
"literature-status:open",
"owr-year:2026"
] | The known bounds for g(n) are between order square root of n and n minus 4, while the conjectured linear growth or n minus O(1) behavior has not been proved. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Let $g(n)$ be the fewest colors needed to edge-color $K_n$ with no two vertex-disjoint color-isomorphic triangles. Determine the order of growth of $g(n)$; in particular, is $g(n)=\Theta(n)$, or even $g(n)=n-O(1)$? | David Conlon Question 14. Let g(n) be the smallest number of colors necessary to edge-color Kn such that there are no two vertex-disjoint color-isomorphic triangles. Estimate g(n). \sqrt{ } It is not hard to show that c n \leq g(n) \leq n − 4 for some c > 0. It is conjectured that g(n) grows linearly in n and it may ev... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,564 | OWR-14299905-039 | Independent Sets in Pseudorandom Regular Graphs | Does there exist an absolute constant $C>0$ such that every $(n,d,\lambda)$-graph with $\lambda>(\log n)^2$ has at most
$$\left(\frac{4e^2\lambda}{\log n}\right)^t$$
independent sets of size $t=Cn\log n/(d+1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79](https://doi.org/10.4171/owr/2026/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.... | 3 | open | null | 2,026 | 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-14299905-039",
"literature-status:open",
"owr-year:2026"
] | The Alon--Rodl estimate controls independent sets only at the larger logarithmic threshold; the proposed stronger threshold with a constant C remains an open question. | [
{
"url": "https://doi.org/10.4171/owr/2026/1",
"label": "Oberwolfach Report 1/2026"
},
{
"url": "https://doi.org/10.4171/JEMS/1359",
"label": "Mubayi--Verstraete, A note on pseudorandom Ramsey graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/1 | null | null | null | Does there exist an absolute constant $C>0$ such that every $(n,d,\lambda)$-graph with $\lambda>(\log n)^2$ has at most
$$\left(\frac{4e^2\lambda}{\log n}\right)^t$$
independent sets of size $t=Cn\log n/(d+1)$? | Does there exist a constant C > 0 such that the following holds? Mubayi and Verstraete [3] noticed that Theorem 15 gives, via sampling from an appropriate C4 -free graph, a lower bound of Ω(t3/2 / log t) on the cycle-complete Ramsey number r(C4 , t), which matches the result of the C4 -free process. The following quest... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/1, pp. 5--79 |
30,006,565 | OWR-14299906-001 | KMS-Symmetric Quantum Markov Semigroups on von Neumann Algebras | Extend the derivation-correspondence characterization of bounded generators of KMS-symmetric quantum Markov semigroups from matrix algebras to arbitrary von Neumann algebras. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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-14299906-001",
"literature-status:open",
"owr-year:2026"
] | The derivation representation is established for matrix algebras and substantial general-von-Neumann-algebra results are known, but the report's full characterization conjecture for arbitrary von Neumann algebras remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
},
{
"url": "https://doi.org/10.1007/s00220-023-04795-6",
"label": "Vernooij--Wirth, Derivations and KMS-Symmetric QMS"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Extend the derivation-correspondence characterization of bounded generators of KMS-symmetric quantum Markov semigroups from matrix algebras to arbitrary von Neumann algebras. | This im- proves upon previous joint work with Vernooij [VW23] in that it fully characterizes KMS-symmetric QMS on matrix algebras, and we conjecture that this continues to hold for arbitrary von Neumann algebras. Noncommutative Harmonic Analysis and Quantum Information 225 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,566 | OWR-14299906-002 | Reverse Approximation Implications for Traces | Is every hyperlinear trace an MF trace? Is every amenable trace quasidiagonal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299906-002",
"literature-status:open",
"owr-year:2026"
] | MF traces imply hyperlinearity and quasidiagonal traces imply amenability, but the reverse implications are explicitly still open. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Is every hyperlinear trace an MF trace? Is every amenable trace quasidiagonal? | The opposite implications are an open problem. Noncommutative Harmonic Analysis and Quantum Information 227 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,567 | OWR-14299906-003 | Quantum Automorphisms in Limiting Cuntz-Krieger Isometry Groups | Let $A$ be a finite zero-one matrix. If $\operatorname{QAut}(A)\neq\operatorname{Aut}(A)$, does the limiting quantum isometry group $G_A^\infty$ contain $\operatorname{QAut}(A)$ as a quantum subgroup? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"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/23071235",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **On a Question of Freslon, Gerontogiannis and Skalski about Quantum Isometries of Cuntz–Krieger Algebras** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23071235) | [
"owr",
"oberwolfach-reports",
"OWR-14299906-003",
"literature-status:open",
"owr-year:2026"
] | The 2026 primary report explicitly says that whether the limiting quantum isometry group contains QAut(A) as a quantum subgroup when QAut(A)\neq Aut(A) is unknown. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Let $A$ be a finite zero-one matrix. If $\operatorname{QAut}(A)\neq\operatorname{Aut}(A)$, does the limiting quantum isometry group $G_A^\infty$ contain $\operatorname{QAut}(A)$ as a quantum subgroup? | Thus the quantum isometry groups of Cuntz-Krieger algebras are much larger than their classical counterparts, which should be contrasted with the fact that quantum isometry groups of classical smooth manifolds coincide with their classical versions ([GJ18]). It turns out that the construction described above yields als... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,568 | OWR-14299906-004 | Ergodic Limiting Quantum Isometry Actions | Establish ergodicity of the limiting quantum isometry action on the path space $\Sigma_A$ for matrices $A$ beyond the full-shift matrix whose entries are all one. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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-14299906-004",
"literature-status:open",
"owr-year:2026"
] | The source report presents ergodicity beyond the full-shift case A=1 as an unanswered question; no later result establishing the general claim was located. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Establish ergodicity of the limiting quantum isometry action on the path space $\Sigma_A$ for matrices $A$ beyond the full-shift matrix whose entries are all one. | Can we establish ergodicity of the quantum isometry action in some cases beyond A = 1? Thus the quantum isometry groups of Cuntz-Krieger algebras are much larger than their classical counterparts, which should be contrasted with the fact that quantum isometry groups of classical smooth manifolds coincide with their cla... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,569 | OWR-14299906-006 | Existence of Nonsofic Groups | Does there exist a nonsofic group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate of canonical problem ALG-008 | [
"ALG-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299906-006",
"literature-status:open",
"owr-year:2026"
] | The extracted text is only a trailing word, `conjecture', followed by proposed research steps; it does not identify a definite mathematical claim whose truth has been established. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Does there exist a nonsofic group? | conjecture. Theorem 4 ([Aru-Man25]). If S is a locally universal tracial von Neumann al- gebra (i.e. approximate homomorphisms into it separate points for every separable tracial von Neumann algebra), then S has no computable presentations. Theorem 5 ([Bow-Cha25]). There is an IRS H of a free group that is non- hyperli... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,570 | OWR-14299906-007 | Quantum Advantage in Threefold Repetition of Feige’s Game | Does the quantum value exceed the classical value for the threefold parallel repetition of Feige’s game? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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-14299906-007",
"literature-status:open",
"owr-year:2026"
] | The 2026 report records that the quantum and classical values agree for two repetitions but leaves the three-fold quantum-versus-classical comparison unresolved; the 2025 primary paper likewise does not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
},
{
"url": "https://arxiv.org/abs/2510.08484",
"label": "Schmidt--Storgaard--Walter--Zhao, Guess your neighbor's input"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Does the quantum value exceed the classical value for the threefold parallel repetition of Feige’s game? | Does the quantum value exceed the classical value for the 3-fold par- allel repetition of Feige’s game? Table 1. Summary of values of the n-fold parallel repetition of Feige’s game. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,571 | OWR-14299906-008 | Semidefinite Relaxations for Quantum Equilibria | Construct a convergent semidefinite-programming hierarchy for maximizing social welfare over quantum correlated equilibria by replacing the explicit tensor-product constraints with suitable commutation constraints. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 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-14299906-008",
