id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,816 | OWR-8415345-006 | The Alekseev–Torossian Symmetry-Group Conjecture | Prove the Alekseev–Torossian symmetry-group identities $KV\cong GT_1\times K$ and $KRV\cong GRT_1\times K$ for Kashiwara–Vergne solutions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | open | null | 2,021 | 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-8415345-006",
"literature-status:open",
"owr-year:2021"
] | The Kashiwara-Vergne conjecture itself is proved, and symmetry groups have structural descriptions and injections from Grothendieck-Teichmuller groups, but the asserted product identifications remain an open conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://annals.math.princeton.edu/2012/175-2/p01",
"label": "Alekseev--Torossian"
},
{
"url": "https://arxiv.org/abs/2106.02373",
"label": "Dancso--Halacheva--Robertson"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | Prove the Alekseev–Torossian symmetry-group identities $KV\cong GT_1\times K$ and $KRV\cong GRT_1\times K$ for Kashiwara–Vergne solutions. | Alekseev--Torossian conjecture: the symmetry groups of Kashiwara--Vergne solutions satisfy KV\cong GT_1\times K and KRV\cong GRT_1\times K. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,817 | OWR-8415345-007 | The Q-Form Classification Conjecture | Q-form conjecture: let $M$ and $M'$ be simply connected $2q$-manifolds with normal $(q-1)$-smoothings $\bar\nu:M\to B$ and $\bar\nu':M'\to B$, where $q$ is even. If $\bar\nu$ and $\bar\nu'$ are bordant and their Q-forms $E_q(M,\bar\nu)$ and $E_q(M',\bar\nu')$ are isomorphic, then $M$ and $M'$ are h-cobordant over $B$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | partially_solved | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Nagy proves the conjecture when Hq(B) is torsion-free, and later extended surgery work confirms this free-homology case; the full conjecture in the stated generality remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://www.cambridge.org/core/journals/compositio-mathematica/article/extended-surgery-theory-for-simplyconnected-4kmanifolds/85B4255F03634F86890D193F39350770",
"label": "Nagy"
},
{
"url": "https://arxiv.... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | Q-form conjecture: let $M$ and $M'$ be simply connected $2q$-manifolds with normal $(q-1)$-smoothings $\bar\nu:M\to B$ and $\bar\nu':M'\to B$, where $q$ is even. If $\bar\nu$ and $\bar\nu'$ are bordant and their Q-forms $E_q(M,\bar\nu)$ and $E_q(M',\bar\nu')$ are isomorphic, then $M$ and $M'$ are h-cobordant over $B$. | Q-form conjecture: let M and M' be simply connected 2q-manifolds with normal (q-1)-smoothings \bar\nu:M\to B and \bar\nu':M'\to B for even q. If \bar\nu and \bar\nu' are bordant and their Q-forms E_q(M,\bar\nu) and E_q(M',\bar\nu') are isomorphic, then M and M' are h-cobordant over B. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,818 | OWR-8415345-008 | Genus-Reducing Local-Knot Concordance in Orientable Three-Manifolds | Does the genus-reducing concordance phenomenon constructed for local knots in non-orientable 3-manifolds also occur in an orientable 3-manifold; equivalently, can the additional topology of an orientable 3-manifold yield more efficient cobordisms between local knots? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-008",
"literature-status:open",
"owr-year:2021"
] | The orientable case of the requested genus-saving cobordism phenomenon is posed as an open question; Boden-Nagel proves only the sliceness implication for local knots, not the requested genus separation. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1112/topo.12051",
"label": "Celoria"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | Does the genus-reducing concordance phenomenon constructed for local knots in non-orientable 3-manifolds also occur in an orientable 3-manifold; equivalently, can the additional topology of an orientable 3-manifold yield more efficient cobordisms between local knots? | Does the genus-reducing concordance phenomenon constructed for local knots in non-orientable 3-manifolds also occur in an orientable 3-manifold; equivalently, can the additional topology of an orientable 3-manifold yield more efficient cobordisms between local knots? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,819 | OWR-8415345-009 | Concordance Rigidity of Positive Braid Knots | Are concordant positive braid knots in $S^3$ necessarily isotopic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-009",
"literature-status:open",
"owr-year:2021"
] | Recent work gives invariants and strong partial results for positive 3-braids, but explicitly leaves open whether concordant positive braid knots must be isotopic. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://ems.press/content/serial-article-files/50050",
"label": "OWR-2024-43"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | Are concordant positive braid knots in $S^3$ necessarily isotopic? | Are concordant positive braid knots in S^3 necessarily isotopic? | corrected_verified | The sphere notation was dollar-delimited without changing the concordance question. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,820 | OWR-8415346-002 | Regularity of Equivariant Monomial-Ideal Filtrations | Let $I=(I_n)_{n\geq1}$ be an $\operatorname{Inc}(\mathbb N)$-invariant filtration of nonzero proper homogeneous ideals with stability index $r$. Is $\operatorname{reg}(I_n)$ eventually linear in $n$? If the filtration is monomial, does there exist a constant $D$ such that $$\operatorname{reg}(I_n)=(w(I_r)-1)n+D$$ for a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396](https://doi.org/10.4171/owr/2021/43)
## Litera... | 3 | open | null | 2,021 | 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-8415346-002",
"literature-status:open",
"owr-year:2021"
] | The cited authors explicitly leave regularity eventually linear open even for non-saturated squarefree monomial filtrations; later work proves only selected saturated or asymptotic cases. | [
{
"url": "https://doi.org/10.4171/owr/2021/43",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2206.15141",
"label": "Le--Nguyen"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/43 | null | null | null | Let $I=(I_n)_{n\geq1}$ be an $\operatorname{Inc}(\mathbb N)$-invariant filtration of nonzero proper homogeneous ideals with stability index $r$. Is $\operatorname{reg}(I_n)$ eventually linear in $n$? If the filtration is monomial, does there exist a constant $D$ such that $$\operatorname{reg}(I_n)=(w(I_r)-1)n+D$$ for a... | But it remains open even for non-saturated filtrations of squarefree monomial ideals. Projective dimension and regularity of equivariant filtrations of ideals Hop D. Nguyen (joint work with Dinh Van Le) | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396 |
30,004,821 | OWR-8415346-003 | Eventual Linearity of Equivariant Projective Dimensions | Let $I=(I_n)_{n\geq 1}$ be an $\operatorname{Inc}(\mathbb{N})$-invariant filtration of nonzero proper homogeneous ideals. Is the sequence $(\operatorname{pd}(R_n/I_n))_{n\geq 1}$ eventually linear? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396](https://doi.org/10.4171/owr/2021/43)
## Litera... | 3 | partially_solved | null | 2,021 | 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-8415346-003",
"literature-status:partially-solved",
"owr-year:2021"
] | The conjecture is proved for saturated chains of monomial ideals, but the stated claim for arbitrary nonzero proper homogeneous Inc-invariant filtrations is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2021/43",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2206.15141",
"label": "Le--Nguyen"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/43 | null | null | null | Let $I=(I_n)_{n\geq 1}$ be an $\operatorname{Inc}(\mathbb{N})$-invariant filtration of nonzero proper homogeneous ideals. Is the sequence $(\operatorname{pd}(R_n/I_n))_{n\geq 1}$ eventually linear? | Conjecture 3 ([3, Conjecture 1.3]). Let I = (In )n\geq1 be an Inc(N)-invariant filtra- tion of non-zero proper homogeneous ideals. Then the sequence (pd(Rn /In ))n\geq1 is eventually linear. For Conjecture 2, we prove an asymptotic version for all (saturated or not) chains of monomial ideals. For Conjecture 3, we prove... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396 |
30,004,822 | OWR-8415346-004 | Spectrahedrality Under the Eigenvalue-Set Transformation | Let $M\subseteq\mathbb R^n$ be invariant under coordinate permutations, let $\mathcal S^n$ be the space of real symmetric $n\times n$ matrices, and define $$\Lambda(M)=\{A\in\mathcal S^n:\lambda(A)\in M\},$$ where $\lambda(A)$ is the ordered eigenvalue vector of $A$. Is $M$ a spectrahedron if and only if $\Lambda(M)$ i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396](https://doi.org/10.4171/owr/2021/43)
## Litera... | 3 | open | null | 2,021 | 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-8415346-004",
"literature-status:open",
"owr-year:2021"
] | Known sufficient conditions and derivative-relaxation cases do not establish the proposed equivalence for all symmetric sets; it remains tied to the unresolved generalized Lax conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/43",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2021.107749",
"label": "Kummer"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/43 | null | null | null | Let $M\subseteq\mathbb R^n$ be invariant under coordinate permutations, let $\mathcal S^n$ be the space of real symmetric $n\times n$ matrices, and define $$\Lambda(M)=\{A\in\mathcal S^n:\lambda(A)\in M\},$$ where $\lambda(A)$ is the ordered eigenvalue vector of $A$. Is $M$ a spectrahedron if and only if $\Lambda(M)$ i... | We conjecture that M is a spectrahedron if and only if Λ(M ) is a spectrahedron. Symmetric spectrahedra with respect to the permutation and orthogonal group Mario Kummer | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396 |
30,004,823 | OWR-8415346-007 | Polynomial Specht Multiplicities in Symmetric-Variety Cohomology | Let a symmetric ideal in the inverse-limit ring of symmetric polynomials define a sequence of symmetric varieties $V_n$, and fix a partition $\lambda$ and an integer $p\geq0$. Is the multiplicity of the Specht module indexed by $\{\lambda\}_n$ in $H^p(V_n;\mathbb Q)$ eventually a polynomial in $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396](https://doi.org/10.4171/owr/2021/43)
## Litera... | 3 | partially_solved | null | 2,021 | 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-8415346-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Polynomial bounds and special cases are known, including the p=0 family reported here, but the eventual-polynomial multiplicity conjecture for arbitrary fixed p and symmetric varieties remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/43",
"label": "OWR report"
},
{
"url": "https://academic.oup.com/imrn/article/2020/7/2054/4989853",
"label": "Basu--Riener"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/43 | null | null | null | Let a symmetric ideal in the inverse-limit ring of symmetric polynomials define a sequence of symmetric varieties $V_n$, and fix a partition $\lambda$ and an integer $p\geq0$. Is the multiplicity of the Specht module indexed by $\{\lambda\}_n$ in $H^p(V_n;\mathbb Q)$ eventually a polynomial in $n$? | Conjecture 1. [2] For any fixed p \geq 0, the multiplicity of the Specht module corresponding to \{\lambda\}n in Hp (Vn , Q) is eventually given by a polynomial in n. We study a special case of this conjecture (joint work with D. Perrucci). We have proved the following theorem. Pd Theorem 1. [1] Let f = i=0 ai \sigmai ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/43, pp. 2365--2396 |
30,004,824 | OWR-8415347-001 | Unspecified Quantum-Groups Workshop Problem | Open Problems Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2450 Makoto Yamashita Open problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vyjayanthi Chari Quantum Affine Algebras and their Representations . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a standalone open problem.) | null | null | null | [
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{
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"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | null | Open Problems Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2450 Makoto Yamashita Open problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vyjayanthi Chari Quantum Affine Algebras and their Representations . . . . ... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a standalone open problem. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,825 | OWR-8415347-002 | Unspecified Quantum-Groups Open Problem | 2452 Nicolás Andruskiewitsch Open problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rowell Open problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Groups – Algebra, Analysis and Category Theory... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a standalone open problem.) | null | null | null | [
"owr",
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"OWR-8415347-002",
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{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | null | 2452 Nicolás Andruskiewitsch Open problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rowell Open problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Groups – Algebra, Analysis and Category Theory... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a standalone open problem. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,826 | OWR-8415347-003 | Classification and K-Theory of Compact Quantum Groups | Determine when the reduced $C^*$-algebra of a compact quantum group is simple and compute its K-theory, even for the basic examples for which these questions remain open. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-003",
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{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Determine when the reduced $C^*$-algebra of a compact quantum group is simple and compute its K-theory, even for the basic examples for which these questions remain open. | Many basic questions, like simplicity of the reduced C∗ -algebra, calculation of K-theory, etc, remain open for even the easiest examples of compact quantum groups. Again, even for basic examples of compact quantum groups, many questions remain open. Can some of them be classified up to isomorphism? As a general introdu... | corrected_verified | The linked report was inspected; the two explicit research tasks were isolated from introductory prose. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,827 | OWR-8415347-004 | Free Actions of Rigid Tensor Categories on the Hyperfinite Factor | Can every rigid $C^*$-tensor category act freely on the hyperfinite $\mathrm{II}_1$ factor? In the nonamenable case, are there infinitely many such actions up to cocycle conjugacy? What happens for the Temperley–Lieb–Jones categories at index values greater than $4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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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-8415347-004",
"literature-status:partially-solved",
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] | Amenable rigid C-star tensor categories have Rohlin and uniqueness results for actions on properly infinite factors, but existence and classification of free actions on the hyperfinite factor beyond the amenable setting remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1812.04222",
"label": "Tomatsu on centrally free actions"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Can every rigid $C^*$-tensor category act freely on the hyperfinite $\mathrm{II}_1$ factor? In the nonamenable case, are there infinitely many such actions up to cocycle conjugacy? What happens for the Temperley–Lieb–Jones categories at index values greater than $4$? | Beyond amenability, almost all basic questions remain open. Can every rigid C∗ -tensor category “act” freely on the hyperfinite II1 factor? Are there, in the nonamenable case, infinitely many such actions up to “cocycle conjugacy”? What about the Temperley-Lieb-Jones categories at index values > 4? Quantum Groups – Algeb... | corrected_verified | The explicit question or conjecture was isolated from surrounding report prose and its mathematical notation was normalized. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,828 | OWR-8415347-005 | Finite-Growth Hopf Algebras in Yetter–Drinfeld Categories | Let $G$ be a finitely generated group. Classify, or at least characterize, all coradically graded connected Hopf algebras $E=\bigoplus_{n\in\mathbb{N}_0}E_n$ in the Yetter–Drinfeld category ${}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ such that $\operatorname{GKdim}(E\#\mathbb{C}G)<\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-005",
"literature-status:partially-solved",
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] | The finite-GK classification program is complete in important diagonal and selected nondiagonal cases, but the requested classification of all coradically graded connected Hopf algebras over finitely generated nilpotent groups is not complete. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/2504.12206",
"label": "Yang on finite-GK pre-Nichols algebras"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Let $G$ be a finitely generated group. Classify, or at least characterize, all coradically graded connected Hopf algebras $E=\bigoplus_{n\in\mathbb{N}_0}E_n$ in the Yetter–Drinfeld category ${}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ such that $\operatorname{GKdim}(E\#\mathbb{C}G)<\infty$. | This is a report on recent progress in the classification of pointed Hopf algebras with finite Gelfand-Kirillov dimension over the field C, specifically within the method proposed long ago by H.-J. Schneider and the speaker. Let G be a finitely-generated group; by a celebrated result of Gromov, we may assume that G is nilpo... | corrected_verified | The linked report was inspected and its numbered Question 1 was transcribed as a self-contained statement. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,829 | OWR-8415347-006 | Finite-Growth Nichols Algebras over Finitely Generated Groups | Let $G$ be a finitely generated group. Classify all Yetter–Drinfeld modules $V\in{}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ such that the bosonized Nichols algebra satisfies $\operatorname{GKdim}(\mathcal{B}(V)\#\mathbb{C}G)<\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415347-006",
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{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
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{
"url": "https://arxiv.org/abs/2212.08169",
"label": "Angiono--Garcia Iglesias"
