id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,116 | OWR-14298805-002 | Moy-Prasad Data and Langlands Parameters | Let $\pi\in\operatorname{Irr}_{\mathrm{sm}}(G(F))$, let $(X,r)$ be its associated Moy-Prasad datum with $r>0$, and let $\phi_\pi$ be its Langlands parameter. Prove that $\phi_\pi|_{W_F^{>r}}=1$ and $\phi_\pi|_{W_F^{=r}}=\phi_X$ in general. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 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-14298805-002",
"literature-status:open",
"owr-year:2024"
] | The 2025 Moy--Prasad-types work constructs restricted parameters and proves compatibility in specified cases, but the extracted claim that the same compatibility always holds is still presented as a conjecture. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2509.07780",
"label": "Chen--DeBacker--Tsai"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | Let $\pi\in\operatorname{Irr}_{\mathrm{sm}}(G(F))$, let $(X,r)$ be its associated Moy-Prasad datum with $r>0$, and let $\phi_\pi$ be its Langlands parameter. Prove that $\phi_\pi|_{W_F^{>r}}=1$ and $\phi_\pi|_{W_F^{=r}}=\phi_X$ in general. | Naturally, we conjecture that the same is always true. Theorem (Chen–DeBacker–Tsai). There is a well-defined construction X 7\to ϕX where ϕX : WF=r \to G∨ is a continuous homomorphism. This construction de- pends only on the associativity class of X and the choice of \psiF . When ϕ\pi is a supercuspidal Langlands param... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,117 | OWR-14298805-003 | Spectral Categorical Langlands for Quasisplit Groups | For a quasisplit group $G$ with Whittaker datum $(U,\psi)$, construct the conjectural canonical $\operatorname{Perf}(\operatorname{Par}_G)$-linear equivalence $\operatorname{Coh}_{\operatorname{Nilp}}(\operatorname{Par}_G)\simeq\operatorname{Shv}(\operatorname{Isoc}_G,\Lambda)^\omega$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 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-14298805-003",
"literature-status:partially-solved",
"owr-year:2024"
] | The full spectral categorical equivalence in the extract remains conjectural, while nontrivial tame and unipotent pieces have been constructed or proved and current work targets broader cases. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2504.07482",
"label": "Zhu, tame categorical LLC"
},
{
"url": "https://arxiv.org/abs/2606.02799",
"label": "Schematic and analytic LLC... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | For a quasisplit group $G$ with Whittaker datum $(U,\psi)$, construct the conjectural canonical $\operatorname{Perf}(\operatorname{Par}_G)$-linear equivalence $\operatorname{Coh}_{\operatorname{Nilp}}(\operatorname{Par}_G)\simeq\operatorname{Shv}(\operatorname{Isoc}_G,\Lambda)^\omega$. | Conjecture 2. Assume that G is quasi-split and let (U, \psi) be a Whittaker datum. There is a canonical Perf(ParG )-linear equivalence CohNilp (ParG ) ≃ Shv(IsocG , Λ)\omega , Spectral action on isocrystals Arnaud Eteve (joint work with Dennis Gaitsgory, Alain Genestier, and Vincent Lafforgue) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,118 | OWR-14298805-004 | Sheaves on Bundles and Isocrystals | Construct the conjectural canonical $\operatorname{Perf}(\operatorname{Par}_G)$-linear equivalence $\operatorname{Shv}(\operatorname{Bun}_G,\Lambda)\simeq\operatorname{Shv}(\operatorname{Isoc}_G,\Lambda)$ in full generality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 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-14298805-004",
"literature-status:partially-solved",
"owr-year:2024"
] | A 2026 primary preprint proves the comparison for torsion coefficients, but the full coefficient-independent equivalence stated in the extract is not yet established in complete generality. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2606.02799",
"label": "Schematic and analytic LLC"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | Construct the conjectural canonical $\operatorname{Perf}(\operatorname{Par}_G)$-linear equivalence $\operatorname{Shv}(\operatorname{Bun}_G,\Lambda)\simeq\operatorname{Shv}(\operatorname{Isoc}_G,\Lambda)$ in full generality. | Conjecture 3. There is a canonical Perf(ParG )-linear equivalence of categories (2) Shv(BunG , Λ) = Shv(IsocG , Λ). While the full equivalence is conjectural, it is a theorem of [17] that the mor- phism (1) constructed out of the spectral action of Fargues–Scholze agrees with the one of Genestier–Lafforgue. Higher near... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,119 | OWR-14298805-006 | Geometric and Local Arthur Packets for Classical Groups | For all local Arthur parameters of a $p$-adic classical group, prove the conjectural comparison between local Arthur packets and the corresponding geometric ABV packets, including the predicted pairing with equivariant perverse sheaves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 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-14298805-006",
"literature-status:partially-solved",
"owr-year:2024"
] | The conjectural packet comparison has proofs for GLn and substantial results for classical groups, including tempered parameters, but the all-parameter classical-group proof described as in progress is not complete. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2302.10300",
"label": "Cunningham--Ray"
},
{
"url": "https://doi.org/10.1093/imrn/rnaf316",
"label": "Chao--Ding--Fang--Zhang"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | For all local Arthur parameters of a $p$-adic classical group, prove the conjectural comparison between local Arthur packets and the corresponding geometric ABV packets, including the predicted pairing with equivariant perverse sheaves. | The proof of the conjecture is in progress for p-adic classical groups in a joint project with Cun- ningham, Hazeltine, Liu, Lo, and Xu. Geometric analogues to local Arthur packets: p-adic classical groups Mishty Ray Πpure \lambda (G) −\to Φe\lambda (G) −\to PerH\lambda (V\lambda )simple /iso \pi 7\to (\phi, \tau ) 7\t... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,120 | OWR-14298805-007 | Vogan Conjecture for Quasisplit Classical Groups | For $G=\operatorname{GL}_n$, $\operatorname{SO}_{2n+1}$, or $\operatorname{Sp}_{2n}$, prove that local Arthur packets equal the corresponding ABV packets and that Arthur's stable distributions and their endoscopic transfers are computed by the normalized vanishing-cycle functors predicted by Vogan's conjecture. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 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-14298805-007",
"literature-status:partially-solved",
"owr-year:2024"
] | The GLn case is proved and tempered classical-group cases have been established, but the full quasisplit classical-group Arthur and endoscopic assertions remain incomplete. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2302.10300",
"label": "Cunningham--Ray"
},
{
"url": "https://doi.org/10.1093/imrn/rnaf316",
"label": "Chao--Ding--Fang--Zhang"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | For $G=\operatorname{GL}_n$, $\operatorname{SO}_{2n+1}$, or $\operatorname{Sp}_{2n}$, prove that local Arthur packets equal the corresponding ABV packets and that Arthur's stable distributions and their endoscopic transfers are computed by the normalized vanishing-cycle functors predicted by Vogan's conjecture. | conjecture. We formulate the quasisplit version (for trivial \delta) of Vogan’s conjecture below. Conjecture 1 (See Conjecture 1 in [1]). Let G be GLn , SO2n+1 , or Sp2n . (a) The local Arthur packet for \psi coincides with the ABV-packet for \phi\psi : Π\psi (G) = ΠABV \phi\psi (G). (b) Arthur’s stable distributions a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,121 | OWR-14298805-008 | Supercuspidal Character Survey Heading | What do characters look like? Supercuspidal Characters: What and How(e) Loren Spice In this extended abstract, we consider only complex representations. This is meant to be, not a comprehensive history, but a story of the development of one strand of thought in the modern character theory of p-adic groups. As such, imp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses “What do characters look like?” as an expository section heading and historical organizing question, not as a preci) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298805-008",
"literature-status:open",
"owr-year:2024"
] | What do characters look like is a broad research question rather than a specific theorem, and the cited supercuspidal-character literature does not make the extracted question resolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | null | What do characters look like? Supercuspidal Characters: What and How(e) Loren Spice In this extended abstract, we consider only complex representations. This is meant to be, not a comprehensive history, but a story of the development of one strand of thought in the modern character theory of p-adic groups. As such, imp... | unrecoverable | The official report uses “What do characters look like?” as an expository section heading and historical organizing question, not as a precise open problem. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,122 | OWR-14298805-012 | Arthur-Langlands Reciprocity | Establish the general Arthur-Langlands reciprocity correspondence between constituents of the discrete automorphic spectrum of a connected reductive group $G$ and the appropriate global Galois or Arthur parameters, compatibly with localization and automorphic $L$-functions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 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-14298805-012",
"literature-status:open",
"owr-year:2024"
] | The extracted reciprocity statement is explicitly a rough Arthur--Langlands conjecture; broad general reciprocity for all reductive groups remains an open program despite major classical-group cases. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://bookstore.ams.org/COLL/61",
"label": "Arthur, Endoscopic Classification"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | Establish the general Arthur-Langlands reciprocity correspondence between constituents of the discrete automorphic spectrum of a connected reductive group $G$ and the appropriate global Galois or Arthur parameters, compatibly with localization and automorphic $L$-functions. | Arthur’s results The Arthur–Langlands conjectures: rough statements. Let F/Q be a finite extension and let G be a connected reductive F -group. A central goal in the theory of automorphic forms is to understand the Hilbert space L2 (G) := L2 (G(F )\G(A)) as a representation of the group G(A). Langlands’ theory of Eisen... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,123 | OWR-14298805-013 | General Langlands Functoriality | Given a homomorphism of dual groups $\xi:\widehat H\to\widehat G$, construct the predicted transfer $\xi_*:\operatorname{AutRep}(H)\to\operatorname{AutRep}(G)$ satisfying $L(s,\xi_*(\pi),\tau)=L(s,\pi,\tau\circ\xi)$ for every finite-dimensional representation $\tau$ of $\widehat G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 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-14298805-013",
"literature-status:open",
"owr-year:2024"
] | The extracted functoriality statement is a rough general conjecture; transfers for important endoscopic settings are known, but the asserted general homomorphism-to-transfer principle is not fully proved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://bookstore.ams.org/COLL/61",
"label": "Arthur, Endoscopic Classification"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | Given a homomorphism of dual groups $\xi:\widehat H\to\widehat G$, construct the predicted transfer $\xi_*:\operatorname{AutRep}(H)\to\operatorname{AutRep}(G)$ satisfying $L(s,\xi_*(\pi),\tau)=L(s,\pi,\tau\circ\xi)$ for every finite-dimensional representation $\tau$ of $\widehat G$. | satisfying L(s, \pi, \tau ) = L(s, \tau ◦ \psi) for each \tau : Ĝ \to GLN (C). Conjecture (Functoriality, rough). A homomorphism ξ : Ĥ \to Ĝ produces a transfer of automorphic representations ξ∗ : AutRep(H) \to AutRep(G) such that L(s, ξ∗ (\pi), \tau ) = L(s, \pi, \tau ◦ ξ). Slightly more precisely, one has to repla... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,124 | OWR-14298805-014 | Weighted Fundamental Lemma for Classical Groups | Prove the weighted fundamental lemma for nonsplit classical groups, thereby making the endoscopic classification of representations of classical groups unconditional. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178](https://doi.org/10.4171/owr/2024/54)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298805-014",
"literature-status:partially-solved",
"owr-year:2024"
] | Arthur's classification theorem establishes the stated classical-group result under its trace-formula and related hypotheses, but the unconditional completion remains conditional on the stated assumptions. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4270/OWR_2024_54.pdf?sequence=1",
"label": "OWR report"
},
{
"url": "https://bookstore.ams.org/COLL/61",
"label": "Arthur, Endoscopic Classification"
},
{
"url": "https://www.claymath.org/library/cw/arthur/pdf/arthur-endoscopic-t... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/54 | null | null | null | Prove the weighted fundamental lemma for nonsplit classical groups, thereby making the endoscopic classification of representations of classical groups unconditional. | Precise statements for classical groups. Arthur proves the following precise version of the Reciprocity Conjecture. Let G be a quasi-split symplectic or or- thogonal group (or a quasi-split unitary group, handled by Mok). One can define a substitute of Ψ(G), called the “set of formal global parameters for G”, using cus... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of \$p\$-adic Groups (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/54, pp. 3103--3178 |
30,006,125 | OWR-14298807-001 | Casimir Substitutes for Kac–Moody Enveloping Algebras | Does a substitute for the Casimir element exist in the universal enveloping algebra of $\mathfrak{k}(A)$, or in a suitable completion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite-Dimensional Kac-Moody Lie Algebras in Supergravity and M Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/53, pp. 3055--3102](https://doi.org/10.4171/owr/202... | 3 | open | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298807-001",
"literature-status:open",
"owr-year:2024"
] | The Kac--Moody report explicitly identifies the existence of a Casimir substitute in the enveloping algebra or a completion as an open question, with no authoritative resolution found. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/67fd7081-be76-40fb-956b-4f1194e2f4f8/download",
"label": "Kac--Moody OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/53 | null | null | null | Does a substitute for the Casimir element exist in the universal enveloping algebra of $\mathfrak{k}(A)$, or in a suitable completion? | Another open question is, if there exists a substitute for the Casimir element within the universal enveloping algebra of k(A) or a completion thereof. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Infinite-Dimensional Kac-Moody Lie Algebras in Supergravity and M Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/53, pp. 3055--3102 |
30,006,126 | OWR-14298807-002 | Higher-Level Generalization of Conformal-Block Operators | Do the conformal-block operators constructed at level $\ell=3$ admit corresponding generalizations at every level $\ell>3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Infinite-Dimensional Kac-Moody Lie Algebras in Supergravity and M Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/53, pp. 3055--3102](https://doi.org/10.4171/owr/202... | 3 | open | null | 2,024 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298807-002",
"literature-status:open",
"owr-year:2024"
] | The level-three operators are presented as a conjectural pattern and the report proposes its extension to every level greater than three; this generalization remains open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/67fd7081-be76-40fb-956b-4f1194e2f4f8/download",
"label": "Kac--Moody OWR report"
},
{
"url": "https://pure.mpg.de/rest/items/item_3633535_2/component/file_3633536/content",
"label": "A string-like realization"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/53 | null | null | null | Do the conformal-block operators constructed at level $\ell=3$ admit corresponding generalizations at every level $\ell>3$? | Hence for level ℓ = 3 we propose yet another set of operators that does exactly this. We conjecture that there exists a generalization of this operator for all ℓ > 3. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Infinite-Dimensional Kac-Moody Lie Algebras in Supergravity and M Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/53, pp. 3055--3102 |
30,006,127 | OWR-14298808-003 | Fixed-Delta Convolution-Body Extremizers | Fix $\delta\in(0,1)$. Among convex bodies $K$ of a prescribed volume, characterize the maximizers of the volume $|C_\delta K|$ of the associated convolution body. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-14298808-003",
"literature-status:open",
"owr-year:2024"
] | The report poses the fixed-delta extremizer problem for C_delta-volume as Question 10, and no authoritative later resolution of the full convex-body classification was found. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, Question 10"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Fix $\delta\in(0,1)$. Among convex bodies $K$ of a prescribed volume, characterize the maximizers of the volume $|C_\delta K|$ of the associated convolution body. | The following natural question remains open: Question 10. Theorem 8. Let K m \subseteq R2 be the (symmetric) radial set defined by ρK m (v) = cos(2mv)2 with v \in [0, 2\pi]. Then for every \delta \in (0, 1) there exists m \in N such that \partial2 C\delta Ktm 2 > 0. \partialt2 t=0 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,128 | OWR-14298808-004 | Classical Busemann-Petty Problem | Does it follow that Voln (K) \leq Voln (L)? Measure comparison problems for dilations of convex bodies Artem Zvavitch (joint work with Malak Lafi) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. A. Zvavitch (joint with M. Lafi; OWR 58/2024, pp. 3333–3334) recalls the Busemann–Petty problem (`-004`) and its answer, yes for n ≤ 4 and no for n ≥ 5 (Gardner, 1994, n = 3; Zhang, 1999, n = 4; Gardner–Koldobsky–Schlumprecht, [Ann. of M... | [
