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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,616 | OWR-14297736-027 | Universal Lower Bounds for Biharmonic Steklov Eigenvalues | Given $\alpha,M>0$, prove that constants $a,b>0$ depending only on $\alpha,M,n$ satisfy $\rho_k(\Omega)\geq ak^{2/(2n-1)}$ for every convex $\Omega\subset\mathbb R^n$ of volume $M$, and $\rho_k(\Omega)\geq bk^{1/n}$ for every such general domain. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297736-027",
"literature-status:open",
"owr-year:2023"
] | This duplicate formulation of the convex and general-domain rho_k lower-bound conjecture remains unresolved beyond the special families motivating it. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Given $\alpha,M>0$, prove that constants $a,b>0$ depending only on $\alpha,M,n$ satisfy $\rho_k(\Omega)\geq ak^{2/(2n-1)}$ for every convex $\Omega\subset\mathbb R^n$ of volume $M$, and $\rho_k(\Omega)\geq bk^{1/n}$ for every such general domain. | Based on the results obtained in [5] for rectangles and unions of rectangles, we conjecture that similar results will hold for convex and general domains in Rn : Conjecture: Given positive numbers \alpha and M , there exist positive constants a and b depending on \alpha, M and n only, such that ρk (Ω) \geq ak 2/(2n−1) ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,617 | OWR-14297736-028 | Curved-Waveguide Simplicity and Surface-Curvature Optimization | For soft or hard-wall curved waveguides, determine whether every discrete eigenvalue above the ground state is simple. Separately, among connected compact smooth surfaces $\Sigma\subset\mathbb R^3$ of fixed area and genus $g\geq 1$, minimize $H_\Sigma=\|k_1-k_2\|_\infty$ and characterize minimizers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297736-028",
"literature-status:open",
"owr-year:2023"
] | The record explicitly says that the finite-eigenvalue question remains open even for hard-wall waveguides, and the cited literature does not provide a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For soft or hard-wall curved waveguides, determine whether every discrete eigenvalue above the ground state is simple. Separately, among connected compact smooth surfaces $\Sigma\subset\mathbb R^3$ of fixed area and genus $g\geq 1$, minimize $H_\Sigma=\|k_1-k_2\|_\infty$ and characterize minimizers. | Let us add a couple of remarks: (a) the question is not void; for suitably chosen Γ and V , one can get any finite number of eigenvalues, (b) the question is open also for ‘hard-wall’ waveguides in which the potential confinement is replaced by Dirichlet condition, and (c) the quasi-onedimensional character is vital; i... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,618 | OWR-14297736-029 | Second Neumann Eigenvalues of Convex Subdomains of a Square | Let $D$ be the unit square. Prove that every convex subdomain $\Omega\subset D$ satisfies $\mu_2(\Omega)\geq\mu_2(D)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-029",
"literature-status:open",
"owr-year:2023"
] | Existence results and proofs for symmetric convex families are known, but the proposed inequality for every convex subdomain of the unit square is still stated as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2312.13747",
"label": "Cavallina--Funano--Henrot--Lemenant--Lucardesi--Sakaguchi, Neumann extremum problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Let $D$ be the unit square. Prove that every convex subdomain $\Omega\subset D$ satisfies $\mu_2(\Omega)\geq\mu_2(D)$. | This leads to the following open problem: Let D be the unit square, prove that for any convex subdomain Ω \subset D, we have µ2 (Ω) \geq µ2 (D). Mikhail Karpukhin: Universal bounds for magnetic and Bakry-Emery Laplacians. Let (M, g) be a closed Riemannian surface. For a real-valued 1-form A on M one has a differential ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,619 | OWR-14297736-030 | Magnetic-Laplacian Eigenvalue Infima on Closed Surfaces | For a closed Riemannian surface $(M,g)$ and $i>1$, prove $\inf_A\overline\lambda_i(M,g,A)\geq C(M,g)>0$ over all real magnetic potentials $A$, and develop a natural construction of critical metric-potential pairs. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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,
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-030",
"literature-status:open",
"owr-year:2023"
] | The fixed-surface positive lower bound for the infimum of normalized magnetic eigenvalues is posed as an open question; available magnetic spectral results do not establish it in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For a closed Riemannian surface $(M,g)$ and $i>1$, prove $\inf_A\overline\lambda_i(M,g,A)\geq C(M,g)>0$ over all real magnetic potentials $A$, and develop a natural construction of critical metric-potential pairs. | This raises a question of whether there is a natural way to obtain crit- ical pairs (g, A). Thus, the open question is to show that for a fixed (M, g) and i > 1 one has inf \lambdāi (M, g, A) ⩾ C(M, g) > 0. Partial monotonicity. It is well-known that Neumann eigenvalues do not satisfy domain monotonicity (by contrast ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,620 | OWR-14297736-031 | Metric-Independent Bounds for Bakry–Émery Eigenvalues | For the normalized eigenvalues $\overline\lambda_i(M,g,e^{-f})$ of the Bakry–Émery Laplacian on a closed surface, find an upper bound independent of the metric $g$ and weight $f$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-031",
"literature-status:open",
"owr-year:2023"
] | Universal upper bounds are known under additional curvature or geometric hypotheses, but independence from both the metric and arbitrary weight in the stated problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00039-013-0215-x",
"label": "Funano--Shioya, weighted eigenvalue bounds under curvature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For the normalized eigenvalues $\overline\lambda_i(M,g,e^{-f})$ of the Bakry–Émery Laplacian on a closed surface, find an upper bound independent of the metric $g$ and weight $f$. | In this case, the open question is: does there exist an upper bound for \lambdāi (M, g, e−f ) independent of g and f ? There is a similar question for Bakry-Emery (or Witten) Laplacian. For \sigma = e−f , f \in C \infty (M ) the operator L\sigma can be defined via Z Z h∇g \phi, ∇g \psii \sigmadvg = \phi(L\sigma \psi) ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,621 | OWR-14297736-032 | High-Index Spectral Optimizers Among Polygons | For polygons with a fixed number $n$ of sides, prove that optimizers of normalized Dirichlet and Neumann eigenvalues converge to the regular $n$-gon as the eigenvalue index tends to infinity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297736-032",
"literature-status:open",
"owr-year:2023"
] | The extracted record stops after defining the class of n-sided polygons and does not state the target extremal claim, so no more specific resolution is identifiable. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For polygons with a fixed number $n$ of sides, prove that optimizers of normalized Dirichlet and Neumann eigenvalues converge to the regular $n$-gon as the eigenvalue index tends to infinity. | I propose the following open problem: let Rn be the class of all polygons with n sides. Richard Laugesen: Neumann and Robin eigenvalues. The Rayleigh quo- tient for the Robin eigenvalue problem on a domain Ω with Robin parameter \alpha is R R 2 Ω |∇u| Rdx + \alpha \partialΩ u2 dS . Ω u2 dx | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,622 | OWR-14297736-033 | Third Neumann Eigenvalue Maximization Under Curvature Bounds | Among simply connected surfaces with curvature bounded above by $K$, prove that the third Neumann eigenvalue is maximized by a disjoint union of two constant-curvature-$K$ disks when $K\neq 0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,023 | 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-14297736-033",
"literature-status:partially-solved",
"owr-year:2023"
] | The two-disk maximizer is proved in Euclidean and hyperbolic constant-curvature settings and for spherical domains, while the broader upper-curvature-bound problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.2422/2036-2145.202010_059",
"label": "Freitas--Laugesen, hyperbolic space"
},
{
"url": "https://arxiv.org/abs/2208.11413",
"label": "Bucur--Martinet--Nahon, sphere"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Among simply connected surfaces with curvature bounded above by $K$, prove that the third Neumann eigenvalue is maximized by a disjoint union of two constant-curvature-$K$ disks when $K\neq 0$. | Is the third Neumann eigenvalue maximal for a disjoint union of two disks with constant curvature K, among simply connected surfaces with curvature bounded above by K? The conjecture is known for K = 0 by Girouard and Polterovich [10], but is open when K < 0, and when K > 0. Note: in the constant curvature setting the ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,623 | OWR-14297736-034 | Critical Points of Second Neumann Eigenfunctions on Acute Triangles | Prove that every second Neumann eigenfunction of an acute planar triangle has at most one nonvertex critical point. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297736-034",
"literature-status:open",
"owr-year:2023"
] | The extracted statement refers to an omitted preceding hot-spots claim; known counterexamples and positive classes do not identify or settle that exact claim, so it remains unclear and is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4007/annals.2020.191.1.3",
"label": "Judge--Mondal, Euclidean triangles"
},
{
"url": "https://doi.org/10.2307/121027",
"label": "Burdzy--Werner, hot-spots counterexample"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Prove that every second Neumann eigenfunction of an acute planar triangle has at most one nonvertex critical point. | The conjecture is known to be false for non-simply connected domains in the plane [5]. Although we were able to give an alternative proof of the hot spots conjecture for all acute triangles in 2021 [11], the above statement still remains an open question. The following is a summary of the open problems presented on Thu... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,624 | OWR-14297737-001 | Rigorous Mesoscopic Limits of Many-Particle Systems | Rigorously justify mesoscopic evolution equations, including the Boltzmann equation, as limits of many-particle systems. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246](https://doi.org/10.4171/owr/2023/38)
## Literature re... | 3 | open | null | 2,023 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"id": 15,
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297737-001",
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] | The extracted question is only a rhetorical phrase about order and chaos, while the surrounding Boltzmann discussion does not specify a mathematical proposition that can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2023/38",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/38 | null | null | null | Rigorously justify mesoscopic evolution equations, including the Boltzmann equation, as limits of many-particle systems. | Can we have a little Order amidst all this Chaos? Systems that involve many elements, be it a gas of particles or a herd of animals, are ubiquitous in our day to day lives. While such systems are of great interest to us, their investigation is hindered by their complexity the amount of (usually coupled) equations that ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246 |
30,005,625 | OWR-14297737-002 | Fluctuation Limits for Moderately Interacting Particle Systems | Prove mean-field convergence for Keller–Segel-type and Dirac-approximating potentials, and obtain the better-than-$N^{-1/2}$ mean-square rate needed to derive intermediate fluctuation limits from smoothed empirical measures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246](https://doi.org/10.4171/owr/2023/38)
## Literature re... | 3 | partially_solved | null | 2,023 | 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-14297737-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Recent mean-field fluctuation results justify smoothed empirical measures and obtain N^{-1/2-epsilon} rates in specific moderately interacting models, but no general explanation or universal rate theorem resolves the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2023/38",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2405.15128",
"label": "mean-field fluctuations for smoothed empirical measures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/38 | null | null | null | Prove mean-field convergence for Keller–Segel-type and Dirac-approximating potentials, and obtain the better-than-$N^{-1/2}$ mean-square rate needed to derive intermediate fluctuation limits from smoothed empirical measures. | Why smoothed empirical measures and why the rate N −1/2−\varepsilon ? On stationary solutions to the discrete velocity Boltzmann equation in the plane Anne Nouri (joint work with Leif Arkeryd) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246 |
30,005,626 | OWR-14297737-003 | Continuation of Nordheim Condensation Beyond Dirac-Mass Formation | After finite-time formation of a Dirac mass at $\omega=0$ in the Nordheim equation, determine whether the solution can be continued as $f(t,\omega)=n(t)\delta_0/\sqrt\omega+h(t,\omega)$ with $h(t,\cdot)$ a function. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246](https://doi.org/10.4171/owr/2023/38)
## Literature re... | 3 | open | null | 2,023 | 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-14297737-003",
"literature-status:open",
"owr-year:2023"
] | The extracted formula and question are malformed and omit the governing equation and hypotheses, so the intended claim cannot be identified or verified. | [
{
"url": "https://doi.org/10.4171/owr/2023/38",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/38 | null | null | null | After finite-time formation of a Dirac mass at $\omega=0$ in the Nordheim equation, determine whether the solution can be continued as $f(t,\omega)=n(t)\delta_0/\sqrt\omega+h(t,\omega)$ with $h(t,\cdot)$ a function. | 1 (1) f (t, \omega) = \sqrt{ } n(t)\delta0 + h(t, \omega), where h(t) is a function? \omega If (1) is plugged in the equation and only homogeneous terms of order two and three are kept, (cf. [2] where such a question is already considered). Moreover, in the limit of weak nonlinear inteactions, it is possible to give an... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246 |
30,005,627 | OWR-14297737-004 | External-Field Stabilization of Unstable Kinetic Equilibria | For an unstable kinetic equilibrium, determine whether an imposed external electric field can stabilize the dynamics and characterize an optimal stabilizing field. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246](https://doi.org/10.4171/owr/2023/38)
## Literature re... | 3 | partially_solved | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297737-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Control theory now gives explicit external fields that suppress instabilities for known equilibria and perturbations, but the general PDE-constrained stabilization problem in the extracted record remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/38",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.jcp.2025.113904",
"label": "Einkemmer--Li--Mouhot--Yue, Vlasov--Poisson control"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/38 | null | null | null | For an unstable kinetic equilibrium, determine whether an imposed external electric field can stabilize the dynamics and characterize an optimal stabilizing field. | For the equilibrium state that are unstable, we ask if it is possible to impose external electric field to stablize the dynamics. Two case studies of PDE-constrained optimization within kinetic framework Qin Li min J(f [H]) H \partialt f + v\partialx f − (H + E[f ])\partialv f = 0 (1) s.t. E[f ] = \partialx G ∗ (1... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Classical and Quantum Mechanical Models of Many-Particle Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/38, pp. 2179--2246 |