},
{
"url": "https://arxiv.org/abs/2312.10505",
"label": "Nichols algebras over Q8"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Let $G$ be a finitely generated group. Classify all Yetter–Drinfeld modules $V\in{}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ such that the bosonized Nichols algebra satisfies $\operatorname{GKdim}(\mathcal{B}(V)\#\mathbb{C}G)<\infty$. | In the situation of Question 1, if V := E 1 \in CG CG YD, then E is a post-Nichols algebra of V . Indeed, the subalgebra of E generated by V is isomorphic to the Nichols algebra B(V ). See the survey [1]. The core of Question 1 is the following. Question 2. Classify all V \in CGCG YD such that GK-dim B(V )\#CG < \infty... | corrected_verified | The linked report was inspected and its numbered Question 2 was transcribed as a self-contained statement. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,830 | OWR-8415347-007 | Classification of Finite-Growth Pre-Nichols Algebras | Let $G$ be a finitely generated group and let $V\in{}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ satisfy $\operatorname{GKdim}(\mathcal{B}(V)\#\mathbb{C}G)<\infty$. Classify the pre-Nichols algebras $R$ of $V$ for which $\operatorname{GKdim}(R\#\mathbb{C}G)<\infty$. In addition, if $\mathcal{O}$ is a finite conjugacy cla... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-007",
"literature-status:partially-solved",
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] | The diagonal finite-GK conjecture and several low-dimensional or block cases have been settled, while the type-C conjecture and the general finite-GK pre-Nichols classification asked here remain open. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
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{
"url": "https://arxiv.org/abs/2504.12206",
"label": "Yang on finite-GK pre-Nichols algebras"
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{
"url": "https://doi.org/10.1112/plms.12559",
"label": "Angiono on nonabelian pointed Hopf algebras"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Let $G$ be a finitely generated group and let $V\in{}^{\mathbb{C}G}_{\mathbb{C}G}\mathcal{YD}$ satisfy $\operatorname{GKdim}(\mathcal{B}(V)\#\mathbb{C}G)<\infty$. Classify the pre-Nichols algebras $R$ of $V$ for which $\operatorname{GKdim}(R\#\mathbb{C}G)<\infty$. In addition, if $\mathcal{O}$ is a finite conjugacy cla... | Question 3. Classify all pre-Nichols algebras R of those V \in CG CG YD with GK-dim B(V )\#CG < \infty such that GK-dim R\#CG < \infty. . Let us focus on Question 2. Using a Theorem of Malcev, we proved recently: Theorem 1. [2] If the support of V contains an infinite conjugacy class, then GK-dim B(V )\#CG = \infty. Let... | corrected_verified | The linked report was inspected; numbered Question 3 and the explicit type-C conjecture were isolated from intervening theorem and survey prose. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,831 | OWR-8415347-009 | Monoidal Invariance of Hopf-Algebra Cohomological Dimension | If Hopf algebras $A$ and $B$ have equivalent linear tensor categories of comodules, must their Hochschild cohomological dimensions agree, $\operatorname{cd}(A)=\operatorname{cd}(B)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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.",
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"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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-8415347-009",
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] | Monoidal invariance of global or cohomological dimension is proved under smoothness, cosemisimplicity, finite-dimensionality, and finite-global-dimension hypotheses, but no unconditional theorem covers the general question. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
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{
"url": "https://arxiv.org/abs/2102.02479",
"label": "Bichon on monoidal invariance"
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{
"url": "https://arxiv.org/abs/2602.12731",
"label": "Bichon on the finite case"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | If Hopf algebras $A$ and $B$ have equivalent linear tensor categories of comodules, must their Hochschild cohomological dimensions agree, $\operatorname{cd}(A)=\operatorname{cd}(B)$? | In this talk, mainly based on [2], I discussed the following question: Question 1. If A and B are Hopf algebras having equivalent linear tensor cate- gories of comodules, do we have cd(A) = cd(B)? Here cd(A) denotes the global dimension of A, which coincides as well with the Hochschild cohomological dimension. The foll... | corrected_verified | The linked report was inspected and numbered Question 1 was isolated from the list of known special cases and talk metadata. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,832 | OWR-8415347-010 | Categorical Determination of KMS-State Structure | Can further information about the structure of KMS states be derived from purely categorical considerations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-8415347-010",
"literature-status:open",
"owr-year:2021"
] | The extracted sentence explicitly leaves open whether categorical data alone determine further structure of KMS states; current categorical classification results do not provide such a general implication. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1603.05519",
"label": "Categorical compact quantum groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Can further information about the structure of KMS states be derived from purely categorical considerations? | However, at present it remains open whether fur- ther information about the structure of KMS-states can be derived from purely categorical considerations. Quantum Groups – Algebra, Analysis and Category Theory 2419 | corrected_verified | The explicit question or conjecture was isolated from surrounding report prose and its mathematical notation was normalized. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,833 | OWR-8415347-011 | Dimension Rigidity of Quantum Automorphism-Group Factors | For a finite-dimensional $C^*$-algebra $B$ equipped with its canonical trace, let $G^+(B)$ denote the compact quantum automorphism group of $B$, and let $L^\infty(G^+(B))$ be its associated von Neumann algebra. For $n = \dim B \geq 5$, does the von Neumann algebra isomorphism class of $L^\infty(G^+(B))$ depend only on ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 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-8415347-011",
"literature-status:open",
"owr-year:2021"
] | The report states the n-only invariance of the isomorphism class as an open problem, and the current search found no primary result proving that the proposed isomorphism class is determined solely by dim B. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | For a finite-dimensional $C^*$-algebra $B$ equipped with its canonical trace, let $G^+(B)$ denote the compact quantum automorphism group of $B$, and let $L^\infty(G^+(B))$ be its associated von Neumann algebra. For $n = \dim B \geq 5$, does the von Neumann algebra isomorphism class of $L^\infty(G^+(B))$ depend only on ... | Let us conclude these results with an open problem: Can Theorem C be used to somehow show that the isomorphism class of L\infty (G+ (B)) only depends on n = dim B? Finally, let us conclude with a strengthening of Theorem A, which says that the embeddings given in that theorem can actually be extended to algebra isomor-... | corrected_verified | The linked report was inspected and the explicit open problem was isolated from the preceding theorem and crossed-product formulas. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,834 | OWR-8415347-012 | Resolved Witt-Group Question on Anisotropic Modular Categories | question: [1, Question 6.8]. Quantum Groups – Algebra, Analysis and Category Theory 2425 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (yes; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; answered in the source)**. E. C. Rowell (joint with S.-H. Ng, Y. Ruan, Y. Wang and Q. Zhang; OWR 44/2021, p. 2425) reports that their work settles Question 6.8 of Davydov–Müger–Nikshych–Ostrik, [J. reine angew. Math. 677 (2013)](https://doi.org/10.1515/crelle... | [
"owr",
"oberwolfach-reports",
"OWR-8415347-012",
"literature-status:open",
"owr-year:2021"
] | The clipped record points to Question 6.8 of the just-infinite C-star algebra paper, asking whether a unique C-star norm on the group algebra forces local finiteness; the published source records this converse as unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://ems.press/content/serial-article-files/43460",
"label": "Just-infinite C-star algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | null | question: [1, Question 6.8]. Quantum Groups – Algebra, Analysis and Category Theory 2425 | unrecoverable | The linked report was inspected: the fragment says that the construction settles the cited Question 6.8, so it does not state a remaining open problem. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,835 | OWR-8415347-013 | Geometric and Sheaf-Theoretic Models of Nichols Algebras | Can bosonization and the reflection functors be interpreted geometrically? Can the associated polynomials be interpreted in geometric terms? Can extensions of local systems, quiver descriptions of perverse sheaves, or asymptotic calculations yield a combinatorial description or finite-presentation results for Nichols a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 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"
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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-8415347-013",
"literature-status:open",
"owr-year:2021"
] | Factorizable perverse sheaves already model a substantial class of Nichols-related braided Hopf algebras, but the report's requested geometric interpretation of bosonization, reflection functors, and the associated polynomial conditions remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1904.09325",
"label": "Shuffle algebras and perverse sheaves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Can bosonization and the reflection functors be interpreted geometrically? Can the associated polynomials be interpreted in geometric terms? Can extensions of local systems, quiver descriptions of perverse sheaves, or asymptotic calculations yield a combinatorial description or finite-presentation results for Nichols a... | Open questions (1) Is it possible to give a geometric interpretation of bosonization and of the reflection functors from I. Can these polynomials be interpreted in geometric terms? 1. Possible directions (1) The extensions j∗ and j!∗ of local systems could be studied by looking at the covering of Sym6= (C) given by Hurw... | corrected_verified | The explicit question or conjecture was isolated from surrounding report prose and its mathematical notation was normalized. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,836 | OWR-8415347-014 | Geometry and Local Systems Behind Finite Nichols Algebras | Can one describe more explicitly the geometry behind $F(K_n)\simeq T_{!*}(V_n)$ for $n=3,4,5$? What can be said about the local systems and sheaves whose Nichols algebras have finite dimension or finite Gelfand–Kirillov dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-014",
"literature-status:open",
"owr-year:2021"
] | The sheaf-theoretic correspondence is established in a broad framework, but an explicit geometric explanation of the stated low-rank identifications and a general description of finite or finite-GK cases are still not known. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1904.09325",
"label": "Shuffle algebras and perverse sheaves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Can one describe more explicitly the geometry behind $F(K_n)\simeq T_{!*}(V_n)$ for $n=3,4,5$? What can be said about the local systems and sheaves whose Nichols algebras have finite dimension or finite Gelfand–Kirillov dimension? | (3) Could one describe more explicitly the geometry behind the fact that F Kn ≃ T!∗ (Vn ) for n = 3, 4, 5? (4) What can we say about the local systems and sheaves for which the cor- responding Nichols algebra is known to be of finite/finite GK dimension? Quantum Groups – Algebra, Analysis and Category Theory 2433 | corrected_verified | The explicit question or conjecture was isolated from surrounding report prose and its mathematical notation was normalized. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,837 | OWR-8415347-015 | Quantum-Group Interpretations of Quasi-Macdonald Polynomials | Do the quasi-polynomial generalizations of symmetric Macdonald polynomials admit natural quantum-group interpretations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-015",
"literature-status:open",
"owr-year:2021"
] | Recent work gives DAHA representations and quasi-polynomial analogues of symmetric Macdonald polynomials, but a natural quantum-group interpretation of these particular generalizations remains an open question. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://doi.org/10.1017/fms.2025.33",
"label": "Quasi-polynomial DAHA representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Do the quasi-polynomial generalizations of symmetric Macdonald polynomials admit natural quantum-group interpretations? | A natural open question is the following: are there natural quantum group in- terpretations of the quasi-polynomial generalisations of the symmetric Macdonald polynomials? Quantum Groups – Algebra, Analysis and Category Theory 2437 | corrected_verified | The linked report was inspected and its explicit open question was isolated verbatim in substance. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,838 | OWR-8415347-016 | Lévy–Khintchine Decomposition for Star-Bialgebras | Characterize the $*$-bialgebras with the Lévy–Khintchine property (LK): every generating functional decomposes into a Gaussian part and a purely non-Gaussian part. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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"
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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-8415347-016",
"literature-status:partially-solved",
"owr-year:2021"
] | The Levy-Khintchine property is proved for commutative bialgebras and several quantum groups, and counterexamples are known, but there is no general characterization of star-bialgebras having property LK. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1510.03292",
"label": "Levy-Khintchine decompositions"
},
{
"url": "https://doi.org/10.1007/s10959-025-01425-w",
"label": "Gaussian functionals on easy quantum groups"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Characterize the $*$-bialgebras with the Lévy–Khintchine property (LK): every generating functional decomposes into a Gaussian part and a purely non-Gaussian part. | In the noncommutative setting, the notion of gaussian GFs was introduced by Schürmann [8] in order to deal with the question whether a similar decomposition would hold for ∗-bialgebras. Still, it remains open to understand which ∗-bialgebras also have the property called (LK), that any GF on it decomposes into the gau... | corrected_verified | The linked report was inspected; the explicit characterization problem was isolated and its terminology retained. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,839 | OWR-8415347-017 | Gaussian Functionals on q-Deformed Compact Lie Groups | Does the Lévy–Khintchine decomposition method for $U_q(n)$ extend to the $q$-deformations $G_q$ of other simple compact Lie groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-017",
"literature-status:partially-solved",
"owr-year:2021"
] | Levy-Khintchine decompositions are established for SUq of arbitrary finite rank and several related quantum groups, while extension to q-deformations of all simple compact Lie groups is not established. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://eprints.lancs.ac.uk/id/eprint/222139/",
"label": "Hunt formula for SUq and Uq"
},
{
"url": "https://arxiv.org/abs/2203.08030",
"label": "Connectedness and Gaussian parts"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Does the Lévy–Khintchine decomposition method for $U_q(n)$ extend to the $q$-deformations $G_q$ of other simple compact Lie groups? | A similar method works also for the quantum group Uq (n), and we conjecture that it can be further extend to q-deformations Gq of other simple compact Lie groups. that they always admit GFs, the latter being necessarily of the form \psi(a) = hv, [\pi(a)−\varepsilon(a)I]vi. In our paper we show that each ηj is determine... | corrected_verified | The linked report was inspected; its concluding conjecture was isolated from a spliced formula and acknowledgements. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,840 | OWR-8415347-018 | Morita Classification of Quantum SU-Two Projective Representations | If $(M_F,\alpha_F)$ is an ergodic coaction of $L^\infty(FO_F)$, does there exist $G\in F_q$ such that $M_G$ is equivariantly $W^*$-Morita equivalent to a coideal von Neumann subalgebra of $L^\infty(FO_G)$? If not, can such coactions be characterized? If $(M,\alpha)$ is an ergodic coaction of $L^\infty(SU_q(2))$ on a ty... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415347-018",
"literature-status:partially-solved",
"owr-year:2021"
] | Projective representations are characterized through actions on type-I factors and cocycle regularity, with explicit SUq of 2 examples, but a complete classification of all such coactions for quantum SUq of 2 remains unavailable. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/1006.2278",
"label": "Projective representations for compact quantum groups"
},
{
"url": "https://arxiv.org/abs/2112.04365",
"label": "Projective representation theory ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | If $(M_F,\alpha_F)$ is an ergodic coaction of $L^\infty(FO_F)$, does there exist $G\in F_q$ such that $M_G$ is equivariantly $W^*$-Morita equivalent to a coideal von Neumann subalgebra of $L^\infty(FO_G)$? If not, can such coactions be characterized? If $(M,\alpha)$ is an ergodic coaction of $L^\infty(SU_q(2))$ on a ty... | • If (MF , \alphaF ) is an ergodic coaction of L\infty (FOF ), does there exist G \in Fq such that MG is equivariantly W∗ -Morita equivalent with a coideal von Neumann subalgebra of L\infty (FOG )? Since one knows explicitly the structure of the von Neumann algebras of coideals of quantum SU (2) [Tom08], this would cla... | corrected_verified | The linked report was inspected and both bullet-point questions were recovered with their hypotheses. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,841 | OWR-8415347-019 | Separated Augmentation Filtrations and Quantum Group Generation | Let $I$ be the augmentation ideal of a Hopf algebra $A$ and set $I^\infty=\bigcap_{n\in\mathbb{N}}I^n$. For which $A$ does $I^\infty=\{0\}$, and more generally how can $A/I^\infty$ be described in terms of $A$? In particular, what is $I^\infty$ for $\mathcal{O}(O_N^+)$? Does there exist a residually torsion-free nilpot... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | partially_solved | null | 2,021 | 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 | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **The Free Orthogonal Quantum Group O_N^+ Is Topologically Generated by SO_N and the Dual of a Free Group Exactly When N ≥ 4: On a Question of Freslon and the Nilpotent Residual of O(O_N^+)** (Alper Ferudun, Mercury Software GmbH). It ... | [