"owr",
"oberwolfach-reports",
"OWR-14298808-004",
"literature-status:partially-solved",
"owr-year:2024"
] | The Busemann--Petty problem has an affirmative answer for n\leq4 and counterexamples for n\geq5, so the dimension-free claim is settled only dimension by dimension. | [
{
"url": "https://annals.math.princeton.edu/articles/12537",
"label": "Gardner--Koldobsky--Schlumprecht, Annals 1999"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | null | Does it follow that Voln (K) \leq Voln (L)? Measure comparison problems for dilations of convex bodies Artem Zvavitch (joint work with Malak Lafi) | unrecoverable | The official report recounts the classical Busemann-Petty question, whose answer is already known: affirmative in dimensions at most four and negative in dimensions at least five. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,129 | OWR-14298808-005 | Busemann-Petty Problem for Arbitrary Measures | It was proved in [6, 7] that the answer to the above question is independent from the “choice” of measure and depends only on the dimension n, i.e. affirmative when n \leq 4, and negative whenever n \geq 5. Does it follow that µ(K) \leq µ(L)? The report passage is retained verbatim as the relevant context for this extr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (answered in the source)**. A. Zvavitch (joint with M. Lafi; OWR 58/2024, pp. 3333–3334) recalls the Busemann–Petty problem (`-004`) and its answer, yes for n ≤ 4 and no for n ≥ 5 (Gardner, 1994, n = 3; Zhang, 1999, n = 4; Gardner–Koldobsky–Schlumprecht, [Ann. of M... | [
"owr",
"oberwolfach-reports",
"OWR-14298808-005",
"literature-status:partially-solved",
"owr-year:2024"
] | For arbitrary measures the Busemann--Petty comparison is affirmative in dimensions n\leq4 and negative in dimensions n\geq5, leaving no single answer independent of dimension. | [
{
"url": "https://doi.org/10.1007/s00208-004-0611-5",
"label": "Zvavitch, Math. Ann. 2005"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | null | It was proved in [6, 7] that the answer to the above question is independent from the “choice” of measure and depends only on the dimension n, i.e. affirmative when n \leq 4, and negative whenever n \geq 5. Does it follow that µ(K) \leq µ(L)? The report passage is retained verbatim as the relevant context for this extr... | unrecoverable | The official report explicitly states that this arbitrary-measure version is settled with the same dimensional dichotomy as the classical problem. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,130 | OWR-14298808-006 | Log-Concave Busemann-Petty Problems | Resolve the following measure-comparison questions. (1) For $n=5$ or $6$, let $\mu$ be a rotation-invariant log-concave measure with strictly decreasing density, and let $K,L\subset\mathbb R^n$ be origin-symmetric convex bodies satisfying $\mu(tK\cap\theta^\perp)\leq\mu(tL\cap\theta^\perp)$ for every $t>0$ and $\theta\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-006",
"literature-status:open",
"owr-year:2024"
] | The stated strictly decreasing log-concave and intersection-body measure questions remain open in the report; Gaussian counterexamples cover n\geq7, while the requested n=5,6 and general intersection-body cases are unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, open problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Resolve the following measure-comparison questions. (1) For $n=5$ or $6$, let $\mu$ be a rotation-invariant log-concave measure with strictly decreasing density, and let $K,L\subset\mathbb R^n$ be origin-symmetric convex bodies satisfying $\mu(tK\cap\theta^\perp)\leq\mu(tL\cap\theta^\perp)$ for every $t>0$ and $\theta\... | We would like to finish with two open problems: Open Problem: Fix n = 5 or n = 6. Does it follow that µ(K) \leq µ(L)? Open Problem: Let µ be a log-concave, measure, so that dµ(x) = e−\phi(kxkM ) , where M is an intersection body. Does it follow that µ(K) \leq µ(L)? The report passage is retained verbatim as the relevan... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,131 | OWR-14298808-007 | Schneider Higher-Order Difference-Body Conjecture | Let $n\geq 3$ and $m\geq 2$. Prove that the minimizers of the normalized volume $\delta_m(K)=|D^m(K)|/|K|^m$ among convex bodies $K\subset\mathbb R^n$ are precisely the ellipsoids. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-007",
"literature-status:partially-solved",
"owr-year:2024"
] | Schneider's higher-order difference-body conjecture remains open in general, although special cases, asymptotic results, and a related polar dual problem have been proved. | [
{
"url": "https://arxiv.org/abs/2503.06191",
"label": "On the polar of Schneider's difference body"
},
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Let $n\geq 3$ and $m\geq 2$. Prove that the minimizers of the normalized volume $\delta_m(K)=|D^m(K)|/|K|^m$ among convex bodies $K\subset\mathbb R^n$ are precisely the ellipsoids. | using the techniques of translative integral geometry, obtained the decomposition of D(K1 , K2 , . . . , Kk ) into multilinear translation-invariant functionals, which he (0) denoted Vm1 ,...,mk (K1 , . . . , Kk ). These functionals coincide with the mixed vol- umes V (ı1 (K)[m1 ], . . . , ık−1 (K)[mk−1 ], −∆(Kk )[mk ]... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,132 | OWR-14298808-009 | Floating-Area and Centro-Affine Entropy Inequalities | Prove the conjectured isoperimetric inequalities $\Omega_1(K)\leq\Omega_1(C_K)$ for floating area, $E_{\mathrm{PW}}(K)\geq E_{\mathrm{PW}}(B_K)$ for centro-affine entropy, and $E^s(K)\geq E^s(C_K)$ for the spherical analogue. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
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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-14298808-009",
"literature-status:partially-solved",
"owr-year:2024"
] | The floating-area, centro-affine entropy, and spherical inequalities remain conjectural in their stated generality, but dimension-two implications and related spherical Lp inequalities provide substantial partial progress. | [
{
"url": "https://arxiv.org/abs/2411.01631",
"label": "Besau--Werner, 2024 preprint"
},
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, open problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Prove the conjectured isoperimetric inequalities $\Omega_1(K)\leq\Omega_1(C_K)$ for floating area, $E_{\mathrm{PW}}(K)\geq E_{\mathrm{PW}}(B_K)$ for centro-affine entropy, and $E^s(K)\geq E^s(C_K)$ for the spherical analogue. | Open Questions We believe that the isoperimetric inequality for the floating area, that is, ? Ω1 (K) \leq Ω1 (CK ), should be true in general for n \geq 2. We conjecture that a similar inequality is also true for the centro-affine entropy, that is, ? A similar question also remains open for the spherical analog: Do we ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,133 | OWR-14298808-010 | Complex and Quaternionic Affine Quermassintegral Inequalities | Let $\mathbb F\in\{\mathbb C,\mathbb H\}$, put $p=\dim_{\mathbb R}\mathbb F$, let $1\leq m<n$, and let $K\subset\mathbb F^n$ be a convex body with nonempty interior. Write $\kappa_j$ for the volume of the Euclidean unit ball in $\mathbb R^j$, equip the Grassmannian $\operatorname{Gr}_m(n,\mathbb F)$ with Haar probabili... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-010",
"literature-status:open",
"owr-year:2024"
] | The real affine-quermassintegral inequality is known, but the complex and quaternionic analogues asked for here are explicitly still open. | [
{
"url": "https://doi.org/10.1007/s00208-025-03279-3",
"label": "Saroglou--Wannerer, Math. Ann. 2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Let $\mathbb F\in\{\mathbb C,\mathbb H\}$, put $p=\dim_{\mathbb R}\mathbb F$, let $1\leq m<n$, and let $K\subset\mathbb F^n$ be a convex body with nonempty interior. Write $\kappa_j$ for the volume of the Euclidean unit ball in $\mathbb R^j$, equip the Grassmannian $\operatorname{Gr}_m(n,\mathbb F)$ with Haar probabili... | As in the real case, the conjecture directly implies the isoperimetric inequalities Z κnp (5) |PE K|dE \geq |K|m/n . κmp Grm (n,F) While these inequalities are highly compelling, they remain open over the complex numbers and the quaternions. The report passage is retained verbatim as the relevant context for this extra... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,134 | OWR-14298808-011 | Growing-Parameter Limits for Convex-Body Functionals | Let $(d_j)$ and $(k_j)$ satisfy $0\leq k_j\leq d_j-1$, $2k_j>d_j+1$, and $d_j\to\infty$. Determine the asymptotic behavior of the standardized random variables $Y^*_{d_j,k_j}$. Find conditions, such as $k_j/d_j\to 1/2$, that imply convergence in distribution, and determine whether any limit is Gaussian. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-011",
"literature-status:open",
"owr-year:2024"
] | The limiting distribution of Y^*_{d,k} in the stated growing-parameter regime remains unresolved; the report records divergent cumulants and asks for the asymptotic behavior. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, open problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Let $(d_j)$ and $(k_j)$ satisfy $0\leq k_j\leq d_j-1$, $2k_j>d_j+1$, and $d_j\to\infty$. Determine the asymptotic behavior of the standardized random variables $Y^*_{d_j,k_j}$. Find conditions, such as $k_j/d_j\to 1/2$, that imply convergence in distribution, and determine whether any limit is Gaussian. | While its characteristic function \psid,k can be explicitly calculated, there are still open questions concerning this distribution. This leaves us with the following open problem: Question. Let (dj ), (kj ) be sequences of integers satisfying 0 \leq kj \leq dj − 1, 2kj > dj + 1 and dj \to \infty, j \to \infty. What is... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,135 | OWR-14298808-012 | Duplicate Growing-Parameter Limit Question | What is the asymptotic behavior of Yd∗j ,kj as j \to \infty? 2. Properties of the limit distribution For 2k > d + 1, let ∗ Yd,k − E[Yd,k ] Yd,k := p V(Yd,k ) (m) be the standardized limit distribution of Fr . While its characteristic function \psid,k can be explicitly calculated, there are still open questions concerni... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | open | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23041944",
"checked_at": "2026-09-29",
"kind": "claim",
"evidence": "unrefereed_claim"
} | Unrecoverable OWR statement (The official report confirms that this extraction is the preamble to, and repeats, the precise asymptotic-distribution question preserved in) | null | null | [Discussion #4 unrefereed claim, 2026-09-29] I have released an unrefereed preprint, **The Critical Window for High-Dimensional Limits of Hyperbolic Poisson k-Plane Processes** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23041944) | [
"owr",
"oberwolfach-reports",
"OWR-14298808-012",
"literature-status:open",
"owr-year:2024"
] | This is the report's repeated asymptotic-distribution question for Y^*_{d_j,k_j}; no authoritative result resolving the general regime was found. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, open problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | null | What is the asymptotic behavior of Yd∗j ,kj as j \to \infty? 2. Properties of the limit distribution For 2k > d + 1, let ∗ Yd,k − E[Yd,k ] Yd,k := p V(Yd,k ) (m) be the standardized limit distribution of Fr . While its characteristic function \psid,k can be explicitly calculated, there are still open questions concerni... | unrecoverable | The official report confirms that this extraction is the preamble to, and repeats, the precise asymptotic-distribution question preserved in the preceding record. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,136 | OWR-14298808-013 | Discrete Log-Concavity Under Self-Convolution | Let $p$ be a probability mass function on $\mathbb Z^d$ that is the restriction of a log-concave function on $\mathbb R^d$. Is the self-convolution $p*p$ again the restriction of a log-concave function on $\mathbb R^d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | solved | null | 2,024 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (no for every d ≥ 2; yes for d = 1)**. M. Fradelizi (joint with L. Gavalakis and M. Rapaport; OWR 58/2024, p. 3360) calls p on Z^d log-concave if it is the restriction of a log-concave function on R^d, and asks whether self-convolution preserves this. | [
"owr",
"oberwolfach-reports",
"OWR-14298808-013",
"literature-status:open",
"owr-year:2024"
] | The report explicitly leaves open whether self-convolution preserves the stated discrete entropy log-concavity, and no later proof or counterexample was found. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, open problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Let $p$ be a probability mass function on $\mathbb Z^d$ that is the restriction of a log-concave function on $\mathbb R^d$. Is the self-convolution $p*p$ again the restriction of a log-concave function on $\mathbb R^d$? | This is an open question to know if self-convolution preserves this definition. On the monotonicity of discrete entropy for log-concave random vectors in Zd Matthieu Fradelizi (joint work with Lampros Gavalakis and Martin Rapaport) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,137 | OWR-14298808-014 | Centroidal-Section Introductory Question | How often do centroids of sections coincide with the centroid of a convex body? We say that K is a convex body in Rn if K is a compact convex subset with non-empty interior. The centroid of K (also known as the center of mass or the barycenter) is defined as Z 1 c(K) = x dx |K| K | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this broad sentence to introduce the precise centroidal-section problem preserved in the following record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-014",
"literature-status:partially-solved",
"owr-year:2024"
] | The centroid-section question is affirmative in dimension 2, while examples with exactly one such section exist for n\geq5; dimensions 3 and 4 remain open. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.110081",
"label": "Myroshnychenko--Tatarko--Yaskin, Adv. Math. 2025"
},
{
"url": "https://doi.org/10.1007/s12220-026-02570-2",
"label": "Haddad--Jimenez--Villa, 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | null | How often do centroids of sections coincide with the centroid of a convex body? We say that K is a convex body in Rn if K is a compact convex subset with non-empty interior. The centroid of K (also known as the center of mass or the barycenter) is defined as Z 1 c(K) = x dx |K| K | unrecoverable | The official report uses this broad sentence to introduce the precise centroidal-section problem preserved in the following record. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,138 | OWR-14298808-015 | Multiplicity of Centroidal Hyperplane Sections | For a convex body $K\subset\mathbb R^n$, must at least $n+1$ distinct hyperplane sections through the centroid $c(K)$ also have centroid $c(K)$? More generally, determine the minimum number $\mu(n)$ of such sections over all convex bodies, especially for $n=3$ and $4$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (no: μ(n) = 1 for n ≥ 3; preprint)**; the dataset currently labels it partially solved. Problems of B. Grünbaum and C. Loewner recalled by K. Tatarko (with S. Myroshnychenko, V. Yaskin), OWR 58/2024, pp. 3361–3362: must the centroid of a convex body in ℝⁿ be the ce... | [
"owr",
"oberwolfach-reports",
"OWR-14298808-015",
"literature-status:partially-solved",
"owr-year:2024"
] | The Loewner-centroid minimum satisfies mu(n)=1 for n\geq5 and mu(2)=3; the values in dimensions 3 and 4 remain open. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.110081",
"label": "Myroshnychenko--Tatarko--Yaskin, Adv. Math. 2025"
},
{
"url": "https://doi.org/10.1007/s12220-026-02570-2",
"label": "Haddad--Jimenez--Villa, 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | For a convex body $K\subset\mathbb R^n$, must at least $n+1$ distinct hyperplane sections through the centroid $c(K)$ also have centroid $c(K)$? More generally, determine the minimum number $\mu(n)$ of such sections over all convex bodies, especially for $n=3$ and $4$. | Is the centroid c(K) of K \subset Rn the centroid of at least n+ 1 different (n − 1)-dimensional sections of K through c(K)? What is the minimum number µ(n) of (n − 1)-dimensional sections of K \subset Rn passing through c(K) whose centroid coincide with c(K), where the minimum is taken over all convex bodies K in Rn ?... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,139 | OWR-14298808-016 | Minkowski Problem for Asymptotic Convex Sets | Characterize the Borel measures on the spherical domain $\Omega$ that arise as surface-area measures of $C$-asymptotic convex sets in dimensions greater than two. In particular, prove or disprove the conjectured necessary condition $\int_0^{\pi/2}S_K(\omega_\alpha)^{1/(n-1)}\,d\alpha<\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-016",
"literature-status:partially-solved",
"owr-year:2024"
] | The C-asymptotic-set Minkowski problem has a complete necessary-and-sufficient characterization in dimension 2, while the higher-dimensional characterization remains incomplete. | [
{
"url": "https://arxiv.org/abs/2409.18699",
"label": "Semenov--Zhao, 2024 preprint"
},
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Characterize the Borel measures on the spherical domain $\Omega$ that arise as surface-area measures of $C$-asymptotic convex sets in dimensions greater than two. In particular, prove or disprove the conjectured necessary condition $\int_0^{\pi/2}S_K(\omega_\alpha)^{1/(n-1)}\,d\alpha<\infty$. | In higher dimensions, while necessary (but not sufficient) and sufficient (but not necessary) conditions exist, the problem is still widely open. In Semenov-Zhao [9], the growth rate of surface area measures for C-asymptotic sets is estimated in higher dimensions. Schneider [8] showed that for any C-asymptotic set K an... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,140 | OWR-14298808-017 | Stable Banach Isometric Subspace Conjecture | Let $V$ be a real or complex $n$-dimensional normed space and $2\leq k<n$. If every pair of $k$-dimensional subspaces $E,E'\subset V$ satisfies $d_{\mathrm{BM}}(E,E')<1+\delta$, prove that $d_{\mathrm{BM}}(V,\ell_2^n)<1+\varepsilon(n,k,\delta)$ with $\varepsilon(n,k,\delta)\to 0$ as $\delta\to 0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376](https://doi.org/10.4171/owr/2024/58)