30,005,628 | OWR-14297738-001 | Geometric Criteria for Benign Overfitting | Identify necessary and sufficient geometric conditions under which, for an arbitrary norm, the associated minimum-norm interpolating estimator exhibits benign overfitting. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376](https://doi.org/10.4171/owr/... | 3 | partially_solved | null | 2,023 | 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-14297738-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Necessary and sufficient conditions are known for minimum-norm linear interpolants in important covariance models, while the arbitrary-norm geometric characterization highlighted in the record remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/41",
"label": "original OWR report"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7720150/",
"label": "Bartlett--Long--Lugosi--Tsigler, benign overfitting"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/41 | null | null | null | Identify necessary and sufficient geometric conditions under which, for an arbitrary norm, the associated minimum-norm interpolating estimator exhibits benign overfitting. | In this talk, two geometrical tools are introduced that should be useful to solve this open problem: the Dvoretsky-Milman theorem and isomorphic and restricted isomorphic properties. A geometrical viewpoint on the benign overfitting phenomenon Guillaume Lecué (joint work with Zong Shang) Planted regression forests Enn... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376 |
30,005,629 | OWR-14297738-002 | Benign, Tempered, and Catastrophic Overfitting Regimes | Characterize when interpolation and overfitting in neural networks or kernel methods is benign, tempered, or catastrophic. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376](https://doi.org/10.4171/owr/... | 3 | partially_solved | null | 2,023 | 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-14297738-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Linear, kernel, and selected neural regimes now have rigorous benign, tempered, or catastrophic classifications, but a general characterization across interpolating methods is still open. | [
{
"url": "https://doi.org/10.4171/owr/2023/41",
"label": "original OWR report"
},
{
"url": "https://papers.neurips.cc/paper_files/paper/2022/hash/08342dc6ab69f23167b4123086ad4d38-Abstract-Conference.html",
"label": "Mallinar et al., overfitting taxonomy"
},
{
"url": "https://proceedings.... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/41 | null | null | null | Characterize when interpolation and overfitting in neural networks or kernel methods is benign, tempered, or catastrophic. | Can we characterize and understand when overfitting is in- deed benign, and when it is catastrophic as classic theory suggests? Tempered and benign overfitting in neural networks and kernels Ohad Shamir (joint work with Guy Kornowski, Gilad Yehudai, Daniel Barzilai) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376 |
30,005,630 | OWR-14297738-003 | Training-Loss Implications for Shallow Neural Networks | Determine what guarantees on prediction or generalization follow from small training loss for shallow neural networks. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376](https://doi.org/10.4171/owr/... | 3 | open | null | 2,023 | 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-14297738-003",
"literature-status:open",
"owr-year:2023"
] | The extracted ambitious implication from training losses to shallow-network behavior is not stated precisely enough for a theorem, and no general result resolves it. | [
{
"url": "https://doi.org/10.4171/owr/2023/41",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/41 | null | null | null | Determine what guarantees on prediction or generalization follow from small training loss for shallow neural networks. | Several open problems that I am intrigued by are summarized below: • An ambitious open problem is showing the implication of training losses for shallow neural networks. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376 |
30,005,631 | OWR-14297738-004 | Convergence to Implicit Geometry under Class Imbalance | Quantify how class imbalance affects the rates at which first-order training methods converge to their asymptotically preferred implicit geometry, and determine how architecture, data, and loss design affect that convergence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376](https://doi.org/10.4171/owr/... | 3 | partially_solved | null | 2,023 | 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-14297738-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Closed-form implicit geometries and imbalance-invariant parameterizations are known in unconstrained-feature and related models, but architecture-independent characterization remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/41",
"label": "original OWR report"
},
{
"url": "https://openreview.net/forum?id=utahaTbcHdP",
"label": "Kini--Vakilian--Behnia--Thrampoulidis, imbalance geometry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/41 | null | null | null | Quantify how class imbalance affects the rates at which first-order training methods converge to their asymptotically preferred implicit geometry, and determine how architecture, data, and loss design affect that convergence. | Is there an implicit bias towards solutions of a certain geometry and how does this vary across architectures and data? We remark that this characterization only holds for balanced data; hence, we ask whether it can be made invariant to class imbalances. Implicit Geometries through the Imbalance Lens Christos Thrampoul... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Interpolation and Over-parameterization in Statistics and Machine Learning (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/41, pp. 2359--2376 |
30,005,632 | OWR-14297739-001 | Recurrence-Coefficient Characterization of Bernstein–Szegő Measures | Characterize Bernstein–Szegő measures completely through recurrence coefficients of their associated multivariate orthogonal spaces, analogously to the known spectral characterization on $\mathbb T^2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Multivariate Orthogonal Polynomials: New synergies with Numerical Analysis (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/43, pp. 2489--2534](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,023 | 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-14297739-001",
"literature-status:open",
"owr-year:2023"
] | Bivariate and special multivariate Bernstein--Szego theories have recurrence and parameterization results, but the requested complete recurrence-coefficient characterization for the stated orthogonal spaces remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/43",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1102.0986",
"label": "Geronimo--Benge, bivariate Bernstein--Szego measures"
},
{
"url": "https://arxiv.org/abs/0710.0035",
"label": "Delgado--Geronimo--Iliev--Xu, two-var... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/43 | null | null | null | Characterize Bernstein–Szegő measures completely through recurrence coefficients of their associated multivariate orthogonal spaces, analogously to the known spectral characterization on $\mathbb T^2$. | A challenging open question is to give a complete characterization of the Bernstein-Szegő measures in terms of appropriate recurrence coefficients for the orthogonal spaces similarly to the spectral character- ization of the Bernstein-Szegő measures on the torus T2 in [3]. l−m M0 Pk,l;µ [x, y] = Tk,l (Pn0 ,m0 −1;µ\om... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Multivariate Orthogonal Polynomials: New synergies with Numerical Analysis (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/43, pp. 2489--2534 |
30,005,633 | OWR-14297740-001 | Unspecified Anabelian Galois Representation Conjecture | conjecture (Takao). Geometric and motivic Galois representations. Concerning the “homology vs homotopy” frontier, this workshop has seen the path between linear and an- abelian methods – a path initiated in the 90’s on one side with the integration of Falting’s p-adic Hodge method in anabelian geometry by Mochizuki and... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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 extraction is workshop-introduction prose ending in a reference to the Coleman conjecture; the report states no separate conjecture at t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297740-001",
"literature-status:open",
"owr-year:2023"
] | The extracted record is a workshop-summary fragment rather than a mathematically stated conjecture, so no stronger resolution can be established from the cited passage; under the queue rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | null | conjecture (Takao). Geometric and motivic Galois representations. Concerning the “homology vs homotopy” frontier, this workshop has seen the path between linear and an- abelian methods – a path initiated in the 90’s on one side with the integration of Falting’s p-adic Hodge method in anabelian geometry by Mochizuki and... | unrecoverable | The extraction is workshop-introduction prose ending in a reference to the Coleman conjecture; the report states no separate conjecture at this location. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,634 | OWR-14297740-002 | Unspecified Anabelian Geometry Conjecture | conjecture. A certain thematic group has appeared, that exploits various flavors of anabelian ℓ-adic Galois representations, in terms of purely anabelian methods (Iijima et al.), of the symmetries of spaces (applied to associators, Shiraishi or to Oda’s conjecture, Philip et al.), or in relation with Deligne-Ihara’s co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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 extraction is a composite workshop overview of several research programs rather than a formulated mathematical problem. No separate clea) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297740-002",
"literature-status:open",
"owr-year:2023"
] | The extracted record is a broad survey paragraph with no uniquely identifiable proposition; the cited material reports research directions rather than a proof or disproof, so it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | null | conjecture. A certain thematic group has appeared, that exploits various flavors of anabelian ℓ-adic Galois representations, in terms of purely anabelian methods (Iijima et al.), of the symmetries of spaces (applied to associators, Shiraishi or to Oda’s conjecture, Philip et al.), or in relation with Deligne-Ihara’s co... | unrecoverable | The extraction is a composite workshop overview of several research programs rather than a formulated mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,635 | OWR-14297740-005 | Profinite Congruence Subgroup Problem for Mapping Class Groups | Let $\Pi_{g,r}$ be the fundamental group of a hyperbolic topological surface of genus $g$ with $r$ punctures, let $\Gamma_{g,r}$ be its mapping class group, and for a class of finite groups $P$ let $\rho^P_{g,r} : \widehat{\Gamma}_{g,r} \to \operatorname{Out}(\Pi_{g,r}^P)$ be the universal pro-$P$ outer monodromy repre... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-005",
"literature-status:partially-solved",
"owr-year:2023"
] | The universal pro-P outer monodromy representation is known to be injective for genus at most two, but the general congruence subgroup problem for mapping class groups remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report with Asada--Boggi results"
},
{
"url": "https://arxiv.org/abs/1804.06322",
"label": "Boggi, congruence topologies"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $\Pi_{g,r}$ be the fundamental group of a hyperbolic topological surface of genus $g$ with $r$ punctures, let $\Gamma_{g,r}$ be its mapping class group, and for a class of finite groups $P$ let $\rho^P_{g,r} : \widehat{\Gamma}_{g,r} \to \operatorname{Out}(\Pi_{g,r}^P)$ be the universal pro-$P$ outer monodromy repre... | Is the universal pro-P outer monodromy representation ρP g,r injec- tive? 2. The congruence subgroup problem of the mapping class group The following problem is known as the congruence subgroup problem of the map- ping class group. For the congruence subgroup problem of the mapping class group, the following affirmativ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,636 | OWR-14297740-006 | Pro-l Congruence Subgroup Problem for Mapping Class Groups | Let $\Gamma_{g,r}$ be the mapping class group of a surface of genus $g$ with $r$ punctures, and for a prime $\ell$ let $\rho^{\ell\text{-csp}}_{g,r}$ denote the pro-$\ell$ congruence-subgroup representation induced by the action of $\Gamma_{g,r}$ on the pro-$\ell$ completion of the surface fundamental group. For which ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The pro-l representation is injective for several cases, including genus zero and genus at most two at l=2, while it is non-injective for genus one and l>7; no general answer is known. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report with the positive and negative theorems"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869318306410",
"label": "Hoshi--Iijima, genus-one pro-l problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $\Gamma_{g,r}$ be the mapping class group of a surface of genus $g$ with $r$ punctures, and for a prime $\ell$ let $\rho^{\ell\text{-csp}}_{g,r}$ denote the pro-$\ell$ congruence-subgroup representation induced by the action of $\Gamma_{g,r}$ on the pro-$\ell$ completion of the surface fundamental group. For which ... | Is ρl-csp g,r injective? The following problem may be regarded as a pro-l version of the congruence subgroup problem of the mapping class group. For the pro-l congruence subgroup problem of the mapping class group, the following affirmative results are known. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,637 | OWR-14297740-007 | Fields of Definition under Gluing of Hurwitz Components | In the arithmetic geometry of Hurwitz spaces parametrizing branched covers of curves with fixed monodromy group and conjugacy classes, let $K$ be a number field over which two irreducible components of Hurwitz spaces are defined. Are the irreducible components of higher-degree Hurwitz spaces obtained by topological glu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-007",
"literature-status:partially-solved",
"owr-year:2023"
] | Fields of Definition of Components of Hurwitz Spaces proves the desired field-of-definition statement in several positive situations, but presents the general gluing question as unresolved. | [
{
"url": "https://arxiv.org/abs/2303.05903",
"label": "Seguin, Fields of Definition of Components of Hurwitz Spaces"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | In the arithmetic geometry of Hurwitz spaces parametrizing branched covers of curves with fixed monodromy group and conjugacy classes, let $K$ be a number field over which two irreducible components of Hurwitz spaces are defined. Are the irreducible components of higher-degree Hurwitz spaces obtained by topological glu... | Are components obtained by gluing components defined over K themselves defined over K? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,638 | OWR-14297740-008 | Anderson-Ihara Maximal Pro-p Extension Conjecture | question: Is Ω∗ equal to the maximal pro-p extension of Q(µp ) unramified outside p? which has motivated further work of Rasmussen and Tamagawa [RT08], and also of Matsumoto, Nakamura, Takao and other on the related Oda’s problem, see Philip’s report in this volume. 1.1. The Deligne-Ihara conjecture. To consider this q... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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 report explicitly says that this historical Anderson–Ihara question has an affirmative answer under the former Deligne–Ihara conjecture,) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297740-008",
"literature-status:partially-solved",
"owr-year:2023"
] | The Anderson--Ihara equality is proved in important cases, including Sharifi's theorem for odd irregular primes, and is implied by the Deligne--Ihara theorem in the relevant setting; the general equality remains open. | [
{
"url": "https://annals.math.princeton.edu/1988/128-2/p05",