"owr",
"oberwolfach-reports",
"OWR-8415347-019",
"literature-status:partially-solved",
"owr-year:2021"
] | The augmentation residual is characterized for classical compact groups and discrete group algebras, and strong connectedness gives useful generation criteria, but the general compact-quantum-group problem and the final O-plus existence question remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://arxiv.org/abs/2203.08030",
"label": "Connectedness and Gaussian parts"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Let $I$ be the augmentation ideal of a Hopf algebra $A$ and set $I^\infty=\bigcap_{n\in\mathbb{N}}I^n$. For which $A$ does $I^\infty=\{0\}$, and more generally how can $A/I^\infty$ be described in terms of $A$? In particular, what is $I^\infty$ for $\mathcal{O}(O_N^+)$? Does there exist a residually torsion-free nilpot... | This is a Hopf ideal in A and the general question is: Question : For which A does I \infty = \{0\} ? This leads us to the final problem: Question : Does there exist a discrete group Γ which is residually torsion-free + nilpotent and such that ON b? is topologically generated by SON and Γ Let A be a Hopf algebra and let... | corrected_verified | The linked report was inspected and all three explicit questions were restored from the OCR-corrupted extraction. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,842 | OWR-8415347-020 | Genuine Finite-Growth Nichols Algebras over Nonabelian Groups | Find a genuine Nichols algebra over a nonabelian group whose support is nonabelian, whose dimension is infinite, and whose Gelfand–Kirillov dimension is finite. In particular, for the rack of transpositions in $S_3$, what is the Nichols algebra corresponding to the constant cocycle $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458](https://doi.org/10.4171/owr/2021/44)
## Literature review (chec... | 3 | open | null | 2,021 | 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-8415347-020",
"literature-status:open",
"owr-year:2021"
] | Finite-dimensional and selected nonabelian Nichols algebras have been determined, but no genuine nonabelian-support Nichols algebra satisfying the requested infinite-dimension and finite-GK conditions has been identified or classified in general. | [
{
"url": "https://doi.org/10.4171/owr/2021/44",
"label": "Oberwolfach Report 44"
},
{
"url": "https://doi.org/10.1112/plms.12559",
"label": "Pointed Hopf algebras over nonabelian groups"
},
{
"url": "https://arxiv.org/abs/2504.12206",
"label": "Finite-GK pre-Nichols algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/44 | null | null | null | Find a genuine Nichols algebra over a nonabelian group whose support is nonabelian, whose dimension is infinite, and whose Gelfand–Kirillov dimension is finite. In particular, for the rack of transpositions in $S_3$, what is the Nichols algebra corresponding to the constant cocycle $1$? | Open problem Nicolás Andruskiewitsch Question. (N.A.) Find a genuine Nichols algebra over a non-abelian group whose support is not abelian, it has infinite dimension and finite GK-dimension. (Here genuine means excluding any trivial example). What is the Nichols algebra corresponding to the constant cocycle equal to 1? ... | corrected_verified | The linked report was inspected; the author label was removed and the example omitted by the extraction was restored. | null | null | null | null | null | Quantum Groups – Algebra, Analysis and Category Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/44, pp. 2397--2458 |
30,004,843 | OWR-8415348-001 | Bilinear Wave–Schrödinger Restriction Without Transversality | Determine the admissible exponents and sharp scale dependence in bilinear restriction estimates for wave–Schrödinger interactions when the transversality assumption is removed. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/45, pp. 2459--2496](https://doi.org/10.4171/owr/2021/45)
## Literatur... | 3 | open | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415348-001",
"literature-status:open",
"owr-year:2021"
] | The transference principle proves bilinear restriction estimates for the stated endpoint space in the available transverse setting, but the sharp estimate after removing the transversality assumption remains open and is tied to Zakharov regularity. | [
{
"url": "https://doi.org/10.4171/owr/2021/45",
"label": "Oberwolfach Report 45"
},
{
"url": "https://arxiv.org/abs/1605.04882",
"label": "Transference of bilinear restriction estimates"
},
{
"url": "https://arxiv.org/abs/2005.09932",
"label": "Energy-critical Zakharov system"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/45 | null | null | null | Determine the admissible exponents and sharp scale dependence in bilinear restriction estimates for wave–Schrödinger interactions when the transversality assumption is removed. | This open problem is of particular interest due to connections with the regularity theory for the Zakharov equation. This talk describes two recent results. The first is joint work with S. Herr and K. Nakanishi [3], and gives a fairly general method to show that bilinear restriction estimates on R4 for free (or homogen... | corrected_verified | The linked report was inspected; the open question following the sharp transverse estimate was recovered from the talk summary. | null | null | null | null | null | MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/45, pp. 2459--2496 |
30,004,844 | OWR-8415348-002 | Local Smoothing for the Euclidean Wave Equation | For the Euclidean half-wave propagator on $\mathbb{R}^n$, prove the local smoothing estimate $\left(\int_0^1\lVert e^{it\sqrt{-\Delta}}f\rVert_{L^p(\mathbb{R}^n)}^p\,dt\right)^{1/p}\leq C_\varepsilon\lVert f\rVert_{W^{\sigma(p)+\varepsilon,p}(\mathbb{R}^n)}$ for every $\varepsilon>0$ in the conjectured range, where $\s... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/45, pp. 2459--2496](https://doi.org/10.4171/owr/2021/45)
## Literatur... | 3 | partially_solved | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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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-8415348-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The local smoothing conjecture is proved in two spatial dimensions and has broad decoupling-based partial ranges, but the full general conjecture, especially in higher dimensions, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/45",
"label": "Oberwolfach Report 45"
},
{
"url": "https://arxiv.org/abs/2106.05101",
"label": "Local smoothing and Hardy spaces"
},
{
"url": "https://arxiv.org/abs/2010.14390",
"label": "Square functions and local smoothing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/45 | null | null | null | For the Euclidean half-wave propagator on $\mathbb{R}^n$, prove the local smoothing estimate $\left(\int_0^1\lVert e^{it\sqrt{-\Delta}}f\rVert_{L^p(\mathbb{R}^n)}^p\,dt\right)^{1/p}\leq C_\varepsilon\lVert f\rVert_{W^{\sigma(p)+\varepsilon,p}(\mathbb{R}^n)}$ for every $\varepsilon>0$ in the conjectured range, where $\s... | Although the local smoothing conjecture is still open in full generality, there are many partial results available, and the conjecture was proved by Guth, Wang and Zhang [2] for n = 2. Local smoothing and Hardy spaces for Fourier integral operators Jan Rozendaal for s = d(p) + \varepsilon, where ( 2s(p) − p1 if p \geq ... | corrected_verified | The linked report was inspected and the full local-smoothing conjecture was reconstructed from its displayed definition and piecewise exponent. | null | null | null | null | null | MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/45, pp. 2459--2496 |
30,004,845 | OWR-8415349-001 | Bubble-Free Criterion for Polygraphic and Nerve Homology | For a two-dimensional polygraph, does its polygraphic homology coincide with the homology of its nerve if and only if the polygraph is bubble-free? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560](https://doi.org/10.4171/owr/2021/46)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-8415349-001",
"literature-status:open",
"owr-year:2021"
] | The clipped record is the bubble-free conjecture: equality of polygraphic homology and nerve homology exactly for bubble-free two-dimensional polygraphs; the primary work states it as a conjecture and does not prove it generally. | [
{
"url": "https://doi.org/10.4171/owr/2021/46",
"label": "Oberwolfach Report 46"
},
{
"url": "https://arxiv.org/abs/2104.12662",
"label": "Homology of strict omega-categories"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/46 | null | null | null | For a two-dimensional polygraph, does its polygraphic homology coincide with the homology of its nerve if and only if the polygraph is bubble-free? | conjecture . . . . . . . . . 2505 Philip Hackney (joint with Viktoriya Ozornova, Emily Riehl, Martina Rovelli) On pasting in (\infty, 2)-categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 Julian Holstein (joint with Andrey Lazarev) Categorical Koszul Duality . . . . . . . . . . . . ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560 |
30,004,846 | OWR-8415349-004 | String Diagram Models of Moduli Spaces | Is the string-diagram cell complex $SD$ homotopy equivalent to the moduli space of Riemann surfaces with boundary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560](https://doi.org/10.4171/owr/2021/46)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415349-004",
"literature-status:open",
"owr-year:2021"
] | String diagrams support chain-level string-topology operations and related graph models have been compared, but the stated homotopy equivalence with the moduli space of Riemann surfaces with boundary remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/46",
"label": "Oberwolfach Report 46"
},
{
"url": "https://arxiv.org/abs/1506.02596",
"label": "Chain-level string topology operations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/46 | null | null | null | Is the string-diagram cell complex $SD$ homotopy equivalent to the moduli space of Riemann surfaces with boundary? | Assocoipahedra and the moduli space of Riemann surfaces. The met- ric condition defining short-branched trees is related to an equivalence relation appearing in Bodigheimer’s work on the moduli space of Riemann surfaces [1]; the short-branched trees in some sense “interpolate” between equivalent cells in his harmonic c... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560 |
30,004,847 | OWR-8415349-005 | $I$-Chain Models of Spaces in Coalgebras and Lie Algebras | Can $I$-chains be used to construct models of spaces in differential graded cocommutative coalgebras and Lie algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560](https://doi.org/10.4171/owr/2021/46)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415349-005",
"literature-status:open",
"owr-year:2021"
] | I-chain homotopy colimits produce E-infinity coalgebras, but the known obstruction to the expected left-induced model structures prevents a complete Lie or cocommutative-coalgebra model of spaces of the requested kind. | [
{
"url": "https://doi.org/10.4171/owr/2021/46",
"label": "Oberwolfach Report 46"
},
{
"url": "https://www.math.uni-hamburg.de/en/personen/richter/ichains100822.pdf",
"label": "Comonoidal properties of I-chains"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/46 | null | null | null | Can $I$-chains be used to construct models of spaces in differential graded cocommutative coalgebras and Lie algebras? | Can we use I-chains to obtain models of spaces in the setting of differential graded cocommutative coalgebras and Lie-algebras? Canonical E\infty -operads involved in homotopy colimits of I-chain complexes Birgit Richter | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560 |
30,004,848 | OWR-8415349-006 | Del Pezzo Surfaces and Iterated Cyclic Loop Spaces | Is there an explicit relation between the del Pezzo surfaces $B_k$ and the iterated cyclic loop spaces $L_c^kS^4$ for $0\leq k\leq8$ that matches their $E_k$ symmetry patterns and relates geometric data such as curve volumes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560](https://doi.org/10.4171/owr/2021/46)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415349-006",
"literature-status:open",
"owr-year:2021"
] | The exceptional E-sub-k data and parabolic symmetries of iterated cyclic or toroidified loop spaces have been constructed, but the conjectured explicit geometric relation to del Pezzo surfaces remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2021/46",
"label": "Oberwolfach Report 46"
},
{
"url": "https://arxiv.org/abs/2111.14810",
"label": "Mysterious Triality and Rational Homotopy"
},
{
"url": "https://arxiv.org/abs/2408.13337",
"label": "Exceptional symmetry of loop spaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/46 | null | null | null | Is there an explicit relation between the del Pezzo surfaces $B_k$ and the iterated cyclic loop spaces $L_c^kS^4$ for $0\leq k\leq8$ that matches their $E_k$ symmetry patterns and relates geometric data such as curve volumes? | Conjecture. There must be an explicit relation between the series of del Pezzo surfaces Bk , 0 \leq k \leq 8, and the series of iterated cyclic loop spaces Lkc S 4 , 0 \leq k \leq 8. This relation should match the Ek symmetry patterns occurring in both series, as well as relate other geometric data, such as the volumes... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560 |
30,004,849 | OWR-8415349-008 | Algebraic Structures and Applications of Two-Dimensional Field Theories | For two-dimensional topological conformal or homological conformal field theories, what are the appropriate algebraic structures, do nontrivial examples exist, and what applications do they have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560](https://doi.org/10.4171/owr/2021/46)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415349-008",
"literature-status:partially-solved",
"owr-year:2021"
] | Costello gives a major algebraic classification of open and open-closed TCFTs through Calabi--Yau A\infty categories, and many nontrivial examples and applications are known; the broader TCFT/HCFT classification and usefulness questions in the record remain incomplete. | [
{
"url": "https://doi.org/10.1016/j.aim.2006.06.004",
"label": "Costello, TCFTs and Calabi--Yau categories"
},
{
"url": "https://ems.press/content/serial-article-files/46922",
"label": "OWR report stating the remaining questions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/46 | null | null | null | For two-dimensional topological conformal or homological conformal field theories, what are the appropriate algebraic structures, do nontrivial examples exist, and what applications do they have? | In this talk, we considered the following questions: (1) What is a 2d–TCFT or 2d–HCFT as an algebraic structure? i.e., what could be an analogue of the above theorem in those cases? (2) Are there non-trivial examples? (3) Are such field theories useful for anything? from CobC 2 ∗ to the dg-category of chain complexes a... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Homotopical Algebra and Higher Structures (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/46, pp. 2497--2560 |
30,004,850 | OWR-8415350-001 | Unspecified Surface Singularity Conjecture | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . 2619 Baldur Sigurðsson (joint with András Némethi) Local Newton nondegenerate Weil divisors in toric varieties . . . . . . . . . . . 2621 Jan Stevens (joint with Gavin Brown and Miles Reid) Tom and Jerry . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 record is only a table-of-contents fragment and contains no identifiable conjecture. No separate clea) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-001",
"literature-status:open",
"owr-year:2021"
] | The extracted record is only a table-of-contents fragment ending in `Conjecture' and does not identify a mathematical claim; under the requested rule an unresolvable claim is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . 2619 Baldur Sigurðsson (joint with András Némethi) Local Newton nondegenerate Weil divisors in toric varieties . . . . . . . . . . . 2621 Jan Stevens (joint with Gavin Brown and Miles Reid) Tom and Jerry . . . . . . . . . . . . . . . . . . . . . . . . . . . .... | unrecoverable | The official report confirms that this record is only a table-of-contents fragment and contains no identifiable conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,851 | OWR-8415350-002 | Non-Archimedean Wilkie-Type Point-Counting Bounds | Conjecture (namely with polylogarithmic instead of subexponential upper bounds). In fact, bounds for rational points on definable sets in non-archimedean set- tings have many faces. On subsets of Qnp , one can count actual rational points of bounded height, where on subsets of C((t))n one rather ”counts” the polynomials... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 reports results in each of the listed non-Archimedean settings, including a proved Pfaffian analogue of Wilkie's c) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-002",
"literature-status:open",
"owr-year:2021"
] | The record truncates the conjecture and mixes several non-archimedean point-counting settings, so its exact claim cannot be uniquely verified; the literature proves Pfaffian/Noetherian special cases but also shows arbitrarily fast growth for general analytic sets. | [
{
"url": "https://doi.org/10.1215/00127094-2022-0013",
"label": "Binyamini--Cluckers--Novikov, non-archimedean point counting"
},