## Literature review (checked 2026-08-22)
*... | 3 | partially_solved | null | 2,024 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298808-017",
"literature-status:partially-solved",
"owr-year:2024"
] | The affine-equivalence reformulation is established and many parameter cases of Banach's conjecture are known, but the general stable Banach isometric problem remains open. | [
{
"url": "https://ems.press/content/serial-article-files/50771",
"label": "OWR 2024/58, Banach conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2024/58 | null | null | null | Let $V$ be a real or complex $n$-dimensional normed space and $2\leq k<n$. If every pair of $k$-dimensional subspaces $E,E'\subset V$ satisfies $d_{\mathrm{BM}}(E,E')<1+\delta$, prove that $d_{\mathrm{BM}}(V,\ell_2^n)<1+\varepsilon(n,k,\delta)$ with $\varepsilon(n,k,\delta)\to 0$ as $\delta\to 0$. | Banach’s conjecture is known to be equivalent to the seemingly stronger one, where affine equivalence replaces linear [2]. The stable Banach isometric problem Dmitry Faifman (joint work with Gautam Aishwarya) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Convex Geometry and its Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2024/58, pp. 3301--3376 |
30,006,141 | OWR-14299081-001 | Workshop Summary Mention of the Erdős–Hajnal Conjecture | The full Mon- day program concluded with an open problem session designed to spark productive discussions for the rest of the week. Later in the week, Tung Nguyen updated the participants on his results on the Erdős–Hajnal conjecture, a major open problem concerning homogeneous subgraphs in hereditary classes of graph... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is workshop-summary prose mentioning the Erdős–Hajnal conjecture, which is stated separate) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-001",
"literature-status:partially-solved",
"owr-year:2025"
] | The Erdos--Hajnal conjecture remains open in general, although the 2026 resolution of the five-vertex path case completes all five-vertex graphs. | [
{
"url": "https://doi.org/10.1112/plms.70133",
"label": "Nguyen--Scott--Seymour, Proc. LMS 2026"
},
{
"url": "https://ems.press/content/serial-article-files/51346",
"label": "OWR 2025/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | The full Mon- day program concluded with an open problem session designed to spark productive discussions for the rest of the week. Later in the week, Tung Nguyen updated the participants on his results on the Erdős–Hajnal conjecture, a major open problem concerning homogeneous subgraphs in hereditary classes of graph... | unrecoverable | The official report confirms that this extraction is workshop-summary prose mentioning the Erdős–Hajnal conjecture, which is stated separately in a canonical record from the same report. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,142 | OWR-14299081-002 | Corrupted Graph-Theory Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . 45 Peter Nelson (joint with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Tony Huynh, Matthew E. Kroeker) Rainbow triangles and the Erdős-Hajnal problem in projective geometries 46 Sang-il Oum (joint with Maria Chudnovsky, Linda Cook, James Davies, Jane Tan) C... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged contents-listing fragment, not a mathematical problem. No separate clean stat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-002",
"literature-status:partially-solved",
"owr-year:2025"
] | The extracted Erdős--Hajnal problem remains open in general; substantial special cases are known, including the completion of all five-vertex cases in 2026. | [
{
"url": "https://doi.org/10.1112/plms.70133",
"label": "Nguyen--Scott--Seymour, Proc. LMS 2026"
},
{
"url": "https://ems.press/content/serial-article-files/51346",
"label": "OWR 2025/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . 45 Peter Nelson (joint with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Tony Huynh, Matthew E. Kroeker) Rainbow triangles and the Erdős-Hajnal problem in projective geometries 46 Sang-il Oum (joint with Maria Chudnovsky, Linda Cook, James Davies, Jane Tan) C... | unrecoverable | The official report confirms that this extraction is a damaged contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,143 | OWR-14299081-003 | Equality Cases for Gerzon’s Equiangular-Line Bound | Are there infinitely many dimensions $r$ in which the maximum number of equiangular lines in $\mathbb{R}^r$ attains Gerzon’s bound $\binom{r+1}{2}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-003",
"literature-status:partially-solved",
"owr-year:2025"
] | Gerzon's bound is known, equality is attained in dimensions 2, 3, 7, and 23, and infinitely many dimensions cannot attain it; whether equality occurs for infinitely many dimensions remains open. | [
{
"url": "https://doi.org/10.1016/j.jcta.2015.09.008",
"label": "Equiangular lines in Euclidean spaces"
},
{
"url": "https://doi.org/10.1007/s10107-021-01638-x",
"label": "Equiangular lines and Gerzon's bound"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Are there infinitely many dimensions $r$ in which the maximum number of equiangular lines in $\mathbb{R}^r$ attains Gerzon’s bound $\binom{r+1}{2}$? | The well-known absolute bound (see e.g. [6]) states that the answer is at most r+1 2 , which is tight up to a multiplica- tive constant and it is a difficult open problem to determine whether there are infinitely many r for which it holds with equality. Equiangular lines via improved eigenvalue multiplicity Matija Bucić ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,144 | OWR-14299081-004 | Structure and Coloring at Large r-Acyclic Width | Fix $r\geq 3$. (1) Is there a function $f:\mathbb{N}\to\mathbb{N}$ such that every graph of $r$-acyclic width at least $f(k)$ contains a subdivided grid of $r$-acyclic width at least $k$? (2) Is there a function $h:\mathbb{N}\to\mathbb{R}$ with $h(r)\to 0$ such that some minimum-width $r$-acyclic $H$-decomposition of e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-004",
"literature-status:open",
"owr-year:2025"
] | The r-acyclic-width problems for subdivided grids and the associated coloring question are posed as open Problems 6--8, with no general resolution found. | [
{
"url": "https://ems.press/content/serial-article-files/51346",
"label": "OWR 2025/1, Problems 6--8"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Fix $r\geq 3$. (1) Is there a function $f:\mathbb{N}\to\mathbb{N}$ such that every graph of $r$-acyclic width at least $f(k)$ contains a subdivided grid of $r$-acyclic width at least $k$? (2) Is there a function $h:\mathbb{N}\to\mathbb{R}$ with $h(r)\to 0$ such that some minimum-width $r$-acyclic $H$-decomposition of e... | A more fundamental question is what certificates of large r-acyclic width, if any, will necessarily occur in graphs of large enough r-acyclic width. Given r \geq 3, is there an N \to N function f such that every graph of r-acyclic width at least f (k) contains a subdivided grid of r-acyclic width at least k? Is there an... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,145 | OWR-14299081-005 | Conditions Forcing Long Induced Paths | For a graph class $\mathcal{G}$, let $f_{\mathcal{G}}(n)$ be the maximum integer $k$ such that every member of $\mathcal{G}$ containing an $n$-vertex path also contains an induced $k$-vertex path. What natural conditions on $\mathcal{G}$ ensure that $f_{\mathcal{G}}(n)\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Recent work proves long induced paths under several natural graph conditions and gives polylogarithmic bounds, but the broad characterization of conditions forcing f_G(n) to diverge remains open. | [
{
"url": "https://doi.org/10.1137/24M1720366",
"label": "Duron--Esperet--Raymond, SIAM J. Discrete Math."
},
{
"url": "https://doi.org/10.37236/11029",
"label": "Hilaire--Raymond, 2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | For a graph class $\mathcal{G}$, let $f_{\mathcal{G}}(n)$ be the maximum integer $k$ such that every member of $\mathcal{G}$ containing an $n$-vertex path also contains an induced $k$-vertex path. What natural conditions on $\mathcal{G}$ ensure that $f_{\mathcal{G}}(n)\to\infty$? | What natural conditions on G ensure that fG (n) \to \infty ? Long induced paths Louis Esperet (joint work with Julien Duron, Jean-Florent Raymond) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,146 | OWR-14299081-007 | Complete Bipartite Subgraphs and Connected Matchings at $\alpha=2$ | Is there a constant $c>0$ such that every $n$-vertex graph $G$ with $\alpha(G)=2$ contains both (1) a complete bipartite graph $K_{n^c,n^c}$ and (2) a connected matching of size $cn$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-007",
"literature-status:open",
"owr-year:2025"
] | The two alpha(G)=2 conjectures on large complete bipartite subgraphs and connected matchings remain unresolved; related minor results do not prove either stated conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/51346",
"label": "OWR 2025/1, conjectures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Is there a constant $c>0$ such that every $n$-vertex graph $G$ with $\alpha(G)=2$ contains both (1) a complete bipartite graph $K_{n^c,n^c}$ and (2) a connected matching of size $cn$? | What can we say about the structure of induced H-free graphs G? In this talk, we discuss some of the major results and open problems in this area, focusing on methods that come from extremal graph theory. Some basic questions remain open, including the following two conjectures. Extremal graph theory methods for forbid... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,147 | OWR-14299081-008 | Polynomial Homogeneous Sets in Induced-Free Graphs | For every graph $H$, is there a constant $c(H)>0$ such that every $n$-vertex induced-$H$-free graph contains a clique or an independent set of size at least $n^{c(H)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299081-009",
"OWR-14299081-010",
"OWR-14299081-020"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The Erdos--Hajnal conjecture remains open in general, despite substantial progress and the 2026 completion of its five-vertex cases. | [
{
"url": "https://doi.org/10.1112/plms.70133",
"label": "Nguyen--Scott--Seymour, Proc. LMS 2026"
},
{
"url": "https://ems.press/content/serial-article-files/51346",
"label": "OWR 2025/1"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | For every graph $H$, is there a constant $c(H)>0$ such that every $n$-vertex induced-$H$-free graph contains a clique or an independent set of size at least $n^{c(H)}$? | Another major open problem in this area is the Erdős-Hajnal conjecture: Theorem 3. If G is an induced H-free graph, then G has edit distance at most \varepsilon|V (G)|2 from a graph G′ such that G′ has an induced homomorphism to an in- duced H-free graph F with at most MH (\varepsilon) vertices. Conjecture 4. For each... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,148 | OWR-14299081-009 | Duplicate Erdős–Hajnal Conjecture Passage | Conjecture 4. For each graph H there is c(H) > 0 such that every induced H-free graph on n vertices contains a clique or independent set of size at least nc . It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the Erdős–Hajnal conjecture represented canonically by OWR-14299081-008. No separa) | [
"OWR-14299081-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-009",
"literature-status:open",
"owr-year:2025"
] | The statement is the Erdős--Hajnal conjecture. It remains open in general; recent work gives stronger-than-classical subpolynomial homogeneous sets but not the required polynomial bound n^c for every forbidden graph H. | [
{
"url": "https://arxiv.org/abs/2301.10147",
"label": "Bucić--Nguyen--Scott--Seymour"
},
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | Conjecture 4. For each graph H there is c(H) > 0 such that every induced H-free graph on n vertices contains a clique or independent set of size at least nc . It is well-known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical... | unrecoverable | The official report confirms that this extraction repeats the Erdős–Hajnal conjecture represented canonically by OWR-14299081-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,149 | OWR-14299081-010 | Duplicate Erdős–Hajnal Conjecture Passage | conjecture. In the recent paper [1], Bucić, Pham, and the speaker proved that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen, Scott and Seymour; Nguyen, Scott and Seymour and Gishboliner and Shapira. We deduce that the family of string gra... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the Erdős–Hajnal conjecture represented canonically by OWR-14299081-008. No separa) | [
"OWR-14299081-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-010",
"literature-status:open",
"owr-year:2025"
] | This fragment is the continuation of the Erdős--Hajnal conjecture recorded in ID ...-009. The general polynomial homogeneous-set assertion remains unproved. | [
{
"url": "https://arxiv.org/abs/2301.10147",
"label": "Bucić--Nguyen--Scott--Seymour"
},
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | conjecture. In the recent paper [1], Bucić, Pham, and the speaker proved that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen, Scott and Seymour; Nguyen, Scott and Seymour and Gishboliner and Shapira. We deduce that the family of string gra... | unrecoverable | The official report confirms that this extraction repeats the Erdős–Hajnal conjecture represented canonically by OWR-14299081-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,150 | OWR-14299081-011 | Truncated Extremal-Graph-Theory Conjecture | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction contains only an isolated conjecture label and no independently recoverable mathematical s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-011",
"literature-status:open",
"owr-year:2025"
] | The extracted record contains only the word `conjecture' and no identifiable mathematical assertion. Under the required uncertainty rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction contains only an isolated conjecture label and no independently recoverable mathematical statement. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,151 | OWR-14299081-013 | Shortest Paths and Cycles of Prescribed Modular Length | Let $\ell,m\geq 0$ with $m\geq 2$. Is there a polynomial-time algorithm that, given a graph and specified vertices $s,t$, finds a shortest $s$–$t$ path whose length is congruent to $\ell\pmod m$, or certifies that none exists? Is there such an algorithm for a shortest cycle whose length is congruent to $\ell\pmod m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-013",
"literature-status:open",
"owr-year:2025"
] | The cited Liu--Yoo results decide whether a path or cycle of a prescribed length residue modulo m exists, but the extracted Problem 5 asks for a shortest such path or cycle. No proof of that optimization question was located; it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Liu--Yoo report and Problem 5"
},
{
"url": "https://doi.org/10.1145/116825.116850",
"label": "Arkin--Papadimitriou--Yannakakis"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Let $\ell,m\geq 0$ with $m\geq 2$. Is there a polynomial-time algorithm that, given a graph and specified vertices $s,t$, finds a shortest $s$–$t$ path whose length is congruent to $\ell\pmod m$, or certifies that none exists? Is there such an algorithm for a shortest cycle whose length is congruent to $\ell\pmod m$? | The k = 1 case of Theorem 1 immediately leads to the following corollary that solves an open problem stated in [1]. Taking H to be a loop in Corollary 3 immediately leads to the following corol- lary, which solves another open problem in [1]. Let ℓ and m be nonnegative integers with m \geq 2. (1) Does there exist a pol... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,152 | OWR-14299081-015 | Tutte’s Four-Flow Conjecture | Does every $2$-connected graph with no Petersen graph minor admit a nowhere-zero $4$-flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-015",
"literature-status:open",
"owr-year:2025"
] | The fragment refers to Tutte's 4-flow conjecture: every 2-connected graph with no Petersen minor should have a nowhere-zero 4-flow. Its cubic restriction was proved, but the unrestricted conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
},
{
"url": "https://doi.org/10.1016/S0021-9800(66)80004-2",
"label": "Tutte, original conjecture"
},
{
"url": "https://doi.org/10.1016/j.jctb.2015.12.006",
"label": "doublecross cubic special case"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Does every $2$-connected graph with no Petersen graph minor admit a nowhere-zero $4$-flow? | Although this conjecture is still open, its special case restricted to cubic graphs was proved in 1997 by Robertson, Seymour, and Thomas [12]. Three-edge-coloring cubic graphs on surfaces of small Euler genus Bojan Mohar (joint work with Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita, Tomohiro Sonobe) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,153 | OWR-14299081-018 | Robertson’s Surface Four-Flow Conjecture | Every $2$-edge-connected graph embedded in the projective plane with face-width at least $4$ has a nowhere-zero $4$-flow. More generally, for every surface $S$, does there exist a constant $r(S)$ such that every $2$-edge-connected graph embedded in $S$ with face-width at least $r(S)$ has a nowhere-zero $4$-flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-018",
"literature-status:open",
"owr-year:2025"
] | The extracted record is the general Robertson conjecture for every surface: a surface-dependent face-width threshold should force a nowhere-zero 4-flow. The projective-plane case is solved, but the all-surfaces assertion remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
},
{
"url": "https://arxiv.org/abs/2405.16586",