"label": "Anderson--Ihara, pro-l branched coverings"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report recording the known cases"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | null | question: Is Ω∗ equal to the maximal pro-p extension of Q(µp ) unramified outside p? which has motivated further work of Rasmussen and Tamagawa [RT08], and also of Matsumoto, Nakamura, Takao and other on the related Oda’s problem, see Philip’s report in this volume. 1.1. The Deligne-Ihara conjecture. To consider this q... | unrecoverable | The report explicitly says that this historical Anderson–Ihara question has an affirmative answer under the former Deligne–Ihara conjecture, now a theorem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,639 | OWR-14297740-010 | Jannsen Finiteness for Galois Cohomology | The finiteness of the second cohomology group is a special case of a conjecture of Jannsen [Jan89, Conjecture 1]. As in the previous section, Gk comes with a descending central filtration \{F m Gk \}m\geq1 on Gk associated to the descending central series \{Π1,1 (m)\}m\geq1 of Π1,1 . We denote the m-th associated grade... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extraction only notes that one finiteness hypothesis in a proved theorem is a special case of Jannsen's broader conjecture and does not ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297740-010",
"literature-status:open",
"owr-year:2023"
] | The finiteness assertion is identified in the report as a special case of Jannsen's finiteness conjecture; only important special cases are known, so the general claim remains open. | [
{
"url": "https://doi.org/10.1007/978-1-4613-9649-9_5",
"label": "Jannsen, l-adic cohomology and Galois cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | null | The finiteness of the second cohomology group is a special case of a conjecture of Jannsen [Jan89, Conjecture 1]. As in the previous section, Gk comes with a descending central filtration \{F m Gk \}m\geq1 on Gk associated to the descending central series \{Π1,1 (m)\}m\geq1 of Π1,1 . We denote the m-th associated grade... | unrecoverable | The extraction only notes that one finiteness hypothesis in a proved theorem is a special case of Jannsen's broader conjecture and does not formulate that conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,640 | OWR-14297740-011 | Tate-Shafarevich Finiteness for Tori over Function Fields | Let $K$ be the function field of a smooth curve $C$ over a number field $k$. For every $K$-torus, or more generally every group of multiplicative type, is the Tate–Shafarevich group $\operatorname{Sha}_C^1(T)$ finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-14297740-011",
"literature-status:partially-solved",
"owr-year:2023"
] | The Tate--Shafarevich finiteness conjecture for tori over function fields is known for stably rational tori and related cases, but the report states the assertion for arbitrary tori as a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "Harari, finiteness theorems in Galois cohomology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $K$ be the function field of a smooth curve $C$ over a number field $k$. For every $K$-torus, or more generally every group of multiplicative type, is the Tate–Shafarevich group $\operatorname{Sha}_C^1(T)$ finite? | The conjecture is known for a stably rational K-torus T (loc. cit.). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,641 | OWR-14297740-012 | Non-Density of Bounded-Rank Galois Loci | Let $X$ be a smooth geometrically connected variety of dimension $\geq 2$ over a number field $k$, let $\rho_\ell : \pi_1(X) \to G_\ell \subset \mathrm{GL}_r(\mathbb{Z}_\ell)$ be an $\ell$-adic Galois representation whose image $G_\ell$ is a $\mathbb{Z}_\ell$-Lie group with finite abelianization, let $|X|_{\leq d}$ be ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-012",
"literature-status:partially-solved",
"owr-year:2023"
] | Cadoret--Tamagawa prove the non-density statement for curves, while the report explicitly says that the dimension-at-least-two case is widely open. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "Cadoret--Stix report with the conjecture and known curve case"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $X$ be a smooth geometrically connected variety of dimension $\geq 2$ over a number field $k$, let $\rho_\ell : \pi_1(X) \to G_\ell \subset \mathrm{GL}_r(\mathbb{Z}_\ell)$ be an $\ell$-adic Galois representation whose image $G_\ell$ is a $\mathbb{Z}_\ell$-Lie group with finite abelianization, let $|X|_{\leq d}$ be ... | Conjecture 1. Assume Gℓ has finite abelianization. Then |X|Vℓ \cap |X|\leqd is not Zariski-dense in X. For X a curve, Conjecture 1 is proved in [CT13]. In contrast, if X has dimension \geq 2, it is widely open. Actually, the strategy of [CT13] provides a heuristic for Conj. 1 when d = 1 - see [Cad23, §4]; this heuristi... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,642 | OWR-14297740-013 | Non-Density of Toric Galois Loci | Under the hypotheses defining the geometric $\ell$-adic local system $V_\ell$ on $X$, is the toric locus $|X|^{\mathrm{tor}}_{V_\ell}\cap|X|$ non-Zariski-dense in $X$? Is this toric locus independent of $\ell$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-013",
"literature-status:partially-solved",
"owr-year:2023"
] | The toric-locus conjecture has a theorem under level conditions at two primes, including non-density and conditional finiteness conclusions, but the unrestricted conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "Cadoret--Stix report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Under the hypotheses defining the geometric $\ell$-adic local system $V_\ell$ on $X$, is the toric locus $|X|^{\mathrm{tor}}_{V_\ell}\cap|X|$ non-Zariski-dense in $X$? Is this toric locus independent of $\ell$? | Conjecture 2. With the above assumptions, |X|tor Vℓ \cap |X| is not Zariski-dense in X. Conjecture 2 follows from Conjecture 1 but it is also a consequence of the Mumford- Tate conjecture and the generalized André-Oort conjecture (an unlikely intersec- tion type conjecture); this implication is deep as it involves the... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,643 | OWR-14297740-014 | Malle Lower Bounds over Rational Function Fields | For a transitive group $G\leq S_m$, prove the conjectural lower bound in Malle's asymptotic for the number $N_{G,\mathbb F_q(t)}(X)$ of degree-$m$ extensions of $\mathbb F_q(t)$ with Galois group $G$ and discriminant norm at most $X$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-014",
"literature-status:partially-solved",
"owr-year:2023"
] | For Malle's conjecture, the abelian case is a theorem and substantial non-abelian upper bounds are known over function fields, but the report notes that the required lower bound is still missing in general. | [
{
"url": "https://arxiv.org/abs/1701.04541",
"label": "Ellenberg--Tran--Westerland, Malle over function fields"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | For a transitive group $G\leq S_m$, prove the conjectural lower bound in Malle's asymptotic for the number $N_{G,\mathbb F_q(t)}(X)$ of degree-$m$ extensions of $\mathbb F_q(t)$ with Galois group $G$ and discriminant norm at most $X$. | conjecture. This method may be summarized as follows: (1) Translate the statistical question over Fq (t) into a question about (asymp- totically) estimating \#Mn (Fq ), where Mn is a moduli stack parameterizing the objects of interest of “complexity” n. (2) Compute \#Mn (Fq ) in terms of Lefschetz numbers in étale coh... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,644 | OWR-14297740-016 | Anabelian Interpretation of Homomorphisms between Fundamental Groups | Is there an anabelian interpretation of $\operatorname{Hom}_{\mathrm{op}}(\Pi_{X_1}^{\bullet},\Pi_{X_2}^{\bullet})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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-14297740-016",
"literature-status:open",
"owr-year:2023"
] | The moduli-space construction and several reconstruction results provide evidence for an anabelian explanation, but the extracted Hom-version question is still posed as an open research problem. | [
{
"url": "https://arxiv.org/abs/2010.01806",
"label": "Yang, moduli spaces of fundamental groups"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Is there an anabelian interpretation of $\operatorname{Hom}_{\mathrm{op}}(\Pi_{X_1}^{\bullet},\Pi_{X_2}^{\bullet})$? | Now, the author considered the following the fundamental question: Does there exist anabelian explanation for Homop (ΠX1• , ΠX2• )? 2. Moduli spaces of fundamental groups def Let Xi• = (Xi , DXi ), i \in \{1, 2\}, be a pointed stable curve of type (g, n) over an algebraically closed field ki of characteristic p > 0. He... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,645 | OWR-14297740-017 | Homeomorphism Conjecture for Moduli of Fundamental Groups | For pointed stable curves of type $(g,n)$ over algebraically closed fields of characteristic $p>0$, is the natural continuous map $\pi_{g,n}^{\mathrm{adm}}:\mathcal M_{g,n}^{\mathrm{adm}}\twoheadrightarrow\Pi_{g,n}$ from Frobenius-equivalence classes of curves to isomorphism classes of their admissible fundamental grou... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-017",
"literature-status:partially-solved",
"owr-year:2023"
] | The homeomorphism conjecture has substantial positive results in special loci and low-dimensional cases, but the asserted homeomorphism for all pointed stable curves in positive characteristic remains conjectural. | [
{
"url": "https://arxiv.org/abs/2010.01806",
"label": "Yang, moduli spaces of fundamental groups"
},
{
"url": "https://arxiv.org/abs/2301.04864",
"label": "Hu--Yang--Zong, topological structures and anabelian geometry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | For pointed stable curves of type $(g,n)$ over algebraically closed fields of characteristic $p>0$, is the natural continuous map $\pi_{g,n}^{\mathrm{adm}}:\mathcal M_{g,n}^{\mathrm{adm}}\twoheadrightarrow\Pi_{g,n}$ from Frobenius-equivalence classes of curves to isomorphism classes of their admissible fundamental grou... | The main conjecture of the theory of moduli spaces of fundamental groups is the following: adm Homeomorphism conjecture: The continuous map \pig,n : Mg,n ։ Πg,n is a homeomorphism. adm Note that the weak Isom-version conjecture only says that \pig,n is a bijection as sets. This means that the homeomorphism conjecture i... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,646 | OWR-14297740-018 | Strict Higher Étale-Homotopy Obstructions over Global Fields | Find varieties over global fields $K$ for which the full étale-homotopy obstruction is strictly stronger than its two-stage truncation; equivalently, find examples with $X(\mathbb{A}_K)^h\subsetneq X(\mathbb{A}_K)^{h,2}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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-14297740-018",
"literature-status:open",
"owr-year:2023"
] | The report explicitly poses the existence of a variety with a strict higher etale-homotopy obstruction as a natural question and cites only progress in work in progress; no demonstrable general example was found. | [
{
"url": "https://arxiv.org/abs/1902.03404",
"label": "Schlank, etale homotopy obstructions of arithmetic spheres"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Find varieties over global fields $K$ for which the full étale-homotopy obstruction is strictly stronger than its two-stage truncation; equivalently, find examples with $X(\mathbb{A}_K)^h\subsetneq X(\mathbb{A}_K)^{h,2}$. | A natural question is to find examples where X(AK )h ( X(AK )h,2 . 6.2. Higher Dimensional Global Fields. There are many fields K for which there is a notion of completions Kv and adele ring AK but for which K has cohomological dimension > 2. A natural example comes from considering a curve C over a field k and taking ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,647 | OWR-14297740-019 | Next-Most-Probable Galois Groups of Random Polynomials | In the large-box model for random integer polynomials of fixed degree, determine the next-most-probable Galois group after the full symmetric group, including whether the alternating group or a point stabilizer dominates and with what asymptotic probability. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | open | null | 2,023 | 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-14297740-019",
"literature-status:open",
"owr-year:2023"
] | Bhargava's 2025 work proves the van der Waerden asymptotic in the large-box model, but the extracted record also includes the Odlyzko--Poonen irreducibility conjecture, which remains unconditional only in special coefficient distributions; the combined extracted claim is therefore open. | [
{
"url": "https://annals.math.princeton.edu/2025/201-2/p01",
"label": "Bhargava, van der Waerden conjecture"
},
{
"url": "https://arxiv.org/abs/1810.13360",
"label": "Breuillard--Varju, conditional Odlyzko--Poonen result"
},
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "O... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | In the large-box model for random integer polynomials of fixed degree, determine the next-most-probable Galois group after the full symmetric group, including whether the alternating group or a point stabilizer dominates and with what asymptotic probability. | Here it is known from about a century that the Galois group is the full symmetric group, and the main question is what is the next most probable group (this is the content of the so-called ”van der Waerden conjecture”). For example, the content of the Odlyzko-Poonen conjecture is that the probability for the polynomial... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,648 | OWR-14297740-020 | Inertia Actions on Torsion Points under Supersingular Reduction | Let $X/K$ be a geometrically connected curve of genus greater than one with Jacobian $J$, and embed $X$ in $J$ using a point $x_0\in X(K)$. If $J$ has supersingular good reduction over $K$, is the inertia action on $X_{\mathrm{tors}}=X(K)\cap J(K)_{\mathrm{tors}}$ trivial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-020",
"literature-status:partially-solved",
"owr-year:2023"
] | The inertia action is proved trivial in the superspecial case and for genus two with supersingular good reduction, while the general supersingular-good-reduction question for higher genus remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "Takao, Coleman conjecture report"
},
{
"url": "https://www.kurims.kyoto-u.ac.jp/~yuichiro/papers_e.html",
"label": "Hoshi, torsion-point ramification results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $X/K$ be a geometrically connected curve of genus greater than one with Jacobian $J$, and embed $X$ in $J$ using a point $x_0\in X(K)$. If $J$ has supersingular good reduction over $K$, is the inertia action on $X_{\mathrm{tors}}=X(K)\cap J(K)_{\mathrm{tors}}$ trivial? | Is the action of IK on Xtors trivial if J has supersingular (good) reduction over K? geometrically connected curve over K of genus g greater than one and write J for its Jacobian variety. Given x0 \in X(K), we have the Albanese embedding ιx0 : X ֒\to J, x 7\to [x − x0 ]. Write J(K)tors for the torsion subgroup of J(K) ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,649 | OWR-14297740-021 | Self-Duality of Quasi-Supersingular Group Schemes | Let $G$ be a $p$-torsion finite flat commutative group scheme over the Witt vectors $W$ of rank $p^{2n}$ whose special fiber $\overline G$ is quasi-supersingular. For $n\geq3$, must $G$ and $\overline G$ be self-dual? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 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-14297740-021",
"literature-status:partially-solved",
"owr-year:2023"
] | The genus-two case of the associated supersingular torsion-point problem is proved affirmative, but the report leaves higher-genus Raynaud-type cases as open strategies and questions. | [
{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "Takao, Coleman conjecture report"
},
{
"url": "https://www.kurims.kyoto-u.ac.jp/~yuichiro/papers_e.html",