"literature-status:open",
"owr-year:2026"
] | The extracted item is explicitly labelled an open question about a semidefinite relaxation of equilibrium behaviours, and the report supplies no resolution. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Construct a convergent semidefinite-programming hierarchy for maximizing social welfare over quantum correlated equilibria by replacing the explicit tensor-product constraints with suitable commutation constraints. | Open question: semidefinite relaxation of equilibrium behaviours? and for all j and tj , X (j) p(t)uj (t, a)Tr ρ(Mat11 ⊗ \cdot \cdot \cdot ⊗ Matjj ⊗ \cdot \cdot \cdot ⊗ Matnn ) = Tr Wtj . t[n]\j ,a | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,572 | OWR-14299906-009 | $L^p$ Approximation for Higher-Rank Group Factors | For $d\geq 2$, does $L^p(L(\operatorname{PSL}_{2d-1}(\mathbb Z)))$ have the completely bounded approximation property for some $p\neq 2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299906-009",
"literature-status:open",
"owr-year:2026"
] | The question asks whether the stated noncommutative Lp-space has the completely bounded approximation property for some p\neq2; the report describes the known result only away from 2 and leaves this extension unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | For $d\geq 2$, does $L^p(L(\operatorname{PSL}_{2d-1}(\mathbb Z)))$ have the completely bounded approximation property for some $p\neq 2$? | The question whether it is also essential for the statement is therefore natural. Does Lp (LPSL2d−1 (Z)) have the completely bounded approximation property for some p 6= 2? The aim of my talk was to present a connection between two different open prob- lems: the Kakeya conjecture in real/harmonic analysis, and Connes’ r... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,573 | OWR-14299906-010 | Kakeya Conjecture in Dimensions Four and Higher | For every integer $d\geq 4$, prove that every Kakeya set in $\mathbb R^d$ has Hausdorff dimension $d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | partially_solved | null | 2,026 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"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-14299906-010",
"literature-status:partially-solved",
"owr-year:2026"
] | The extracted discussion records the Kakeya conjecture as proved in dimension 3, while explicitly leaving higher dimensions open; thus the all-dimensional problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
},
{
"url": "https://arxiv.org/abs/2502.17655",
"label": "Wang--Zahl, Volume estimates and the Kakeya set conjecture in three dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | For every integer $d\geq 4$, prove that every Kakeya set in $\mathbb R^d$ has Hausdorff dimension $d$. | Noncommutative Harmonic Analysis and Quantum Information 255 The Kakeya conjecture is a classical theorem in dimension 2 [4], and more precisely Keich’s construction [8] of Besicovitch sets gives that c C \leq f2 (\delta) \leq | log \delta| | log \delta| In dimension 3, a solution has recently been given in a celebrate... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,574 | OWR-14299906-011 | Duplicate Higher-Dimensional Kakeya Status | The Kakeya conjecture is a classical theorem in dimension 2 [4], and more precisely Keich’s construction [8] of Besicovitch sets gives that c C \leq f2 (\delta) \leq | log \delta| | log \delta| In dimension 3, a solution has recently been given in a celebrated breakthrough by Wang and Zahl [17, Theorem 1.12]; in higher... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | partially_solved | null | 2,026 | 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"
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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 | Unrecoverable OWR statement (The official report confirms that this extraction only repeats the higher-dimensional status of the Kakeya conjecture preserved in the prece) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299906-011",
"literature-status:partially-solved",
"owr-year:2026"
] | The statement is a current status report rather than a new conjecture: dimensions 2 and 3 are settled, but the Kakeya conjecture in dimensions at least 4 remains open. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
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},
{
"url": "https://arxiv.org/abs/2502.17655",
"label": "Wang--Zahl, Volume estimates and the Kakeya set conjecture in three dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | null | The Kakeya conjecture is a classical theorem in dimension 2 [4], and more precisely Keich’s construction [8] of Besicovitch sets gives that c C \leq f2 (\delta) \leq | log \delta| | log \delta| In dimension 3, a solution has recently been given in a celebrated breakthrough by Wang and Zahl [17, Theorem 1.12]; in higher... | unrecoverable | The official report confirms that this extraction only repeats the higher-dimensional status of the Kakeya conjecture preserved in the preceding record. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,575 | OWR-14299906-012 | Foundations for Quantum Measurable Spaces | Define a category of quantum measurable spaces and quantum channels whose commutative subcategory is equivalent to suitable measurable spaces and Markov kernels, and in which positive operator-valued measurements are equivalent to quantum-to-classical channels. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275](https://doi.org/10.4171/owr/2026/4)
## Literature review (checke... | 3 | open | null | 2,026 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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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-14299906-012",
"literature-status:open",
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] | The source identifies the lack of a satisfactory general notion of quantum measurable space as an open foundational problem; existing von Neumann-algebraic formalisms do not resolve the stated categorical and measurement requirements. | [
{
"url": "https://doi.org/10.4171/owr/2026/4",
"label": "Oberwolfach Report 4/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/4 | null | null | null | Define a category of quantum measurable spaces and quantum channels whose commutative subcategory is equivalent to suitable measurable spaces and Markov kernels, and in which positive operator-valued measurements are equivalent to quantum-to-classical channels. | What are quantum measurable spaces? It is often said that von Neumann algebras are the right setting for noncommuta- tive measure theory. Although this makes sense, I will point out that we do not have a good notion of noncommutative measurable space. Having such a notion would be relevant for infinite-dimensional quant... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Noncommutative Harmonic Analysis and Quantum Information (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/4, pp. 217--275 |
30,006,576 | OWR-14299907-001 | Mesh Structures Behind Even-Odd Superconvergence | Consider the surface finite-element discretization of the surface Stokes equations on a smooth two-dimensional surface $\Gamma\subset\mathbb{R}^3$, using discrete geometries $\Gamma_h^k=\Phi_h^k(\widehat\Gamma_h)$ obtained from a uniformly refined reference triangulation $\widehat\Gamma_h$ by a piecewise polynomial par... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Numerical Analysis for Geometric and Nonlinear PDEs (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/5, pp. 277--344](https://doi.org/10.4171/owr/2026/5)
## Literature review (checked 202... | 3 | open | null | 2,026 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299907-001",
"literature-status:open",
"owr-year:2026"
] | The primary workshop report explicitly labels both the necessary mesh structure and the explanation without visible mirrored pairs as central open questions; the displayed analysis is not a resolution. | [
{
"url": "https://doi.org/10.4171/owr/2026/5",
"label": "Oberwolfach Report 5/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/5 | null | null | null | Consider the surface finite-element discretization of the surface Stokes equations on a smooth two-dimensional surface $\Gamma\subset\mathbb{R}^3$, using discrete geometries $\Gamma_h^k=\Phi_h^k(\widehat\Gamma_h)$ obtained from a uniformly refined reference triangulation $\widehat\Gamma_h$ by a piecewise polynomial par... | Two central open questions are: • Which internal mesh structure is necessary for the even-odd superconver- gence effect? Is the mirrored-pair structure from our analysis only one representative, or the main mechanism? • How can observed even/odd behavior be explained in settings, where a mirrored-pair structure is not e... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Numerical Analysis for Geometric and Nonlinear PDEs (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/5, pp. 277--344 |