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | null | Conjecture (namely with polylogarithmic instead of subexponential upper bounds). In fact, bounds for rational points on definable sets in non-archimedean set- tings have many faces. On subsets of Qnp , one can count actual rational points of bounded height, where on subsets of C((t))n one rather ”counts” the polynomials... | unrecoverable | The official contribution reports results in each of the listed non-Archimedean settings, including a proved Pfaffian analogue of Wilkie's conjecture, rather than posing the extracted statement as an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,852 | OWR-8415350-003 | Floer Cohomology and Contact Loci of Jets | 4. Main result We have the following conjecture: Conjecture 2 ([BdBLN20]). There is an isomorphism HF ∗ (\phid ) \sim f = H ∗+2nd+n−1 (χd (f )) c ∗ where Hc means compactly supported cohomology. Such a conjecture was verified by the same authors when d is equal to the multiplicity of f at 0. Theorem 3 (M., in progress).... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 states immediately after the displayed conjecture that the asserted isomorphism is true in general as a theorem in) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-003",
"literature-status:partially-solved",
"owr-year:2021"
] | The general arc--Floer isomorphism remains open, but it is proved in the original work when the iterate equals the multiplicity and in important special families; hyperplane arrangements and 2025 semihomogeneous results establish substantial further cases. | [
{
"url": "https://doi.org/10.4310/jdg/1649953456",
"label": "Budur--Fernández de Bobadilla--Lê--Nguyen, cohomology of contact loci"
},
{
"url": "https://arxiv.org/abs/2506.18805",
"label": "de Lorenzo Poza--Huang, semihomogeneous contact loci"
},
{
"url": "https://doi.org/10.4171/owr/202... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | null | 4. Main result We have the following conjecture: Conjecture 2 ([BdBLN20]). There is an isomorphism HF ∗ (\phid ) \sim f = H ∗+2nd+n−1 (χd (f )) c ∗ where Hc means compactly supported cohomology. Such a conjecture was verified by the same authors when d is equal to the multiplicity of f at 0. Theorem 3 (M., in progress).... | unrecoverable | The official contribution states immediately after the displayed conjecture that the asserted isomorphism is true in general as a theorem in progress, so it is not presented there as a still-open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,853 | OWR-8415350-004 | Pair-of-Pants Products on Contact Loci of Jets | Under the isomorphisms $HF^*(\phi_f^d)\cong H_c^{*+2nd+n-1}(\chi_d(f))$, which operation on $\bigoplus_dH_c^*(\chi_d(f))$ corresponds to the pair-of-pants product on $\bigoplus_dHF^*(\phi_f^d)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 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-8415350-004",
"literature-status:open",
"owr-year:2021"
] | The report explicitly poses the pair-of-pants product correspondence as a further direction; the subsequent arc--Floer literature establishes cohomological cases but does not identify this product in general. | [
{
"url": "https://ems.press/content/serial-article-files/46924",
"label": "OWR report posing the product question"
},
{
"url": "https://doi.org/10.4310/jdg/1649953456",
"label": "Cohomology of contact loci"
},
{
"url": "https://arxiv.org/abs/2506.18805",
"label": "Recent special-case... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | Under the isomorphisms $HF^*(\phi_f^d)\cong H_c^{*+2nd+n-1}(\chi_d(f))$, which operation on $\bigoplus_dH_c^*(\chi_d(f))$ corresponds to the pair-of-pants product on $\bigoplus_dHF^*(\phi_f^d)$? | What does this product correspond to in ⊕d Hc∗ (χd (f ))? 4. Main result We have the following conjecture: Conjecture 2 ([BdBLN20]). There is an isomorphism HF ∗ (\phid ) \sim f = H ∗+2nd+n−1 (χd (f )) c ∗ where Hc means compactly supported cohomology. Such a conjecture was verified by the same authors when d is equal t... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,854 | OWR-8415350-005 | Arc-Space Models of Contact Homology | Can the contact-homology algebra be computed from the space of short arcs? Is there an arc-space version of its spectral sequence? For a two-dimensional singularity, can the embedded contact homology of its link be described in terms of arcs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-005",
"literature-status:open",
"owr-year:2021"
] | Short-arc spaces are understood for surface singularities and isolated quotient singularities, but the proposed algebraic computation of contact homology and an arc-space spectral sequence for embedded contact homology remain open research directions. | [
{
"url": "https://doi.org/10.1007/s00222-014-0530-3",
"label": "Kollár--Némethi, holomorphic and short arcs"
},
{
"url": "https://ems.press/content/serial-article-files/46924",
"label": "OWR report posing the contact-homology question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | Can the contact-homology algebra be computed from the space of short arcs? Is there an arc-space version of its spectral sequence? For a two-dimensional singularity, can the embedded contact homology of its link be described in terms of arcs? | Can one compute such an algebra from the space of short arcs on A [KN14]? Is there an arc space version of this spectral sequence? If the singularity A is of dimension 2, then can one describe embedded contact homology [Hut14] of its link in terms of arcs? The report passage is retained verbatim as the relevant context... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,855 | OWR-8415350-006 | Igusa Bounds for Finite-Ring Exponential Sums | Let $f\in\mathbb Z[x_1,\ldots,x_n]$ be nonconstant of degree $d>1$, let $f_d$ be its highest-degree homogeneous part, and let $s$ be the dimension of the critical locus of $f_d$. For every $\varepsilon>0$ and prime $p$, is there a $C_{p,\varepsilon}>0$ such that
$$
|E_f(p,m)|\leq C_{p,\varepsilon}p^{m(-(n-s)/d+\varepsi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** partially so... | 3 | partially_solved | null | 2,021 | 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-8415350-006",
"literature-status:partially-solved",
"owr-year:2021"
] | Igusa-type bounds are proved for nonrational singularities and in several special cases, including at most three variables for the rational-singularity case and at most four variables or nondegenerate polynomials for the stated exponent; the general conjecture remains unresolved. | [
{
"url": "https://doi.org/10.1017/fmp.2019.3",
"label": "Cluckers--Mustaţă--Nguyen, optimal nonrational estimates"
},
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "OWR report recording the remaining cases"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | Let $f\in\mathbb Z[x_1,\ldots,x_n]$ be nonconstant of degree $d>1$, let $f_d$ be its highest-degree homogeneous part, and let $s$ be the dimension of the critical locus of $f_d$. For every $\varepsilon>0$ and prime $p$, is there a $C_{p,\varepsilon}>0$ such that
$$
|E_f(p,m)|\leq C_{p,\varepsilon}p^{m(-(n-s)/d+\varepsi... | conjecture. To go further on applications of Igusa’s conjecture on exponential sums, we need to work with the case of rational singularities. Recently, in a joint work with Veys, we proved this conjecture when f is in at most three variables. The proof follows by the classification for rational singularities of polynomi... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,856 | OWR-8415350-007 | Negativity of Log Divisors on Q-Acyclic Surfaces | If $S$ is a complex $\mathbb Q$-acyclic surface and $(X,D)$ is a log-smooth completion, is
$$
\kappa\!\left(K_X+\frac12D\right)=-\infty
$$
? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415350-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-007",
"literature-status:open",
"owr-year:2021"
] | The Negativity Conjecture for every complex Q-acyclic surface is still open; Pełka completely classifies the smooth Q-homology planes satisfying the conjecture, which is a conditional classification rather than a proof of the universal assertion. | [
{
"url": "https://doi.org/10.1112/jlms.12779",
"label": "Pełka, smooth Q-homology planes satisfying negativity"
},
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "OWR statement that the conjecture remains open"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | If $S$ is a complex $\mathbb Q$-acyclic surface and $(X,D)$ is a log-smooth completion, is
$$
\kappa\!\left(K_X+\frac12D\right)=-\infty
$$
? | Conjecture (Negativity Conjecture, [Pal19, 4.7]). Let S be a complex Q-acyclic surface and let (X, D) be a log smooth completion. Then κ(KX + 12 D) = −\infty. Finding almost log exceptional curves allowed to group rational cuspidal curves into series in which one curve is obtained inductively from another in a simple m... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,857 | OWR-8415350-008 | Unspecified Rank-One Del Pezzo Surface Conjecture | So far the latter conjecture remains open. Theorem. Let X be a normal del Pezzo surface of rank 1 defined over an alge- braically closed field k. Assume that char k 6= 2. Then X \sim = P2 or the minimal log resolution (X, D) of X has a P1 -fibration such that f \cdot D \leq 4 for a general fiber f . | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 phrase 'the latter conjecture remains open' refers back to the Negativity Conjecture retained in OWR-8415350-007; the following rank-one) | [
"OWR-8415350-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415350-008",
"literature-status:open",
"owr-year:2021"
] | The record says that the latter conjecture remains open but omits the antecedent, so the exact mathematical claim cannot be identified or checked; it is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | null | So far the latter conjecture remains open. Theorem. Let X be a normal del Pezzo surface of rank 1 defined over an alge- braically closed field k. Assume that char k 6= 2. Then X \sim = P2 or the minimal log resolution (X, D) of X has a P1 -fibration such that f \cdot D \leq 4 for a general fiber f . | unrecoverable | The phrase 'the latter conjecture remains open' refers back to the Negativity Conjecture retained in OWR-8415350-007; the following rank-one del Pezzo statement is explicitly a theorem, not another conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,858 | OWR-8415350-009 | Topological Determination of Polar Curve Positions | Does the topological type of a complex surface germ $(X,0)$ restrict the possible relative positions of its polar-curve families? For which classes of surface germs are those relative positions determined by the topological type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 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-8415350-009",
"literature-status:open",
"owr-year:2021"
] | Polar-exploration work proves finite topological bounds and determines substantial combinatorial data, but the exact relative-position determination asked for in the record is not established in general. | [
{
"url": "https://arxiv.org/abs/2103.15444",
"label": "Belotto da Silva--Fantini--Némethi--Pichon, polar exploration"
},
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "OWR formulation of the question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | Does the topological type of a complex surface germ $(X,0)$ restrict the possible relative positions of its polar-curve families? For which classes of surface germs are those relative positions determined by the topological type? | Does the topological type of (X, 0) “restrict” the possibilities of relative positions between these families of curves? Can we find special classes of surfaces (X, 0) for which the relative positions between these families of curves are determined by the topological type? Polar exploration of complex surface germs Anne... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,859 | OWR-8415350-011 | Zariski's Multiplicity Conjecture | Let $f,g:(\mathbb C^n,0)\to(\mathbb C,0)$ be reduced complex analytic functions. If there is a homeomorphism $\phi:(\mathbb C^n,0)\to(\mathbb C^n,0)$ with $\phi(V(f))=V(g)$, must $m(V(f),0)=m(V(g),0)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639](https://doi.org/10.4171/owr/2021/47)
## Literature review (checked 2026-08-22)
**Status:** open
**Asse... | 3 | open | null | 2,021 | 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-8415350-011",
"literature-status:open",
"owr-year:2021"
] | The report explicitly states that the referenced problem is still open and that the real case does not satisfy the complex formulation in the same way; no later primary result located here settles the general claim. | [
{
"url": "https://doi.org/10.4171/owr/2021/47",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/47 | null | null | null | Let $f,g:(\mathbb C^n,0)\to(\mathbb C,0)$ be reduced complex analytic functions. If there is a homeomorphism $\phi:(\mathbb C^n,0)\to(\mathbb C^n,0)$ with $\phi(V(f))=V(g)$, must $m(V(f),0)=m(V(g),0)$? | This is still an open problem, and in the real case it does not hold in the same form as in the complex case. On the Fukui-Kurdyka-Paunescu Conjecture José Edson Sampaio (joint work with Alexandre Fernandes and Zbigniew Jelonek) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Singularities (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/47, pp. 2573--2639 |
30,004,860 | OWR-8415352-001 | Deciding Positivity in Star Algebras | How can one decide whether an element of a $*$-algebra is positive, meaning that it maps to a positive operator in every $*$-representation on a Hilbert space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 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-8415352-001",
"literature-status:partially-solved",
"owr-year:2021"
] | There is no single test for arbitrary star-algebras, but the problem is sharply resolved in important classes: free-group positivity has effective procedures, whereas positivity in tensor products of free algebras is coRE-hard and hence undecidable in the algorithmic sense. | [
{
"url": "https://doi.org/10.4171/JEMS/1786",
"label": "Mehta--Slofstra--Zhao, positivity is undecidable in tensor products"
},
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR formulation and free-group special case"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | How can one decide whether an element of a $*$-algebra is positive, meaning that it maps to a positive operator in every $*$-representation on a Hilbert space? | How do we test if an element of a ∗-algebra is positive? (For this talk, an element of a ∗-algebra is positive if it maps to a positive operator in every ∗-representation on a Hilbert space). Decision problems for positivity and sums of squares William Slofstra (joint work with Arthur Mehta, Yuming Zhao) | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,861 | OWR-8415352-003 | Submultiplicativity Gaps for Stabilizer Extent | How large can the submultiplicativity gap between $\xi(\phi\otimes\psi)$ and $\xi(\phi)\xi(\psi)$ be for quantum states $\phi$ and $\psi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415352-003",
"literature-status:partially-solved",
"owr-year:2021"
] | The gap is known to be positive because strict submultiplicativity exists, and multiplicativity is proved for several low-qubit and structured families; the general extremal size or asymptotic behavior of the gap remains open. | [
{
"url": "https://doi.org/10.22331/q-2021-02-24-400",
"label": "Heimendahl--Montealegre-Mora--Vallentin--Gross"
},
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR statement of the gap question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | How large can the submultiplicativity gap between $\xi(\phi\otimes\psi)$ and $\xi(\phi)\xi(\psi)$ be for quantum states $\phi$ and $\psi$? | Open questions An interesting open question is how large the gap can get between ξ(\phi ⊗ \psi) and ξ(\phi)ξ(\phi) for states |\phii and |\psii. That is, even if X X \psi= cs s, \phi= ds s, s\inStabn s\inStabn p P p P are optimal (i.e. such that ξ(\psi) = Ps |cs | and ξ(\phi) = s |ds |), it can hap- pen that the decomp... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,862 | OWR-8415352-004 | Mutually Unbiased Bases in Non-Prime-Power Dimensions | For which pairs $(d,k)$ do there exist $k$ mutually unbiased bases in dimension $d$, particularly when $d$ is not a prime power? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-8415352-004",
"literature-status:partially-solved",
"owr-year:2021"
] | For prime-power dimensions a complete set of d+1 mutually unbiased bases exists, while the maximum number in non-prime-power dimensions remains unknown; dimension six already lacks a proof of whether four bases exist despite strong computational evidence. | [
{
"url": "https://doi.org/10.1016/0003-4916(89)90322-9",
"label": "Wootters--Fields, prime-power construction"
},
{
"url": "https://doi.org/10.1103/PhysRevA.83.062303",
"label": "Raynal--Lü--Englert, dimension-six evidence"
},
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | For which pairs $(d,k)$ do there exist $k$ mutually unbiased bases in dimension $d$, particularly when $d$ is not a prime power? | A natural question is for which pairs (d, k) there exist k mutually unbiased bases in dimension d. However, for all d that are not a power of a prime the question is wide open. This conjecture is widely believed, but there is no formal proof. Mutually unbiased bases, polynomial optimization \& symmetry Sander Gribling ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,863 | OWR-8415352-005 | Symmetry Structure of Mutually Unbiased Bases | What is the symmetry in the MUB problem? 1For t = 1 the separate actions of S on C[d]t and S on C[k]t are transitive and the analytic d k decomposition can be obtained for example from [5, Thrm. 3.1.1]. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this question as an expository heading and immediately identifies the wreath-product symmetry acting on the mutuall) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415352-005",
"literature-status:open",
"owr-year:2021"
] | The symmetry question is posed without a precise mathematical target, and the current MUB literature supplies constructions and constraints but no general symmetry principle answering this record. | [
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR report posing the symmetry question"
},
{
"url": "https://doi.org/10.1103/PhysRevA.83.062303",
"label": "Primary dimension-six MUB analysis"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | null | What is the symmetry in the MUB problem? 1For t = 1 the separate actions of S on C[d]t and S on C[k]t are transitive and the analytic d k decomposition can be obtained for example from [5, Thrm. 3.1.1]. | unrecoverable | The official report uses this question as an expository heading and immediately identifies the wreath-product symmetry acting on the mutually unbiased bases problem; it is not a distinct unresolved claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,864 | OWR-8415352-006 | Algorithms for Symmetry-Reduced Semidefinite Programs | Can the small number of variables in symmetry-reduced semidefinite programs be exploited to obtain faster algorithms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415352-006",
"literature-status:open",