"label": "Hoshi, finite-flat group-scheme results"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $G$ be a $p$-torsion finite flat commutative group scheme over the Witt vectors $W$ of rank $p^{2n}$ whose special fiber $\overline G$ is quasi-supersingular. For $n\geq3$, must $G$ and $\overline G$ be self-dual? | 2. Other strategies In this section, we shall discuss possible new ideas to overcome the obstacle raised by Proposition 1 and to solve Problem 1. 2.1. Self-duality of J[p]. Although J has a natural principal polarization, this fact is not reflected in Proposition 1. It would therefore be natural to examine whether cond... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,650 | OWR-14297740-022 | Field Reconstruction from Rationalized Milnor K-Theory | Let $F$ be a field of Kronecker dimension at least $2$. Is the isomorphism type of its inseparable closure $F^i$ determined by the graded $\mathbb{Q}$-algebra $K_*^M(F)\otimes\mathbb{Q}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488](https://doi.org/10.4171/owr/2023/42)
## Literature rev... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Properties of integers, prime numbers, Diophantine equations.",
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"created_at": "2026-07-31T15:26:25.670Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14297740-022",
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] | Topaz proves reconstruction of the perfect closure from rationalized Milnor K-theory under transcendence-degree-at-least-five hypotheses, while the stated Kronecker-dimension-at-least-two extension remains a conjecture. | [
{
"url": "https://arxiv.org/abs/2211.14665",
"label": "Topaz, algebraic dependence and Milnor K-theory"
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{
"url": "https://doi.org/10.4171/owr/2023/42",
"label": "OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/42 | null | null | null | Let $F$ be a field of Kronecker dimension at least $2$. Is the isomorphism type of its inseparable closure $F^i$ determined by the graded $\mathbb{Q}$-algebra $K_*^M(F)\otimes\mathbb{Q}$? | As usual in anabelian geometry, the process which reconstructs the field from its Milnor K-theory in the proof of this theorem is actually functorial in a suitable sense. However, as soon as F is multiplicatively divisible, the quotient F \times /torsion becomes a vector space over Q, and thus multiplication by nonzero... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | MFO–RIMS Tandem Workshop: Arithmetic Homotopy and Galois Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/42, pp. 2377--2488 |
30,005,651 | OWR-14297741-001 | Equivariant Stable Connectivity in Higher Representation Dimension | Let $G$ be a finite group with an irreducible representation of dimension greater than one. If a spectral presheaf on smooth $G$-schemes is Nisnevich-locally connected, must its equivariant $\mathbb A^1$-localization remain connected? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "topology",
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"description": "Properties preserved under continuous deformations.",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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] | The report presents stable connectivity as an open question beyond the elementary examples and gives no general proof for groups with higher-dimensional irreducible representations. | [
{
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"label": "OWR report"
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{
"url": "https://arxiv.org/abs/2205.13926",
"label": "Bachmann, motivic spectral Mackey functors"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Let $G$ be a finite group with an irreducible representation of dimension greater than one. If a spectral presheaf on smooth $G$-schemes is Nisnevich-locally connected, must its equivariant $\mathbb A^1$-localization remain connected? | Open question. Does stable connectivity still hold? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,652 | OWR-14297741-002 | Picard and Brauer Groups of Stable Module Blocks | Can the Picard and Brauer groups of principal blocks of stable module categories be computed completely by descent spectral sequences based on their associated spectral schemes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14297741-002",
"literature-status:partially-solved",
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{
"url": "https://arxiv.org/abs/1601.03098",
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{
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"url": "https://doi.org/10.1112/topo.70020",
"label": "Krause, Pic... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Can the Picard and Brauer groups of principal blocks of stable module categories be computed completely by descent spectral sequences based on their associated spectral schemes? | Can the Picard and Brauer groups of the principal blocks for stable module categories be completely computed by a descent spectral sequence based on their associated spectral schemes? A key example of categories satisfying the above include the principal blocks of any \infty-categorical enhancement of the stable module... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,653 | OWR-14297741-003 | Spectral Moduli Interpretations for Stable Module Blocks | Do the spectral schemes associated with principal blocks of stable module categories admit natural spectral moduli-theoretic interpretations beyond the case of elementary abelian groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297741-003",
"literature-status:partially-solved",
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] | Natural spectral interpretations are available for elementary abelian groups and related support constructions, but the report states that the general moduli-theoretic interpretation question remains unanswered. | [
{
"url": "https://doi.org/10.4171/owr/2023/40",
"label": "OWR report"
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{
"url": "https://arxiv.org/abs/1510.06773",
"label": "Benson--Iyengar--Krause, stratification for finite group schemes"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Do the spectral schemes associated with principal blocks of stable module categories admit natural spectral moduli-theoretic interpretations beyond the case of elementary abelian groups? | Question 12. Do the spectral schemes appearing in the equivalences above admit natural spectral moduli-theoretic interpretations? I am presently able to provide an affirmative answer only for elementary abelian groups. Question 11. Can the Picard and Brauer groups of the principal blocks for stable module categories be... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,654 | OWR-14297741-004 | Kasparov-Theory Heading Fragment | conjecture. The difference is that, this time, we know how to calculate Spc\omega (CellG ) at least in the case of some small finite groups (and possibly also rationally for all finite groups; work in progress!). The way this works for G finite is that we observe that Stratification in Kasparov theory Ivo Dell’Ambrogio... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction combines the end of preceding exposition with the heading of the Kasparov-theory contribut) | null | null | null | [
"owr",
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{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | null | conjecture. The difference is that, this time, we know how to calculate Spc\omega (CellG ) at least in the case of some small finite groups (and possibly also rationally for all finite groups; work in progress!). The way this works for G finite is that we observe that Stratification in Kasparov theory Ivo Dell’Ambrogio... | unrecoverable | The official report confirms that this extraction combines the end of preceding exposition with the heading of the Kasparov-theory contribution and states no separate open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,655 | OWR-14297741-005 | Balmer Spectra of Equivariant Eilenberg–MacLane Modules | For a finite group $G$ and a Mackey functor $M$, describe the Balmer spectrum $\operatorname{Spc}(\operatorname{Perf}_G(HM))$ of compact modules over the equivariant Eilenberg–MacLane spectrum $HM$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297741-005",
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] | The Balmer spectrum for the constant Mackey Eilenberg--MacLane spectrum is computed in important field and integral cases, but a general description for arbitrary commutative rings remains open. | [
{
"url": "https://doi.org/10.1007/s00222-024-01301-0",
"label": "Quillen stratification in equivariant homotopy theory"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | For a finite group $G$ and a Mackey functor $M$, describe the Balmer spectrum $\operatorname{Spc}(\operatorname{Perf}_G(HM))$ of compact modules over the equivariant Eilenberg–MacLane spectrum $HM$. | Can we describe the Balmer spectrum Spc(Perf G (HM ))? as tt-categories. For the Balmer spectrum of compact objects, we write = Spc(Dperf (R)) \sim Spc(Perf(HR)) = Spc(HR−Modc ) \sim = Spec(R) where the last isomorphism is due to Hopkins–Neeman [6, 7] in the case where R is Noetherian and Thomason [10] for general R. E... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,656 | OWR-14297741-006 | Balmer Spectra for Constant Mackey Functors | For $G=C_p$ and $R$ a constant Mackey functor associated with a commutative ring, describe $\operatorname{Spc}(\operatorname{Perf}_{C_p}(HR))$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
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] | The spectrum is known for several coefficients, including fields and some integral cases, and its underlying set has a geometric fixed point description; the topology and gluing for general commutative rings are not fully determined. | [
{
"url": "https://doi.org/10.1007/s00222-024-01301-0",
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{
"url": "https://math.ucla.edu/~balmer/Pubfile/PmMfAm.pdf",
"label": "Balmer and Gallauer on permutation modules"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | For $G=C_p$ and $R$ a constant Mackey functor associated with a commutative ring, describe $\operatorname{Spc}(\operatorname{Perf}_{C_p}(HR))$. | In fact, Balmer and Gallauer do much more. For G a finite group and k a field of characteristic p > 0, they describe Spc(Perf G (Hk)). In their previous work on Artin–Tate motives [2] they also describe Spc(Perf C2 (H Z)) using C2 as the Galois group. So we consider the case of a more general ring. Question 8. For G = ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,657 | OWR-14297741-009 | Compactly Generated t-Structures on Schemes and dg Rings | Classify suitable compactly generated t-structures on $D(\operatorname{Qcoh}(X))$ for a Noetherian scheme $X$ and on $D(R)$ for a cohomologically nonpositive, bounded commutative dg ring $R$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
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"description": "Properties preserved under continuous deformations.",
"slug": "topology",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297741-009",
"literature-status:partially-solved",
"owr-year:2023"
] | Tensor-compatible compactly generated t-structures on noetherian schemes are classified by Thomason filtrations, while the broader question including arbitrary suitable t-structures and connective dg rings remains unresolved. | [
{
"url": "https://arxiv.org/abs/2204.05015",
"label": "Sahoo--Dubey, Compactly generated tensor t-structures"
},
{
"url": "https://arxiv.org/abs/1806.00078",
"label": "Hrbek, Compactly generated t-structures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Classify suitable compactly generated t-structures on $D(\operatorname{Qcoh}(X))$ for a Noetherian scheme $X$ and on $D(R)$ for a cohomologically nonpositive, bounded commutative dg ring $R$. | Our first, more down to earth, open question is whether such a classification extends to settings not entirely distant from commutative algebra. Can one classify (suitable) compactly generated t-structures in (1) D = D(Qcoh(X)), where X is a noetherian scheme? (2) D = D(R), where R is a cohomologically non-positive and... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,658 | OWR-14297741-011 | Support-Filtration Classification of Compactly Generated t-Structures | Let $A$ be a connective bounded commutative differential graded ring, let $\mathcal D=D(A)$ be its derived category, and set $X=\operatorname{Spec}(\operatorname{End}_{\mathcal D}(\mathbf 1))$. Are the compactly generated $t$-structures on $\mathcal D$ whose nonpositive aisle is a tensor ideal classified by support fil... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"literature-status:open",
"owr-year:2023"
] | Support-filtration classifications are established for ordinary commutative rings, but no general theorem was found for the connective bounded commutative dg-ring setting stated in the surrounding question. | [
{
"url": "https://arxiv.org/abs/1806.00078",
"label": "Hrbek, Compactly generated t-structures"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4102/OWR_2023_40.pdf?sequence=4",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Let $A$ be a connective bounded commutative differential graded ring, let $\mathcal D=D(A)$ be its derived category, and set $X=\operatorname{Spec}(\operatorname{End}_{\mathcal D}(\mathbf 1))$. Are the compactly generated $t$-structures on $\mathcal D$ whose nonpositive aisle is a tensor ideal classified by support fil... | Are then compactly generated t-structures classified by filtrations by supports of Spec(EndD (1))? (i) the compactly generated t-structures (D\leq0 , D\geq0 ) for which D\leq0 is a t-⊗- ideal and (ii) filtrations by supports f : Z \to 2X ? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,659 | OWR-14297741-012 | Quantum-Symmetric Classes of Artin–Schelter Regular Algebras | Determine the full quantum-symmetric equivalence class of an Artin–Schelter regular algebra. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 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-14297741-012",
"literature-status:open",
"owr-year:2023"
] | Quantum-symmetric equivalence preserves Artin--Schelter regularity and unifies fixed-dimensional Koszul examples, but the full quantum-symmetric equivalence class of an Artin--Schelter regular algebra is still not determined. | [
{
"url": "https://arxiv.org/abs/2209.11621",
"label": "Twisting Manin's universal quantum groups and comodule algebras"
},
{
"url": "https://arxiv.org/abs/2507.05612",
"label": "Quantum-symmetric equivalence for superpotential algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Determine the full quantum-symmetric equivalence class of an Artin–Schelter regular algebra. | It remains an open question to fully determine the quantum-symmetric equivalence class of an Artin–Schelter regular algebra. Noncommutative algebra via tensor categories Kent Vashaw (joint work with Hongdi Huang, Daniel Nakano, Van Nguyen, Charlotte Ure, Padmini Veerapen, Xingting Wang, Milen Yakimov) | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,660 | OWR-14297741-013 | Spectrum Comparison for Finite Tensor Categories | Let $\mathcal T$ be a finite tensor category, let $\underline{\mathcal T}$ be its stable category, and let $C_{\mathcal T}^{\bullet}$ be the categorical center of its cohomology ring. Is the continuous central-support comparison map $$\rho:\operatorname{Spc}(\underline{\mathcal T})\longrightarrow\operatorname{Proj} C_{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358](https://doi.org/10.4171/owr/2023/40)
## Literature review (checked 2026-08... | 3 | open | null | 2,023 | 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-14297741-013",
"literature-status:open",
"owr-year:2023"
] | The comparison map from the Balmer spectrum to the homogeneous spectrum of the categorical center is a homeomorphism under stronger hypotheses and in many examples, but the assertion for every finite tensor category remains conjectural. | [
{
"url": "https://arxiv.org/abs/2112.11170",
"label": "Nakano--Vashaw--Yakimov, On the spectrum and support theory"
},
{
"url": "https://doi.org/10.2140/ant.2024.18.1081",
"label": "Vashaw, Balmer spectra and Drinfeld centers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/40 | null | null | null | Let $\mathcal T$ be a finite tensor category, let $\underline{\mathcal T}$ be its stable category, and let $C_{\mathcal T}^{\bullet}$ be the categorical center of its cohomology ring. Is the continuous central-support comparison map $$\rho:\operatorname{Spc}(\underline{\mathcal T})\longrightarrow\operatorname{Proj} C_{... | We conjecture that the map ρ is a homeomorphism for every finite tensor category. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tensor-Triangular Geometry and Interactions (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/40, pp. 2303--2358 |