30,006,577 | OWR-14299908-001 | Workshop-Summary Extraction Artifact | Conjecture. Jonathan Kirby then introduced the classes of exponentially-algebraic functions and presented results investigating when such functions appear as solutions of algebraic differential equations. Peter Jossen delivered the final talk on conjectures and outlooks that intertwine transcendence properties of values ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"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,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 extraction starts with the final word of a preceding reference to Schanuel's conjecture and then continues with workshop-summary prose; ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-001",
"literature-status:open",
"owr-year:2026"
] | The extracted statement is only the word `conjecture' followed by workshop prose, so no identifiable mathematical claim is available to classify as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | null | Conjecture. Jonathan Kirby then introduced the classes of exponentially-algebraic functions and presented results investigating when such functions appear as solutions of algebraic differential equations. Peter Jossen delivered the final talk on conjectures and outlooks that intertwine transcendence properties of values ... | unrecoverable | The extraction starts with the final word of a preceding reference to Schanuel's conjecture and then continues with workshop-summary prose; it does not state a separate conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,578 | OWR-14299908-002 | Algebraic Effective-Period Complex Conjecture | Let $D=\{z\in\mathbb C:\lvert z\rvert\leq1\}$, and let $\widetilde{\Omega}_{\infty-\bullet}^{\mathrm{alg}}(D_\infty)$ be the boundary-vanishing complex of codegree forms on $D_\infty$ whose coefficients are holomorphic near the closed polydiscs and algebraic over $\mathbb Q(z_1,z_2,\ldots)$. Is this complex acyclic out... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 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-14299908-002",
"literature-status:open",
"owr-year:2026"
] | The extracted complex is tied to the conjectural acyclicity and injectivity of the period map, with the report relating the second part to the still-open Kontsevich--Zagier period conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Let $D=\{z\in\mathbb C:\lvert z\rvert\leq1\}$, and let $\widetilde{\Omega}_{\infty-\bullet}^{\mathrm{alg}}(D_\infty)$ be the boundary-vanishing complex of codegree forms on $D_\infty$ whose coefficients are holomorphic near the closed polydiscs and algebraic over $\mathbb Q(z_1,z_2,\ldots)$. Is this complex acyclic out... | alg (D ) is acyclic except in degree zero and the Conjecture 2. The complex Ω\infty−● \infty map ̂ alg (D )) \to C, H0 (Ω\infty−● \varnothing ↦∫ \infty (2) f ⋅ dz f, [0,1]\infty deduced from (1), is injective. Remark 3. The image of the map (2) is precisely the ring of effective periods. The second assertion in Conjectu... | corrected_verified | The official Oberwolfach report was checked directly. The clean statement preserves the complete open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,579 | OWR-14299908-003 | Adic Effective-Period Complex Conjecture | Let $K=\mathbb Q$ with a $p$-adic valuation, or let $K=k(\pi)$ with the $\pi$-adic valuation, where $k$ has characteristic zero, and write $\widehat K$ for the completion of $K$. For the infinite-dimensional Tate ball $B_\infty$ over $\widehat K$, let $\widetilde{\Omega}_{\infty-\bullet}^{K\text{-}\mathrm{alg}}(B_\inft... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 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-14299908-003",
"literature-status:open",
"owr-year:2026"
] | This is the p-adic or pi-adic analogue of the preceding period conjecture; the report states it as a conjecture and gives no proof of the asserted acyclicity and integral map property. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Let $K=\mathbb Q$ with a $p$-adic valuation, or let $K=k(\pi)$ with the $\pi$-adic valuation, where $k$ has characteristic zero, and write $\widehat K$ for the completion of $K$. For the infinite-dimensional Tate ball $B_\infty$ over $\widehat K$, let $\widetilde{\Omega}_{\infty-\bullet}^{K\text{-}\mathrm{alg}}(B_\inft... | By analogy with Conjecture 2, we make the following conjecture. Conjecture 5. Assume that K = Q, with the p-adic valuation, or K = k(\pi), with K-alg (B ) is acyclic except in degree the \pi-adic valuation. Then, the complex Ω\infty−● \infty zero and the map H0 (Ω\infty−● ̂ ̂ K-alg (B )) \to K, \varnothing ↦∫ \infty (4... | corrected_verified | The official Oberwolfach report was checked directly. The clean statement preserves the complete open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,580 | OWR-14299908-004 | Model Companions and Geometry of Globally Valued Fields | Do existentially closed globally valued fields form a first-order class; equivalently, does the theory $\mathrm{GVF}_e$ have a model companion? Is there a Berkovich-type geometry whose closed points represent global heights on residue rings of algebras? What is the asymptotic first-order theory of number fields viewed ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-004",
"literature-status:open",
"owr-year:2026"
] | The existence of a model companion for the theories GVF_e remains conjectural in the current foundations text; known existential-closure results for selected fields do not establish the full theory or the other listed questions. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid:0526cc37-8e0d-4c41-bc2d-a62178aae2e1/files/d736665338",
"label": "Ben Yaacov--Destic--Hrushovski--Szachniewicz, Globally Valued Fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Do existentially closed globally valued fields form a first-order class; equivalently, does the theory $\mathrm{GVF}_e$ have a model companion? Is there a Berkovich-type geometry whose closed points represent global heights on residue rings of algebras? What is the asymptotic first-order theory of number fields viewed ... | Is the class of existentially closed globally valued fields first order? In other words, does there exist a model companion of the theory GVFe ? Can one find such a geometry in the case of globally valued fields? Does there exist a geometry of Berkovich type where closed points represent global heights on residue rings of ... | corrected_verified | The official Oberwolfach report was checked directly. The clean statement preserves the complete open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,581 | OWR-14299908-005 | Effective G-Function Bounds for Unlikely Intersections | Determine the strongest fully explicit G-function height bounds for unlikely intersections in algebraic tori and abelian varieties. In particular, extend the current explicit bounds from line sections in $\mathbb G_m^3$ to arbitrary algebraic curves in $\mathbb G_m^n$, and develop analogous explicit bounds for curves i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** pa... | 3 | partially_solved | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-005",
"literature-status:partially-solved",
"owr-year:2026"
] | Explicit height bounds are known in the classical torus setting, and Orr's July 2026 preprint obtains explicit G-function bounds and applications to lines in tori; the broader very-unlikely-intersection program is not fully resolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
},
{
"url": "https://arxiv.org/abs/2607.09565",
"label": "Orr, Explicit height bounds for G-functions and unlikely intersections with lines in tori"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Determine the strongest fully explicit G-function height bounds for unlikely intersections in algebraic tori and abelian varieties. In particular, extend the current explicit bounds from line sections in $\mathbb G_m^3$ to arbitrary algebraic curves in $\mathbb G_m^n$, and develop analogous explicit bounds for curves i... | Explicit height bounds for (very) unlikely intersections using G-functions Martin Orr The following theorem of Bombieri, Masser and Zannier [4] is one of the founda- tional theorems in the theory of unlikely intersections. Theorem 1. Let G = Gnm with n \geq 2. For a positive integer d, let Σd denote the union of all al... | corrected_verified | The official Oberwolfach report was checked directly. The clean statement preserves the complete open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,582 | OWR-14299908-006 | Expository h-Minimality Passage | O-minimality is a framework coming from model theory in which one can carry out analytic arguments with guaranteed tameness. By “analytic arguments” we specifically mean arguments from real or complex analysis. The success of o- minimality in important arithmetic geometry problems is now well-established, see for exampl... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 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 contribution is expository text introducing h-minimality and summarizing applications; the extracted passage contains no separa) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-006",
"literature-status:open",
"owr-year:2026"