"owr-year:2021"
] | Symmetry reduction is effective for the reported SDPs, but the record asks for a further general exploitation of the reduced variable count and gives no theorem resolving that algorithmic question. | [
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR report posing the SDP question"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | Can the small number of variables in symmetry-reduced semidefinite programs be exploited to obtain faster algorithms? | A second, more open problem is whether it is possible to further exploit the small number of variables in the symmetry reduced SDPs. Table 1. We give the number of rows of the original t-th level SDP, and for the symmetry reduced SDP the number of variables, the sum and max of the block sizes, and the solver status. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,865 | OWR-8415352-007 | Completeness of Realignment and SIC-POVM Entanglement Tests | Without preliminary reshuffling of the subsystems, is the family of realignment and SIC-POVM entanglement tests complete? Which multipartite mixed states can these tests detect, and how do the two families compare in detection performance? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415352-007",
"literature-status:partially-solved",
"owr-year:2021"
] | The tester framework proves completeness for bipartite states after allowing index permutations and detects all entangled pure multipartite states, but completeness without reshuffling and for general mixed multipartite states remains open. | [
{
"url": "https://doi.org/10.1007/s00023-022-01187-9",
"label": "Jivulescu--Lancien--Nechita, multipartite entanglement testers"
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{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR report listing the unresolved cases"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | Without preliminary reshuffling of the subsystems, is the family of realignment and SIC-POVM entanglement tests complete? Which multipartite mixed states can these tests detect, and how do the two families compare in detection performance? | Another natural question that we ask is whether our family of entanglement criteria is complete, i.e. in other words, whether any entangled state can be detected by a tester. Are there interesting classes of multipartite mixed states whose entanglement can be detected by the realignment or SIC POVM testers? Geometry an... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,866 | OWR-8415352-008 | Spin-Alignment Entropy Conjecture | Fix a mixed one-spin state $Q$. Consider $n$-spin density operators formed as convex combinations of states in which a chosen subset of spins is fixed to a product of copies of $Q$ and the remaining spins have variable joint states. Is the entropy minimized when every variable joint state is a product of copies of one ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415352-008",
"literature-status:partially-solved",
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] | The spin-alignment conjecture is proved for several special cases, including integer Schatten norms, classical freely chosen states, and two-state mixtures with projector Q; the full entropy-minimization conjecture remains unresolved. | [
{
"url": "https://doi.org/10.1007/s00220-024-04980-1",
"label": "Alhejji--Knill, towards a resolution of spin alignment"
},
{
"url": "https://doi.org/10.4171/owr/2021/49",
"label": "OWR statement of the conjecture"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | Fix a mixed one-spin state $Q$. Consider $n$-spin density operators formed as convex combinations of states in which a chosen subset of spins is fixed to a product of copies of $Q$ and the remaining spins have variable joint states. Is the entropy minimized when every variable joint state is a product of copies of one ... | Spin alignment conjecture. We now provide a short description of a conjecture about the entropy of spins. Subject to this conjecture, Q(1) (Ns ) = Q(Ns ). First, consider a single spin-1/2 particle whose density operator ρ is a convex combina- tion of a given mixed state Q and some variable state \omega. The minimum en... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,867 | OWR-8415352-009 | Analytical Performance Theory for QAOA and RQAOA | Develop an analytical account of the performance and limitations of QAOA and RQAOA in the resource-limited NISQ regime. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "computer_science",
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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",
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"OWR-8415352-009",
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] | Analytical bounds and limitation results for QAOA and RQAOA have accumulated, but a general theory of performance, scaling, and parameter choice remains an open problem, as the record states. | [
{
"url": "https://doi.org/10.1103/PhysRevLett.124.090504",
"label": "Akshay--Philathong--Morales--Biamonte, QAOA reachability deficits"
},
{
"url": "https://doi.org/10.4171/owr/2021/49",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | Develop an analytical account of the performance and limitations of QAOA and RQAOA in the resource-limited NISQ regime. | Especially in the resource limited NISQ era, further analytical understanding of both QAOA and RQAOA is an important open problem. Figure 1. Approximation ratios for (n, d) = (60, 6) (left) and (300, 6) (right), respectively. The guaranteed worst-case approxi- mation ratio of Newman’s algorithm is indicated by the hori... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,868 | OWR-8415352-010 | Quantum Complexity of High-Precision Matrix Scaling | Can a quantum algorithm improve the $\widetilde O(m^{3/2})$ high-precision running time for general matrix scaling while retaining polylogarithmic dependence on $1/\varepsilon$? For a dense nonnegative $n\times n$ matrix whose entries sum to at most $1$, what is the quantum query complexity of approximating its row-sum... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415352-010",
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{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol219-stacs2022/LIPIcs.STACS.2022.35/LIPIcs.STACS.2022.35.pdf",
"label": "Gribling--Nieuwboer, quantum matrix-scaling bounds"
},
{
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"label": "OWR formulation of the open problem"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | Can a quantum algorithm improve the $\widetilde O(m^{3/2})$ high-precision running time for general matrix scaling while retaining polylogarithmic dependence on $1/\varepsilon$? For a dense nonnegative $n\times n$ matrix whose entries sum to at most $1$, what is the quantum query complexity of approximating its row-sum... | However, some open problems remain. For general matrices, the interior-point method of [10] has the best guarantees in the high-precision regime, finding an e m1.5 ; a natural question is whether this can be reduced \varepsilon-ℓ1 -scaling in time O with a quantum algorithm while retaining the polylogarithmic 1/\vareps... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,869 | OWR-8415352-012 | Polyhedral Cones of Graph Profile Inequality Exponents | For a finite collection $U$ of connected graphs, do the exponents of binomial inequalities valid on the profile $G_U$ form a polyhedral cone, and if so is it necessarily a rational polyhedral cone? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720](https://doi.org/10.4171/owr/2021/49)
## Literature review (checked 20... | 3 | open | null | 2,021 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415352-012",
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] | Blekherman, Raymond, Singh, and Thomas prove convexity and compute important special cases, but state the general polyhedral and rational-polyhedral questions for graph-profile binomial exponents as open. | [
{
"url": "https://arxiv.org/abs/2004.05207",
"label": "Blekherman--Raymond--Singh--Thomas"
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/49 | null | null | null | For a finite collection $U$ of connected graphs, do the exponents of binomial inequalities valid on the profile $G_U$ form a polyhedral cone, and if so is it necessarily a rational polyhedral cone? | Question 2. Let U be a finite collection of connected graphs. Do exponents of binomial inequalities valid on the profile GU form a polyhedral cone. If yes, then is it necessarily a rational polyhedral cone? Sos profiles and sos-testable functions. For a fixed positive integer d, define the d-sos-profile,Pdenoted as Sd ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Geometry and Optimization in Quantum Information (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/49, pp. 2665--2720 |
30,004,870 | OWR-8415353-001 | Open Problems in Thin Groups and Super-Approximation | Conjecture . . . . . . . . . . . 2745 Daniele Dona Approximate subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2747 Edna Jones Local-global I: Apollonian packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2750 Manuel Luethi Mixing and the decay of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790](https://doi.org/10.4171/owr/2021/50)
## Literature review (ch... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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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 source passage is a table-of-contents fragment and contains no mathematical claim. No separate clean statement is promoted; the) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415353-001",
"literature-status:open",
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] | The extracted text is a table-of-contents fragment rather than an identifiable mathematical claim, so no determinate resolution can be established. | [
{
"url": "https://doi.org/10.4171/owr/2021/50",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/50 | null | null | null | null | Conjecture . . . . . . . . . . . 2745 Daniele Dona Approximate subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2747 Edna Jones Local-global I: Apollonian packings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2750 Manuel Luethi Mixing and the decay of ... | unrecoverable | The official source passage is a table-of-contents fragment and contains no mathematical claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790 |
30,004,871 | OWR-8415353-002 | Thinness of Hyperbolic Hypergeometric Monodromy Groups | For hyperbolic hypergeometric monodromy groups $\Gamma_{\alpha,\beta}$, which are arithmetic and which are thin; in particular, are all but finitely many such groups thin? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790](https://doi.org/10.4171/owr/2021/50)
## Literature review (ch... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415353-002",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/50 | null | null | null | For hyperbolic hypergeometric monodromy groups $\Gamma_{\alpha,\beta}$, which are arithmetic and which are thin; in particular, are all but finitely many such groups thin? | question. Question 8. Which Γ\alpha,\beta are arithmetic and which Γ\alpha,\beta are thin? It is known that Γ\alpha,\beta are arithmetic for n \in \{2, 3\}. There have been further work for the above question [10, 28, 27] when G\alpha,\beta = Spn . We now briefly describe the work of Fuchs–Meiri–Sarnak [13]. Suppose G\... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790 |
30,004,872 | OWR-8415353-003 | Zaremba Conjecture for Bounded Continued Fraction Digits | Does there exist a constant $A$ such that every natural number is the denominator of a reduced fraction whose continued-fraction partial quotients are all at most $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790](https://doi.org/10.4171/owr/2021/50)
## Literature review (ch... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | [
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"owr",
"oberwolfach-reports",
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{
"url": "https://arxiv.org/abs/2603.14116",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/50 | null | null | null | Does there exist a constant $A$ such that every natural number is the denominator of a reduced fraction whose continued-fraction partial quotients are all at most $A$? | conjecture. Let A \subset N be a finite subset. Denote by DA the set of denominators d of reduced rational numbers b 1 = d 1 a1 + 1 a2 + .. 1 .+ ak whose coefficients a1 , a2 , . . . , ak in its continued fraction expansion are all in A. The following was conjectured by Zaremba, motivated by applications in random numb... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790 |
30,004,873 | OWR-8415353-004 | Zaremba Conjecture for Bounded Continued Fraction Digits | Conjecture. It is well known that every number x \in (0, 1) admits a continued fraction expansion: 1 x = [a1 , a2 , \cdot \cdot \cdot ] := a1 + 1 .. a2 + . The integers a1 , a2 , \cdot \cdot \cdot are called partial quotients for x. If x is rational, the length of the expansion is finite. Motivated by constructing sets... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790](https://doi.org/10.4171/owr/2021/50)
## Literature review (ch... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report states the same Zaremba conjecture already represented by the source-verified record OWR-8415353-003 in this report. No ) | [
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}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/50 | null | null | null | null | Conjecture. It is well known that every number x \in (0, 1) admits a continued fraction expansion: 1 x = [a1 , a2 , \cdot \cdot \cdot ] := a1 + 1 .. a2 + . The integers a1 , a2 , \cdot \cdot \cdot are called partial quotients for x. If x is rational, the length of the expansion is finite. Motivated by constructing sets... | unrecoverable | The official report states the same Zaremba conjecture already represented by the source-verified record OWR-8415353-003 in this report. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790 |
30,004,874 | OWR-8415353-006 | Spectral-Gap Conjecture for Compact Simple Lie Groups | Let $\mu$ be a symmetric probability measure on a compact connected simple Lie group. Does $\mu$ have a spectral gap if and only if it is nondegenerate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790](https://doi.org/10.4171/owr/2021/50)
## Literature review (ch... | 3 | open | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415353-006",
"literature-status:open",
"owr-year:2021"
] | Benoist and de Saxce show that spectral gap is equivalent to the almost-Diophantine property and state that it is unknown whether every adapted, hence non-degenerate, measure is almost Diophantine; the extracted conjecture is therefore unresolved. | [
{
"url": "https://doi.org/10.1007/s00222-015-0636-2",
"label": "Benoist--de Saxce"
},
{
"url": "https://arxiv.org/abs/1405.1808",
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{
"url": "https://doi.org/10.4171/owr/2021/50",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/50 | null | null | null | Let $\mu$ be a symmetric probability measure on a compact connected simple Lie group. Does $\mu$ have a spectral gap if and only if it is nondegenerate? | Definition 3. The measure µ has spectral gap if ||\lambdaG (µ)|L20 (G) ||op < 1. Conjecture 4. (Spectral Gap Conjecture) Let µ be a symmetric probability mea- sure on a compact connected simple Lie group. Then µ has spectral gap if and only if µ is non-degenerate. As argued above, spectral gap implies equidistribution ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Arbeitsgemeinschaft: Thin Groups and Super-approximation (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/50, pp. 2721--2790 |
30,004,875 | OWR-8415354-001 | Indecomposable Representations of Quantum Loop Algebras | Classify the finite-dimensional indecomposable representations of quantum loop algebras; equivalently, split their Grothendieck groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415354-001",
"literature-status:open",
"owr-year:2021"
] | The extracted statement contains only the heading ``Open problem'' and omits the mathematical question, so its resolution is indeterminate and is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | Classify the finite-dimensional indecomposable representations of quantum loop algebras; equivalently, split their Grothendieck groups. | In addition, the participants shared ideas about open problems in each theory, as well as possible a priori connections among them. The discussion between David Hernandez and Valerio Toledano Laredo (online) led to the following open problem: Open problem. The report passage is retained verbatim as the relevant context... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,876 | OWR-8415354-002 | Langlands-Dual Parametrization of Non-Simply-Laced Truncation Modules | Are simple modules of a non-simply-laced truncation parametrized by data from the Langlands-dual quantum affine Lie algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,021 | 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"
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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-8415354-002",
"literature-status:partially-solved",
"owr-year:2021"
] | Hernandez states the Langlands-dual parametrization as a conjecture; later work proves descent of simple shifted-quantum-affine modules to truncations for predicted parameters, but not the full non-simply-laced parametrization. | [
{
"url": "https://arxiv.org/abs/2010.06996",
"label": "Hernandez"
},
{
"url": "https://arxiv.org/abs/2501.16859",
"label": "Hernandez--Zhang"
},
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | Are simple modules of a non-simply-laced truncation parametrized by data from the Langlands-dual quantum affine Lie algebra? | We propose a conjectural parameterization of simple modules of a non simply- laced truncation in terms of the Langlands dual quantum affine Lie algebra (this has various motivations, including the symplectic duality relating Coulomb branch- es and quiver varieties). HT• (X) , s99 ee❑❑ ss ❑❑ ss ❑❑ ss ❑ StabC′ ❑❑ ss Stab... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,877 | OWR-8415354-003 | Origins of Yangian R-Matrix Factors | Can the diagonal factor $R_0(s)$ of a Yangian R-matrix be derived from four-dimensional Chern–Simons theory, and what is the interpretation of its lower-triangular factor $R_-(s)$ in Maulik–Okounkov geometry? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,021 | 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.",
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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-8415354-003",