30,005,661 | OWR-14297742-001 | Periodic Ground States in Gross–Pitaevskii Theory | For superstable, sufficiently decaying pair interactions $w$ whose Fourier transform takes negative values, must every infinite-volume ground state of $(-\Delta+w*|u|^2)u=\mu u$ be periodic when $\mu$ exceeds the fluid–solid transition value $\mu_c$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302](https://doi.org/10.4171/owr/2023/39)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297742-001",
"literature-status:open",
"owr-year:2023"
] | The positive-density Gross--Pitaevskii theory now proves the fluid-to-solid transition and loss of the constant ground state, but the conjectured periodic or crystalline form of the solid ground state remains unproved in general. | [
{
"url": "https://doi.org/10.2140/pmp.2025.6.647",
"label": "Lewin--Nam, Positive-density ground states of the Gross--Pitaevskii equation"
},
{
"url": "https://doi.org/10.4171/EMSS/13",
"label": "Blanc--Lewin, The crystallization conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/39 | null | null | null | For superstable, sufficiently decaying pair interactions $w$ whose Fourier transform takes negative values, must every infinite-volume ground state of $(-\Delta+w*|u|^2)u=\mu u$ be periodic when $\mu$ exceeds the fluid–solid transition value $\mu_c$? | conjecture. For Bose-Einstein condensates, Phase Transition in Gross-Pitaevskii Theory Mathieu Lewin (joint work with Phan Thành Nam) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302 |
30,005,662 | OWR-14297742-002 | Adiabatic Expansions for Gapless Quantum Systems | Can the adiabatic-expansion framework, whose convergence follows from imaginary-time correlation estimates for gapped systems, be extended to gapless quantum systems even without interactions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302](https://doi.org/10.4171/owr/2023/39)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297742-002",
"literature-status:open",
"owr-year:2023"
] | The expansion and adiabatic results are rigorous for gapped many-body systems, with thermodynamic-limit control in those regimes, but the requested extension to gapless systems remains open. | [
{
"url": "https://doi.org/10.1007/s00220-023-04903-6",
"label": "Greenblatt--Marcelli--Lange--Porta, Adiabatic Evolution"
},
{
"url": "https://arxiv.org/abs/2211.16836",
"label": "Adiabatic Evolution of Low-Temperature Many-Body Systems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/39 | null | null | null | Can the adiabatic-expansion framework, whose convergence follows from imaginary-time correlation estimates for gapped systems, be extended to gapless quantum systems even without interactions? | In particular, the convergence of the expansion (4) actually only relies on suitable integrability properties of imaginary-time correlation functions, which hold true for many-body perturbations of gapped systems; it is an inter- esting open problem to understand how to apply this framework to study gapless quantum sys... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302 |
30,005,663 | OWR-14297742-003 | Accelerated Information Propagation in Bosonic Lattices | When does accelerated information propagation occur in bosonic lattice systems with nearest-neighbor or long-range interactions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302](https://doi.org/10.4171/owr/2023/39)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,023 | 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-14297742-003",
"literature-status:partially-solved",
"owr-year:2023"
] | Rigorous work exhibits accelerated information propagation in bosonic systems and derives improved bounds under extra interaction or symmetry assumptions, while the standard nearest-neighbor Bose--Hubbard case and a general long-range criterion remain unresolved. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC10957968/",
"label": "Effective light cone and digital quantum simulation of interacting bosons"
},
{
"url": "https://doi.org/10.1007/s00023-026-01733-9",
"label": "Symmetry-enhanced Lieb--Robinson bounds for bosons"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/39 | null | null | null | When does accelerated information propagation occur in bosonic lattice systems with nearest-neighbor or long-range interactions? | Understanding rigorously if and when this accelerated bosonic information propagation occurs, both for nearest-neighbor and long-range interactions is a fundamental open problem. Theorem 2 (Microscopic particle transport [FLS22a, KVS22, LRZ23]). Let p \geq 1. Suppose that \alpha > 2dp + 1. Then there exists v > 0 such ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302 |
30,005,664 | OWR-14297742-004 | Aubin–Talenti Optimizers for Critical Dirac Potentials | In dimensions $d>1$ at the critical parameter $\alpha=\alpha_*(p,d)$, is the optimizing nonnegative potential for the Dirac spectral-gap problem of Aubin–Talenti form $V(x)=A/(1+B|x|^2)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302](https://doi.org/10.4171/owr/2023/39)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 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-14297742-004",
"literature-status:open",
"owr-year:2023"
] | The critical value and the optimal potential are characterized variationally, and the one-dimensional case is solved, but the higher-dimensional Aubin--Talenti potential formula is still explicitly conjectural. | [
{
"url": "https://ems.press/content/serial-article-files/47481?nt=1",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2210.03091",
"label": "Keller and Lieb--Thirring estimates for Dirac operators"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/39 | null | null | null | In dimensions $d>1$ at the critical parameter $\alpha=\alpha_*(p,d)$, is the optimizing nonnegative potential for the Dirac spectral-gap problem of Aubin–Talenti form $V(x)=A/(1+B|x|^2)$? | In higher dimension, and for the critical point \alpha = \alpha∗ , we conjecture that the optimal potential is also A of the Aubin–Talentin form V (x) = 1+B|x| 2 . critical value \alpha∗ (p, d) has the explicit formula p−d d 2 Γ(p − d2 ) \alpha∗ (p, d)p = pp \pi 2 . p−d Γ(p) This is confirmed by numerical simulations. F... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302 |
30,005,665 | OWR-14297742-005 | Lee–Huang–Yang Upper Bound for Hard-Sphere Bosons | For a dilute hard-sphere Bose gas in the thermodynamic limit, prove the second-order upper bound matching the Lee–Huang–Yang expansion $e(\rho)=4\pi a\rho^2\bigl(1+128(\rho a^3)^{1/2}/(15\sqrt\pi)+o((\rho a^3)^{1/2})\bigr)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302](https://doi.org/10.4171/owr/2023/39)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | solved | null | 2,023 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] - Duplicate of `OWR-14297742-005`. | [
"owr",
"oberwolfach-reports",
"OWR-14297742-005",
"literature-status:partially-solved",
"owr-year:2023"
] | Thermodynamic-limit energy expansions and Gross--Pitaevskii asymptotics are rigorously known in several dilute regimes, but the proposed extension of the method to the fixed-density torus regime with the stated singularity remains open. | [
{
"url": "https://doi.org/10.1103/PhysRevA.61.043602",
"label": "Lieb--Seiringer--Yngvason, Gross--Pitaevskii energy"
},
{
"url": "https://arxiv.org/abs/2211.16836",
"label": "Adiabatic Evolution of Low-Temperature Many-Body Systems"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/70504... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/39 | null | null | null | For a dilute hard-sphere Bose gas in the thermodynamic limit, prove the second-order upper bound matching the Lee–Huang–Yang expansion $e(\rho)=4\pi a\rho^2\bigl(1+128(\rho a^3)^{1/2}/(15\sqrt\pi)+o((\rho a^3)^{1/2})\bigr)$. | In this talk I will also address the natural question of whether the same method could be pushed to cover more singular regimes, and in particular whether it allows to treat the thermodynamic limit in which N bosons are confined to a torus ΛL of side length L in the limit N, L \to +\infty with particle density ρ = N/L3 ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Many-Body Quantum Systems (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/39, pp. 2247--2302 |
30,005,666 | OWR-14297743-001 | Rigid Subgraphs of the Curve Complex | Which subgraphs of the curve complex are rigid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892](https://doi.org/10.4171/owr/2023/33)
## Literature review (ch... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297743-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Finite rigid sets are known for the full curve complex and several subcomplexes, but there is no general classification of which subgraphs are rigid as asked in the extracted passage. | [
{
"url": "https://arxiv.org/abs/1206.3114",
"label": "Aramayona--Leininger, Finite rigid sets in curve complexes"
},
{
"url": "https://doi.org/10.1016/j.topol.2022.108078",
"label": "Finite rigid sets and the separating curve complex"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/33 | null | null | null | Which subgraphs of the curve complex are rigid? | As the complex serves as a ”natural” counterexample to the Ivanov’s metaconjecture, McCarthy-Papadopoulos posed the open problem of understanding which of its subgraphs are rigid. The curve complex via model theory Valentina Disarlo (joint work with Javier de la Nuez Gonzalez and Thomas Koberda) 1.1. Stability in model... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892 |
30,005,667 | OWR-14297743-002 | Group Actions with Differentiability Obstructions | Does there exist a countable or finitely generated group $\Gamma_{r,M}\leq\operatorname{Diff}^r(M)$ such that, for every $s>r$, every action of $\Gamma_{r,M}$ on $M$ by $C^s$ diffeomorphisms is trivial or has a large kernel? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892](https://doi.org/10.4171/owr/2023/33)
## Literature review (ch... | 3 | partially_solved | null | 2,023 | 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-14297743-002",
"literature-status:partially-solved",
"owr-year:2023"
] | The proposed regularity obstruction is proved for compact one-manifolds, including finitely generated examples, but the analogous existence question in higher dimensions remains open. | [
{
"url": "https://arxiv.org/abs/2106.15532",
"label": "Kim--Koberda, Structure and regularity of group actions"
},
{
"url": "https://doi.org/10.1090/noti2252",
"label": "Koberda, Diffeomorphism groups of critical regularity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/33 | null | null | null | Does there exist a countable or finitely generated group $\Gamma_{r,M}\leq\operatorname{Diff}^r(M)$ such that, for every $s>r$, every action of $\Gamma_{r,M}$ on $M$ by $C^s$ diffeomorphisms is trivial or has a large kernel? | Does there exist a countable, or perhaps finitely generated group Γr,M \leq Diff r (M ) such that for all s > r, all actions of Γr,M on M by C s diffeomorphisms are trivial (or have a large kernel at least)? First order theory of homeomorphism groups of manifolds, and applications Thomas Koberda (joint work with Sang-h... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892 |
30,005,668 | OWR-14297743-003 | Linearity of Mapping Class Groups | Is the mapping class group of a surface $\Sigma$ linear, and can the question be formulated intrinsically in terms of $\Sigma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892](https://doi.org/10.4171/owr/2023/33)
## Literature review (ch... | 3 | open | null | 2,023 | 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-14297743-003",
"literature-status:open",
"owr-year:2023"
] | The mapping class groups of the torus and genus two are linear and positive-characteristic representations are ruled out in higher genus, but linearity over characteristic zero for genus at least three remains open. | [
{
"url": "https://arxiv.org/abs/math/0010310",
"label": "Bigelow--Budney, The mapping class group of genus two"
},
{
"url": "https://arxiv.org/abs/1610.08464",
"label": "Button, Mapping class groups are not linear in positive characteristic"
},
{
"url": "https://arxiv.org/abs/1108.3241",... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/33 | null | null | null | Is the mapping class group of a surface $\Sigma$ linear, and can the question be formulated intrinsically in terms of $\Sigma$? | Is the mapping class group of Σ a linear group? Can this question be understood in a way that is more intrinsic to Σ? Teichmüller Theory: Classical, Higher, Super and Quantum 1869 | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892 |
30,005,669 | OWR-14297743-004 | Canonical Harmonic Metrics on Noncompact Riemann Surfaces | Given holomorphic differentials $\vec q=(q_2,\ldots,q_n)$ on a noncompact Riemann surface $X$, does there exist a compatible harmonic metric on the associated Higgs bundle, and is there a canonical best such metric that exists uniquely? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892](https://doi.org/10.4171/owr/2023/33)
## Literature review (ch... | 3 | partially_solved | null | 2,023 | 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-14297743-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Existence of a compatible harmonic metric is proved for arbitrary holomorphic differential tuples on noncompact hyperbolic surfaces, and uniqueness is proved under boundedness or completeness conditions; unrestricted uniqueness is not settled. | [
{
"url": "https://arxiv.org/abs/2307.03365",
"label": "Li--Mochizuki, Higgs bundles in the Hitchin section"
},
{
"url": "https://arxiv.org/abs/2010.05401",
"label": "Li--Mochizuki, Complete solutions of Toda equations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/33 | null | null | null | Given holomorphic differentials $\vec q=(q_2,\ldots,q_n)$ on a noncompact Riemann surface $X$, does there exist a compatible harmonic metric on the associated Higgs bundle, and is there a canonical best such metric that exists uniquely? | Given a tuple of holomorphic differentials q⃗ = (q2 , ⋯, qn ) on a non-compact Riemann surface X, (1) does there exist a harmonic metric on (KX,n , \theta(⃗ q )) compatible with CK,X,n ? (2) If so, can one find a notion of “best” harmonic metric such that it uniquely exists? Teichmüller Theory: Classical, Higher, Supe... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Teichmüller Theory: Classical, Higher, Super and Quantum (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/33, pp. 1843--1892 |
30,005,670 | OWR-14297744-001 | Equivariant Homotopy-Theory Workshop Abstract | Abstract. The workshop brought together experts in homotopy theory from many areas, including chromatic homotopy theory, algebraic K-theory, de- rived algebra and equivariant homotopy theory. We had a lecture series on the recent disproof of the telescope conjecture. In addition to a total of 24 research talks we had t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a workshop abstract and contains no standalone open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-001",
"literature-status:open",
"owr-year:2023"
] | The extracted text is a report abstract describing the recent disproof of the telescope conjecture, not a separate mathematical problem statement. | [
{
"url": "https://doi.org/10.4171/OWR/2023/34",
"label": "OWR Homotopy Theory report"
},
{
"url": "https://arxiv.org/abs/2310.17459",
"label": "K-theoretic counterexamples to Ravenel's telescope conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | null | Abstract. The workshop brought together experts in homotopy theory from many areas, including chromatic homotopy theory, algebraic K-theory, de- rived algebra and equivariant homotopy theory. We had a lecture series on the recent disproof of the telescope conjecture. In addition to a total of 24 research talks we had t... | unrecoverable | The official report confirms that this extraction is a workshop abstract and contains no standalone open problem. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,671 | OWR-14297744-002 | Equivariant Homotopy-Theory Table-of-Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1897 Shachar Carmeli (joint with Shay Ben-Moshe, Tomer Schlank, Lior Yanovski) Cyclotomic Redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1902 Mona Merling (joint with Tom Gooodwillie, Kiyoshi Igusa... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a table-of-contents fragment, not a standalone open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-002",