"label": "projective-plane special case"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Every $2$-edge-connected graph embedded in the projective plane with face-width at least $4$ has a nowhere-zero $4$-flow. More generally, for every surface $S$, does there exist a constant $r(S)$ such that every $2$-edge-connected graph embedded in $S$ with face-width at least $r(S)$ has a nowhere-zero $4$-flow? | Robertson made a more general conjecture: Conjecture 5 (Robertson, 1994). Every 2-edge-connected graph on the projective plane whose face-width is at least 4, has a nowhere-zero 4-flow. Conjecture 6 (Robertson, 1994). For every surface S, there is a constant r such that every 2-edge-connected graph embedded in S with f... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,154 | OWR-14299081-020 | Duplicate Erdős–Hajnal Conjecture Lead-In | A 1977 conjecture of Erdős and Hajnal [5] predicts a very different behaviour in graphs with a forbidden induced subgraph; formally, their conjecture says that: Conjecture 1 (Erdős–Hajnal). This conjecture remains open despite a substantial body of work. Recent work on the Erdős–Hajnal conjecture Tung Nguyen (joint w... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction is another occurrence of the Erdős–Hajnal conjecture represented canonically by OWR-142990) | [
"OWR-14299081-008"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-020",
"literature-status:open",
"owr-year:2025"
] | The extracted statement is the general Erdős--Hajnal conjecture for induced H-free graphs. It remains open despite substantial progress for particular forbidden graphs and improved general subpolynomial bounds. | [
{
"url": "https://arxiv.org/abs/2301.10147",
"label": "Bucić--Nguyen--Scott--Seymour"
},
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | A 1977 conjecture of Erdős and Hajnal [5] predicts a very different behaviour in graphs with a forbidden induced subgraph; formally, their conjecture says that: Conjecture 1 (Erdős–Hajnal). This conjecture remains open despite a substantial body of work. Recent work on the Erdős–Hajnal conjecture Tung Nguyen (joint w... | unrecoverable | The official report confirms that this extraction is another occurrence of the Erdős–Hajnal conjecture represented canonically by OWR-14299081-008. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,155 | OWR-14299081-021 | The Multicolored Geometric Erdős–Hajnal Conjecture | For every prime power $q$, all $k,s\in\mathbb{N}$, and every $s$-coloring $c_0$ of $\operatorname{PG}(k-1,q)$, do constants $\delta,C>0$ exist such that, for every $n$ and every $c_0$-free $s$-coloring of $\operatorname{PG}(n-1,q)$, some subspace of dimension at least $Cn^\delta$ uses at most $s-1$ colors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** partially solved
**... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-021",
"literature-status:partially-solved",
"owr-year:2025"
] | The multicoloured geometric Erdős--Hajnal conjecture is not proved in general. The cited work resolves all cases for (k,q)=(2,2) and several cases for (2,3) and (3,2), leaving the general assertion open. | [
{
"url": "https://arxiv.org/abs/2505.13781",
"label": "Chun--Douthitt--Ge--Huynh--Kroeker--Nelson"
},
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | For every prime power $q$, all $k,s\in\mathbb{N}$, and every $s$-coloring $c_0$ of $\operatorname{PG}(k-1,q)$, do constants $\delta,C>0$ exist such that, for every $n$ and every $c_0$-free $s$-coloring of $\operatorname{PG}(n-1,q)$, some subspace of dimension at least $Cn^\delta$ uses at most $s-1$ colors? | conjecture. Conjecture 1 (Multicoloured geometric Erdős-Hajnal conjecture). For every prime power q, all k, s \in N and every s-colouring c0 of PG(k − 1, q), there exists \delta, C > 0 such that, for all n \in N and every c0 -free colouring c of G \sim = PG(n − 1, q), there is a subspace of G with dimension at least C... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,156 | OWR-14299081-023 | Truncated Graph-Theory Conjecture | Conjecture. Namely, we will take X The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a truncated conjecture fragment with no independently recoverable mathematical statemen) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-023",
"literature-status:open",
"owr-year:2025"
] | The extracted record is only a truncated lead-in to a conjecture and does not preserve the mathematical claim. It therefore cannot be verified and is classified as open under the required rule. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | Conjecture. Namely, we will take X The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is a truncated conjecture fragment with no independently recoverable mathematical statement. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,157 | OWR-14299081-024 | Solved Design-Conjecture Prose Fragment | The true benefit of our new proof of the Existence Conjecture is in the ro- bustness of the proof structure. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is prose about a new proof of the design Existence Conjecture, not a new open problem. No ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-024",
"literature-status:open",
"owr-year:2025"
] | The extracted text is a consequence or motivation for a new proof, not a complete conjecture or theorem statement. Because no definite claim can be assessed from the record, it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | null | The true benefit of our new proof of the Existence Conjecture is in the ro- bustness of the proof structure. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction is prose about a new proof of the design Existence Conjecture, not a new open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,158 | OWR-14299081-025 | The Log-Log Factor for Rainbow Cycles | Is the $\log\log n$ factor in the $O(\log n\log\log n)$ average-degree bound necessary to guarantee a rainbow cycle in a properly edge-colored graph? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-025",
"literature-status:open",
"owr-year:2025"
] | The best current theorem gives average degree O(\log n\log\log n) to force a rainbow cycle, with matching lower-order precision only up to the \log\log n factor. The authors explicitly leave necessity of that factor open. | [
{
"url": "https://arxiv.org/abs/2309.04460",
"label": "Alon--Bucić--Sauermann--Zakharov--Zamir"
},
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Is the $\log\log n$ factor in the $O(\log n\log\log n)$ average-degree bound necessary to guarantee a rainbow cycle in a properly edge-colored graph? | Is the log log n factor in the bound for the average degree in Theo- rem 1 necessary in order to guarantee a rainbow cycle? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,159 | OWR-14299081-029 | Hamiltonicity of Connected Vertex-Transitive Graphs | Does every connected vertex-transitive graph contain a Hamilton path and, apart from the five known exceptions, a Hamilton cycle? In particular, is every connected Cayley graph Hamiltonian, and is a random connected Cayley graph generated by $C\log|G|$ elements asymptotically almost surely Hamiltonian? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74](https://doi.org/10.4171/owr/2025/1)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299081-029",
"literature-status:open",
"owr-year:2025"
] | This is Lovász's conjecture that every connected vertex-transitive graph has a Hamilton path and, apart from five known exceptions, a Hamilton cycle. It remains open; the abelian Cayley-graph case and several dense or pseudorandom cases are known. | [
{
"url": "https://doi.org/10.4171/owr/2025/1",
"label": "Oberwolfach Report 1/2025"
},
{
"url": "https://arxiv.org/abs/2402.06603",
"label": "Hamiltonicity of expanders"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/1 | null | null | null | Does every connected vertex-transitive graph contain a Hamilton path and, apart from the five known exceptions, a Hamilton cycle? In particular, is every connected Cayley graph Hamiltonian, and is a random connected Cayley graph generated by $C\log|G|$ elements asymptotically almost surely Hamiltonian? | Conjecture 6. Every connected vertex-transitive graph contains a Hamilton path, and, except for five known examples, a Hamilton cycle. As Cayley graphs are vertex-transitive and none of the five known exceptions in Conjecture 6 are Cayley graphs, Lovász’s conjecture implies the following earlier conjecture, posed in 19... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Graph Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/1, pp. 5--74 |
30,006,160 | OWR-14299082-001 | Descriptive-Set-Theory Table-of-Contents Fragment | conjecture . . . . . . 100 Eyal Kaplan Consistency results regarding the Ketonen order and the Lipschitz order 101 Matthew Foreman Filter Games and Ineffable Cardinals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Moti Gitik Some new ways of blowing up the power of a measurable cardinal . . . . . . 10... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is table-of-contents debris ending in the word “conjecture,” not a recoverable mathematica) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-001",
"literature-status:open",
"owr-year:2025"
] | The extract is only a fragment ending in the word conjecture followed by table-of-contents text, so no testable mathematical proposition is recoverable. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | null | conjecture . . . . . . 100 Eyal Kaplan Consistency results regarding the Ketonen order and the Lipschitz order 101 Matthew Foreman Filter Games and Ineffable Cardinals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Moti Gitik Some new ways of blowing up the power of a measurable cardinal . . . . . . 10... | unrecoverable | The official report confirms that this extraction is table-of-contents debris ending in the word “conjecture,” not a recoverable mathematical statement. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,161 | OWR-14299082-003 | Generic Maximal Chains on Exceptional Surfaces | Does the action of $\operatorname{Homeo}(X)$ on the hyperspace $\Phi(X)$ of maximal chains of connected closed subsets have a comeager orbit when $X=S^2$? Does it have one when $X=\mathbb{RP}^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-003",
"literature-status:open",
"owr-year:2025"
] | The primary report labels the generic-chain questions for the sphere and real projective plane as still open, and no later primary resolution was located by the checked date. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Does the action of $\operatorname{Homeo}(X)$ on the hyperspace $\Phi(X)$ of maximal chains of connected closed subsets have a comeager orbit when $X=S^2$? Does it have one when $X=\mathbb{RP}^2$? | A more rigorous way to formulate this question is asking whether, given X, there is C \in Φ(X) such that its orbit under the action Homeo(X) y Φ(X) is comeager in Φ(X), endowed with its natural compact hyperspace topology. The following questions are still open Question 3 ([1]*Question 1.3). Is there a generic chain on... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,162 | OWR-14299082-004 | Generic Point Property for Exceptional Surface Homeomorphisms | Does $\operatorname{Homeo}_0(S^2)$ have the generic point property? Does $\operatorname{Homeo}_0(\mathbb{RP}^2)$ have the generic point property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-004",
"literature-status:open",
"owr-year:2025"
] | The report proves failure of the generic point property for all other closed surfaces but explicitly leaves the sphere and real projective plane unresolved. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2412.05659",
"label": "Basso--Zucker, Topological groups with tractable minimal dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Does $\operatorname{Homeo}_0(S^2)$ have the generic point property? Does $\operatorname{Homeo}_0(\mathbb{RP}^2)$ have the generic point property? | The following open problem is tightly related to Question 3. Does Homeo0 (S 2 ), where S 2 is the sphere, have the generic point property? What about the real projective plane? Corollary 4. If X is a closed surface which is not the sphere or the real projective plane, then Homeo0 (X) does not have the generic point pro... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,163 | OWR-14299082-005 | Duplicate Generic Point Property Question | Does Homeo0 (S 2 ), where S 2 is the sphere, have the generic point property? What about the real projective plane? The following open problem is tightly related to Question 3. Theorem 2 can be used to deduce the failure of the generic point property for Homeo(X) for spaces X (not necessarily manifolds) for which the a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction repeats Question 5, which is preserved in the preceding record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-005",
"literature-status:open",
"owr-year:2025"
] | The two cases in the extracted question are exactly the exceptional cases left open after the report's theorem for other closed surfaces, with no later primary resolution found. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2412.05659",
"label": "Basso--Zucker, Topological groups with tractable minimal dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | null | Does Homeo0 (S 2 ), where S 2 is the sphere, have the generic point property? What about the real projective plane? The following open problem is tightly related to Question 3. Theorem 2 can be used to deduce the failure of the generic point property for Homeo(X) for spaces X (not necessarily manifolds) for which the a... | unrecoverable | The official report confirms that this extraction repeats Question 5, which is preserved in the preceding record. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,164 | OWR-14299082-006 | Mouse-Set Property Without a Cone Restriction | Assume $\mathrm{ZF}+\mathrm{AD}+V=L(\mathbb R)$. Let $[\alpha,\gamma]$ be a weak $\Sigma_1$ gap, or let $\gamma=\beta+1$ for a strong gap $[\alpha,\beta]$, and let $e$ be least such that $\rho_{e+1}^{J_\gamma(\mathbb R)}=\mathbb R$. Is $\mathrm{OD}^{*\mathbb R}_{\gamma,e+2}$ a mouse set without restricting to a cone of... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-006",
"literature-status:open",
"owr-year:2025"
] | The 2024 mouse-set results settle higher complexity levels and cone versions, but the no-cone case at the extracted level is explicitly stated to remain open. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2307.08856",
"label": "Schlutzenberg, The Mouse Set Theorem Just Past Projective"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Assume $\mathrm{ZF}+\mathrm{AD}+V=L(\mathbb R)$. Let $[\alpha,\gamma]$ be a weak $\Sigma_1$ gap, or let $\gamma=\beta+1$ for a strong gap $[\alpha,\beta]$, and let $e$ be least such that $\rho_{e+1}^{J_\gamma(\mathbb R)}=\mathbb R$. Is $\mathrm{OD}^{*\mathbb R}_{\gamma,e+2}$ a mouse set without restricting to a cone of... | But in general, it remains open whether OD\gamma,e+2 is a mouse set (without the cone). These results also relate to the correctness conjecture of Rudominer and Steel in [1], that, also assuming ZF + AD + V = L(R), given any (0, \omega1 + 1)-iterable mouse M , there are ordinals \gammā, \gamma and n < \omega such that... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,165 | OWR-14299082-010 | Idealistic Equivalence Relations and Orbit Relations | Is every idealistic equivalence relation on a standard Borel space Borel bireducible with an orbit equivalence relation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-010",
"literature-status:open",
"owr-year:2025"
] | The 2026 primary manuscript still calls the general Borel bireducibility question open, although it proves a strong obstruction for a related classwise embedding formulation. | [
{
"url": "https://sites.math.rutgers.edu/~fc327/idealistic.pdf",
"label": "Calderoni--Motto Ros, Structural results on idealistic equivalence relations"
},
{
"url": "https://doi.org/10.4171/owr/2025/2",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Is every idealistic equivalence relation on a standard Borel space Borel bireducible with an orbit equivalence relation? | Although orbit equivalence relations have been widely studied in the literature, very little is known about idealistic equivalence relations and their structure up to the pre-order of Borel reducibility. (E.g., see [KecLou].) The following funda- mental question is still open and motivates our work. Is every idealistic... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,166 | OWR-14299082-012 | Hyperfiniteness of Generic Wreath-Product Actions | Is the generic action of the wreath product $\mathbb Z\wr\mathbb Z$ on Cantor space hyperfinite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-012",
"literature-status:open",
"owr-year:2025"
] | The primary report explicitly lists the generic action of the wreath product of the integers with the integers as open; known finite-asymptotic-dimension results do not cover this group. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2409.03078",
"label": "Iyer--Shinko, Asymptotic dimension and hyperfiniteness"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Is the generic action of the wreath product $\mathbb Z\wr\mathbb Z$ on Cantor space hyperfinite? | Is the generic action of Z ≀ Z on Cantor space hyperfinite? The proof of Theorem 1 uses the connection between finite Borel asymptotic dimension and hyperfiniteness developed in [1]. Following Theorem 1, there are still many groups for which we do not know if their generic action is hyperfinite, even among the amenable gr... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,167 | OWR-14299082-014 | HOD Failure at Uncountable Cofinality | Is it consistent with ZFC that the HOD hypothesis holds and there are cardinals $\kappa<\lambda$ such that $\kappa$ is $<\lambda$-extendible, $\lambda$ is a strong-limit cardinal with $\operatorname{cf}(\lambda)=\omega_1$, and $(\lambda^+)^{\mathrm{HOD}}<\lambda^+$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-014",
"literature-status:open",
"owr-year:2025"
] | The 2025 primary paper still presents the analogous HOD failure configuration at uncountable cofinality as an open consistency question, including cofinality omega one. | [
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/compactness-phenomena-in-hod/FFD6AD92EFDDDAC2D53A98CDE7A396AD",
"label": "Goldberg--Poveda, Compactness phenomena in HOD"
},