] | The extracted passage is expository context about h-minimality and does not state a resolved theorem or a precise solved problem; the associated non-Archimedean tameness agenda remains active. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | null | O-minimality is a framework coming from model theory in which one can carry out analytic arguments with guaranteed tameness. By “analytic arguments” we specifically mean arguments from real or complex analysis. The success of o- minimality in important arithmetic geometry problems is now well-established, see for exampl... | unrecoverable | The official contribution is expository text introducing h-minimality and summarizing applications; the extracted passage contains no separately formulated open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,583 | OWR-14299908-007 | Dimension-Independent Nonminimality of Difference Equations | Let $K\subset\mathcal U\models\mathrm{ACFA}$ be difference fields with distinguished automorphism $\sigma$, let $V$ be an algebraic variety, and let $\phi:V\dashrightarrow V^\sigma$ be a rational map over $K$. For a generic solution $a$ of $\sigma(a)=\phi(a)$ whose type over $K$ is nonminimal, must $\operatorname{nmdeg... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-007",
"literature-status:open",
"owr-year:2026"
] | The displayed conjecture asks for a dimension-independent bound of 3 on the degree of nonminimality for algebraic difference equations; the report describes this as conjectural and gives no proof. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Let $K\subset\mathcal U\models\mathrm{ACFA}$ be difference fields with distinguished automorphism $\sigma$, let $V$ be an algebraic variety, and let $\phi:V\dashrightarrow V^\sigma$ be a rational map over $K$. For a generic solution $a$ of $\sigma(a)=\phi(a)$ whose type over $K$ is nonminimal, must $\operatorname{nmdeg... | later date is given in [2]), but a well-known conjecture of Poizat predicted that al- most every nonlinear equation should be minimal. We conjecture that one can, in general replace dim(V ) + 3 by 3. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly. The clean statement preserves the complete open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,584 | OWR-14299908-008 | Elementary Equivalences for Ordered Exponential Fields | Let $R$ be an ordered field equipped with an everywhere continuous and differentiable function $\exp:R\to R$ satisfying $\exp'=\exp$ and $\exp(0)=1$. Are the following conditions equivalent: $R$ has the same first-order theory as the real exponential field $\mathbb R_{\exp}$; $R$ is o-minimal; and $R$ is definably comp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"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,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299908-008",
"literature-status:open",
"owr-year:2026"
] | Two implications are established, while the remaining implication from definable completeness to the complete theory of R_exp is conditional on Schanuel-type reasoning; the unconditional equivalence is therefore open. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
},
{
"url": "https://arxiv.org/abs/2603.08365",
"label": "On the elementary theory of the real exponential field"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Let $R$ be an ordered field equipped with an everywhere continuous and differentiable function $\exp:R\to R$ satisfying $\exp'=\exp$ and $\exp(0)=1$. Are the following conditions equivalent: $R$ has the same first-order theory as the real exponential field $\mathbb R_{\exp}$; $R$ is o-minimal; and $R$ is definably comp... | Are the following equivalent? (1) R has the same first-order theory as Rexp . (2) R is o-minimal. (3) R is definably complete. 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 open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,585 | OWR-14299908-009 | Polynomial Boundedness of Definably Complete Restricted Exponential Fields | Is every definably complete restricted exponential field polynomially bounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216](https://doi.org/10.4171/owr/2026/3)
## Literature review (checked 2026-08-22)
**Status:** op... | 3 | open | null | 2,026 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
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"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
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"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-14299908-009",
"literature-status:open",
"owr-year:2026"
] | The report explicitly concludes that it is unknown whether every definably complete restricted exponential field is polynomially bounded; current results only prove this under a Schanuel-type hypothesis. | [
{
"url": "https://doi.org/10.4171/owr/2026/3",
"label": "Oberwolfach Report 3/2026"
},
{
"url": "https://arxiv.org/abs/2603.08365",
"label": "On the elementary theory of the real exponential field"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/3 | null | null | null | Is every definably complete restricted exponential field polynomially bounded? | I conclude with an open question. Is every definably complete restricted exponential field polynomially bounded? 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 open target while repairing OCR, notation, and source-dependent wording. | null | null | null | null | null | Model Theory and Arithmetic (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/3, pp. 157--216 |
30,006,586 | OWR-14299909-001 | Lie Structure of Formal $q$-Zeta Algebras | Prove that the balanced quasi-shuffle relations and $\tau$-invariance generate all algebraic relations among balanced multiple $q$-zeta values, giving $\mathcal G^{\mathrm f}\cong\mathcal G=\mathcal Z_q$. Prove that the primitive space $\mathfrak{bm}_0$ is a Lie algebra under its proposed bracket and establish $\mathca... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-001",
"literature-status:open",
"owr-year:2026"
] | The conjectural identification of the formal q-zeta algebra and the primitive space b_m_0 as a Lie algebra is still presented as conjectural in the 2026 report and related primary work. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://arxiv.org/abs/2602.08176",
"label": "Bachmann--Kanno, Relations and Derivatives of Multiple Eisenstein Series"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Prove that the balanced quasi-shuffle relations and $\tau$-invariance generate all algebraic relations among balanced multiple $q$-zeta values, giving $\mathcal G^{\mathrm f}\cong\mathcal G=\mathcal Z_q$. Prove that the primitive space $\mathfrak{bm}_0$ is a Lie algebra under its proposed bracket and establish $\mathca... | The previously mentioned conjecture is equivalent to having an algebra isomorphism G f ≃ G = Zq . We conjecture that bm0 is a Lie algebra, and an explicit formula for the Lie bracket on bm0 is given in [5]. We want to understand the term D(x) in the dimension conjecture, which corre- sponds to a derivation of weight 2 ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,587 | OWR-14299909-002 | Derivative Formula for Multiple Eisenstein Series | For every word $w\in\mathbb Q\langle z_2,z_3,\ldots\rangle$, prove the conjectural derivative identity $2\pi i\,\frac{d}{d\tau}G(w)=G(\theta(w))$, where $\theta=-D\circ\varphi$ is defined using the Drop1 operator. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-002",
"literature-status:open",
"owr-year:2026"
] | The conjecture involving the derivation theta and the formal multiple-Eisenstein relations is stated as an open conjecture; the 2026 primary paper proves structural results but does not prove this full assertion. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://arxiv.org/abs/2602.08176",
"label": "Bachmann--Kanno, Relations and Derivatives of Multiple Eisenstein Series"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | For every word $w\in\mathbb Q\langle z_2,z_3,\ldots\rangle$, prove the conjectural derivative identity $2\pi i\,\frac{d}{d\tau}G(w)=G(\theta(w))$, where $\theta=-D\circ\varphi$ is defined using the Drop1 operator. | Setting \theta(w) := −D(ϕ(w)), we conjecture: d Conjecture ([2]). For example, R(z2 , z2 ) yields the weight 6 relation 6G3,3 − 3G4,2 − G6 = 0. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,588 | OWR-14299909-003 | Duplicate Multiple-Eisenstein Relations Preamble | Conjectures on all relations We conjecture that all relations among multiple Eisenstein series can be obtained from the relations and the derivative. Xk d 2\pii Gk (\tau ) = (2k − 1)Gk+2 (\tau ) − (k + j − 1)Gk+2−j,j (\tau ) − G2,k (\tau ) . d\tau j=2 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
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"created_at": "2026-07-31T15:26:25.670Z"
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is an informal lead-in to the precise kernel conjecture preserved in the following record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-003",
"literature-status:open",
"owr-year:2026"
] | The claim that all relations among multiple Eisenstein series arise from known relations and differentiation remains conjectural; the 2026 paper verifies the framework in depth one but not in all depths. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://arxiv.org/abs/2602.08176",
"label": "Bachmann--Kanno, Relations and Derivatives of Multiple Eisenstein Series"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | null | Conjectures on all relations We conjecture that all relations among multiple Eisenstein series can be obtained from the relations and the derivative. Xk d 2\pii Gk (\tau ) = (2k − 1)Gk+2 (\tau ) − (k + j − 1)Gk+2−j,j (\tau ) − G2,k (\tau ) . d\tau j=2 | unrecoverable | The official report confirms that this extraction is an informal lead-in to the precise kernel conjecture preserved in the following record. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,589 | OWR-14299909-004 | Kernel Presentation for Multiple Eisenstein Relations | Let $G$ map words in $H^{\geq 2}=\mathbb Q\langle z_2,z_3,\ldots\rangle$ to multiple Eisenstein series, and set $\operatorname{DR}^*=\operatorname{span}_{\mathbb Q}\{\theta^n(R(u,v))*w:n\geq 0,\ u,v,w\in H^{\geq 2}\}$. Prove that $\operatorname{DR}^*=\ker G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"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-14299909-004",