"literature-status:partially-solved",
"owr-year:2021"
] | The report gives explicit meromorphic constructions answering the first two R-matrix questions, while the Chern--Simons and Maulik--Okounkov interpretations remain posed as open questions. | [
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2007.09218",
"label": "Appel--Vlaar"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | Can the diagonal factor $R_0(s)$ of a Yangian R-matrix be derived from four-dimensional Chern–Simons theory, and what is the interpretation of its lower-triangular factor $R_-(s)$ in Maulik–Okounkov geometry? | How to interpret RV,W (s) as a function of one complex variable? Can we get an explicit construction of RV,W (s)? How can we obtain R0 (s) from 4-dimensional Chern-Simons theory of Costello-Witten-Yamazaki? What is the interpretation of R− (s) in the geometric setting of Maulik-Okounkov? The report passage is retained ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,878 | OWR-8415354-004 | Pole Orders and Extensions of Kirillov–Reshetikhin Modules | For Kirillov–Reshetikhin modules $V$ and $W$, is the order of the pole at $z=1$ of the normalized R-matrix between $V$ and $W$ equal to the dimension of the first extension group between their generic-kernel modules over the associated generalized preprojective algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
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"description": "Group theory, ring theory, field theory, and algebraic structures.",
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"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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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-8415354-004",
"literature-status:open",
"owr-year:2021"
] | The extracted sentence refers to an omitted conjecture and an unspecified left-hand side, so the mathematical claim cannot be identified or verified and is classified open. | [
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | For Kirillov–Reshetikhin modules $V$ and $W$, is the order of the pole at $z=1$ of the normalized R-matrix between $V$ and $W$ equal to the dimension of the first extension group between their generic-kernel modules over the associated generalized preprojective algebra? | At this moment, we can check that this conjecture is true as long as the left hand side is known. potential. The algebra P fi also appeared in the context of theoretical physics [1] and in the representation theory of the quantum loop algebras [6]. We can equip the algebras Π and P fi with a Z-grading following [6]. As... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,879 | OWR-8415354-005 | Invariant Involutions for Quantum Affine Evaluation Modules | For every quantum affine evaluation module $V(z)$, does there exist an invariant automorphism $\zeta$ of the second kind such that $\zeta_q^*V=V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"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-8415354-005",
"literature-status:partially-solved",
"owr-year:2021"
] | The reflection-equation conjecture is verified for U_q of affine sl_2, but the asserted existence for arbitrary evaluation modules and affine types remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
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{
"url": "https://arxiv.org/abs/2007.09218",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | For every quantum affine evaluation module $V(z)$, does there exist an invariant automorphism $\zeta$ of the second kind such that $\zeta_q^*V=V$? | Thus given a pair of involutions of the second kind one obtains a solution of the universal reflection equation (2) in a completion of Uq g⊗2 . Evaluating (2) on a tensor product of Oint -modules, we obtain a representation of a defining relation of the type B (or “cylindrical”) ribbon Artin braid groupoid. Here the tw... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,880 | OWR-8415354-006 | Trigonometric and Elliptic R-Matrices from Three-Dimensional WZW Models | Can three-dimensional Wess–Zumino–Witten models be generalized to produce trigonometric and elliptic R-matrices for broader choices of the defining differential form? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825](https://doi.org/10.4171/owr/2021/51)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
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"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
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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-8415354-006",
"literature-status:open",
"owr-year:2021"
] | The report explicitly poses generalization to trigonometric and elliptic R-matrices as an open question, and no complete general construction was found in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2021/51",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/51 | null | null | null | Can three-dimensional Wess–Zumino–Witten models be generalized to produce trigonometric and elliptic R-matrices for broader choices of the defining differential form? | An open question is whether these results can be generalized to derive trigono- metric and elliptic R-matrices (note that 3d WZW models for other choices of \omega can be obtained by generalizing the methods of [3]). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Three Facets of R-Matrices (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/51, pp. 2791--2825 |
30,004,881 | OWR-8415355-001 | Open Problems in Geometric Representation Theory | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 2861 Geordie Williamson Towards combinatorial invariance for Kazhdan-Lusztig polynomials . . . . 2863 Olivier Schiffmann (joint with E. Diaconescu, M. Porta, F. Sala and E. Vasserot) Cohomological Hall algebras of sheaves on surfaces and affine Yangians (in... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "algebra",
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"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 | Unrecoverable OWR statement (The official source passage is a table-of-contents fragment and contains no mathematical claim. No separate clean statement is promoted; the) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-001",
"literature-status:open",
"owr-year:2021"
] | The extracted text is another table-of-contents fragment rather than an identifiable mathematical claim, so no determinate resolution can be established. | [
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 2861 Geordie Williamson Towards combinatorial invariance for Kazhdan-Lusztig polynomials . . . . 2863 Olivier Schiffmann (joint with E. Diaconescu, M. Porta, F. Sala and E. Vasserot) Cohomological Hall algebras of sheaves on surfaces and affine Yangians (in... | unrecoverable | The official source passage is a table-of-contents fragment and contains no mathematical claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,882 | OWR-8415355-002 | Structure of Cohomological Hall Algebras of Preprojective Algebras | What is the structure of the entire cohomological Hall algebra $A_{\Pi_Q}$ of the preprojective algebra $\Pi_Q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-002",
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] | Davison identifies the perverse-exact subalgebra of A_Pi_Q with a BPS Lie algebra, but the extracted question asks for the structure of the entire algebra, which remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/52",
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{
"url": "https://arxiv.org/abs/2007.03289",
"label": "Davison"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | What is the structure of the entire cohomological Hall algebra $A_{\Pi_Q}$ of the preprojective algebra $\Pi_Q$? | So a natural question is: what is the structure of the entire algebra AΠQ ? L Furthermore there is a lift of the heis+ action to an action of d\geq1 ∆d,∗ QA2 ,vir (with the trivial bracket) on q∗ QX ζ ,vir . (•,1) Theorem 1. Let L0 AΠQ \subset AΠQ be the subalgebra of “perverse-exact raising op- erators” (to be introdu... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,883 | OWR-8415355-003 | Primitive Generators of Preprojective Cohomological Hall Algebras | Let $Q$ be a quiver with preprojective algebra $\Pi_Q$, let $\mathcal{A}_{\Pi_Q}$ be its cohomological Hall algebra (CoHA), and for a dimension vector $d$ let $\operatorname{IC}(X_d)$ denote the intersection cohomology of the coarse moduli space $X_d$ of semisimple $\Pi_Q$-modules of dimension vector $d$. Does $\operat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Theorem 3 realizes IC(X_d) as a canonical subspace of primitive degree-d generators, but the authors leave completeness of that subspace as a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2007.03289",
"label": "Davison"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | Let $Q$ be a quiver with preprojective algebra $\Pi_Q$, let $\mathcal{A}_{\Pi_Q}$ be its cohomological Hall algebra (CoHA), and for a dimension vector $d$ let $\operatorname{IC}(X_d)$ denote the intersection cohomology of the coarse moduli space $X_d$ of semisimple $\Pi_Q$-modules of dimension vector $d$. Does $\operat... | We conjecture that IC(Xd ) is a complete space of primitive degree d generators. L0 AΠQ = H(p \tau \leq0 JH∗ Qvir ). Theorem 1 is proved by realising the category of ΠQ - modules as the “dimensional reduction” of the category of ΠQ [x]-modules, and then studying the cohomological DT theory of this 3CY category: see [1]... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,884 | OWR-8415355-004 | Simple Modules of Nonsimply-Laced Quantum-Group Truncations | Can the simple modules of a nonsimply laced truncation be parametrized in terms of the Langlands dual quantum affine Lie algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415355-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-004",
"literature-status:partially-solved",
"owr-year:2021"
] | The Langlands-dual parametrization is stated as a conjecture; later work proves descent to truncations for predicted parameters but does not establish the full non-simply-laced classification. | [
{
"url": "https://arxiv.org/abs/2010.06996",
"label": "Hernandez"
},
{
"url": "https://arxiv.org/abs/2501.16859",
"label": "Hernandez--Zhang"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | Can the simple modules of a nonsimply laced truncation be parametrized in terms of the Langlands dual quantum affine Lie algebra? | We propose a conjectural parametrization of simple modules of a non simply-laced truncation in terms of the Langlands dual quantum affine Lie algebra (this has various motivations, including the symplectic duality relating Coulomb branches and quiver varieties). Representations of shifted quantum groups (or quantized C... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,885 | OWR-8415355-005 | Langlands Dual Parametrization from Baxter Polynomiality | Hence the statement of our conjecture is also motivated by the symplectic duality and the Langlands duality. A main evidence for the Conjecture is the following, obtained as a consequence of the Baxter polynomiality. 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:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 passage only gives evidence for the Langlands-dual parametrization conjecture already represented by OWR-8415355-004 in this re) | [
"OWR-8415355-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-005",
"literature-status:open",
"owr-year:2021"
] | The extracted sentence refers to an omitted conjecture and gives only evidence from Baxter polynomiality, so the claim cannot be identified or shown resolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | null | Hence the statement of our conjecture is also motivated by the symplectic duality and the Langlands duality. A main evidence for the Conjecture is the following, obtained as a consequence of the Baxter polynomiality. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official passage only gives evidence for the Langlands-dual parametrization conjecture already represented by OWR-8415355-004 in this report. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,886 | OWR-8415355-007 | Splitting Subgroups of General Linear Supergroups | In the representation theory of the general linear supergroup $G = \mathrm{GL}(m|n)$ (with $m \geq n$), a subgroup $K \subseteq G$ is called a *splitting subgroup* if the restriction of every projective $G$-module to $K$ remains projective, and let $H = \mathrm{SL}(1|1)^n \subseteq \mathrm{GL}(m|n)$ be the minimal stan... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-007",
"literature-status:partially-solved",
"owr-year:2021"
] | The subgroup H=SL(1|1)^n is proved splitting, but the conjecture that every splitting subgroup of GL(m|n) contains a conjugate of H remains explicitly open in the 2026 literature. | [
{
"url": "https://arxiv.org/abs/2206.07693",
"label": "Serganova--Sherman"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2026.108277",
"label": "Entova-Aizenbud--Serganova--Sherman"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | In the representation theory of the general linear supergroup $G = \mathrm{GL}(m|n)$ (with $m \geq n$), a subgroup $K \subseteq G$ is called a *splitting subgroup* if the restriction of every projective $G$-module to $K$ remains projective, and let $H = \mathrm{SL}(1|1)^n \subseteq \mathrm{GL}(m|n)$ be the minimal stan... | Furthermore, we conjecture that every splitting subgroup K of GL(m|n) con- tains a subgroup conjugate to H. Theorem 2 confirms the conjecture of T. Enveloping Algebras and Geometric Representation Theory 2841 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,887 | OWR-8415355-008 | Affine Springer Cohomology and Quantum-Group Centers | For an affine Springer fiber $\mathcal F\ell^J_\gamma$, a small quantum group $u^J_\zeta$, the coweight lattice $\check\Lambda$, and the affine Weyl group $W_{\mathrm{af}}$, are there canonical isomorphisms $$H^\bullet(\mathcal F\ell^J_\gamma)^{\check\Lambda}\cong Z(u^J_\zeta)^{\check T},\qquad H^\bullet(\mathcal F\ell... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-008",
"literature-status:partially-solved",
"owr-year:2021"
] | The authors establish the equivariant cohomology/center isomorphism and an injective nonequivariant invariant map; the conjectured invariant isomorphism remains only partially confirmed, including type-A progress. | [
{
"url": "https://arxiv.org/abs/2205.05951",
"label": "Bezrukavnikov--Boixeda Alvarez--Shan--Vasserot"
},
{
"url": "https://arxiv.org/abs/2205.09700",
"label": "Hemelsoet--Kivinen--Lachowska"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For an affine Springer fiber $\mathcal F\ell^J_\gamma$, a small quantum group $u^J_\zeta$, the coweight lattice $\check\Lambda$, and the affine Weyl group $W_{\mathrm{af}}$, are there canonical isomorphisms $$H^\bullet(\mathcal F\ell^J_\gamma)^{\check\Lambda}\cong Z(u^J_\zeta)^{\check T},\qquad H^\bullet(\mathcal F\ell... | Corollary. Consider the C\times -action on Gr by loop rotation. Then we have a canon- ical isomorphism H • (0 Grζ\gammaℓ )Λ \sim = Z(uζ )T and H • (0 Grζ\gammaℓ )Waf \sim = Z(uζ )G . We will check (based on results of the second author with Losev) that dim(H • (F ℓ\gamma )Waf ) = (h + 1)r where h is the Coxeter number ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,888 | OWR-8415355-010 | Operator Relations on Yified Khovanov–Rozansky Homology | What are the relations in the algebra acting on y-ified Khovanov–Rozansky homology that is generated by $x_i$, $y_i$, $F_k$, and the $\mathfrak{sl}_2$ operators $f$ and $h$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-010",
"literature-status:partially-solved",
"owr-year:2021"
] | Known relations are [F_k,F_m]=0, [F_k,x_i]=0, and [F_k,y_i]=k x_i^{k-1}, with F_2 extending to an sl_2 action; the complete algebra of relations asked for remains open. | [
{
"url": "https://arxiv.org/abs/2103.01212",
"label": "Gorsky--Hogancamp--Mellit"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | What are the relations in the algebra acting on y-ified Khovanov–Rozansky homology that is generated by $x_i$, $y_i$, $F_k$, and the $\mathfrak{sl}_2$ operators $f$ and $h$? | What are the relations in the algebra that acts on the y-ified Khovanov- Rozansky homology generated by xi , yi , Fk and the sl2 -operators f, h? Theorem. Any complex of the form HH i (F\beta ) admits and action of the dg-algebra CA. The resulting CA-module is a link invariant. In particular, passing to the y-ified hom... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,889 | OWR-8415355-011 | Unitarity from Nilpotent-Orbit Boundary Codimension | Let $G$ be a real reductive Lie group and call an irreducible Harish–Chandra module unipotent when it is annihilated by a unipotent ideal associated with a nilpotent orbit $\mathcal O$. If $$\operatorname{codim}(\partial\mathcal O,\mathcal O)\geq4,$$ must every such unipotent module be unitary? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-011",
"literature-status:partially-solved",
"owr-year:2021"
] | Results prove Vogan-type structure statements under codimension at least four and establish broad classical-group cases, but the exact unitarity conjecture for all real reductive groups is not fully settled. | [
{
"url": "https://arxiv.org/abs/1805.12038",
"label": "Mason-Brown"
},
{
"url": "https://arxiv.org/abs/2108.03453",
"label": "Losev--Mason-Brown--Matvieievskyi"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | Let $G$ be a real reductive Lie group and call an irreducible Harish–Chandra module unipotent when it is annihilated by a unipotent ideal associated with a nilpotent orbit $\mathcal O$. If $$\operatorname{codim}(\partial\mathcal O,\mathcal O)\geq4,$$ must every such unipotent module be unitary? | In addition, we show that all unipotent bimod- ules are, as G-representations, of a very special form, proving a conjecture of Vogan ([V3]). We conjecture that this problem disappears if we impose the condition codim(\partial O, O) \geq 4. Enveloping Algebras and Geometric Representation Theory 2851 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,890 | OWR-8415355-014 | Combinatorial Invariance of Kazhdan–Lusztig Polynomials | For a Coxeter group $(W,S)$ and elements $x,y\in W$, does the Kazhdan–Lusztig polynomial $P_{x,y}$ depend only on the isomorphism class of the Bruhat interval $[x,y]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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"
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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-8415355-014",
"literature-status:partially-solved",
"owr-year:2021"