"literature-status:open",
"owr-year:2023"
] | The extracted record is a table-of-contents fragment ending in the word conjecture and contains no identifiable mathematical claim to verify. | [
{
"url": "https://doi.org/10.4171/OWR/2023/34",
"label": "OWR Homotopy Theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1897 Shachar Carmeli (joint with Shay Ben-Moshe, Tomer Schlank, Lior Yanovski) Cyclotomic Redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1902 Mona Merling (joint with Tom Gooodwillie, Kiyoshi Igusa... | unrecoverable | The official report confirms that this extraction is a table-of-contents fragment, not a standalone open problem. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,672 | OWR-14297744-004 | Orphaned Equivariant h-Cobordism Conjecture Label | conjecture. Moduli spaces of equivariant h-cobordisms Mona Merling (joint work with Tom Gooodwillie, Kiyoshi Igusa, and Cary Malkiewich) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is only an orphaned heading and conjecture label; the complete problems are preserved in t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-004",
"literature-status:open",
"owr-year:2023"
] | The extracted record is only the word conjecture attached to a talk title and does not state a mathematical proposition that can be assessed. | [
{
"url": "https://doi.org/10.4171/OWR/2023/34",
"label": "OWR Homotopy Theory report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | null | conjecture. Moduli spaces of equivariant h-cobordisms Mona Merling (joint work with Tom Gooodwillie, Kiyoshi Igusa, and Cary Malkiewich) | unrecoverable | The official report confirms that this extraction is only an orphaned heading and conjecture label; the complete problems are preserved in the following records. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,673 | OWR-14297744-005 | Equivariant Splitting of A-Theory | For a compact smooth $G$-manifold $M$, prove an equivariant splitting $A_G(M)\simeq\Sigma_G^\infty M_+\times\operatorname{Wh}_G(M)$ with $\Omega^{\infty+1}\operatorname{Wh}_G(M)^G\simeq H_G^\infty(M)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-005",
"literature-status:partially-solved",
"owr-year:2023"
] | Equivariant A-theory maps to the suspension spectrum with a fiber described by stable h-cobordism spectra, and stable equivariant h-cobordism splittings are known; the full A-theory product splitting for every compact smooth G-manifold remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2022.108242",
"label": "Malkiewich--Merling, Equivariant parametrized h-cobordism"
},
{
"url": "https://arxiv.org/abs/2303.14892",
"label": "Goodwillie--Igusa--Malkiewich--Merling, h-cobordism functoriality"
},
{
"url": "https://doi.org/10.4171/OWR... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | For a compact smooth $G$-manifold $M$, prove an equivariant splitting $A_G(M)\simeq\Sigma_G^\infty M_+\times\operatorname{Wh}_G(M)$ with $\Omega^{\infty+1}\operatorname{Wh}_G(M)^G\simeq H_G^\infty(M)$. | Equivariant A- theory of a G-space AG (X) was constructed in [14] using the machinery of spectral Mackey functors [6, 7, 10, 5, 4].1 The main question/conjecture is the following. For a compact smooth G-manifold M , is there a splitting (2) AG (M ) ≃ Σ\infty G M \times WhG (M ) analogous to the nonequivariant one from ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,674 | OWR-14297744-006 | Equivariant Algebraic K-Theory of Stable h-Cobordisms | Describe the stable moduli space $H_G^\infty(M)$ of equivariant $h$-cobordisms in terms of equivariant algebraic $K$-theory. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-006",
"literature-status:open",
"owr-year:2023"
] | The report explicitly leaves the description of the stable equivariant h-cobordism space in terms of equivariant algebraic K-theory as a question. Later work gives functoriality and stable splittings, but not the requested identification. | [
{
"url": "https://doi.org/10.4171/owr/2023/34",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2303.14892",
"label": "Goodwillie-Igusa-Malkiewich-Merling"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | Describe the stable moduli space $H_G^\infty(M)$ of equivariant $h$-cobordisms in terms of equivariant algebraic $K$-theory. | We can now ask the analogous question as before about this moduli space of equivariant h-cobordisms: \infty Can we describe HG (M ) in terms of equivariant algebraic K-theory? Combined with the results of [16], we obtain a sequence in G-spectra AG (M ) \to Σ\infty G M \to WhG (M ) where Ω\infty+1 WhG (M )G ≃ HG \infty ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,675 | OWR-14297744-007 | Coherence of Equivariant Formal-Group Moduli Stacks | For every compact Lie group $G$, prove that the stacks $\mathcal M_{\mathrm{FG}}^G$ are coherent, meaning that coherent sheaves corresponding to comodules with finitely presented underlying modules form an abelian category. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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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-14297744-007",
"literature-status:open",
"owr-year:2023"
] | Hausmann and Meier prove the universal support theorem and the Balmer-spectrum homeomorphism for compact abelian Lie groups, but the stated coherence conjecture for the equivariant formal-group stacks remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2023/34",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2309.00850",
"label": "Hausmann-Meier"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | For every compact Lie group $G$, prove that the stacks $\mathcal M_{\mathrm{FG}}^G$ are coherent, meaning that coherent sheaves corresponding to comodules with finitely presented underlying modules form an abelian category. | We conjecture: Conjecture 1. X 7\to support of F∗X is the universal support theory on finite G-spectra. This induces a homeomorphism fin |MG F G | \to Spc(SpG ) to the Balmer spectrum of finite G-spectra. 3. Further results and the road ahead The points in MF G corresponds to the invariant prime ideals Ip,n \subseteq \... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,676 | OWR-14297744-008 | Topological Modular Forms over Generalized Elliptic Curves | Extend topological modular-form operations to the moduli stack of generalized elliptic curves; identify $\lim_{\mathrm{Isog}}\mathcal O^{\mathrm{top}}$; and determine whether its map from the TMF-local sphere yields integral or near-integral resolutions of that sphere. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-008",
"literature-status:open",
"owr-year:2023"
] | The construction of the isogeny-indexed sheaf on the elliptic-curve moduli stack is established, but the report still asks for its compactified extension to generalized elliptic curves and for the corresponding integral limit description of the TMF-local sphere. | [
{
"url": "https://doi.org/10.4171/owr/2023/34",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2212.06208",
"label": "Davies on Hecke operators"
},
{
"url": "https://arxiv.org/abs/2104.13407",
"label": "Davies on dualisable Tmf"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | Extend topological modular-form operations to the moduli stack of generalized elliptic curves; identify $\lim_{\mathrm{Isog}}\mathcal O^{\mathrm{top}}$; and determine whether its map from the TMF-local sphere yields integral or near-integral resolutions of that sphere. | We ask: can the theorem above can be extended to moduli stack of generalised elliptic curves? Is there an approach to Tmf similar to Lurie’s approach to TMF in [5]? top Secondly, just as the definition of TMF is as the limit of OGHM , one might ask the question: what is the limit of Otop over Isog? Is this map a good a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,677 | OWR-14297744-010 | Fully Faithful Enveloping Algebras for Spectral Lie Algebras | Prove that the universal enveloping algebra functor from $T(n)$-local spectral Lie algebras to $T(n)$-local spectral Hopf algebras is fully faithful. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-010",
"literature-status:partially-solved",
"owr-year:2023"
] | The universal-enveloping functor is fully faithful on abelian T(n)-local spectral Lie algebras, including infinite-loop cases, but the conjecture for all T(n)-local spectral Lie algebras is not proved. | [
{
"url": "https://doi.org/10.4171/owr/2023/34",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2501.03116",
"label": "Antolin-Camarena-Brantner-Heuts"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | Prove that the universal enveloping algebra functor from $T(n)$-local spectral Lie algebras to $T(n)$-local spectral Hopf algebras is fully faithful. | We conjecture the following parallel of the Milnor–Moore theorem in this setting: Conjecture A. 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 | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,678 | OWR-14297744-011 | Fully Two-Segal Waldhausen S-Constructions | Characterize the Waldhausen categories whose $S_\bullet$-construction is fully $2$-Segal rather than merely left $2$-Segal, and find natural examples that are left but not fully $2$-Segal. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952](https://doi.org/10.4171/owr/2023/34)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297744-011",
"literature-status:open",
"owr-year:2023"
] | The report poses the extension from categories with cofibrations and pullbacks to general Waldhausen categories as a natural question; the cited equivariant and scissors-congruence results do not settle this generalization. | [
{
"url": "https://doi.org/10.4171/owr/2023/34",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/34 | null | null | null | Characterize the Waldhausen categories whose $S_\bullet$-construction is fully $2$-Segal rather than merely left $2$-Segal, and find natural examples that are left but not fully $2$-Segal. | A natural question is what happens for Waldhausen categories, where one has cofibrations (horizontal morphisms) and suitable pushouts, but lacks another dis- tinguished vertical class of morphisms and pullback data. 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 | Homotopy Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/34, pp. 1893--1952 |
30,005,679 | OWR-14297745-001 | Duality and Convergence Rates in Lasserre Hierarchies | For Lasserre's hierarchy, when does strong duality hold, do the moment relaxations converge to an optimal measure, and what is their convergence rate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/35, pp. 1953--2016](https://doi.org/10.4171/owr/2023/35)
## Litera... | 3 | partially_solved | null | 2,023 | 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-14297745-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Strong duality and convergence of moment-SOS relaxations are proved under standard compactness and regularity hypotheses, and quantitative rates are known for important domains such as simplices and spheres; no uniform rate answers the full general formulation. | [
{
"url": "https://arxiv.org/abs/2011.08139",
"label": "Tacchi"
},
{
"url": "https://arxiv.org/abs/1405.7334",
"label": "Josz-Henrion"
},
{
"url": "https://doi.org/10.1007/s11590-022-01851-3",
"label": "Kirschner-de Klerk"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/35 | null | null | null | For Lasserre's hierarchy, when does strong duality hold, do the moment relaxations converge to an optimal measure, and what is their convergence rate? | Lasserre’s hierarchy usually comes with three questions: (1) does strong duality hold for the GMP and its relaxations? (2) Does (yk⋆ ) converge to an optimal solution µ⋆ of (5a)? (3) What is the convergence rate of the relaxations? Mixed-integer Nonlinear Optimization 1973 n o (8b) fk′ := max \gamma \in R f − \gamma \i... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/35, pp. 1953--2016 |
30,005,680 | OWR-14297745-002 | Double Cap Conjecture | Is the largest measurable subset of $S^{n-1}$ containing no orthogonal pair the union of two open antipodal spherical caps of angular radius $\pi/4$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/35, pp. 1953--2016](https://doi.org/10.4171/owr/2023/35)
## Litera... | 3 | open | null | 2,023 | 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-14297745-002",
"literature-status:open",
"owr-year:2023"
] | The double-cap conjecture remains unresolved in general. Recent work proves strong structural properties of near-optimal orthogonal-pair-free sets, but does not establish optimality of the double cap. | [
{
"url": "https://doi.org/10.4171/owr/2023/35",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2403.18404",
"label": "Bekker-Kuryatnikova-de Oliveira Filho-Vera"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/35 | null | null | null | Is the largest measurable subset of $S^{n-1}$ containing no orthogonal pair the union of two open antipodal spherical caps of angular radius $\pi/4$? | Witsenhausen’s problem [6] asks for the largest measurable set on a unit sphere such that no two points in the set are orthogonal. More precisely, let S n−1 = \{x \in Rn : kxk = 1\} be the n-dimensional unit sphere, \omega be the standard surface measure, and \omegan the total measure of the sphere. We define \alphan =... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/35, pp. 1953--2016 |
30,005,681 | OWR-14297746-001 | CAM Actions of Residually Finite Groups | Does every residually finite group admit a chaotic almost minimal (CAM) action? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 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-14297746-001",
"literature-status:open",
"owr-year:2023"
] | The report states that whether every residually finite group admits a chaotic almost minimal action remains open; no later primary result located by the cutoff resolves this existence problem. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://sites.math.northwestern.edu/~kra/papers/CAM.pdf",
"label": "Cyr-Kra-Schmieding"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | Does every residually finite group admit a chaotic almost minimal (CAM) action? | On the other side, if G admits a CAM action, G is residually finite, and it is still an open question whether any residually finite group admits actions of this type. 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 | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,682 | OWR-14297746-002 | Convergence of Multiplicative Polynomial Averages | Let $f:\mathbb N\to\mathbb R$ be bounded and completely multiplicative, and let $P\in\mathbb Z[x,y]$ be homogeneous and positive on $\mathbb N^2$. Does the limit $\lim_{N\to\infty}N^{-2}\sum_{m,n=1}^N f(P(m,n))$ exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 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-14297746-002",
"literature-status:open",
"owr-year:2023"
] | The displayed polynomial average is a special case of the Frantzikinakis-Host question, which the report explicitly says is still out of reach; existing Gaussian-integer averages cover narrower multiplicative situations. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2309.07249",
"label": "Donoso-Le-Moreira-Sun"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | Let $f:\mathbb N\to\mathbb R$ be bounded and completely multiplicative, and let $P\in\mathbb Z[x,y]$ be homogeneous and positive on $\mathbb N^2$. Does the limit $\lim_{N\to\infty}N^{-2}\sum_{m,n=1}^N f(P(m,n))$ exist? | Does the limit limN Ñ8 N12 m,n“1 f pP pm, nqq exist? Main ideas. Theorem 3 follows from a more general theorem, and uses the idea of multiplicative actions of Gaussian integers (such actions have been studied in the past in, for instance, [2, 4, 7]). Recall that G :“ tm ` in : m, n P Nu and G˚ “ Gzt0u. Denote by P the ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,683 | OWR-14297746-003 | Diffraction Scaling and Mahler-Function Asymptotics | Relate the order of scaling near zero of a substitution system's diffraction measure to the radial asymptotics of its associated Mahler function. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297746-003",
"literature-status:open",
"owr-year:2023"