"literature-status:open",
"owr-year:2026"
] | The equality DR^*=ker G is the conjectural presentation of all relations; the cited 2026 work proves the formal quotient has an sl_2 structure but does not establish the equality with the analytic kernel. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://arxiv.org/abs/2602.08176",
"label": "Bachmann--Kanno, Relations and Derivatives of Multiple Eisenstein Series"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Let $G$ map words in $H^{\geq 2}=\mathbb Q\langle z_2,z_3,\ldots\rangle$ to multiple Eisenstein series, and set $\operatorname{DR}^*=\operatorname{span}_{\mathbb Q}\{\theta^n(R(u,v))*w:n\geq 0,\ u,v,w\in H^{\geq 2}\}$. Prove that $\operatorname{DR}^*=\ker G$. | Conjecture ([2]). We have DR∗ = ker G, where DR∗ := spanQ \{\thetan (R(u, v)) ∗ w | n \geq 0, u, v, w \in H\geq2 \}. This leads to the notion of the space formal multiple Eisenstein, defined by \geq2 . Eff := H∗ DR . ∗ By above conjecture we have Eff \sim = E. It is conjectured in [1] that E is an sl2 -algebra. We show ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,590 | OWR-14299909-005 | Critical-Value Conjecture Preamble | 1.1. Period polynomials. Let k \geq 4 be even. The period polynomial Pf (X, Y ) \in C[X, Y ] associated to a cusp form f \in Sk (SL2 (Z)) is the homogeneous polynomial of degree k − 2 given by Z i\infty X k−2 Pf (X, Y ) := f (z)(X − Y z)k−2 dz = (−1)s−1 Λ(f ; s)X r−1Y s−1 , 0 s − 1 r+s=k r,s\geq1 R i\infty where we set... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
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"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
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"created_at": "2026-07-31T15:26:25.670Z"
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"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 | Unrecoverable OWR statement (The official report confirms that this extraction is background on period polynomials immediately preceding the complete critical-value conj) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-005",
"literature-status:open",
"owr-year:2026"
] | The extracted passage identifies a folklore conjecture asserting the maximal expected rational dimension of parity-separated critical L-values; it is supported by period-polynomial bounds but is not proved in general. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | null | 1.1. Period polynomials. Let k \geq 4 be even. The period polynomial Pf (X, Y ) \in C[X, Y ] associated to a cusp form f \in Sk (SL2 (Z)) is the homogeneous polynomial of degree k − 2 given by Z i\infty X k−2 Pf (X, Y ) := f (z)(X − Y z)k−2 dz = (−1)s−1 Λ(f ; s)X r−1Y s−1 , 0 s − 1 r+s=k r,s\geq1 R i\infty where we set... | unrecoverable | The official report confirms that this extraction is background on period polynomials immediately preceding the complete critical-value conjecture preserved in the following record. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,591 | OWR-14299909-006 | Rational Dimensions of Critical Modular $L$-Values | Let $f\in S_k(\operatorname{SL}_2(\mathbb Z))$ be a normalized Hecke eigenform. If $L_f^+$ and $L_f^-$ are the $\mathbb Q$-spans of its odd and even critical values $\Lambda(f;s)$, respectively, prove that $\dim_{\mathbb Q}L_f^\pm=\dim_{\mathbb C}S_k(\operatorname{SL}_2(\mathbb Z))$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
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"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"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-14299909-006",
"literature-status:open",
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] | The report proves only the upper bound for the critical-value spaces; the asserted equality is explicitly presented as a folklore conjecture and remains tied to the unproved Maeda conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Let $f\in S_k(\operatorname{SL}_2(\mathbb Z))$ be a normalized Hecke eigenform. If $L_f^+$ and $L_f^-$ are the $\mathbb Q$-spans of its odd and even critical values $\Lambda(f;s)$, respectively, prove that $\dim_{\mathbb Q}L_f^\pm=\dim_{\mathbb C}S_k(\operatorname{SL}_2(\mathbb Z))$. | Conjecture 1. For a normalized Hecke eigenform f \in Sk (SL2 (Z)), let L\pm f be the Q-vector space spanned by the critical values Λ(f ; s), s ≡ \delta\pm mod 2, where we set \delta+ = 1 and \delta− = 0: L+ f := hΛ(f ; s) | s = 1, 3, 5, . . . , k − 1iQ , L− f := hΛ(f ; s) | s = 2, 4, 6, . . . , k − 2iQ . ? Then we have... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,592 | OWR-14299909-007 | Duplicate Critical-Value and Maeda Discussion | conjecture. To see this, recall that for a newform f , the ratio Λ(f ; s)/Λ(f ; s′ ) of critical values with s ≡ s′ mod 2 lies in the Hecke field Q(f ) (cf. [6]). Thus, the dimension of the space L\pm f is bounded above by the extension degree [Q(f ) : Q]. On the other hand, Maeda’s conjecture, which asserts that the He... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
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"created_at": "2026-07-31T15:26:25.670Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is the explanatory continuation of the critical-value conjecture preserved in the precedin) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-007",
"literature-status:open",
"owr-year:2026"
] | This continuation says the desired bound is obtained only conditionally from Maeda's conjecture, and notes that the critical-value conjecture would imply Maeda; no unconditional proof is reported. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | null | conjecture. To see this, recall that for a newform f , the ratio Λ(f ; s)/Λ(f ; s′ ) of critical values with s ≡ s′ mod 2 lies in the Hecke field Q(f ) (cf. [6]). Thus, the dimension of the space L\pm f is bounded above by the extension degree [Q(f ) : Q]. On the other hand, Maeda’s conjecture, which asserts that the He... | unrecoverable | The official report confirms that this extraction is the explanatory continuation of the critical-value conjecture preserved in the preceding record, not a second standalone problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,593 | OWR-14299909-008 | Ramanujan Tau Nonvanishing from Double Eisenstein Series | Use double-Eisenstein-series representations of the discriminant modular form to prove that Ramanujan’s $\tau(n)$ never vanishes, or at least that $\tau(p)=0$ for only finitely many primes $p$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-008",
"literature-status:open",
"owr-year:2026"
] | The report records this as an open application of a new formula to the non-vanishing of the Ramanujan tau function and says the proposed argument remains heuristic. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Use double-Eisenstein-series representations of the discriminant modular form to prove that Ramanujan’s $\tau(n)$ never vanishes, or at least that $\tau(p)=0$ for only finitely many primes $p$. | Can we apply this formula to the non-vanishing problem of \tau (n)? 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 | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,594 | OWR-14299909-009 | Relations Among Multiple Weierstrass Function Spaces | For the spaces $\mathcal P_k$ of multiple Weierstrass functions and Eisenstein-series spaces $\mathcal E_k$, prove that $C_n(\mathcal P_{k+n})=\mathcal E_k$ for all $k\geq 0$ and $n\geq 3$, and that $\frac{d}{dz}(\mathcal E\cdot\mathcal P)\subseteq\mathcal P$. Also prove $\mathcal E_k\cap\mathcal P_k=\Delta\mathcal E_{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-009",
"literature-status:open",
"owr-year:2026"
] | The extracted record truncates the conjecture; the underlying report states that the needed dimension conjectures for the indicated spaces were not available, so the claim is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | For the spaces $\mathcal P_k$ of multiple Weierstrass functions and Eisenstein-series spaces $\mathcal E_k$, prove that $C_n(\mathcal P_{k+n})=\mathcal E_k$ for all $k\geq 0$ and $n\geq 3$, and that $\frac{d}{dz}(\mathcal E\cdot\mathcal P)\subseteq\mathcal P$. Also prove $\mathcal E_k\cap\mathcal P_k=\Delta\mathcal E_{... | The following conjecture is an analogue of Theorem 4. Furthermore, we propose the following conjecture for C0 (Pk ) and C2 (Pk ). From the above statement, since a dimension conjecture for Ek has already been given by Okounkov[5] and Bachmann–Kühn[1], one can obtain a dimension con- jecture for Pk by determining the d... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,595 | OWR-14299909-010 | Modularity of Higher-$t$ Generating-Function Coefficients | Determine whether the coefficients of higher powers of $t$ in the hypergeometric generating function for the integrals $R_{k,1}(X)$ are modular forms or higher-order modular antiderivatives, and rigorously identify the corresponding structure for $R_{k,\ell}(X)$ when $\ell>1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-010",
"literature-status:open",
"owr-year:2026"