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/onl... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Is it consistent with ZFC that the HOD hypothesis holds and there are cardinals $\kappa<\lambda$ such that $\kappa$ is $<\lambda$-extendible, $\lambda$ is a strong-limit cardinal with $\operatorname{cf}(\lambda)=\omega_1$, and $(\lambda^+)^{\mathrm{HOD}}<\lambda^+$? | Thus, we ask: Question 10 (Goldberg-P.). Is the above configuration consistent (with ZFC) for a cardinal \lambda with cf(\lambda) = \omega1 ? In the same paper, Cummings–Friedman–Golshani asked whether or not below the first supercompact cardinal \delta, κ+HOD < κ+ for all cardinals κ. We answer this is negatively, with... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,168 | OWR-14299082-015 | Measurable-Cardinal Strength of Minimal Namba Collapse | Does the consistency of regular cardinals $\nu$ and $\mu=\nu^{++}$ admitting a $|\mu|=\nu^+$-minimal forcing extension that preserves the regularity of $\mu^+$ require the consistency strength of a measurable cardinal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-015",
"literature-status:open",
"owr-year:2025"
] | Levine's primary paper retains the measurable-cardinal consistency question as an explicit remaining question; the theorem gives only the current upper bound. | [
{
"url": "https://resolve.cambridge.org/core/services/aop-cambridge-core/content/view/139989528588848BDDFD80F18AF63ED9/S2050509425101060a.pdf/on-namba-forcing-and-minimal-collapses.pdf",
"label": "Levine, On Namba Forcing and Minimal Collapses"
},
{
"url": "https://content.ems.press/assets/public/fu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Does the consistency of regular cardinals $\nu$ and $\mu=\nu^{++}$ admitting a $|\mu|=\nu^+$-minimal forcing extension that preserves the regularity of $\mu^+$ require the consistency strength of a measurable cardinal? | Does the conclusion of Theorem 1 require consistency of a measurable cardinal? There is also the question of the extent to which the main theorem can be stratified. Can we find a forcing like the one used in Theorem 1 that preserves cardinals ν \leq \lambda? It should be noted that there are a number of open questions—e... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,169 | OWR-14299082-016 | Cardinal-Preserving Namba-Type Forcing | Assume $\operatorname{LIP}(\lambda,\mu)$, where $\omega<\kappa<\lambda<\mu$ are regular cardinals. Is there a Namba-type minimal forcing that preserves every cardinal $\nu\leq\lambda$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-016",
"literature-status:open",
"owr-year:2025"
] | Levine's primary paper retains the cardinal-preservation question for the Namba-style forcing as an explicit open question, with no general preservation theorem resolving it. | [
{
"url": "https://resolve.cambridge.org/core/services/aop-cambridge-core/content/view/139989528588848BDDFD80F18AF63ED9/S2050509425101060a.pdf/on-namba-forcing-and-minimal-collapses.pdf",
"label": "Levine, On Namba Forcing and Minimal Collapses"
},
{
"url": "https://content.ems.press/assets/public/fu... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Assume $\operatorname{LIP}(\lambda,\mu)$, where $\omega<\kappa<\lambda<\mu$ are regular cardinals. Is there a Namba-type minimal forcing that preserves every cardinal $\nu\leq\lambda$? | Can we find a forcing like the one used in Theorem 1 that preserves cardinals ν \leq \lambda? It should be noted that there are a number of open questions—even besides those highlighted by Bukovský and Copláková—regarding whether Namba-style forcings produce cardinal collapses and whether they embed certain forcing ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,170 | OWR-14299082-017 | Chaining and Weak Mixing for Measure-Class-Preserving Actions | For measure-class-preserving actions, is chaining equivalent to weak mixing? Does there exist a measure-class-preserving action that is chaining but not $1$-chaining? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | partially_solved | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"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": "2026-10-10",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-10] **partially solved (first question: no; second: open)**. J. Zomback (with A. Tserunyan), Oberwolfach Report 2/2025, p. 122, Questions 5 and 6; chaining there means k-chaining for some k. A. Tserunyan, J. Zomback, *Bounded chaining in measurable dynamics*, arXiv:2609.18061v2... | [
"owr",
"oberwolfach-reports",
"OWR-14299082-017",
"literature-status:open",
"owr-year:2025"
] | The report proves equivalence of chaining, weak mixing, and one-chaining for probability-preserving actions but explicitly leaves both measure-class-preserving questions unresolved. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2012.10522",
"label": "Tserunyan--Zomback, A backward ergodic theorem along trees"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | For measure-class-preserving actions, is chaining equivalent to weak mixing? Does there exist a measure-class-preserving action that is chaining but not $1$-chaining? | Is chaining equivalent to weak mixing for measure-class-preserving actions? Are there measure-class-preserving actions that are chaining but not 1-chaining? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,171 | OWR-14299082-018 | ABCD Conjecture Under Determinacy | Assume $\mathrm{ZF}+\mathrm{AD}$. Let $\alpha,\beta,\gamma,\delta<\Theta$ with $\beta\leq\alpha$ and $\delta\leq\gamma$. Prove that $|\alpha^\beta|\leq|\gamma^\delta|$ if and only if $|\beta|\leq|\delta|$ and $|\alpha|\leq|\gamma|$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-018",
"literature-status:open",
"owr-year:2025"
] | The extracted ABCD conjecture is explicitly still open under only ZF plus AD, although the primary report records a proof under the stronger AD-plus hypothesis. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Assume $\mathrm{ZF}+\mathrm{AD}$. Let $\alpha,\beta,\gamma,\delta<\Theta$ with $\beta\leq\alpha$ and $\delta\leq\gamma$. Prove that $|\alpha^\beta|\leq|\gamma^\delta|$ if and only if $|\beta|\leq|\delta|$ and $|\alpha|\leq|\gamma|$. | Specifically the conjecture is the following. In full generality, that is, just assuming ZF + AD, the conjecture is still open, although special cases have been established just from this hypothesis (which we mention below). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,172 | OWR-14299082-019 | Function-Space Measure Embedding Values | Let $\nu$ be the function-space measure on $^{\omega_1}\omega_1$. Compute $j_\nu(\omega_2)$, and more generally determine the values of the associated elementary embedding on relevant cardinals. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-019",
"literature-status:open",
"owr-year:2025"
] | The report identifies computation of the next value of the function-space measure invariant as an open problem and gives only a strict upper bound for a lower value. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Let $\nu$ be the function-space measure on $^{\omega_1}\omega_1$. Compute $j_\nu(\omega_2)$, and more generally determine the values of the associated elementary embedding on relevant cardinals. | There are a number of interesting open problems about these functions space measures (for example computing jν (\omega2 ) where ν is the function space measure on \omega1\omega1 ; Chan has shown that jν (\omega1 ) < \delta 13 ). Infinite Structural Ramsey Theory: A progress report Natasha Dobrinen The simplest form of ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,173 | OWR-14299082-020 | Hyperfiniteness of Minimal-Subshift Conjugacy | Is the topological-conjugacy equivalence relation on minimal symbolic subshifts hyperfinite? In particular, is its restriction to Toeplitz subshifts hyperfinite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-020",
"literature-status:open",
"owr-year:2025"
] | The primary report states that hyperfiniteness of conjugacy for minimal symbolic subshifts remains unknown; 2025 work proves hyperfiniteness only for a proper generalized Oxtoby subclass. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
},
{
"url": "https://arxiv.org/abs/2502.14978",
"label": "Deka--Peng, Generalized Oxtoby subshifts and hyperfiniteness"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Is the topological-conjugacy equivalence relation on minimal symbolic subshifts hyperfinite? In particular, is its restriction to Toeplitz subshifts hyperfinite? | It remains unknown whether the conjugacy of minimal symbolic subshifts is hyperfinite, which is connected to a conjecture of Thomas on the isomorphism of complete groups. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,174 | OWR-14299082-021 | Classification of Symbolic Systems with Specification | Classify symbolic dynamical systems with the specification property. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140](https://doi.org/10.4171/owr/2025/2)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessment.*... | 3 | open | null | 2,025 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299082-021",
"literature-status:open",
"owr-year:2025"
] | The extract is only a fragment saying that an open-problem list is maintained, without identifying a mathematical claim, so it cannot support a solved or refuted classification. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299082/online/10.4171-owr-2025-2.pdf",
"label": "Oberwolfach Report 2/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/2 | null | null | null | Classify symbolic dynamical systems with the specification property. | list of open problems, which is now maintained on the webpage [32]. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Set Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/2, pp. 75--140 |
30,006,175 | OWR-14299083-001 | Similarity Metrics for Stochastic Processes | How can one define similarity metrics between stochastic processes? Optimal transport distances for Markov chains Gergely Neu (joint work with Sergio Calo, Anders Jonsson, Ludovic Schwartz, and Javier Segovia-Aguas) Overparametrization, Regularization, Identifiability and Uncertainty in ML 197 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208](https://doi.org/10.4171/owr/2025/... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report poses this broad question and then presents an optimal-transport construction, proving that the relevant bisimulation me) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299083-001",
"literature-status:partially-solved",
"owr-year:2025"
] | Optimal-transport and bisimulation constructions now give principled similarity distances for Markov chains, including efficient computation, but no universal metric theory for all stochastic processes is established. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299083/online/10.4171-owr-2025-4.pdf",
"label": "Oberwolfach Report 4/2025"
},
{
"url": "https://arxiv.org/abs/2406.04056",
"label": "Calo et al., Bisimulation metrics are optimal transport distances"
},
{
"u... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/4 | null | null | null | null | How can one define similarity metrics between stochastic processes? Optimal transport distances for Markov chains Gergely Neu (joint work with Sergio Calo, Anders Jonsson, Ludovic Schwartz, and Javier Segovia-Aguas) Overparametrization, Regularization, Identifiability and Uncertainty in ML 197 | unrecoverable | The official report poses this broad question and then presents an optimal-transport construction, proving that the relevant bisimulation metrics are optimal-transport distances and giving a finite-dimensional algorithm for Markov chains. | null | null | null | null | null | Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208 |
30,006,176 | OWR-14299083-002 | Generalization Guarantees for Self-Supervised Representations | Establish statistical generalization guarantees across downstream prediction tasks for representations obtained by self-supervised pretraining on large unlabeled augmented datasets, beyond the presently understood kernel and infinite-width regimes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208](https://doi.org/10.4171/owr/2025/... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299083-002",
"literature-status:partially-solved",
"owr-year:2025"
] | Kernel self-supervised models and wide-network limits have rigorous PCA-like equivalences in restricted regimes, but the claim is not established for self-supervised models in general. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299083/online/10.4171-owr-2025-4.pdf",
"label": "Oberwolfach Report 4/2025"
},
{
"url": "https://ojs.aaai.org/index.php/AAAI/article/view/29077",
"label": "Esser--Fleissner--Ghoshdastidar, Non-parametric representati... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/4 | null | null | null | Establish statistical generalization guarantees across downstream prediction tasks for representations obtained by self-supervised pretraining on large unlabeled augmented datasets, beyond the presently understood kernel and infinite-width regimes. | Are self-supervised models doing kernel PCA? I have introduced this framework and the foundations of the most recent algorith- mic developments, as well as discussed the potential for representation learning in more detail. This talk will have two parts. In the first part, I will briefly introduce self- supervised pret... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208 |
30,006,177 | OWR-14299083-003 | Adam Optimization Performance | Why does Adam work so well? Adam has been shown to outperform gradient descent in optimizing large language transformers empirically, and by a larger margin than on other tasks, but it is unclear why this happens. We show that the heavy-tailed class imbalance found in language modeling tasks leads to difficulties in th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208](https://doi.org/10.4171/owr/2025/... | 3 | partially_solved | null | 2,025 | 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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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 the title of a talk and then supplies its proposed mechanism: heavy-tailed class imbalance creates) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299083-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The primary study identifies heavy-tailed class imbalance and normalization as a mechanism explaining Adam's advantage in several settings, but it is not a complete explanation of all cases in which Adam works well. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299083/online/10.4171-owr-2025-4.pdf",
"label": "Oberwolfach Report 4/2025"
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{
"url": "https://proceedings.neurips.cc/paper_files/paper/2024/hash/350e718ff74062b4bac2c6ffd9e1ac66-Abstract-Conference.html",
"label":... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/4 | null | null | null | null | Why does Adam work so well? Adam has been shown to outperform gradient descent in optimizing large language transformers empirically, and by a larger margin than on other tasks, but it is unclear why this happens. We show that the heavy-tailed class imbalance found in language modeling tasks leads to difficulties in th... | unrecoverable | The official report uses this question as the title of a talk and then supplies its proposed mechanism: heavy-tailed class imbalance creates ill-conditioning that Adam’s normalization counteracts. | null | null | null | null | null | Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208 |
30,006,178 | OWR-14299083-004 | Definition of a Causal Representation | What is a causal representation? 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:** [Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208](https://doi.org/10.4171/owr/2025/... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents this as a broad epistemological framing question rather than a precise mathematical problem with stated hypothe) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299083-004",
"literature-status:open",
"owr-year:2025"
] | The extracted question is foundational and under-specified: the literature proposes multiple causal representation formalisms and identifiability conditions, but no generally accepted definition resolves it. | [
{
"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/1/14299083/online/10.4171-owr-2025-4.pdf",
"label": "Oberwolfach Report 4/2025"
},
{
"url": "https://nips.cc/virtual/2024/108171",
"label": "Scholkopf, What is a causal representation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/4 | null | null | null | null | What is a causal representation? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report presents this as a broad epistemological framing question rather than a precise mathematical problem with stated hypotheses and conclusion. | null | null | null | null | null | Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208 |
30,006,179 | OWR-14299083-005 | Criteria for a Good Representation | What makes a good representation? 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:** [Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208](https://doi.org/10.4171/owr/2025/... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report poses this as a philosophical organizing question in an expository discussion, not as a standalone mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299083-005",
"literature-status:open",
"owr-year:2025"
] | No generally accepted task-independent criterion for a good learned representation has emerged; current work gives task-dependent criteria such as downstream utility, alignment, symmetry, and robustness, so the extracted question remains open. | [
{
"url": "https://representational-alignment.github.io/",
"label": "ICLR 2024 Representational Alignment workshop"
},
{
"url": "https://arxiv.org/abs/2203.09250",
"label": "Symmetry-Based Representations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/4 | null | null | null | null | What makes a good representation? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report poses this as a philosophical organizing question in an expository discussion, not as a standalone mathematical problem. | null | null | null | null | null | Overparametrization, Regularization, Identifiability and Uncertainty in Machine Learning (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/4, pp. 175--208 |