] | The full combinatorial invariance conjecture for Kazhdan--Lusztig polynomials remains open, but the coefficient of q is now combinatorially invariant for arbitrary Coxeter groups and this yields the conjecture for intervals of length at most six, alongside earlier special cases. | [
{
"url": "https://arxiv.org/abs/2601.07793",
"label": "Barkley--Gaetz--Lam, coefficient of q"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-024-00972-0",
"label": "Gurevich--Wang, hypercube decomposition"
},
{
"url": "https://arxiv.org/abs/2111.15161",
"label": "Blund... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For a Coxeter group $(W,S)$ and elements $x,y\in W$, does the Kazhdan–Lusztig polynomial $P_{x,y}$ depend only on the isomorphism class of the Bruhat interval $[x,y]$? | Let (W, S) be a Coxeter group. To any pair of elements x, y \in W one may associate the Kazhdan-Lusztig polynomial Px,y \in Z[q]. This polynomial is at the heart of many problems, and participants working in Geo- metric Representation Theory need no convincing of the importance of Kazhdan- Lusztig polynomials. In the 1... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,891 | OWR-8415355-015 | Hypercube Decomposition of Kazhdan–Lusztig Polynomial Derivatives | For permutations $x\leq y$ in Bruhat order and the canonical element $c$, does the proposed decomposition $$\partial P_{x,y}=I_{x,y,c}+H_{x,y,c}$$ hold, with the inductive and hypercube-cluster terms determined by the corresponding Bruhat-interval data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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-8415355-015",
"literature-status:partially-solved",
"owr-year:2021"
] | The q-derivative decomposition into an inductive piece and a hypercube piece is proved for the canonical or standard decomposition and has algebraic extensions, but the proposed formula for arbitrary admissible decompositions is not established in full. | [
{
"url": "https://arxiv.org/abs/2111.15161",
"label": "Blundell et al., hypercube formula"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-024-00972-0",
"label": "Gurevich--Wang, parabolic recursions"
},
{
"url": "https://doi.org/10.1093/imrn/rnag022",
"label": "BBDVW l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For permutations $x\leq y$ in Bruhat order and the canonical element $c$, does the proposed decomposition $$\partial P_{x,y}=I_{x,y,c}+H_{x,y,c}$$ hold, with the inductive and hypercube-cluster terms determined by the corresponding Bruhat-interval data? | conjecture. Let us describe the formula in vague terms.1 Consider permutations x, y \in Sn+1 , which we view as permutations of 0, 1, . . . , n. Suppose that x \leq y in Bruhat order. The set of elements \{z \in Sn+1 | x(n) = z(n)\} has a unique maximum c. Moreover, the interval [x, c] consists exactly of the intersect... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,892 | OWR-8415355-016 | Diamond-Complete Hypercube Formulas for Kazhdan–Lusztig Polynomials | Does the proposed hypercube-cluster formula hold for every $c'\in[x,y]$ such that $[x,c']$ is diamond complete and the edges leaving it span a hypercube cluster? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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-8415355-016",
"literature-status:partially-solved",
"owr-year:2021"
] | The conjectured formula for every diamond-complete hypercube decomposition with a hypercube cluster is proved for lower intervals and several standard or stronger subclasses, while the universal type-A assertion remains unresolved. | [
{
"url": "https://doi.org/10.1093/imrn/rnag022",
"label": "BBDVW lower-interval theorem"
},
{
"url": "https://arxiv.org/abs/2605.13304",
"label": "Zannoni, standard decompositions"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-024-00972-0",
"label": "Gurevich--Wang, h... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | Does the proposed hypercube-cluster formula hold for every $c'\in[x,y]$ such that $[x,c']$ is diamond complete and the edges leaving it span a hypercube cluster? | The most important of these properties appear to be the fact that [x, c] is “diamond complete” (a notion introduced by Patimo [2]) and the fact that the edges leaving [x, c] from any vertex v \in [x, c] “span a hypercube cluster”. (Basically, one asks for the existence of lcms, so that the above formula for the hypercu... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,893 | OWR-8415355-018 | Quantum Grothendieck Rings Beyond Simply-Laced Types | For a category $\mathcal C$ of finite-dimensional representations of a quantum affine algebra, does the bilinear product $*$ constructed from the monoidal Jantzen filtration make $(K(\mathcal C)_t,*)$ an algebra with anti-involution, isomorphic to the quantum Grothendieck ring $K_t(\mathcal C)$ with its standard bases ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | partially_solved | null | 2,021 | 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-8415355-018",
"literature-status:partially-solved",
"owr-year:2021"
] | The proposed quantum Grothendieck-ring conjecture is proved for simply-laced quantum loop algebras and in additional special categories, but associativity and the claimed isomorphism in the general non-simply-laced setting remain conjectural. | [
{
"url": "https://doi.org/10.1016/j.aim.2026.110963",
"label": "Fujita--Hernandez, Advances in Mathematics"
},
{
"url": "https://arxiv.org/abs/2402.13544",
"label": "Fujita--Hernandez, Monoidal Jantzen filtrations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For a category $\mathcal C$ of finite-dimensional representations of a quantum affine algebra, does the bilinear product $*$ constructed from the monoidal Jantzen filtration make $(K(\mathcal C)_t,*)$ an algebra with anti-involution, isomorphic to the quantum Grothendieck ring $K_t(\mathcal C)$ with its standard bases ... | Now we propose the following : Conjecture 4. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,894 | OWR-8415355-020 | Semicuspidal and Schur Algebras of Affine Quivers | For any affine-type quiver $Q$ over $k=\mathbb{F}_q$, is $C(n\delta)\simeq S_n(\mathbb{Z}^{Q_0})\otimes_{\mathbb{Z}}\mathbb{F}_q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | open | null | 2,021 | 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-8415355-020",
"literature-status:open",
"owr-year:2021"
] | The affine-quiver identification of the semicuspidal algebra with the proposed Schur algebra is not proved in the report; the authors explicitly leave the microlocal argument unfinished, and later related KLR and Schur-algebra work does not establish this exact conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "Oberwolfach Report 52, affine KLR"
},
{
"url": "https://academic.oup.com/imrn/article/2023/8/6976/6554160",
"label": "Maksimau--Minets, KLR and Schur algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For any affine-type quiver $Q$ over $k=\mathbb{F}_q$, is $C(n\delta)\simeq S_n(\mathbb{Z}^{Q_0})\otimes_{\mathbb{Z}}\mathbb{F}_q$? | Conjecture 6. For any quiver of affine type Q and k = Fq , we have C(n\delta) ≃ Sen (ZQ0 ) ⊗Z Fq . Unfortunately, our previous approach fails to work. The reason is that while restriction to the semistable locus always provides a quotient of R(n\delta), for other affine quivers its kernel is strictly bigger than Iµ(n\d... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,895 | OWR-8415355-021 | Coefficient Criterion for Irredundant String-Cone Inequalities | For a string cone presented by linear inequalities, is the presentation irredundant if and only if every coefficient in every defining linear form belongs to $\{-1,0,1\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-021",
"literature-status:open",
"owr-year:2021"
] | The equivalence between the coefficient criterion and non-redundancy of tropical string-cone inequalities is still stated as a conjecture; the primary paper proves only the sufficient direction and records the equivalence as unresolved. | [
{
"url": "https://doi.org/10.1007/s10801-022-01144-z",
"label": "Koshevoy--Schumann, Journal of Algebraic Combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "Oberwolfach Report 52, string cones"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | For a string cone presented by linear inequalities, is the presentation irredundant if and only if every coefficient in every defining linear form belongs to $\{-1,0,1\}$? | We conjecture that the above theorem is indeed an equivalence. String cones and cluster varieties Bea Schumann (joint work with Gleb Koshevoy) Enveloping Algebras and Geometric Representation Theory 2883 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,896 | OWR-8415355-022 | Coefficient Criterion for Redundant Tropical String Inequalities | Does a term of the potential $W|_{T_i^\vee}$ yield a redundant inequality after tropicalization if and only if its coefficient is at most $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891](https://doi.org/10.4171/owr/2021/52)
## Literature review (che... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415355-022",
"literature-status:open",
"owr-year:2021"
] | The proposed if-and-only-if criterion that a coefficient greater than one exactly detects a redundant tropical inequality remains a conjecture; the primary paper gives examples and sufficient criteria but no general proof or counterexample. | [
{
"url": "https://doi.org/10.1007/s10801-022-01144-z",
"label": "Koshevoy--Schumann, Journal of Algebraic Combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2021/52",
"label": "Oberwolfach Report 52, string cones"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/52 | null | null | null | Does a term of the potential $W|_{T_i^\vee}$ yield a redundant inequality after tropicalization if and only if its coefficient is at most $1$? | we replace multiplication by addition and addition by taking the minimum. By cluster magic magic the potential W |TΣ∨ \in C[TΣ∨ ] has only non-positive exponents and our theorem in this language reads as follows. Theorem 3 ([3]). If each exponent of any variable in W |Ti∨ is in the set \{−1, 0\}, then the inequalities ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Enveloping Algebras and Geometric Representation Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/52, pp. 2827--2891 |
30,004,897 | OWR-8415356-001 | Unspecified Combinatorial Optimization Problem | 2939 Chandra Chekuri Open Problem: Approximating Symmetric Submodular Functions by Hypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2941 Laura Sanità Open Problem: Computing the diameter of the bipartite perfect matching polytope . . . . . . . . . . . . . ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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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 official report shows that the extract is a table-of-contents fragment listing several later contributions, not a standalone mathematica) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-001",
"literature-status:open",
"owr-year:2021"
] | The record is an index fragment listing several distinct open-problem titles rather than one determinate mathematical claim; no single resolved statement can be assigned, so the extracted item remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53, problem index"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | null | 2939 Chandra Chekuri Open Problem: Approximating Symmetric Submodular Functions by Hypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2941 Laura Sanità Open Problem: Computing the diameter of the bipartite perfect matching polytope . . . . . . . . . . . . . ... | unrecoverable | The official report shows that the extract is a table-of-contents fragment listing several later contributions, not a standalone mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,898 | OWR-8415356-002 | Complexity of Submodular $k$-Partition | For fixed $k$, what is the computational complexity of minimizing the sum of a submodular function over a partition into $k$ nonempty parts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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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-8415356-002",
"literature-status:partially-solved",
"owr-year:2021"
] | Polynomial algorithms are known for general submodular 3-partition and, by the 2023 result, minimum 4-partition, but the complexity of the general value-oracle problem for all fixed k remains unresolved for larger k. | [
{
"url": "https://doi.org/10.1137/1.9781611977554.ch64",
"label": "Chandrasekaran et al., minimum 4-partition"
},
{
"url": "https://arxiv.org/abs/2204.09178",
"label": "Chekuri et al., hypergraph k-partition"
},
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Re... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For fixed $k$, what is the computational complexity of minimizing the sum of a submodular function over a partition into $k$ nonempty parts? | The talk will discuss these results with the goal of highlighting the open problem of resolving the complexity of Submodular k-Partition. Submodular k-Partitioning and Hypergraph k-Cut Chandra Chekuri (joint work with Karthik Chandrasekaran) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,899 | OWR-8415356-004 | Integer Programming with Bounded Subdeterminants | For a fixed integer $\Delta\geq3$, can integer programs whose constraint matrices have every square subdeterminant bounded in absolute value by $\Delta$ be solved in polynomial time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-004",
"literature-status:partially-solved",
"owr-year:2021"
] | The unrestricted constant-subdeterminant integer-programming question remains open beyond the known small cases, but a strongly polynomial algorithm now solves the important subclass with at most two nonzero entries per row or per column. | [
{
"url": "https://doi.org/10.1145/3695985",
"label": "Fiorini et al., Journal of the ACM"
},
{
"url": "https://arxiv.org/abs/2407.09477",
"label": "Aprile et al., nearly totally unimodular matrices"
},
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53, b... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For a fixed integer $\Delta\geq3$, can integer programs whose constraint matrices have every square subdeterminant bounded in absolute value by $\Delta$ be solved in polynomial time? | It is an open question whether such integer programs can be solved in polynomial time if the absolute value of the determinant of every square submatrix of A is bounded by some constant ∆. However, the question is open in the case ∆ \geq 3. Integer programs with bounded subdeterminants and two nonzeros per row Samuel F... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,900 | OWR-8415356-006 | Extension Complexity of Inscribed Fixed-Dimensional Polytopes | For every fixed $d\geq2$, does every $d$-dimensional polytope with $n$ vertices on a common sphere have extension complexity $O(\sqrt n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-006",
"literature-status:partially-solved",
"owr-year:2021"
] | The common-sphere extension-complexity question remains open in dimensions greater than two; the cited work proves the planar bound, in fact with order square-root of n rather than merely linear order, and gives related random-polytope results in every fixed dimension. | [
{
"url": "https://doi.org/10.1090/tran/8614",
"label": "Kwan--Sauermann--Zhao, Transactions of the AMS"
},
{
"url": "https://arxiv.org/abs/2006.08836",
"label": "Kwan--Sauermann--Zhao, low-dimensional polytopes"
},
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For every fixed $d\geq2$, does every $d$-dimensional polytope with $n$ vertices on a common sphere have extension complexity $O(\sqrt n)$? | Is it true that for every fixed d \geq 2, every d-dimensional n-vertex polytope \sqrt{ } with all vertices on a common sphere has extension complexity at most O( n)? This question is also open, but we prove that the answer is “Yes” for d = 2: Theorem 3. The report passage is retained verbatim as the relevant context fo... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,901 | OWR-8415356-007 | Arborescences Induced by Linear-Programming Pivot Rules | For a fixed linear-programming objective, how do the induced arborescences vary with the memoryless pivot rule, and for a fixed memoryless pivot rule, how do they vary with the objective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-007",
"literature-status:partially-solved",
"owr-year:2021"
] | For normalized-weight memoryless pivot rules, pivot-rule polytopes and neighbotopes explicitly describe how the arborescences vary with the objective and auxiliary weight; the corresponding question for unrestricted pivot rules remains open. | [
{
"url": "https://doi.org/10.1137/22M1475910",
"label": "Black et al., SIAM Journal"
},
{
"url": "https://arxiv.org/abs/2201.05134",
"label": "Black et al., pivot-rule geometry"
},
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53, pivot rules"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For a fixed linear-programming objective, how do the induced arborescences vary with the memoryless pivot rule, and for a fixed memoryless pivot rule, how do they vary with the objective? | The two main questions that we address in this paper are (1) How do the arborescences vary for fixed objective function c and varying pivot rule? (2) How do the arborescences vary for fixed pivot rule and varying objective function c? Definition 2. A memory-less pivot rule is one where its footprint for every LP is an ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,902 | OWR-8415356-009 | Near-Optimal Algorithms for Mixed-Integer Convex Optimization | Can mixed-integer convex optimization be solved with running time matching its information-complexity bound up to lower-order factors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-009",
"literature-status:open",
"owr-year:2021"
] | Later work sharpened information-complexity bounds for mixed-integer convex optimization, but the requested algorithm attaining a substantially closer running time to the information bound, especially through nontrivial cutting planes, remains unresolved. | [
{
"url": "https://doi.org/10.1007/s10107-024-02099-8",
"label": "Basu et al., Information Complexity"
},
{
"url": "https://doi.org/10.1007/s10107-022-01789-5",
"label": "Basu et al., branch-and-cut complexity"
},