] | The Thue-Morse and Rudin-Shapiro examples show matching exponents in selected cases, but the report leaves open whether diffraction scaling near zero is generally governed by radial Mahler-function asymptotics. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1088/1742-5468/2019/05/054003",
"label": "Baake-Grimm"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | Relate the order of scaling near zero of a substitution system's diffraction measure to the radial asymptotics of its associated Mahler function. | The big question is whether one really can relate the order of the scaling of the diffraction measure near zero with the radial asymptotics of the associated Mahler function. Are these coincidences coincidental? Unfortunately, the asymptotics for this function cannot be provided by my above- mentioned result with Bell.... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,684 | OWR-14297746-005 | Random Perturbations of Aperiodic Schrödinger Potentials | What happens if one adds some random noise on top of an aperiodic potential, or, more generally, a given ergodic potential? On spectrum of aperiodic Schrödinger operators with random noise Anton Gorodetski (joint work with A. Avila, D. Damanik, V. Kleptsyn) spectrum of Hx , denoted by \sigmapHx q, is almost surely ind... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks this introductory question and then answers it with localization and spectral-structure theorems; the remaining Fib) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297746-005",
"literature-status:open",
"owr-year:2023"
] | Randomly perturbed ergodic potentials with connected base are understood and have interval spectrum, but the general aperiodic-noise question and disconnected Fibonacci hull remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2211.02173",
"label": "Avila-Damanik-Gorodetski"
},
{
"url": "https://arxiv.org/abs/2504.08153",
"label": "Damanik-Gorodetski-Kleptsyn"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | null | What happens if one adds some random noise on top of an aperiodic potential, or, more generally, a given ergodic potential? On spectrum of aperiodic Schrödinger operators with random noise Anton Gorodetski (joint work with A. Avila, D. Damanik, V. Kleptsyn) spectrum of Hx , denoted by \sigmapHx q, is almost surely ind... | unrecoverable | The official report asks this introductory question and then answers it with localization and spectral-structure theorems; the remaining Fibonacci case is preserved in the following record. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,685 | OWR-14297746-006 | Spectrum of Randomly Perturbed Fibonacci Hamiltonians | Let $H$ be the Fibonacci Hamiltonian and let $W_\omega$ be a random perturbation. Determine the topological structure of the almost-sure spectrum of $H+W_\omega$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 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-14297746-006",
"literature-status:open",
"owr-year:2023"
] | The report labels the Fibonacci random-perturbation question as open. Connected-base theorems do not apply to the Fibonacci hull, and no primary result found gives its full spectral topology. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2211.02173",
"label": "Avila-Damanik-Gorodetski"
},
{
"url": "https://arxiv.org/abs/1403.7823",
"label": "Damanik-Gorodetski-Yessen"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | Let $H$ be the Fibonacci Hamiltonian and let $W_\omega$ be a random perturbation. Determine the topological structure of the almost-sure spectrum of $H+W_\omega$. | We will formulate a specific open question. Corollary 3. If X is connected, the almost sure spectrum Σ1 is given by a finite union of non-degenerate compact intervals. Question 4. Let H be the Fibonacci Hamiltonian (the discrete Schrödinger opera- tor with the potential given by the Fibonacci substitution sequence). W... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,686 | OWR-14297746-007 | Duplicate Random-Perturbation Question | What can one say about topological structure of the spectrum of its random perturbation H `W\omega ? Notice that the condition that X is connected cannot be removed, and, while it holds in many important cases (e.g., almost Mathieu potential as background), it also excludes many interesting models. We will formulate a ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction repeats Question 4, which is preserved in the preceding record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297746-007",
"literature-status:open",
"owr-year:2023"
] | The specific Fibonacci question is explicitly posed as open in the report; known interval-spectrum results require connectedness of the deterministic base and therefore do not resolve it. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2211.02173",
"label": "Avila-Damanik-Gorodetski"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | null | What can one say about topological structure of the spectrum of its random perturbation H `W\omega ? Notice that the condition that X is connected cannot be removed, and, while it holds in many important cases (e.g., almost Mathieu potential as background), it also excludes many interesting models. We will formulate a ... | unrecoverable | The official report confirms that this extraction repeats Question 4, which is preserved in the preceding record. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,687 | OWR-14297746-010 | Settled Frobenius Elements in Arboreal Representations | Let $f$ be a polynomial of degree $d\geq 2$ over a number field $K$, let $\alpha\in K$, and let $\operatorname{Gal}_{f,\alpha}\subseteq\operatorname{Aut}(T_d)$ be the image of the associated arboreal representation. Prove that the images of Frobenius elements are settled, and hence that settled elements are dense in $\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 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-14297746-010",
"literature-status:partially-solved",
"owr-year:2023"
] | Settled Frobenius behavior is proved for several large-image, postcritically finite, and specified quadratic cases, with further 2026 results for periodic postcritical orbits; the general number-field polynomial conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2106.00631",
"label": "Cortez-Lukina"
},
{
"url": "https://arxiv.org/abs/2604.04524",
"label": "Ejder-Kocak"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | Let $f$ be a polynomial of degree $d\geq 2$ over a number field $K$, let $\alpha\in K$, and let $\operatorname{Gal}_{f,\alpha}\subseteq\operatorname{Aut}(T_d)$ be the image of the associated arboreal representation. Prove that the images of Frobenius elements are settled, and hence that settled elements are dense in $\... | One of the open questions about arboreal representations of Galois groups is the properties of the images of Frobenius elements in GalpK\{Kq under such rep- resentations.} 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 | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,688 | OWR-14297746-012 | Spectra of Operators from Heisenberg Substitutions | For a nonperiodic configuration $\omega$ arising from a symbolic substitution system over the discrete Heisenberg group, determine the spectrum $\sigma(H_\omega)$ and its spectral distribution function. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178](https://doi.org/10.4171/owr/2023/37)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 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-14297746-012",
"literature-status:partially-solved",
"owr-year:2023"
] | For primitive nonperiodic Heisenberg substitutions, the integrated density of states has a Pastur-Shubin limit and periodic spectra approximate the aperiodic spectrum exponentially; a complete description of the spectrum or distribution function is not known. | [
{
"url": "https://doi.org/10.4171/owr/2023/37",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2109.15210",
"label": "Beckus-Hartnick-Pogorzelski"
},
{
"url": "https://arxiv.org/abs/2110.05763",
"label": "Beckus-Takase"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/37 | null | null | null | For a nonperiodic configuration $\omega$ arising from a symbolic substitution system over the discrete Heisenberg group, determine the spectrum $\sigma(H_\omega)$ and its spectral distribution function. | Can one say something about the spectrum \sigmapH\omega q of H\omega , or its spectral distribution function? Symbolic substitution systems. We must first determine the class of non- periodic \omega that we would like to consider. One rich source of examples is given by symbolic substitution systems developed recently ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Aspects of Aperiodic Order (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/37, pp. 2107--2178 |
30,005,689 | OWR-14298001-002 | Controlled McKean-Vlasov Problems without Weak Monotonicity | Can the weak monotonicity hypotheses in the controlled McKean–Vlasov problem be weakened or removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Challenges in the Interplay between Finance and Insurance (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/44, pp. 2547--2635](https://doi.org/10.4171/owr/2023/44)
## Literature revie... | 3 | open | null | 2,023 | 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-14298001-002",
"literature-status:open",
"owr-year:2023"
] | The report explicitly records relaxing the weak monotonicity conditions in the cited controlled McKean-Vlasov theory as an open problem; no complete primary resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/44",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2310.00928",
"label": "Criens"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/44 | null | null | null | Can the weak monotonicity hypotheses in the controlled McKean–Vlasov problem be weakened or removed? | The talk is concluded with the open problem to relax some weak monotonicity conditions from [3]. New Challenges in the Interplay between Finance and Insurance 2627 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | New Challenges in the Interplay between Finance and Insurance (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/44, pp. 2547--2635 |
30,005,690 | OWR-14298003-001 | Algebraic Framework for Stochastic Gauge Symmetries | Is there a common algebraic framework for the renormalization and gauge symmetries arising in geometric stochastic heat equations, two-dimensional Yang–Mills Langevin dynamics, and three-dimensional stochastic Yang–Mills–Higgs theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102](https://doi.org/10.4171/owr/... | 3 | open | null | 2,023 | 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-14298003-001",
"literature-status:open",
"owr-year:2023"
] | The cited results establish several separate algebraic and gauge symmetries, but the report poses their unifying algebraic framework as an unresolved natural question. | [
{
"url": "https://doi.org/10.4171/owr/2023/54",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.4171/JEMS/1025",
"label": "Bruned-Chandra-Chevyrev-Hairer"
},
{
"url": "https://arxiv.org/abs/2201.03487",
"label": "Chandra-Chevyrev-Hairer-Shen"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/54 | null | null | null | Is there a common algebraic framework for the renormalization and gauge symmetries arising in geometric stochastic heat equations, two-dimensional Yang–Mills Langevin dynamics, and three-dimensional stochastic Yang–Mills–Higgs theory? | This argument raises the natural question of whether there is an algebraic framework to describe and unify the symmetries appearing in [1, 2, 3]. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102 |
30,005,691 | OWR-14298003-002 | Integration by Parts and Itô Formulas for Rough Paths | Which additional classes of rough paths satisfy integration-by-parts identities and therefore an Itô formula? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102](https://doi.org/10.4171/owr/... | 3 | partially_solved | null | 2,023 | 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-14298003-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Integration-by-parts and Itô-type change-of-variable formulas are established for branched and quasi-geometric rough paths, with newer planarly branched results, while the report records further classes as an open direction. | [
{
"url": "https://doi.org/10.4171/owr/2023/54",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2312.04523",
"label": "Bellingeri-Ferrucci-Tapia"
},
{
"url": "https://arxiv.org/abs/2501.11886",
"label": "Li-Gao"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/54 | null | null | null | Which additional classes of rough paths satisfy integration-by-parts identities and therefore an Itô formula? | What other kinds of rough paths can be show to satisfy integration-by-parts, and therefore an Itô formula? where the integrals are defined in the rough sense. In the case of quadratic drift, i.e., an Itô SDE, (1) coincides with the classical Itô formula. The definition of Fq fully relies on the pre-Lie structure of ... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102 |
30,005,692 | OWR-14298003-005 | Free Structures and Operadic Symmetries for Rough Paths | Find new combinatorial models and free structures for rough paths, develop an operadic account of them, and describe chain-rule and Itô-isometry symmetries through maps from free Novikov structures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102](https://doi.org/10.4171/owr/... | 3 | open | null | 2,023 | 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-14298003-005",
"literature-status:open",
"owr-year:2023"
] | Subsequent work develops multi-index and chain-rule machinery, but no complete classification of the other free structures or general operadic symmetry theory requested here was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/54",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2403.17066",
"label": "Bruned--Dotsenko"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/54 | null | null | null | Find new combinatorial models and free structures for rough paths, develop an operadic account of them, and describe chain-rule and Itô-isometry symmetries through maps from free Novikov structures. | They are several applications/open problems to such a result: • One can try to find other combinatorial sets and their free structures that will be different from multi-indices and decorated trees. • One can get a more operadic perspective as it was initiated in [14] that recovers as an example the multi-Novikov algebr... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/54, pp. 3063--3102 |
30,005,693 | OWR-14298004-001 | Discrete First Cohomology of Totally Disconnected Groups | Let $G=\operatorname{Aut}_F(E)$, where $F$ has characteristic zero and $E/F$ has finite transcendence degree. Compute the discrete cohomology group $dH^1(G,E^\times)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 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-14298004-001",
"literature-status:open",
"owr-year:2023"
] | The source explicitly leaves this specialized discrete cohomology calculation unanswered; later general theory of rational discrete first cohomology does not compute this coefficient case. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1017/S0305004118000762",
"label": "Castellano"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Let $G=\operatorname{Aut}_F(E)$, where $F$ has characteristic zero and $E/F$ has finite transcendence degree. Compute the discrete cohomology group $dH^1(G,E^\times)$. | What is dH 1 (G, E\times )? Discrete cohomology, the Hattori-Stallings rank, the Euler characteristic and formal Dirichlet series for t.d.l.c. groups Thomas Weigel (joint work with Ilaria Castellano, Gianmarco Chinello, Bianca Marchionna and George Willis) | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,694 | OWR-14298004-002 | Projectivity and Cohomological Dimension without Boundedness or Unimodularity | If $P$ is projective in the category of discrete $\mathbb Q[G]$-modules and $M$ is a rational discrete $G$-module, must $P\otimes_{\mathbb Q}M$ be projective? Separately, does the Stallings–Swan theorem for compactly generated totally disconnected locally compact groups of rational cohomological dimension at most one r... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-002",
"literature-status:open",