30,006,180 | OWR-14299084-001 | Foundational Assumptions for Obfuscation, FHE, and SNARGs | Determine whether indistinguishability obfuscation can be based on weaker standard assumptions and made post-quantum secure; whether any meaningful virtual-black-box obfuscation can be constructed; whether fully homomorphic encryption can be based on objects other than integer lattices; and whether SNARGs for every NP ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 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-14299084-001",
"literature-status:partially-solved",
"owr-year:2025"
] | General virtual-black-box obfuscation is unconditionally impossible for circuits, while indistinguishability obfuscation now has constructions from well-founded assumptions; plausibly post-quantum iO from standard well-studied assumptions and the broader SNARG and non-lattice FHE questions remain unresolved. | [
{
"url": "https://people.seas.harvard.edu/~salil/research/obfuscate-abs.html",
"label": "Barak et al., obfuscation impossibility"
},
{
"url": "https://doi.org/10.1145/3785007",
"label": "Jain et al., iO from well-founded assumptions"
},
{
"url": "https://ems.press/content/serial-article-... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Determine whether indistinguishability obfuscation can be based on weaker standard assumptions and made post-quantum secure; whether any meaningful virtual-black-box obfuscation can be constructed; whether fully homomorphic encryption can be based on objects other than integer lattices; and whether SNARGs for every NP ... | The area is rife with exciting and difficult open questions including: (a) can we reduce the mathematical assumptions required for program obfuscation? (b) can we construct a program obfuscation scheme that is post-quantum secure, e.g. from hardness assumptions on integer lattices? and (c) can we construct obfuscators ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,181 | OWR-14299084-003 | Efficient Verification of Distribution Properties | Characterize the properties of an unknown distribution for which an untrusted server can generate, in polynomial time, a short interactive proof of an approximately correct assertion that a verifier can check using fewer samples and less computation than independent analysis would require. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 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-14299084-003",
"literature-status:partially-solved",
"owr-year:2025"
] | Interactive protocols now verify broad classes of distribution analyses with fewer samples and less verifier computation, including computationally sound protocols for any efficiently decidable distribution property; lower bounds and limitations on proof generation mean the unrestricted formulation is not fully settled... | [
{
"url": "https://arxiv.org/abs/2409.06594",
"label": "Herman and Rothblum, distribution-property arguments"
},
{
"url": "https://eccc.weizmann.ac.il/report/2023/161/revision/1/download/",
"label": "Herman and Rothblum, doubly-efficient proofs"
},
{
"url": "https://ems.press/content/seri... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Characterize the properties of an unknown distribution for which an untrusted server can generate, in polynomial time, a short interactive proof of an approximately correct assertion that a verifier can check using fewer samples and less computation than independent analysis would require. | Can the untrusted data server prove that its assertions are approxi- mately correct? Can a short efficiently verifiable proof be generated in polynomial time? Can Alice efficiently verify Bob’s claims using fewer resources (say in terms of samples and computation) than would be needed to run the analysis herself? Verif... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,182 | OWR-14299084-004 | Information-Theoretic Additive Randomized Encodings | Characterize the functions $f(x_1,\ldots,x_n)$ that admit information-theoretically secure additive randomized encodings: local randomized maps $g_i(x_i)$ into a finite abelian group whose sum reveals $f$ and essentially nothing else about the inputs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 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-14299084-004",
"literature-status:partially-solved",
"owr-year:2025"
] | ARE constructions and reductions are known for important classes, including computational constructions from bilinear-group assumptions and later public-key encryption; information-theoretic feasibility has sharp positive and negative results but the general local-reduction question remains open. | [
{
"url": "https://eprint.iacr.org/2023/870.pdf",
"label": "Halevi, Ishai, Kushilevitz, and Rabin, ARE"
},
{
"url": "https://eprint.iacr.org/2025/104.pdf",
"label": "Bitansky, Erabelli, and Garg, ARE from PKE"
},
{
"url": "https://ems.press/content/serial-article-files/51349",
"label"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Characterize the functions $f(x_1,\ldots,x_n)$ that admit information-theoretically secure additive randomized encodings: local randomized maps $g_i(x_i)$ into a finite abelian group whose sum reveals $f$ and essentially nothing else about the inputs. | Can we reduce the general case to this special case by first locally mapping each xi to x′i in G, and then securely computing the sum of all x′i ? In this part, I will present positive results, negative results, and open questions about the existence of ARE with information-theoretic security. Additive Randomized Encod... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,183 | OWR-14299084-005 | Minimal Assumptions for Additive Randomized Encodings | Determine the weakest computational assumptions under which efficient, fully secure additive randomized encodings can be constructed. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 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-14299084-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Public-key encryption suffices for computational ARE, and one-sided ARE can be obtained from one-way functions, while information-theoretic security is available in restricted or inefficient settings; minimal assumptions for efficient general ARE are still unknown. | [
{
"url": "https://eprint.iacr.org/2025/104.pdf",
"label": "Bitansky, Erabelli, and Garg, ARE from PKE"
},
{
"url": "https://eprint.iacr.org/2023/870.pdf",
"label": "Halevi, Ishai, Kushilevitz, and Rabin, ARE"
},
{
"url": "https://ems.press/content/serial-article-files/51349",
"label"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Determine the weakest computational assumptions under which efficient, fully secure additive randomized encodings can be constructed. | What are the minimal computational assumptions under which additive random- ized encodings can be constructed? Additive Randomized Encodings: Part 2 Nir Bitansky (joint work with Saroja Erabeli and Rachit Garg) Better Garbling via Algebraic Assumptions Rachel Lin (joint work with Marshall Ball, Yuval Ishai, Hanjun Li, ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,184 | OWR-14299084-006 | Power of Shared Randomness in Distributed Computation | Characterize the power of a public random string shared by multiple parties performing a joint task, particularly when the parties' inputs may depend on that string. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299084-006",
"literature-status:partially-solved",
"owr-year:2025"
] | Recent work characterizes concrete gains and losses from preset public coins and relates shared randomness to computational hardness in distributed locally checkable problems; the full power of a shared random string across general multiparty tasks remains open. | [
{
"url": "https://arxiv.org/abs/2504.17583",
"label": "Hadad and Naor, shared randomness in LCL problems"
},
{
"url": "https://ems.press/content/serial-article-files/51349",
"label": "OWR 2025/3 Cryptography report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Characterize the power of a public random string shared by multiple parties performing a joint task, particularly when the parties' inputs may depend on that string. | What is the power of a shared random string known to several parties in a system who wish to perform some joint task? Shared Randomness: Friend or Foe? Moni Naor (joint work with Shahar Cohen and Adar Hadad) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,185 | OWR-14299084-007 | Duplicate Distribution-Verification Question | Can the untrusted data server prove that its assertions are approximately correct? Can a short efficiently verifiable proof be generated in polynomial time? Verifying Properties of Distributions: Constructions Tal Herman | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report repeats the two motivating questions already preserved in the earlier verifiable-data-science record and then gives the ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299084-007",
"literature-status:partially-solved",
"owr-year:2025"
] | Short interactive proofs with efficient verification are known for broad distribution properties, including label-invariant properties with near-square-root sample and communication complexity; the formulation without restrictions on the property or proof-generation model remains unresolved. | [
{
"url": "https://arxiv.org/abs/2409.06594",
"label": "Herman and Rothblum, distribution-property arguments"
},
{
"url": "https://eccc.weizmann.ac.il/report/2023/161/revision/1/download/",
"label": "Herman and Rothblum, doubly-efficient proofs"
},
{
"url": "https://ems.press/content/seri... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | null | Can the untrusted data server prove that its assertions are approximately correct? Can a short efficiently verifiable proof be generated in polynomial time? Verifying Properties of Distributions: Constructions Tal Herman | unrecoverable | The official report repeats the two motivating questions already preserved in the earlier verifiable-data-science record and then gives the label-invariant construction. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,186 | OWR-14299084-008 | Evasive-LWE Research-Direction Discussion | Should we move away from private-coin evasive LWE to public-coin evasive LWE and succinct LWE? Discussion group: Which direction(s) should evasive LWE research take? Chris Brzuska | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** partially solved
... | 3 | partially_solved | null | 2,025 | 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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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 records an open-ended discussion about which research direction to pursue after counterexamples, not a mathematically te) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299084-008",
"literature-status:partially-solved",
"owr-year:2025"
] | Private-coin evasive-LWE variants used in earlier constructions have published counterexamples, whereas public-coin evasive LWE and succinct LWE have cleaner falsifiable formulations and imply useful constructions; this supports the proposed shift but does not settle all variants or security assumptions. | [
{
"url": "https://eprint.iacr.org/2025/375.pdf",
"label": "Brzuska, Uenal, and Woo, evasive-LWE attacks and variants"
},
{
"url": "https://eprint.iacr.org/2024/1416.pdf",
"label": "Lattice construction from public-coin evasive LWE"
},
{
"url": "https://ems.press/content/serial-article-fi... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | null | Should we move away from private-coin evasive LWE to public-coin evasive LWE and succinct LWE? Discussion group: Which direction(s) should evasive LWE research take? Chris Brzuska | unrecoverable | The official report records an open-ended discussion about which research direction to pursue after counterexamples, not a mathematically testable problem statement. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,187 | OWR-14299084-010 | Cryptographic Equivalences for High-Energy Phenomena | Find further high-energy-physics phenomena whose computational hardness is equivalent to the existence of standard cryptographic primitives, extending the known equivalence for decoding Hawking radiation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174](https://doi.org/10.4171/owr/2025/3)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessmen... | 3 | open | null | 2,025 | 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-14299084-010",
"literature-status:open",
"owr-year:2025"
] | An existential equivalence between black-hole radiation decoding and several quantum-cryptographic primitives is proved, but the proposed extension to further high-energy phenomena is explicitly conjectural and has not been established in general. | [
{
"url": "https://arxiv.org/abs/2211.05491",
"label": "Brakerski, Black-Hole Radiation Decoding is Quantum Cryptography"
},
{
"url": "https://ems.press/content/serial-article-files/51349",
"label": "OWR 2025/3 Cryptography report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/3 | null | null | null | Find further high-energy-physics phenomena whose computational hardness is equivalent to the existence of standard cryptographic primitives, extending the known equivalence for decoding Hawking radiation. | We propose to study equivalence relations between phenomena in high-energy physics and the existence of standard cryptographic primitives, and show the first example where such an equivalence holds [Bra23]. We conjecture that such connections may be found in other high-energy physics phenomena. When the Universe Speaks... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Cryptography (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/3, pp. 141--174 |
30,006,188 | OWR-14299085-002 | Lieb–Robinson Bounds for Nonrelativistic Fermions | Can the local estimate $\lvert\operatorname{tr} O_z(\widehat{x})(\gamma^{(1)}_{N,t}-\omega_{N,t})\rvert\leq C(t)\varepsilon^{-2}$, proved for pseudo-relativistic high-density fermions, be extended to nonrelativistic fermion dynamics, where the one-particle velocity is unbounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374](https://doi.org/10.4171/owr/2025/7)
## Literature review (che... | 3 | open | null | 2,025 | 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-14299085-002",
"literature-status:open",
"owr-year:2025"
] | Continuum Lieb-Robinson bounds for non-relativistic fermions have been substantially improved, but the published results still assume ultraviolet-regularized interactions; they do not establish the full unregularized extension with unbounded single-particle velocity posed here. | [
{
"url": "https://doi.org/10.1007/s00023-024-01453-y",
"label": "Hinrichs, Lemm, and Siebert, continuum fermion bounds"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4236/OWR_2025_07.pdf?isAllowed=y&sequence=1",
"label": "OWR 2025/7 correlated systems report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/7 | null | null | null | Can the local estimate $\lvert\operatorname{tr} O_z(\widehat{x})(\gamma^{(1)}_{N,t}-\omega_{N,t})\rvert\leq C(t)\varepsilon^{-2}$, proved for pseudo-relativistic high-density fermions, be extended to nonrelativistic fermion dynamics, where the one-particle velocity is unbounded? | It is an interesting open problem to extend the result (5) to the case of non-relativistic fermions, in which the single particle velocity is a priori unbounded. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374 |
30,006,189 | OWR-14299085-003 | Low-Temperature Order in Quantum Heisenberg Ferromagnets | For the short-range quantum Heisenberg ferromagnet in dimension $d\geq 3$, prove that sufficiently low temperature produces long-range order; specifically, prove that $\lim_{\Lambda\nearrow\mathbb{Z}^d}|\Lambda|^{-2}\sum_{x,y\in\Lambda}\langle\widetilde S_x\cdot\widetilde S_y\rangle_{T,\Lambda}>0$ for all sufficiently ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374](https://doi.org/10.4171/owr/2025/7)
## Literature review (che... | 3 | open | null | 2,025 | 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-14299085-003",
"literature-status:open",
"owr-year:2025"
] | The low-temperature long-range-order statement for the short-range quantum Heisenberg ferromagnet in dimension at least three remains a longstanding unproved problem; available rigorous results cover antiferromagnets, ground states, or different interaction regimes, not this claim. | [
{
"url": "https://web.math.princeton.edu/~aizenman/OpenProblems_MathPhys/9901.HeisenbergFerr.html",
"label": "Lieb, long-range order problem"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4236/OWR_2025_07.pdf?isAllowed=y&sequence=1",
"label": "OWR 2025/7 correlated systems report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/7 | null | null | null | For the short-range quantum Heisenberg ferromagnet in dimension $d\geq 3$, prove that sufficiently low temperature produces long-range order; specifically, prove that $\lim_{\Lambda\nearrow\mathbb{Z}^d}|\Lambda|^{-2}\sum_{x,y\in\Lambda}\langle\widetilde S_x\cdot\widetilde S_y\rangle_{T,\Lambda}>0$ for all sufficiently ... | We recall basic properties of this model, as well as the famous open problem concerning the appearance of long- range order at low temperature: for d \geq 3 and T small enough, it is expected that 1 X D\textasciitilde{} \textasciitilde{} E lim Sx \cdot Sy >0 Λ\toZd |Λ|2 T,Λ x,y\inΛ −HΛ /T −HΛ /T where h \cdot iT,Λ = Tr... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374 |
30,006,190 | OWR-14299085-004 | Strong Continuity Without Ultraviolet Regularization | Does strong continuity of the many-body dynamics persist when the ultraviolet regularization is removed, that is, in the limit $\sigma\to 0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374](https://doi.org/10.4171/owr/2025/7)
## Literature review (che... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299085-004",
"literature-status:open",
"owr-year:2025"
] | The unregularized limit of strong continuity is still identified as an open issue: recent work constructs continuous dynamics on suitable extensions or subalgebras, but does not prove norm continuity on the full algebra after removing the ultraviolet regulator. | [
{
"url": "https://doi.org/10.1007/s11005-025-01919-y",
"label": "Siebert, thermodynamic limit of continuum fermions"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4236/OWR_2025_07.pdf?isAllowed=y&sequence=1",