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach R... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Can mixed-integer convex optimization be solved with running time matching its information-complexity bound up to lower-order factors? | It is a major open question to design an al- gorithm with improved running time closer to the information complexity bound of O (n + d)2n log MR ρǫ . However, the algorithms that achieve O 2n log(n+d) log MR ρǫ complexity do not explicitly utilize non-trivial cutting planes, i.e., halfspaces H such that C 6\subseteq H ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,903 | OWR-8415356-014 | Linear Bounds for Minimally Integer-Infeasible Systems | Let $P=\{x\in\mathbb R^n:Ax\leq b\}$ be full-dimensional and minimally integer-infeasible, and let $\Delta$ be the maximum absolute subdeterminant of $A$. Do functions $f$ and $g$ exist such that the number $m$ of inequalities satisfies $m\leq nf(\Delta)+g(\Delta)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415356-015"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-014",
"literature-status:open",
"owr-year:2021"
] | The desired linear bound for minimally integer-infeasible systems is known for determinant bounds one and two, but the first unresolved case Delta equal to three remains open; no general linear bound has been established. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53, integer infeasible subsystems"
},
{
"url": "https://doi.org/10.1145/3695985",
"label": "Fiorini et al., bounded subdeterminants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Let $P=\{x\in\mathbb R^n:Ax\leq b\}$ be full-dimensional and minimally integer-infeasible, and let $\Delta$ be the maximum absolute subdeterminant of $A$. Do functions $f$ and $g$ exist such that the number $m$ of inequalities satisfies $m\leq nf(\Delta)+g(\Delta)$? | Open Problem: Integer infeasible subsystems Robert Weismantel (joint work with Marcel Celaya) Let A be an integral m \times n matrix and b an integral vector with m components. Can we upper bound m as a linear function of n, provided that ∆ is con- stant? where \delta(v) indicates the edges of G with one endpoint being... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,904 | OWR-8415356-015 | Linear Bounds for Minimally Integer-Infeasible Systems | Can we upper bound m as a linear function of n, provided that ∆ is con- stant? Open Problem: Integer infeasible subsystems Robert Weismantel (joint work with Marcel Celaya) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the minimally integer-infeasible systems problem retained in OWR-8415356) | [
"OWR-8415356-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-015",
"literature-status:open",
"owr-year:2021"
] | The exact bound for minimally integer-infeasible subsystems remains unresolved; later bounded-subdeterminant work gives related size bounds but does not settle this formulation. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://doi.org/10.1016/j.jcta.2024.106003",
"label": "JCTA bounded-subdeterminant bounds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | null | Can we upper bound m as a linear function of n, provided that ∆ is con- stant? Open Problem: Integer infeasible subsystems Robert Weismantel (joint work with Marcel Celaya) | unrecoverable | The official report confirms that this is a duplicate extraction of the minimally integer-infeasible systems problem retained in OWR-8415356-014. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,905 | OWR-8415356-016 | Half-Integral Extreme Points for Feedback Vertex Set | For every extreme point $x^*$ of the standard feedback-vertex-set relaxation, must some vertex $v$ satisfy $x^*(v)\geq\tfrac12$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, for graphs with a cycle; unrefereed preprint)**. S. Fiorini (OWR 53/2021, p. 2944) asks whether every extreme point x\* of the Chudak–Goemans–Hochbaum–Williamson strong-density LP has some x\*(v) ≥ 1/2. | [
"owr",
"oberwolfach-reports",
"OWR-8415356-016",
"literature-status:open",
"owr-year:2021"
] | The stated half-integrality conjecture for the strong-density feedback-vertex-set LP is still unresolved; known results prove weaker density variants, not the claimed one-half bound. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://chekuri.cs.illinois.edu/papers/fvs-polyhedral-mpa.pdf",
"label": "Polyhedral aspects of feedback vertex set"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For every extreme point $x^*$ of the standard feedback-vertex-set relaxation, must some vertex $v$ satisfy $x^*(v)\geq\tfrac12$? | Open Problem: Iterative rounding for feedback vertex set Samuel Fiorini The (undirected) feedback vertex set problem is to find, given a vertex-weighted graph (G, c) a minimum cost set X such that G − X is a forest. Is it true that for every extreme solution x∗ to the LP, there is a vertex v with ∗ x (v) \geq 1/2? Open... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,906 | OWR-8415356-017 | Approximating Maximum Nonsymmetric Principal Subdeterminants | Let $L$ be a matrix such that $L+L^\mathsf T$ is positive semidefinite. Is there a $2^{O(k)}$-approximation algorithm for maximizing $\det L_{S,S}$ over all index sets $S$ of size $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-017",
"literature-status:partially-solved",
"owr-year:2021"
] | The general problem has a k^{O(k)}-time local-search algorithm, while the stronger 2^{O(k)} target is known only in special symmetric positive-semidefinite cases. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://drops.dagstuhl.de/opus/volltexte/2020/12659/pdf/LIPIcs-APPROX56.pdf",
"label": "Maximum determinant principal submatrix"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Let $L$ be a matrix such that $L+L^\mathsf T$ is positive semidefinite. Is there a $2^{O(k)}$-approximation algorithm for maximizing $\det L_{S,S}$ over all index sets $S$ of size $k$? | Open Problem: Maximizing Subdeterminants in Nonsymmetric Matrices Nima Anari Given a matrix L \in Rn\timesn with L + L⊺ 0, and an integer k \in \{1, 2, . . . , n\}, find the k \times k principal submatrix of L that has the maximum determinant: [n] max det(LS,S ) S \in . k This is NP-hard to even approximately solve wit... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,907 | OWR-8415356-018 | Better-Than-Two Approximation for Multiplicative Connectivity Augmentation | For every fixed $\alpha>1$, does $\alpha$-multiplicative connectivity augmentation admit an approximation factor strictly below $2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415356-019"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-018",
"literature-status:partially-solved",
"owr-year:2021"
] | The exact better-than-two goal for alpha-multiplicative connectivity augmentation remains open, although stronger approximations are known for important unit-connectivity and unweighted special cases. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://arxiv.org/abs/2209.07860",
"label": "Weighted connectivity augmentation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For every fixed $\alpha>1$, does $\alpha$-multiplicative connectivity augmentation admit an approximation factor strictly below $2$? | Open Problem: \alpha-Multiplicative Connectivity Augmentation and Polygon Augmentation Nathan Klein Let \alpha > 1 be a constant, let G = (V, E) be a k-edge-connected graph, and let L be a weighted multiset of edges that may be added to the graph G called links (to distinguish them from the edges of G). Therefore, we p... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,908 | OWR-8415356-019 | Better-Than-Two Approximation for Multiplicative Connectivity Augmentation | Therefore, we propose first studying \alpha-multiplicative connectivity augmentation for \alpha \leq 6/5 which may alternately be called polygon augmentation, following the naming convention of the problems tree augmentation and cactus augmentation in which the goal is to increase the connectivity of a graph by 1. The ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the multiplicative connectivity augmentation problem retained in OWR-841) | [
"OWR-8415356-018"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-019",
"literature-status:partially-solved",
"owr-year:2021"
] | The continuation asks for the same better-than-two approximation in the general alpha-multiplicative setting; special-case advances do not resolve the stated problem. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://arxiv.org/abs/2209.07860",
"label": "Weighted connectivity augmentation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | null | Therefore, we propose first studying \alpha-multiplicative connectivity augmentation for \alpha \leq 6/5 which may alternately be called polygon augmentation, following the naming convention of the problems tree augmentation and cactus augmentation in which the goal is to increase the connectivity of a graph by 1. The ... | unrecoverable | The official report confirms that this is a duplicate extraction of the multiplicative connectivity augmentation problem retained in OWR-8415356-018. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,909 | OWR-8415356-020 | Approximating Submodular Functions by Matroid Rank Functions | Is there a universal constant $\alpha$ such that every normalized nonnegative monotone submodular function $f:2^V\to\mathbb R_{\geq0}$ with $f(\{i\})=1$ for all $i\in V$ admits a matroid rank function $r$ satisfying $r(S)\leq f(S)\leq\alpha r(S)$ for every $S\subseteq V$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-020",
"literature-status:open",
"owr-year:2021"
] | No constant-factor representation of every normalized monotone submodular function by a matroid rank function is known; existing approximation results address different, generally weaker guarantees. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://doi.org/10.1137/1.9781611973068.59",
"label": "Approximating submodular functions everywhere"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Is there a universal constant $\alpha$ such that every normalized nonnegative monotone submodular function $f:2^V\to\mathbb R_{\geq0}$ with $f(\{i\})=1$ for all $i\in V$ admits a matroid rank function $r$ satisfying $r(S)\leq f(S)\leq\alpha r(S)$ for every $S\subseteq V$? | Open problem: Approximating submodular functions by matroid rank functions László Végh Let f : 2V \to R+ be a nonnegative and monotone increasing submodular function with f (\varnothing) = 0. The question is whether a non-integer function f can still be well-approximated by a matroid rank? That is, does there exists... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,910 | OWR-8415356-021 | Balanced Signings in the Subtour Polytope | For every point of the subtour-elimination polytope and every even terminal set, does there exist a balanced signing realizable by a capacitated transshipment? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415356-022"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-021",
"literature-status:open",
"owr-year:2021"
] | The existence of the requested balanced signing and transshipment for every subtour-polytope point remains unresolved; related near-mincut structure results do not prove this signing statement. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://pubsonline.informs.org/doi/10.1287/opre.2022.2338",
"label": "Polygon structure for near-minimum cuts"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | For every point of the subtour-elimination polytope and every even terminal set, does there exist a balanced signing realizable by a capacitated transshipment? | Open problem: Signings in the subtour polytope Michel Goemans Consider the subtour polytope P of the TSP on G = (V, E) (where we have dropped the degree constraints, without loss of generality, for the question below): P = \{x \in RE : x(\delta(S)) \geq 2 for all S \subseteq V, x \geq 0\}. But is the following true: Op... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,911 | OWR-8415356-022 | Balanced Signings in the Subtour Polytope | But is the following true: Open question 1. For any x \in P and for any T \subseteq VPof even cardinality, does there exist a signing s : T \to \{−1, +1\} (with s(T ) := v\inT s(v) = 0) such that there exists a transshipment (flow) f in G with capacities \{ue : e \in E\} and whose excess at vertex v is s(v) for v \in T... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the balanced-signing question retained in OWR-8415356-021. No separate c) | [
"OWR-8415356-021"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-022",
"literature-status:open",
"owr-year:2021"
] | This continuation of the signing problem remains open; available polygon and near-mincut results do not establish the required universal signing construction. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://pubsonline.informs.org/doi/10.1287/opre.2022.2338",
"label": "Polygon structure for near-minimum cuts"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | null | But is the following true: Open question 1. For any x \in P and for any T \subseteq VPof even cardinality, does there exist a signing s : T \to \{−1, +1\} (with s(T ) := v\inT s(v) = 0) such that there exists a transshipment (flow) f in G with capacities \{ue : e \in E\} and whose excess at vertex v is s(v) for v \in T... | unrecoverable | The official report confirms that this is a duplicate extraction of the balanced-signing question retained in OWR-8415356-021. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,912 | OWR-8415356-023 | Compact Representations of Four-Thirds Near-Mincuts | Can all cuts of weight at most $\tfrac43$ times the minimum-cut value in an $n$-vertex graph be represented compactly, exploiting the fact that there are at most $n^2$ such cuts? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-023",
"literature-status:open",
"owr-year:2021"
] | Compact representation is known below the six-fifths threshold, but the stated four-thirds near-mincut representation problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://math.mit.edu/~goemans/PAPERS/BenczurGoemans-2008-PolygonRepresentation.pdf",
"label": "Polygon representation of near-mincuts"
},
{
"url": "https://pubsonline.informs.org/doi/10.128... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Can all cuts of weight at most $\tfrac43$ times the minimum-cut value in an $n$-vertex graph be represented compactly, exploiting the fact that there are at most $n^2$ such cuts? | Open problem: Representation for 4/3-near-mincuts Michel Goemans In the recent result of Anna Karlin, Nathan Klein and Shayan Oveis Gharan on the subtour polytope [3] presented at this workshop, the polygon representation of approximately mincuts played an important role (among other tools). Finding a compact represent... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,913 | OWR-8415356-024 | Better Approximations for Unrelated Graph Balancing | Does unrelated graph balancing admit an approximation factor below $2$, even for simple graphs in which every orientation-dependent edge weight belongs to $\{1,k\}$ for a fixed $k$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-024",
"literature-status:partially-solved",
"owr-year:2021"
] | For unrelated graph balancing the general two-approximation barrier remains, while improved ratios are proved for restricted cases such as bounded optimum or uniform weights. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://arxiv.org/abs/1011.4957",
"label": "Configuration LP for graph balancing"
},
{
"url": "https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.74/LIPIcs... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Does unrelated graph balancing admit an approximation factor below $2$, even for simple graphs in which every orientation-dependent edge weight belongs to $\{1,k\}$ for a fixed $k$? | Open problem: Unrelated graph balancing Nicole Megow Let G = (V, E) be an undirected graph. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,914 | OWR-8415356-025 | Deterministic Optimization of Top-$k$ Perfect-Matching Edges | Given a weighted graph and an integer $k$, is there a deterministic polynomial-time algorithm that finds a perfect matching maximizing the total weight of its $k$ heaviest edges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415356-026"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-025",
"literature-status:partially-solved",
"owr-year:2021"
] | The top-k perfect-matching problem has randomized polynomial-time algorithms and equivalent formulations, but deterministic polynomial time for the general problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://arxiv.org/abs/2209.09661",
"label": "Exact matching and top-k perfect matching"
},
{
"url": "https://arxiv.org/abs/2510.12552",
"label": "Restricted top-k matching algorithms"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | Given a weighted graph and an integer $k$, is there a deterministic polynomial-time algorithm that finds a perfect matching maximizing the total weight of its $k$ heaviest edges? | Open problem: Perfect matching that maximizes the k-heaviest edges Ola Svensson Given a bipartite graph G = (V, E) with edge-weights w : E \to R, efficient algorithms for finding a perfect matching of maximum weight can be traced back to the work of Jacobi over a century ago [2]. It remains open if we can get a determi... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
30,004,915 | OWR-8415356-026 | Deterministic Optimization of Top-k Perfect-Matching Edges | It remains open if we can get a deterministic polynomial-time algorithm for this problem. In addition, the complexity of the problem (without restrictions on the edge-weights) remains open. Open problem: Perfect matching that maximizes the k-heaviest edges Ola Svensson | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954](https://doi.org/10.4171/owr/2021/53)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,021 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the top-k perfect-matching question retained in OWR-8415356-025. No sepa) | [
"OWR-8415356-025"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415356-026",
"literature-status:partially-solved",
"owr-year:2021"
] | The continuation remains unresolved in the unrestricted deterministic setting; randomized algorithms and progress for restricted instances are known. | [
{
"url": "https://doi.org/10.4171/owr/2021/53",
"label": "Oberwolfach Report 53/2021"
},
{
"url": "https://arxiv.org/abs/2209.09661",
"label": "Exact matching and top-k perfect matching"
},
{
"url": "https://arxiv.org/abs/2510.12552",
"label": "Restricted top-k matching algorithms"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/53 | null | null | null | null | It remains open if we can get a deterministic polynomial-time algorithm for this problem. In addition, the complexity of the problem (without restrictions on the edge-weights) remains open. Open problem: Perfect matching that maximizes the k-heaviest edges Ola Svensson | unrecoverable | The official report confirms that this is a duplicate extraction of the top-k perfect-matching question retained in OWR-8415356-025. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorial Optimization (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/53, pp. 2893--2954 |
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