] | The report gives modular identifications only for low powers and says that higher powers and the general higher-depth structure remain difficult and unproved. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Determine whether the coefficients of higher powers of $t$ in the hypergeometric generating function for the integrals $R_{k,1}(X)$ are modular forms or higher-order modular antiderivatives, and rigorously identify the corresponding structure for $R_{k,\ell}(X)$ when $\ell>1$. | What about higher powers in t, do they connect with modular forms? to write linear differential equations for them. Already the structure of Rk,2 (X) is highly challenging to analyse, and we only have some partial results for these. At the same time, our analysis of the integrals Rk,1 (X) reveals the following nice gene... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,596 | OWR-14299909-011 | Modular $q$-Analogues of Ramanujan’s 9801 Series | Construct a modular or mock-modular $q$-analogue of Ramanujan’s 9801 series for $1/\pi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-011",
"literature-status:open",
"owr-year:2026"
] | Modular or mock-modular q-analogues are known for several other Ramanujan formulas, but the cited literature does not establish one for the displayed 9801-series; the proposed problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://arxiv.org/abs/2509.05897",
"label": "Campbell, q-analogues of pi-formulas"
},
{
"url": "https://doi.org/10.1080/10652469.2018.1454448",
"label": "Guo--Zudilin, Ramanujan-type q-an... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Construct a modular or mock-modular $q$-analogue of Ramanujan’s 9801 series for $1/\pi$. | (Proposed by Kam Cheong Au) Does there exist a q-analogue of some of Ramanujan’s 1/\pi series [2], such as 1 3 X 1 n 1 9801 2 n 4 n 4 n 8 4 3 (26390n + 1103) = \sqrt{ } , 3 11 (1)n 2 2\pi n\geq0 that exhibits modular properties? Note that for the simpler identity X 1 n 1 3 16 2 n (42n + 5) = 26 (1)n \pi n\geq0 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,597 | OWR-14299909-012 | Algebraicity Under Central-Binomial Untwisting | Let $f(x)=\sum_{n\geq 0}a_nx^n\in\mathbb Z[[x]]$ and $F(x)=\sum_{n\geq 0}\binom{2n}{n}a_nx^n$. If $F$ satisfies a second-order homogeneous linear differential equation with polynomial coefficients and regular singularities, must $f$ be algebraic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486](https://doi.org/10.4171/owr/2026/7)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299909-012",
"literature-status:open",
"owr-year:2026"
] | The 2025 primary paper formulates this same central-binomial untwisting question and reports evidence against a broad positive answer, but gives neither a proof nor a counterexample; it therefore remains open. | [
{
"url": "https://doi.org/10.4171/owr/2026/7",
"label": "Oberwolfach Report 7/2026"
},
{
"url": "https://doi.org/10.48550/arXiv.2306.04921",
"label": "van Hoeij--van Straten--Zudilin, Hyperelliptic saga"
},
{
"url": "https://jexpmath.org/index.php/jem/article/view/Vol-1Issue-2Paper-5",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/7 | null | null | null | Let $f(x)=\sum_{n\geq 0}a_nx^n\in\mathbb Z[[x]]$ and $F(x)=\sum_{n\geq 0}\binom{2n}{n}a_nx^n$. If $F$ satisfies a second-order homogeneous linear differential equation with polynomial coefficients and regular singularities, must $f$ be algebraic? | Is f (x) algebraic? Show that if k \geq 1 and k is not a multiple of 29, then b(29k + 21) ≡ 0 (mod 4). | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Multiple Zeta Values and Modular Forms (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/7, pp. 433--486 |
30,006,598 | OWR-14299910-001 | Socles of Products from Lusztig Components | Let $C$ and $D$ be irreducible components of Lusztig nilpotent varieties of Dynkin type $A$, with associated simple modules $\pi(C)$ and $\pi(D)$. If $C$ is rigid, prove that $\operatorname{soc}(\pi(C)\times\pi(D))=\pi(C*D)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432](https://doi.org/10.4171/owr/2026/6)
## Literature review... | 3 | open | null | 2,026 | 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-14299910-001",
"literature-status:open",
"owr-year:2026"
] | The socle identity is still called a conjecture in the 2026 report; the primary paper verifies it only in special cases, including a stated rigidity class. | [
{
"url": "https://doi.org/10.4171/owr/2026/6",
"label": "Oberwolfach Report 6/2026"
},
{
"url": "https://arxiv.org/abs/2111.05162",
"label": "Lapid--Minguez, binary operation on nilpotent varieties II"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/6 | null | null | null | Let $C$ and $D$ be irreducible components of Lusztig nilpotent varieties of Dynkin type $A$, with associated simple modules $\pi(C)$ and $\pi(D)$. If $C$ is rigid, prove that $\operatorname{soc}(\pi(C)\times\pi(D))=\pi(C*D)$. | Modeled by these conjectures, we conjectured in [LM25] that if C is rigid, then soc(\pi(C) \times \pi(D)) = \pi(C ∗ D). 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 | Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432 |
30,006,599 | OWR-14299910-004 | Homological Interpretation of Semidistributive Rowmotion | For a finite semidistributive lattice $L$, find a homological interpretation of its rowmotion bijection extending the Auslander-Reiten interpretation available for distributive lattices. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432](https://doi.org/10.4171/owr/2026/6)
## Literature review... | 3 | open | null | 2,026 | 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-14299910-004",
"literature-status:open",
"owr-year:2026"
] | The report poses this as Question 1 and explains that the known Auslander--Reiten interpretation applies to distributive lattices, leaving the semidistributive non-distributive case unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2026/6",
"label": "Oberwolfach Report 6/2026"
},
{
"url": "https://arxiv.org/abs/2507.18230",
"label": "Defant et al., Rowmotion and echelonmotion"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/6 | null | null | null | For a finite semidistributive lattice $L$, find a homological interpretation of its rowmotion bijection extending the Auslander-Reiten interpretation available for distributive lattices. | For L semidistributive, is there a homological interpretation of the rowmotion bijection? Φ\pi (dim Pi ) = − dim Ii For a lattice L, consider \pi a reverse linear extension of L, i.e., we number the elements of L from top to bottom. We say that a matrix is P U if it is of the form wU , with w a permutation matrix, and ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432 |
30,006,600 | OWR-14299910-005 | Connectivity of Cluster-Tilting Exchange Graphs | For a stably $2$-Calabi-Yau Frobenius category $\mathcal C$, is the exchange graph whose vertices are cluster-tilting objects and whose edges are mutations always connected? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432](https://doi.org/10.4171/owr/2026/6)
## Literature review... | 3 | open | null | 2,026 | 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-14299910-005",
"literature-status:open",
"owr-year:2026"
] | The source explicitly says that connectivity of the full exchange graph of cluster-tilting objects is an open question, although important subclasses are known to be connected. | [
{
"url": "https://doi.org/10.4171/owr/2026/6",
"label": "Oberwolfach Report 6/2026"
},
{
"url": "https://arxiv.org/abs/1302.6045",
"label": "Bruestle--Yang, Ordered exchange graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/6 | null | null | null | For a stably $2$-Calabi-Yau Frobenius category $\mathcal C$, is the exchange graph whose vertices are cluster-tilting objects and whose edges are mutations always connected? | We need the notion reachable here: in general, it is an open question whether the “exchange graph of C” is connected (this graph has as vertices the cluster-tilting objects and its edges are given by mutation). Representation Theory of Quivers and Finite-Dimensional Algebras 413 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432 |
30,006,601 | OWR-14299910-006 | Universal $F$-Polynomial Configuration-Space Identities | For every finite-dimensional algebra $\Lambda$, prove that the configuration spaces defined by its universal $F$-polynomials and its $u$-equations satisfy $\widetilde{\mathcal M}_\Lambda=\widetilde{\mathcal U}_\Lambda$ and $\mathcal M_\Lambda=\mathcal U_\Lambda$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432](https://doi.org/10.4171/owr/2026/6)
## Literature review... | 3 | open | null | 2,026 | 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-14299910-006",
"literature-status:open",
"owr-year:2026"
] | The universal F-polynomial equality is stated as Conjecture 7; the report lists Dynkin path algebras and several families where it is known, but not a general proof. | [
{
"url": "https://doi.org/10.4171/owr/2026/6",
"label": "Oberwolfach Report 6/2026"
},
{
"url": "https://arxiv.org/abs/2501.09447",