"label": "OWR 2025/7 correlated systems report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/7 | null | null | null | Does strong continuity of the many-body dynamics persist when the ultraviolet regularization is removed, that is, in the limit $\sigma\to 0$? | An open question is if the strong continuity still persists when the regularization gets removed, i.e., in the limit \sigma \to 0. Mini-Workshop: New Directions in Correlated Quantum Systems 365 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374 |
30,006,191 | OWR-14299085-005 | Counterexamples to Strongly Continuous Many-Fermion Dynamics | For the unregularized continuum fermion Hamiltonian, find an interaction $V$ and states for which the Heisenberg evolution of $a(f)$ fails to be strongly continuous. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374](https://doi.org/10.4171/owr/2025/7)
## Literature review (che... | 3 | open | null | 2,025 | 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-14299085-005",
"literature-status:open",
"owr-year:2025"
] | No explicit interaction and state family proving failure of strong continuity for the unregularized many-fermion dynamics was located; recent work explains why such counterexamples are expected and replaces the full algebra by a continuous subalgebra, leaving the requested construction open. | [
{
"url": "https://doi.org/10.1007/s11005-025-01919-y",
"label": "Siebert, thermodynamic limit of continuum fermions"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4236/OWR_2025_07.pdf?isAllowed=y&sequence=1",
"label": "OWR 2025/7 correlated systems report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/7 | null | null | null | For the unregularized continuum fermion Hamiltonian, find an interaction $V$ and states for which the Heisenberg evolution of $a(f)$ fails to be strongly continuous. | The open question is to find a particular interaction V and states to see that (1) for HΛ is not strongly continuous. Here ρ = N/|Λ| ≫ 1 in the limit |Λ|, N \to \infty. The proposed approach is to adapt recent techniques developed for fermionic systems in order to demonstrate that the many-body evolution can be locally... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: New Directions in Correlated Quantum Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/7, pp. 339--374 |
30,006,192 | OWR-14299086-001 | Generating Sets Realizing Minimal Growth | Let $G=F_n\rtimes_\phi\mathbb Z$ be a free-by-cyclic group, and let $\xi(G)=\{e(G,X):X\text{ is a finite generating set of }G\}$. Characterize the finite generating sets $X$ for which $e(G,X)=\min\xi(G)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-001",
"literature-status:open",
"owr-year:2025"
] | Existence and finiteness properties of the set of growth rates are known, including attainment of a minimum in relevant groups, but no characterization of all finite generating sets realizing the minimum for free-by-cyclic groups was found. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/6f61d540-8e50-41f3-97a8-6e8214672460/content",
"label": "OWR 2025/6 geometric group theory report"
},
{
"url": "https://doi.org/10.1007/s00222-023-01200-w",
"label": "Fujiwara and Sela, rates of growth"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Let $G=F_n\rtimes_\phi\mathbb Z$ be a free-by-cyclic group, and let $\xi(G)=\{e(G,X):X\text{ is a finite generating set of }G\}$. Characterize the finite generating sets $X$ for which $e(G,X)=\min\xi(G)$. | An immediate question is the following Problem 4. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,193 | OWR-14299086-003 | $L^p$ Cohomology at the Semisimple Rank Threshold | Let $F$ be a local field, let $G$ be the $F$-points of a semisimple algebraic group over $F$, and let $r=\operatorname{rk}_F(G)$. Is $H^k_{\mathrm{ct}}(G,L^p(G))=0$ for every $1<p<\infty$ and $k<r$? Does there exist $1<p<\infty$ such that $H^r_{\mathrm{ct}}(G,L^p(G))\neq 0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-003",
"literature-status:partially-solved",
"owr-year:2025"
] | For real and non-Archimedean semisimple groups, substantial vanishing below the rank and nonvanishing in the rank degree are proved in important ranges, including large p and many group types; the all-local-field, all-p formulation remains open. | [
{
"url": "https://doi.org/10.5802/jep.232",
"label": "Bourdon and Remy, nonvanishing Lp-cohomology"
},
{
"url": "https://arxiv.org/abs/2302.09307",
"label": "Lopez Neumann, vanishing in degree two"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/6f61d540-8e50-41f3-97a8-6... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Let $F$ be a local field, let $G$ be the $F$-points of a semisimple algebraic group over $F$, and let $r=\operatorname{rk}_F(G)$. Is $H^k_{\mathrm{ct}}(G,L^p(G))=0$ for every $1<p<\infty$ and $k<r$? Does there exist $1<p<\infty$ such that $H^r_{\mathrm{ct}}(G,L^p(G))\neq 0$? | 253] Let F be a local field (Archimedean or not), let G be the F -points of a semisimple algebraic group defined over F and let r = rkF (G). (1) Do we have Hctk (G, Lp (G)) = \{0\} for 1 < p < \infty and k < r? r (2) Does there exist some 1 < p < \infty such that Hct (G, Lp (G)) 6= \{0\}? The report passage is retained... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,194 | OWR-14299086-005 | Profinite Reconstruction of Complex Projective Varieties | Let $X$ be a smooth complex projective variety. Can its homeomorphism type be recovered from its algebraic fundamental group $\pi_1^{\mathrm{alg}}(X)$? Can its topological fundamental group $\pi_1(X)$ be recovered up to isomorphism from $\pi_1^{\mathrm{alg}}(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Profinite rigidity and homeomorphism recovery are proved for important families such as products of hyperbolic Riemann surfaces, but the two questions for arbitrary smooth complex projective varieties remain open. | [
{
"url": "https://arxiv.org/abs/2501.13761",
"label": "Hughes et al., profinite rigidity of Kahler groups"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/6f61d540-8e50-41f3-97a8-6e8214672460/content",
"label": "OWR 2025/6 geometric group theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Let $X$ be a smooth complex projective variety. Can its homeomorphism type be recovered from its algebraic fundamental group $\pi_1^{\mathrm{alg}}(X)$? Can its topological fundamental group $\pi_1(X)$ be recovered up to isomorphism from $\pi_1^{\mathrm{alg}}(X)$? | Let X be a smooth complex projective variety: (1) Can we recover X up to homeomorphism from \pi1alg (X)? (2) Can we recover \pi1 (X) up to isomorphism from \pi1alg (X)? Profinite rigidity of Kähler groups Claudio Llosa Isenrich (joint work with Sam Hughes, Pierre Py, Matthew Stover, Stefano Vidussi) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,195 | OWR-14299086-006 | Profinite Genera and Simple Kähler Groups | Is the Kähler-profinite genus of every residually finite Kähler group finite? Does there exist a simple Kähler group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The report explicitly leaves finiteness of the K-profinite genus and existence of a simple Kahler group open, while the related question of a non-residually-finite Kahler group was answered positively by Toledo; hence the extracted multi-part record is only partially solved. | [
{
"url": "https://ora.ox.ac.uk/objects/uuid%3A3212138f-4ec5-43d4-9af3-49789a6dce51/files/r6395w9580",
"label": "OWR 2025/6 Kahler-group report"
},
{
"url": "https://arxiv.org/abs/2501.13761",
"label": "Hughes et al., profinite rigidity of Kahler groups"
},
{
"url": "https://library.slmat... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Is the Kähler-profinite genus of every residually finite Kähler group finite? Does there exist a simple Kähler group? | We end with the following related questions that to our knowledge remain open: Question 6. Is the K-profinite genus of every residually finite Kähler group finite? Is there a simple Kähler group? Question 7 is a well-known variation of Serre’s question whether there is a non-residually finite Kähler group; the latte... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,196 | OWR-14299086-007 | Profinite Rigidity with Free Edge Groups | Let $\Lambda$ be an amalgamated product $F_1*_H F_2$ or an HNN extension $F_1*_H$ of free groups, where $H$ is an arbitrary finitely generated free group. If the profinite completion of $\Lambda$ is isomorphic to that of a free group or a surface group $\Gamma$, must $\Lambda\cong\Gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-007",
"literature-status:open",
"owr-year:2025"
] | The cyclic case has been proved, but the report states that the corresponding profinite-rigidity assertion for an arbitrary free group remains open; nearby results for free and surface groups do not remove this general gap. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/6f61d540-8e50-41f3-97a8-6e8214672460/content",
"label": "OWR 2025/6 geometric group theory report"
},
{
"url": "https://arxiv.org/abs/2211.12390",
"label": "Jaikin-Zapirain and Morales, free and surface groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Let $\Lambda$ be an amalgamated product $F_1*_H F_2$ or an HNN extension $F_1*_H$ of free groups, where $H$ is an arbitrary finitely generated free group. If the profinite completion of $\Lambda$ is isomorphic to that of a free group or a surface group $\Gamma$, must $\Lambda\cong\Gamma$? | The case when H is an arbitrary free group remains open. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,197 | OWR-14299086-009 | Duplicate Free-Group Word-Measure Conjecture | Theorem 2 above has applications to the study of profinite rigidity. Since the abelianizations of all finite-index subgroups of a given group are a profinite in- variant of that group, the theorem implies that free products of free and surface groups are profinitely rigid among hyperbolic graphs of free groups with cyc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction contains contextual material followed by the same Conjecture 4 preserved in the next recor) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-009",
"literature-status:partially-solved",
"owr-year:2025"
] | The conjecture remains open in general; primary work proves substantial cases including primitive words, powers, commutators, and partial-surface words. | [
{
"url": "https://doi.org/10.4171/owr/2025/6",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2020.03.013",
"label": "Hanany--Meiri--Puder"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | null | Theorem 2 above has applications to the study of profinite rigidity. Since the abelianizations of all finite-index subgroups of a given group are a profinite in- variant of that group, the theorem implies that free products of free and surface groups are profinitely rigid among hyperbolic graphs of free groups with cyc... | unrecoverable | The official report confirms that this extraction contains contextual material followed by the same Conjecture 4 preserved in the next record. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,198 | OWR-14299086-010 | Free-Group Word-Measure Conjecture | Let $F$ be a nonabelian free group of finite rank, and let $w,w'\in F$. If $w$ and $w'$ induce the same word measure on every finite group, prove that some $\varphi\in\operatorname{Aut}(F)$ satisfies $\varphi(w)=w'$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-010",
"literature-status:partially-solved",
"owr-year:2025"
] | The stated word-measure conjecture is unresolved in full, while the literature establishes several nontrivial families, including powers, commutators, and surface-type words. | [
{
"url": "https://doi.org/10.4171/owr/2025/6",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2020.03.013",
"label": "Hanany--Meiri--Puder"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Let $F$ be a nonabelian free group of finite rank, and let $w,w'\in F$. If $w$ and $w'$ induce the same word measure on every finite group, prove that some $\varphi\in\operatorname{Aut}(F)$ satisfies $\varphi(w)=w'$. | Conjecture 4. Let F be a non-abelian free group of rank n and let w \in F . For every finite group G, w induces a word map w : Gn \to G and a word measure −1 given by Pw (A \subset G) = |w|G|(A)| n . If two words w, w′ \in F induce the same word measure on every finite group, then there exists f \in Aut(F ) such that f... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,199 | OWR-14299086-012 | Profinite Rigidity of Coxeter Groups | Write $\mathcal W$ for all Coxeter groups. If $W_\Gamma,W_\Lambda\in\mathcal W$ have isomorphic profinite completions, must $W_\Gamma\cong W_\Lambda$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338](https://doi.org/10.4171/owr/2025/6)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299086-012",
"literature-status:partially-solved",
"owr-year:2025"
] | The general W-profinite-rigidity question remains open, but affine, right-angled, minimal non-spherical, triangle, and other subclasses are proved rigid. | [
{
"url": "https://doi.org/10.4171/owr/2025/6",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1007/s00209-025-03799-3",
"label": "Affine Coxeter rigidity"
},
{
"url": "https://arxiv.org/abs/2505.08701",
"label": "Profinite properties of Coxeter groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/6 | null | null | null | Write $\mathcal W$ for all Coxeter groups. If $W_\Gamma,W_\Lambda\in\mathcal W$ have isomorphic profinite completions, must $W_\Gamma\cong W_\Lambda$? | Are Coxeter groups W-profinitely rigid? Despite much effort, the isomorphism prob- lem amongst Coxeter groups remains open. v 2 for all v \in V (Γ), (vw)2 if \{v, w\} \in / E(Γ), WΓ := V (Γ) . (vw)m(\{v,w\}) if \{v, w\} \in E(Γ) and m(\{v, w\}) < \infty Since the edge-label 3 appears very often in the study of Coxeter ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Structures in Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/6, pp. 275--338 |
30,006,200 | OWR-14299088-001 | Optimization Workshop Contents Fragment | Conjecture . . 416 Luis Felipe Vargas (joint with Alex Bortolotti, Monaldo Mastrolilli) On the degree automatability of SoS proofs . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Dmitriy (Tim) Kunisky (joint with Maximilian Jerdee, Cristopher Moore, Alexander S. Wein) Tensor networks, tensor cumulants, tensor P... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299088-001",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a table-of-contents fragment with no identifiable mathematical proposition, so its truth cannot be tested and it is retained as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | null | Conjecture . . 416 Luis Felipe Vargas (joint with Alex Bortolotti, Monaldo Mastrolilli) On the degree automatability of SoS proofs . . . . . . . . . . . . . . . . . . . . . . . . . . 416 Dmitriy (Tim) Kunisky (joint with Maximilian Jerdee, Cristopher Moore, Alexander S. Wein) Tensor networks, tensor cumulants, tensor P... | unrecoverable | The official report confirms that this extraction is a damaged table-of-contents fragment, not a mathematical conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,201 | OWR-14299088-003 | Degree Automatability of Sum-of-Squares Proofs | Characterize meaningful conditions under which low-degree sum-of-squares proofs can be found in polynomial time with polynomially bounded coefficients. In particular, determine when the degree-$d$ sum-of-squares relaxation is algorithmically computable in time polynomial in the natural input size for fixed $d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | partially_solved | null | 2,025 | 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-14299088-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The general degree-automatability problem remains open; a 2025 primary paper supplies broader sufficient criteria and refutation results for important finite-domain classes. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2504.17756",
"label": "Bortolotti--Mastrolilli--Vargas"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Characterize meaningful conditions under which low-degree sum-of-squares proofs can be found in polynomial time with polynomially bounded coefficients. In particular, determine when the degree-$d$ sum-of-squares relaxation is algorithmically computable in time polynomial in the natural input size for fixed $d$. | O’Donnell (2017) posed the open problem of identifying meaningful conditions that ensure that “small” SoS proofs can be found. An initial elegant solution to this question is provided by Raghavendra and Weitz, which is based on the Nullstellensatz proof system. where si , hi \in R[x1 , . . . , xn ]. Moreover, we say th... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,202 | OWR-14299088-004 | Additive Orthogonal Bases for Invariant Polynomials | For invariant-polynomial rings under general group actions, characterize approximately orthogonal bases and determine when such a basis can also be chosen to satisfy an additive property analogous to that of tensor cumulants. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | partially_solved | null | 2,025 | 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-14299088-004",
"literature-status:partially-solved",
"owr-year:2025"
] | Tensor cumulants give a near-orthogonal additive basis for orthogonally invariant tensor polynomials, but the requested construction for general group actions remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2404.18735",
"label": "Tensor cumulants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | For invariant-polynomial rings under general group actions, characterize approximately orthogonal bases and determine when such a basis can also be chosen to satisfy an additive property analogous to that of tensor cumulants. | Based on this surprising result, we propose an intriguing direction for future research. We ask: in general, what do approximately orthogonal bases for invariant polynomials under various group actions look like? Can such general bases be chosen to also satisfy the additivity property above? Optimization, Theoretical C... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,203 | OWR-14299088-005 | Decidability of Symmetric Polynomial Nonnegativity | Determine whether nonnegativity of a symmetric polynomial is decidable when there is only one group of variables, and whether the analogous problem is decidable for a single matrix variable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-005",
"literature-status:open",
"owr-year:2025"
] | Undecidability is known for several groups of variables, but decidability for one group of variables or one matrix remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2408.04616",
"label": "Symmetric nonnegative functions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Determine whether nonnegativity of a symmetric polynomial is decidable when there is only one group of variables, and whether the analogous problem is decidable for a single matrix variable. | It remains an open problem whether the problem is decidable in the setting of a single group of variables or, respectively, in the case of a single matrix. Symmetric nonnegative functions and the Vandermonde map Sebastian Debus (joint work with Jose Acevedo, Grigoriy Blekherman, Cordian Riener) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,204 | OWR-14299088-006 | Graph Distances in Associahedra | Given two vertices of an associahedron, determine their graph distance, equivalently the minimum number of flips or rotations connecting the corresponding triangulations or trees. Develop an exact structural characterization or efficient algorithm beyond the known complexity classification. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | partially_solved | null | 2,025 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299088-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The diameter is solved and a 2026 primary result establishes NP-completeness of flip or rotation distance, but a full exact algorithmic characterization of associahedron distance remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2602.22874",
"label": "Flip-distance complexity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Given two vertices of an associahedron, determine their graph distance, equivalently the minimum number of flips or rotations connecting the corresponding triangulations or trees. Develop an exact structural characterization or efficient algorithm beyond the known complexity classification. | The first question is to determine the graph distance between two vertices in a polytope. The second question is to determine the graph diameter of a polytope, where the graph diameter is defined as the maximum graph distance over all pairs of vertices. On the other hand, the distance computation in associahedra is a lon... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,205 | OWR-14299088-007 | Generic Point Identification from Polynomial Measurements | Extend the known generic-identification result from dimension two to higher dimensions. More generally, characterize polynomial measurement maps for which generic points can be identified from nongeneric measurements. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-007",
"literature-status:open",
"owr-year:2025"
] | Known results cover dimension two, random hypergraphs, and tensor-identifiability settings, but the higher-dimensional and general-polynomial extensions explicitly remain open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2402.18190",
"label": "Generic global rigidity in ell-p spaces"
},
{
"url": "https://arxiv.org/abs/2305.18990",
"label": "Algebraic hypergraph rigidity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Extend the known generic-identification result from dimension two to higher dimensions. More generally, characterize polynomial measurement maps for which generic points can be identified from nongeneric measurements. | It remains an open problem to extend this result to higher dimensions. (ii) When g(x1 , x2 , . . . , xk ) = (x1 ⊙ x2 ⊙ \cdot \cdot \cdot ⊙ xk ) \cdot 1, where ⊙ denotes the Hadamard product, \cdot denotes the dot product, and 1 denotes the all-one vector. We believe that this phenom- enon holds for other polynomial map... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,206 | OWR-14299088-008 | Complexity-Bounded Computation of Maximum Destabilizing Subgroups | Construct an algorithm that computes the maximum destabilizing one-parameter subgroup represented by the limiting direction of the relevant gradient flow, and prove explicit complexity bounds for the algorithm. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-008",
"literature-status:open",
"owr-year:2025"
] | Recent gradient-flow work identifies the limiting maximally destabilizing direction in broad settings, but a general complexity-bounded algorithm to compute it is still not known. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1287/moor.2025.0939",
"label": "Hirai--Sakabe"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Construct an algorithm that computes the maximum destabilizing one-parameter subgroup represented by the limiting direction of the relevant gradient flow, and prove explicit complexity bounds for the algorithm. | Especially, limi\to\infty xi \in M \infty corresponds to the maximum destabilizing 1-parameter subgroup in this case, and one open problem is to construct an algorithm to compute it with some complexity bounds. where the last limit exists in the sense of the cone topology. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,207 | OWR-14299088-009 | Irreducible Components of Landau Varieties | Determine whether the proposed elimination-theoretic construction identifies every irreducible component of the Landau variety, and characterize which candidate components genuinely occur. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | partially_solved | null | 2,025 | 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-14299088-009",
"literature-status:partially-solved",
"owr-year:2025"
] | Elimination and Euler-discriminant methods give the Landau variety in important families and examples, but the general irreducible-decomposition question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.cpc.2024.109278",
"label": "Principal Landau determinants"
},
{
"url": "https://arxiv.org/abs/2407.18176",
"label": "Euler stratifications"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Determine whether the proposed elimination-theoretic construction identifies every irreducible component of the Landau variety, and characterize which candidate components genuinely occur. | Does it contributes to the irreducible decomposition of the Landau variety as suggested by the method [2]? \partialf \partialf 1 − yf (x; z), νi − syxi (x), ξj + sy (x; z). \partialxi \partialzj The generators of J0 are obtained from (4) by a replacement \sigmas \to y, \sigmaνi \to xi , \partialj \to ξj . Now we set I0... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,208 | OWR-14299088-010 | Dimension-Free Separation Exponents for Affine and Positive Semidefinite Sets | Find an algebraic-geometric invariant that yields a dimension-free exponent in the separation inequality between an affine subspace and the cone $S_+^n$ of positive semidefinite matrices. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-015"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299088-010",
"literature-status:open",
"owr-year:2025"
] | Known separation exponents depend on dimension or singularity parameters; the requested algebraic-geometric dimension-free exponent remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jmaa.2024.129070",
"label": "Alternating projections for the PSD cone"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Find an algebraic-geometric invariant that yields a dimension-free exponent in the separation inequality between an affine subspace and the cone $S_+^n$ of positive semidefinite matrices. | Motivated by this observation, I propose the following problem. Is there a quantity in algebraic geometry that can provide a dimension- free exponent for the separation inequality for an affine subspace and Sn+ ? Alternating Projections in Low Dimensions Yoshiyuki Sekiguchi (joint work with Hiroyuki Ochiai, Hayato Waki) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,209 | OWR-14299088-011 | Komlos Discrepancy Conjecture and Unsatisfiable Formulas | Determine whether discrepancy instances constructed from unsatisfiable Boolean formulas can have lower bound greater than $1+\sqrt{2}$. More broadly, prove the Komlós conjecture that vectors of Euclidean norm at most one admit signs with uniformly bounded coordinate discrepancy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299088-011",
"literature-status:open",
"owr-year:2025"
] | The Komlos conjecture remains open; unsatisfiable-matrix constructions improve the lower bound to 1 plus square-root of 2 but do not prove a dimension-free upper bound. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1137/22M149819X",
"label": "Kunisky"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Determine whether discrepancy instances constructed from unsatisfiable Boolean formulas can have lower bound greater than $1+\sqrt{2}$. More broadly, prove the Komlós conjecture that vectors of Euclidean norm at most one admit signs with uniformly bounded coordinate discrepancy. | Unsatisfiable Boolean formulas and the Komlós conjecture Contributed by Dmitriy (Tim) Kunisky The startlingly simple-looking Komlós conjecture is one of the main open problems in the field of discrepancy theory and has remained open for at least 30 years. Can \sqrt{ } such constructions of dis- crepancy instances ever... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,210 | OWR-14299088-012 | Inverse-Polynomial Influence Thresholds on the Boolean Cube | Let $f$ and $g$ be degree-$d$ multilinear real polynomials on $\{-1,1\}^n$ such that every variable has relative influence at most $\delta$ in both polynomials. Can $\delta$ be chosen inverse-polynomially in $d$ while still guaranteeing a point $x\in\{-1,1\}^n$ for which $f(x)\neq0$ and $g(x)\neq0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-012",
"literature-status:open",
"owr-year:2025"
] | The exponential and inverse-quadratic influence bounds are known, but whether the threshold can be polynomial in the degree remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1007/978-3-031-15979-4_6",
"label": "Austrin--Chung--Chung--Fu--Lin--Mahmoody"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Let $f$ and $g$ be degree-$d$ multilinear real polynomials on $\{-1,1\}^n$ such that every variable has relative influence at most $\delta$ in both polynomials. Can $\delta$ be chosen inverse-polynomially in $d$ while still guaranteeing a point $x\in\{-1,1\}^n$ for which $f(x)\neq0$ and $g(x)\neq0$? | The main question is whether \delta can be taken to be some polynomial in d. in n variables x1 , . . . , xn with real-valued coefficients \{fS \}, the (relative) influence of xi on f is the squared ℓ2 mass of coefficients fS of terms containing xi , relative to the total squared ℓ2 mass, i.e., , X X RelInf i (f ) = 2 fS fS2... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,211 | OWR-14299088-013 | Real Components of Two Multi-Affine Polynomial Zero Sets | Is the number of connected components of the common real zero set of two multi-affine polynomials bounded solely in terms of their degrees, independently of the number $n$ of variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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 | {
"source_url": "https://zenodo.org/records/23049180",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] OWR-14299088-013: a counterexample to Basu and Perrucci's degree-only bound for two multi-affine polynomials is now public. (https://zenodo.org/records/23049180) | [
"owr",
"oberwolfach-reports",
"OWR-14299088-013",
"literature-status:open",
"owr-year:2025"
] | The one-polynomial bound and unbounded three-polynomial constructions are established, while the corresponding dimension-independent bound for two multi-affine polynomials remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2204.01595",
"label": "Basu--Perrucci"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Is the number of connected components of the common real zero set of two multi-affine polynomials bounded solely in terms of their degrees, independently of the number $n$ of variables? | Does there exist a bound on the number of connected components of the real zeros of a system of two multi-affine polynomials in terms of a bound on their degrees, independent of n ? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,212 | OWR-14299088-014 | Dimension-Free Sum-of-Squares Certificates for Two Quadratic Constraints | Let $Q_1,Q_2,Q_3$ be quadratic forms in $n$ variables, with $Q_1$ nonnegative on the variety $Q_2=Q_3=0$. Find the least degree $2d$ for which there are homogeneous polynomials $P,R_2,R_3$ of degree $2d$, with $P$ a sum of squares, such that $PQ_1+R_2Q_2+R_3Q_3$ is a sum of squares. Can $d$ be bounded independently of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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-14299088-014",
"literature-status:open",
"owr-year:2025"
] | The S-lemma settles one quadratic constraint, but no dimension-independent degree guarantee for certificates on the variety of two quadratics is established in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Let $Q_1,Q_2,Q_3$ be quadratic forms in $n$ variables, with $Q_1$ nonnegative on the variety $Q_2=Q_3=0$. Find the least degree $2d$ for which there are homogeneous polynomials $P,R_2,R_3$ of degree $2d$, with $P$ a sum of squares, such that $PQ_1+R_2Q_2+R_3Q_3$ is a sum of squares. Can $d$ be bounded independently of ... | What happens if we instead ask for certificate of nonnegativity of Q1 on the variety defined by two quadratics Q2 and Q3 ? The previously considered certificate had degree 2d equal to 0, and now we ask in what degree 2d is this certificate guaranteed to exist? Is the degree 2d of the certificate independent of the number of... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,213 | OWR-14299088-015 | Duplicate Dimension-Free Separation-Exponent Problem | Is there any quantity in algebraic geometry that can be used to express a dimension-free exponent for separation of an affine set and the set of positive semidefinite matrices? Is there a symbolic or a randomized algorithm to give such an exponent? Sum-of-Squares certificates for non-negativity of Quadratics Contributed b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | open | null | 2,025 | 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 open-problem-session extraction repeats the dimension-free separation-exponent problem represented ca) | [
"OWR-14299088-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299088-015",
"literature-status:open",
"owr-year:2025"
] | Singularity degree gives useful dimension-dependent separation and convergence bounds, with sharp low-dimensional examples, but the requested dimension-free algebraic-geometric exponent and algorithm remain open. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jmaa.2024.129070",
"label": "Ochiai--Sekiguchi--Waki"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | null | Is there any quantity in algebraic geometry that can be used to express a dimension-free exponent for separation of an affine set and the set of positive semidefinite matrices? Is there a symbolic or a randomized algorithm to give such an exponent? Sum-of-Squares certificates for non-negativity of Quadratics Contributed b... | unrecoverable | The official report confirms that this open-problem-session extraction repeats the dimension-free separation-exponent problem represented canonically by OWR-14299088-010. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,214 | OWR-14299088-016 | Incident-Variety Description of Euler Discriminants | Find an intrinsic incident-variety description of the Euler discriminant analogous to the established geometric picture for classical discriminants. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450](https://... | 3 | partially_solved | null | 2,025 | 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-14299088-016",
"literature-status:partially-solved",
"owr-year:2025"
] | Euler-discriminant elimination is proved for important families, including hyperplane complements, but an intrinsic general incident-variety description is still unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/9",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2411.19696",
"label": "Euler discriminants of hyperplane complements"
},
{
"url": "https://arxiv.org/abs/2505.13163",
"label": "Hypergeometric discriminants"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/9 | null | null | null | Find an intrinsic incident-variety description of the Euler discriminant analogous to the established geometric picture for classical discriminants. | Can we find the same picture for Euler discriminant? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | MFO-RIMS Tandem Workshop: Optimization, Theoretical Computer Science and Algebraic Geometry: Convexity and Beyond (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/9, pp. 405--450 |
30,006,215 | OWR-14299089-001 | Quotients and Presentations of L-Convex Objects | Describe the correspondence between the two flow-based presentations of $L$-convex sets and functions. Define natural quotient operations for $L$-convex sets and $L$-convex functions, and establish their basic structural properties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558](https://doi.org/10.4171/owr/2025/12)
## Literature review (... | 3 | open | null | 2,025 | 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-14299089-001",
"literature-status:open",
"owr-year:2025"
] | The correspondence between the two flow-based presentations and quotients of L-convex objects remain workshop-level open questions; no definitive general solution was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/12",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/12 | null | null | null | Describe the correspondence between the two flow-based presentations of $L$-convex sets and functions. Define natural quotient operations for $L$-convex sets and $L$-convex functions, and establish their basic structural properties. | followed by an open problem session and working groups in the afternoons. What is the correspondence between these two presentations? • How can we define quotients of L-convex sets and L-convex functions? Mini-Workshop: Alcoved Polytopes in Physics and Optimization 533 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Alcoved Polytopes in Physics and Optimization (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/12, pp. 531--558 |
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