"label": "Klasz--Marczinzik--Thomas, Auslander regular algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/6 | null | null | null | For every finite-dimensional algebra $\Lambda$, prove that the configuration spaces defined by its universal $F$-polynomials and its $u$-equations satisfy $\widetilde{\mathcal M}_\Lambda=\widetilde{\mathcal U}_\Lambda$ and $\mathcal M_\Lambda=\mathcal U_\Lambda$. | We always have M If follows from [2] that the conjecture is true for path algebras of Dynkin quivers. As a corollary, setting FbX = 1 for all X, we recover the u-equations. Definition 6. The configuration spaces associated to Λ are MfΛ = Spec C[uX | X \in ind KΛ ]/hFbX − 1 | X \in ind KΛ i MΛ = Spec C[u\pm1 b X | X \in i... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representation Theory of Quivers and Finite-Dimensional Algebras (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/6, pp. 345--432 |
30,006,602 | OWR-14299911-001 | Median Geometry Workshop Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 Pénélope Azuelos Median metric groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Montserrat Casals-Ruiz (joint with Mark Hagen, Ilya Kazachkov) Universal real cubings . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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"
} | {
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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 | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment, not a mathematical conjecture. No separate clean statemen) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299911-001",
"literature-status:open",
"owr-year:2026"
] | The record contains only the word conjecture and table-of-contents prose, so no definite mathematical claim is identifiable; under the triage rule it is open. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 Pénélope Azuelos Median metric groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Montserrat Casals-Ruiz (joint with Mark Hagen, Ilya Kazachkov) Universal real cubings . .... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment, not a mathematical conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,603 | OWR-14299911-002 | Common Refinements of PL-Homeomorphic Simplicial Complexes | Given two PL-homeomorphic simplicial complexes, does there exist a common refinement reachable from both by elementary moves? Determine the corresponding factorization relation and its analogues in toric geometry. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,026 | 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-14299911-002",
"literature-status:partially-solved",
"owr-year:2026"
] | Milnor disproved the unrestricted homeomorphic-complex version of the Hauptvermutung, while Adiprasito--Pak proved the modified PL version and the weighted strong-factorization result stated in the report. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
},
{
"url": "https://arxiv.org/abs/2404.05930",
"label": "Adiprasito--Pak, All triangulations have a common stellar subdivision"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Given two PL-homeomorphic simplicial complexes, does there exist a common refinement reachable from both by elementary moves? Determine the corresponding factorization relation and its analogues in toric geometry. | How can they be related? Given two homeomorphic simplicial complexes, is there a common refinement that is reached by elementary moves? Given two PL homeomor- phic simplicial complexes, is there a common refinement that is reached by ele- mentary moves? A similar conjecture emerged in toric geometry, often called the str... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,604 | OWR-14299911-005 | Thiagarajan Grid-Free Decidability Conjecture | For a trace-regular event structure, is its monadic second-order theory decidable if and only if the event structure is grid-free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | solved | null | 2,026 | 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"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"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": "resolution",
"evidence": "published"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299911-005",
"literature-status:partially-solved",
"owr-year:2026"
] | Chalopin–Chepoi construct a trace-regular, grid-free event structure with undecidable MSO theory. The report itself describes this counterexample. The removed second sentence conflated this MSO conjecture with Thiagarajan’s different conjecture about special cube complexes; the MSO counterexample is itself virtually sp... | [
{
"url": "https://doi.org/10.1145/3322095",
"label": "J. Chalopin and V. Chepoi, 1-Safe Petri Nets and Special Cube Complexes (2019)"
},
{
"url": "https://arxiv.org/abs/1810.03395",
"label": "Chalopin–Chepoi — manuscript"
},
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Me... | 2026-09-28T00:00:00 | J. Chalopin and V. Chepoi, 1-Safe Petri Nets and Special Cube Complexes (2019): https://doi.org/10.1145/3322095
Chalopin–Chepoi — manuscript: https://arxiv.org/abs/1810.03395
Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540: https://doi.org/10.4171/owr/2026/8 | https://doi.org/10.4171/owr/2026/8 | null | null | null | For a trace-regular event structure, is its monadic second-order theory decidable if and only if the event structure is grid-free? | In [1] we proved that Thiagarajan’s conjecture is true for event structures whose domains arise as principal filters of universal covers of finite special cube com- plexes. The conjecture on decidability of MSO logic. Thiagarajan and Yang (2014) defined the monadic second order (MSO) theory of an event structure unfolding... | corrected_verified | Reviewed against the cited source on 2026-09-28; the correction and its scope are explained in the current literature review. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,605 | OWR-14299911-007 | Weighted Centers on Bounded-Dimensional Median Graphs | Is there an almost-linear-time algorithm for the Weighted Center problem on median graphs of bounded cube dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-007",
"literature-status:open",
"owr-year:2026"
] | The report labels this an open problem; known results give almost-linear algorithms for unweighted centers and restricted subclasses, not the weighted bounded-cube-dimension case. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
},
{
"url": "https://arxiv.org/abs/2105.12150",
"label": "Chepoi et al., Diameter, radius and all eccentricities"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Is there an almost-linear-time algorithm for the Weighted Center problem on median graphs of bounded cube dimension? | Open problem 1. Is there an almost linear-time algorithm for the Weighted Center problem on median graphs of bounded cube-dimension? or metric spaces the classical Center problem corresponds to the particular case of the all-one profile \pi, which has attracted considerable attention in algorithmic graph theory, and in ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,606 | OWR-14299911-008 | Radius-Function Unimodality in Bounded-Dimensional Median Graphs | Does there exist an absolute constant $c>0$ such that every median graph of cube dimension $d$ has all of its radius functions $G_{cd}$-unimodal? Extend the theory, if possible, to suitably edge-weighted median graphs and to useful families of partial cubes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-008",
"literature-status:open",
"owr-year:2026"
] | The report gives the bounded-cube-dimension question as an open problem and records only the cube-dimension-two case; no general constant c is established. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
},
{
"url": "https://arxiv.org/abs/2503.15011",
"label": "Dragan et al., G-unimodality of radius functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Does there exist an absolute constant $c>0$ such that every median graph of cube dimension $d$ has all of its radius functions $G_{cd}$-unimodal? Extend the theory, if possible, to suitably edge-weighted median graphs and to useful families of partial cubes. | Open problem 2. In particular, does there exist some constant c > 0 such that every me- dian graph of cube-dimension d has all its radius functions that are Gc\cdotd -unimodal? 2. Perspectives It was asked during the talk whether the results above can be extended to edge- weighted median graphs. This is likely to requi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,607 | OWR-14299911-009 | Special Cube Complexes Talk Transition | and median graphs. We then turn to a discussion of Haglund and Wise’s devel- opment of special complexes, a setting in which Stallings approach for building of covers of graphs can be generalized to building covers of non-positively curved cube complexes. Finally, we discuss how this led to Agol’s solution of the virtu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is expository narrative ending with an unspecific reference to questions and then crossing) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299911-009",
"literature-status:open",
"owr-year:2026"
] | The record is an incomplete narrative fragment ending with a reference to further questions, so no definite solved or disproved claim can be extracted. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | null | and median graphs. We then turn to a discussion of Haglund and Wise’s devel- opment of special complexes, a setting in which Stallings approach for building of covers of graphs can be generalized to building covers of non-positively curved cube complexes. Finally, we discuss how this led to Agol’s solution of the virtu... | unrecoverable | The official report confirms that this extraction is expository narrative ending with an unspecific reference to questions and then crossing into the next talk title; it contains no recoverable standalone question. No separate clean statement is promoted; the original record remains publicly visible and retained for pr... | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,608 | OWR-14299911-010 | Classification of Strongly Prime Smooth Graphs | Characterize and classify the strongly prime smooth graphs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-010",
"literature-status:open",
"owr-year:2026"
] | The source explicitly calls identification of the strongly prime smooth graphs an interesting open problem; the cited results classify broad smooth subclasses but not the strongly prime ones. | [
{
"url": "https://doi.org/10.4171/owr/2026/8",
"label": "Oberwolfach Report 8/2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Characterize and classify the strongly prime smooth graphs. | It remains an interesting open problem to identify the strongly prime smooth graphs. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,609 | OWR-14299911-011 | Median Geometry Problem-List Introduction | This section contains a collection of open problems, some of which are well-known. 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:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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 confirms that this extraction is only an introductory sentence for a problem list; the individual mathematical questions) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299911-011",
"literature-status:open",
"owr-year:2026"
] | The record only says that the report contains open problems and names no mathematical claim; it therefore remains open under the queue rule. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | null | This section contains a collection of open problems, some of which are well-known. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is only an introductory sentence for a problem list; the individual mathematical questions are represented by the subsequent records. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,610 | OWR-14299911-012 | Median Actions and Residual Finiteness for Hyperbolic Groups with Sphere Boundary | Let $G$ be a hyperbolic group with boundary homeomorphic to $S^2$. Can one prove that $G$ admits an action with unbounded orbits on a median space, equivalently that $G$ does not have Kazhdan's property $(T)$? More generally, is every medianized hyperbolic group cubulable, or can one at least prove that it is residuall... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299911-012",
"literature-status:open",
"owr-year:2026"
] | This is a fragment of Problem 1(iii)-(iv), including the unresolved residual-finiteness question; the source report lists it as open and no resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Let $G$ be a hyperbolic group with boundary homeomorphic to $S^2$. Can one prove that $G$ admits an action with unbounded orbits on a median space, equivalently that $G$ does not have Kazhdan's property $(T)$? More generally, is every medianized hyperbolic group cubulable, or can one at least prove that it is residuall... | Is it related to the previous question? Can you even prove residually finite? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,611 | OWR-14299911-013 | Wall Structures on Symmetric-Group Cayley Graphs | Does there exist a sequence of generating sets $X_n$ for $S_n$, of uniformly bounded size, such that the Cayley graphs $\operatorname{Cay}(S_n,X_n)$ admit wall structures whose wall metrics are uniformly coarsely equivalent to their word metrics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-013",
"literature-status:open",
"owr-year:2026"
] | Problem 2(i) is explicitly posed as an open question about bounded-degree generating sets of symmetric groups with wall metrics coarsely equivalent to word metrics; no resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Does there exist a sequence of generating sets $X_n$ for $S_n$, of uniformly bounded size, such that the Cayley graphs $\operatorname{Cay}(S_n,X_n)$ admit wall structures whose wall metrics are uniformly coarsely equivalent to their word metrics? | Question i) Does there exist a sequence of generating sets Xn of Sn such that the sizes |Xn | are uniformly bounded and the corresponding sequence of Cayley graphs (Cay(Sn , Xn ))n admits a wall structure whose wall metric is coarsely equivalent to the word length metric (i.e., to the graph metric) on (Cay(Sn , Xn ))n ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,612 | OWR-14299911-014 | Hilbert-Space Coarse Embeddings of Coarse Median Spaces | Does every coarse median space admit a coarse embedding into a Hilbert space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-014",
"literature-status:open",
"owr-year:2026"
] | The report poses the universal coarse-median-to-Hilbert coarse-embedding question directly and supplies no proof or counterexample; no resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Does every coarse median space admit a coarse embedding into a Hilbert space? | Does every coarse median space coarsely embed into a Hilbert space? Problem 2. Symmetric groups and wall structures, Arzhantseva Let Sn denote the permutation group on a finite set of n elements. Question i) Does there exist a sequence of generating sets Xn of Sn such that the sizes |Xn | are uniformly bounded and the c... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,613 | OWR-14299911-015 | Coarse Buneman Models for Countable Preference Data | Extend the Buneman-graph model of single-peaked preference data to a countably infinite set of alternatives. Construct a coarse Buneman graph that accommodates missing or uncertain half-space assignments and computes medians with controlled error. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-015",
"literature-status:open",
"owr-year:2026"
] | This extracted text combines unresolved countable-single-peakedness and coarse Buneman-graph questions; the report gives no solution and no later resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | Extend the Buneman-graph model of single-peaked preference data to a countably infinite set of alternatives. Construct a coarse Buneman graph that accommodates missing or uncertain half-space assignments and computes medians with controlled error. | What happens when we allow X 530 Oberwolfach Report 8/2026 to be infinite countable? Is there a coarse variant of the Buneman graph that can model this data, allowing us to compute medians up to controlled error? Problem 3. Coarse median spaces, Arzhantseva A coarse median space is a metric space endowed with a ternary ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,614 | OWR-14299911-016 | Coarse Buneman Graphs for Partial Data | When half-space membership data are missing or noisy, construct a coarse analogue of the Buneman graph that represents the partial data and permits computation of medians up to a controlled error. Determine when the resulting metric space retains quantitatively controlled median geometry. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-016",
"literature-status:open",
"owr-year:2026"
] | Problem 5 asks for a coarse Buneman-graph model for uncertain half-space data and controlled-error medians; it is presented as open with no resolving result found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | When half-space membership data are missing or noisy, construct a coarse analogue of the Buneman graph that represents the partial data and permits computation of medians up to a controlled error. Determine when the resulting metric space retains quantitatively controlled median geometry. | Is there a coarse variant of the Buneman graph that can model this data, allowing us to compute medians up to controlled error? to be infinite countable? Once the peak has been chosen, the minimum might be on the boundary, is it well-defined? Problem 6. Graphs of hyperplanes, Genevois Let X be a median graph. • Its trans... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
30,006,615 | OWR-14299911-017 | Computing Transversality Degrees of Graphs | For a graph $G$, let $\operatorname{TD}(G)$ be the minimum degree of a median graph whose transversality graph is isomorphic to $G$. Develop an algorithm to compute $\operatorname{TD}(G)$, and obtain structural or complexity bounds for this invariant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 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-14299911-017",
"literature-status:open",
"owr-year:2026"
] | Problem 6(ii) asks how to compute transversality degree; the report records only definitions and examples, not an algorithm or classification, and no resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/53603",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2026/8 | null | null | null | For a graph $G$, let $\operatorname{TD}(G)$ be the minimum degree of a median graph whose transversality graph is isomorphic to $G$. Develop an algorithm to compute $\operatorname{TD}(G)$, and obtain structural or complexity bounds for this invariant. | Question ii) How can one compute the transversality degree of a graph? Problem 5. Partial data, Huber, interpreted by Chatterji \& Niblo Suppose that in constructing the Buneman graph we encounter some uncertainties in determining which half spaces some vertices lie in. This can occur because of missing data, or measur... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540 |
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