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] | The tensor-projectivity question remains unanswered, and the 2025 Stallings--Swan result still assumes both boundedness and unimodularity, so the requested unrestricted extensions remain open. | [
{
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{
"url": "https://doi.org/10.1007/s00208-025-03116-7",
"label": "Castellano--Marchionna--Weigel"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | If $P$ is projective in the category of discrete $\mathbb Q[G]$-modules and $M$ is a rational discrete $G$-module, must $P\otimes_{\mathbb Q}M$ be projective? Separately, does the Stallings–Swan theorem for compactly generated totally disconnected locally compact groups of rational cohomological dimension at most one r... | Is P ⊗Q M necessarily a projective object in Q[G] dis? Does Theorem 2 remain true without the hypothesis of c/o bound- edness, and/or unimodularity? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,695 | OWR-14298004-003 | Rational Duality among Crystallographic Coxeter Groups | Which crystallographic Coxeter groups are rational duality groups of dimension $d\geq1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-14298004-003",
"literature-status:open",
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] | Affine and crystallographic hyperbolic groups give examples, but the report records no general classification of crystallographic Coxeter groups as rational duality groups. | [
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{
"url": "https://doi.org/10.1016/j.jalgebra.2016.01.008",
"label": "Castellano--Weigel"
},
{
"url": "https://doi.org/10.1112/jtopol/jtt047",
"label": "Davis--Kahle"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Which crystallographic Coxeter groups are rational duality groups of dimension $d\geq1$? | What crystallographic Coxeter groups are Q-duality groups of di- mension d \geq 1? Mini-Workshop: Homological aspects of TDLC-groups 3113 Let G be a t.d.l.c. group which is (i) unimodular, (ii) rationally of type FP\infty , (iii) of finite rational cohomological dimension. For such a group let (P• , \partial• ) be a fi... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,696 | OWR-14298004-004 | Euler Characteristics from Formal Dirichlet Series of Merohoric Pairs | For which meromorphic pairs $(G,O)$, with $G$ unimodular, rationally of type $\mathrm{FP}_\infty$, and of finite rational cohomological dimension, does $\chi_G=\widehat\zeta_{G,O}(-1)\,\mu_O$ hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-004",
"literature-status:open",
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] | The identity is proved for several Bruhat-decomposition families, but counterexamples exist among general meromorphic pairs and no characterization of all pairs is known. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | For which meromorphic pairs $(G,O)$, with $G$ unimodular, rationally of type $\mathrm{FP}_\infty$, and of finite rational cohomological dimension, does $\chi_G=\widehat\zeta_{G,O}(-1)\,\mu_O$ hold? | For which merohoric pairs (G, O) satisfying (i)-(iii) is it true that (9) χG = ζG,O1(−1) \cdot µO 3. Formal Dirichlet series associated to t.d.l.c. groups. Let G be a t.d.l.c. group, let µ be a left-invariant Haar measure of G, let O \subseteqc/o G and let R \subset G be a set of coset representatives for O\G/O. One sa... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,697 | OWR-14298004-005 | Gorenstein Equivalences under One-Sided Finiteness | Can the equivalence among the complete-cohomology, singularity, totally acyclic complex, and stable Gorenstein-projective or Gorenstein-injective categories for $A_G$ be proved assuming finiteness of only one of $\operatorname{silp}(A_G)$ and $\operatorname{spli}(A_G)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-005",
"literature-status:open",
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] | Theorem C is proved under finiteness of both invariants, while the source explicitly leaves the one-sided finiteness variant as an ending open question. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Can the equivalence among the complete-cohomology, singularity, totally acyclic complex, and stable Gorenstein-projective or Gorenstein-injective categories for $A_G$ be proved assuming finiteness of only one of $\operatorname{silp}(A_G)$ and $\operatorname{spli}(A_G)$? | Ending open question. Can we achieve Theorem C with a finiteness assump- tion on just one of silp(AG ) and spli(AG )? \ 0 (ii) (AG , ExtAG ( , )) (here, the objects are all modules in AG and the Hom- sets are given by the zero-th complete cohomology groups computed with injective resolutions) (iii) Db (AG )/ Kb (Proj -... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,698 | OWR-14298004-006 | Profinite Invariance among Finite-Rank Coxeter Groups | Which homological and cohomological properties or invariants of finite-rank Coxeter groups are determined by their profinite completions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"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.",
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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-14298004-006",
"literature-status:open",
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] | The extracted record contains only a problem label; its source identifies Problem 10 as a broad open program on profinite cohomological invariants of finite-rank Coxeter groups. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Which homological and cohomological properties or invariants of finite-rank Coxeter groups are determined by their profinite completions? | We pose: Problem 10. Mini-Workshop: Homological aspects of TDLC-groups 3123 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,699 | OWR-14298004-007 | TAP Infinity for Free-by-Cyclic Groups | Does every finitely generated free-by-cyclic group belong to $\operatorname{TAP}_\infty(R)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-007",
"literature-status:open",
"owr-year:2023"
] | Known TAP results cover LERF and products of limit groups, while the 2025 free-by-cyclic work does not prove TAP infinity for every finitely generated free-by-cyclic group. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.1112/plms.70059",
"label": "Hughes--Kudlinska"
},
{
"url": "https://arxiv.org/abs/2206.11347",
"label": "Profinite rigidity of fibring"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Does every finitely generated free-by-cyclic group belong to $\operatorname{TAP}_\infty(R)$? | Conjecture 6. Do all \{finitely generated free\}-by-cyclic groups lie in TAP\infty (R)? Mini-Workshop: Homological aspects of TDLC-groups 3127 | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,700 | OWR-14298004-008 | Condensed-Set Equivalence of CH and Regular Model Structures | After replacing the ambient category by condensed sets, do the weak equivalences in the compactly generated Hausdorff and regular model structures coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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-14298004-008",
"literature-status:open",
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] | The source states this replacement by condensed sets as a conjecture; no later proof equating the resulting weak equivalences in the two model structures was located. | [
{
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{
"url": "https://doi.org/10.3390/axioms8030090",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | After replacing the ambient category by condensed sets, do the weak equivalences in the compactly generated Hausdorff and regular model structures coincide? | I conjecture that if one replaces U with the category of condensed sets, the weak equivalences in the CH-structure and the regular structure will be the same; this should strengthen the equivalent of Theorem 1 and allow further results to be proved in this direction. Mini-Workshop: Homological aspects of TDLC-groups 31... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,701 | OWR-14298004-009 | BNSR Invariants of Algebraic Bieri–Strebel Groups | Determine the Bieri–Neumann–Strebel–Renz invariant of every algebraic Bieri–Strebel group, extending the known computation for $F_\tau$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"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.",
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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-14298004-009",
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] | The golden-mean case and further subclasses have been computed, but the BNSR invariant for Algebraic Bieri--Strebel groups in general remains unsolved. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://nyjm.albany.edu/j/2024/30-23.html",
"label": "Molyneux--Nucinkis--Santos Rego"
},
{
"url": "https://arxiv.org/abs/2602.08748",
"label": "Molyneux"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Determine the Bieri–Neumann–Strebel–Renz invariant of every algebraic Bieri–Strebel group, extending the known computation for $F_\tau$. | Molyneux, Nucinkis and Santos Rego [7] were able to apply Bieri, Geoghegan and Kochloukova’s method in order to calculate the BNSR-invariant of F\tau , but the BNSR-invariant for Algebraic Bieri-Strebel groups in general remains an open problem. Finiteness Properties of Algebraic Bieri-Strebel Groups Lewis Molyneux (jo... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,702 | OWR-14298004-010 | Higher Finiteness Embeddings and TDLC Analogues | Does every finitely presented group embed in a group of type $F_3$? Does every group of type $\mathrm{FP}_2$ embed in a group of type $\mathrm{FP}_3$? Formulate and prove, or disprove, a totally disconnected locally compact analogue of the intended embedding theorem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
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"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-010",
"literature-status:open",
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] | Leary proved the embedding theorem into type FP2, but the type F3 and FP3 questions remain explicitly open and the totally disconnected locally compact analogue is only posed. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.1007/s00208-018-1689-5",
"label": "Leary"
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{
"url": "https://eprints.gla.ac.uk/359114/2/359114.pdf",
"label": "Boone--Higman progress survey"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Does every finitely presented group embed in a group of type $F_3$? Does every group of type $\mathrm{FP}_2$ embed in a group of type $\mathrm{FP}_3$? Formulate and prove, or disprove, a totally disconnected locally compact analogue of the intended embedding theorem. | Leary This talk gave a survey of three embedding theorems and discussed some related open questions. The questions of whether every finitely presented group embeds in a group of type F3 and whether every group of type F P2 embeds in a group of type F P3 remain open. Can one state and either prove or find a counterexamp... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,703 | OWR-14298004-011 | Integral Finiteness from Rational or Modular Finiteness | Let $G$ be of type $\mathrm{FP}_n(F)$ for $F\in\{\mathbb Q,\mathbb F_p:p\text{ prime}\}$. For which classes of groups must $G$ be of type $\mathrm{FP}_n(\mathbb Z)$? Does this hold when there is an exact sequence $G\to H\to\mathbb Z$ with $H$ of type $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
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"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-011",
"literature-status:open",
"owr-year:2023"
] | The source poses both the classification and exact-sequence questions as unresolved, and no later result establishing the stated finiteness implication in general was located. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Let $G$ be of type $\mathrm{FP}_n(F)$ for $F\in\{\mathbb Q,\mathbb F_p:p\text{ prime}\}$. For which classes of groups must $G$ be of type $\mathrm{FP}_n(\mathbb Z)$? Does this hold when there is an exact sequence $G\to H\to\mathbb Z$ with $H$ of type $F$? | In general, G is not of type FPn (Z) (n \geq 1), but there exist examples where it holds (e.g. right-angled Artin group (RAAG)). (i) In which classes of groups is it true? (ii) Is it true if there exists an exact sequence G \to H \to Z, where H of type F? The mini-workshop also featured a discussion session on the open... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,704 | OWR-14298004-012 | TDLC Analogue of Finite-Subgroup Conjugacy | For totally disconnected locally compact groups satisfying appropriate analogues of membership in Kropholler's hierarchy and type $\mathrm{FP}_\infty(\mathbb Z)$, are there only finitely many conjugacy classes of finite elementary abelian $p$-subgroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-012",
"literature-status:open",
"owr-year:2023"
] | The discrete theorem is quoted, but its totally disconnected locally compact analogue is explicitly posed without a general formulation or proof. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2016.01.008",
"label": "Castellano--Weigel"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | For totally disconnected locally compact groups satisfying appropriate analogues of membership in Kropholler's hierarchy and type $\mathrm{FP}_\infty(\mathbb Z)$, are there only finitely many conjugacy classes of finite elementary abelian $p$-subgroups? | Is it possible to formulate a TDLC version of this theorem? 1. Dawid Kielak Question 1. Let G be a group of type FPn (F), for F \in \{Q, Fp : p prime\}. In general, G is not of type FPn (Z) (n \geq 1), but there exist examples where it holds (e.g. right-angled Artin group (RAAG)). (i) In which classes of groups is it t... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,705 | OWR-14298004-013 | Quasi-Isometry Invariance and RAAG Analogues for TDLC Groups | If compactly generated totally disconnected locally compact groups $G$ and $H$ are quasi-isometric and have finite rational cohomological dimension, must $\operatorname{cd}_{\mathbb Q}G=\operatorname{cd}_{\mathbb Q}H$? Is there a useful totally disconnected locally compact analogue of right-angled Artin groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-013",
"literature-status:open",
"owr-year:2023"
] | A 2026 preprint supplies a concrete topological right-angled Artin group construction, but it does not settle quasi-isometry invariance of rational discrete cohomological dimension, so the compound record remains open. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2605.28963",
"label": "Castellano--Marchionna--Nucinkis--Santos Rego"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | If compactly generated totally disconnected locally compact groups $G$ and $H$ are quasi-isometric and have finite rational cohomological dimension, must $\operatorname{cd}_{\mathbb Q}G=\operatorname{cd}_{\mathbb Q}H$? Is there a useful totally disconnected locally compact analogue of right-angled Artin groups? | Does cdQ (G) = cdQ (H)? Is there a suitable TDLC analogue of right-angled Artin groups (RAAGs)? 2. Rudradip Biswas Theorem 1. [1, Theorem 19.1] Let Γ \in LHF (locally in Kropholler’s Hierarchy with all finite groups as the base class), and suppose Γ is of type FP\infty (Z). Then Γ has only finitely many conjugacy class... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,706 | OWR-14298004-014 | Embedding $\sigma$-Compact TDLC Groups | Does every $\sigma$-compact totally disconnected locally compact group embed into a compactly generated totally disconnected locally compact group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-014",
"literature-status:open",
"owr-year:2023"
] | The report poses the embedding, totally disconnected locally compact Atiyah, and irrational-covolume lattice questions; no general solution to any of these three was located. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00208-025-03116-7",
"label": "Castellano--Marchionna--Weigel"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Does every $\sigma$-compact totally disconnected locally compact group embed into a compactly generated totally disconnected locally compact group? | Does G embed into a compactly generated TDLC group? Does a version of the Atiyah conjecture hold for TDLC groups? Are there examples of compactly generated TDLC groups with lattices of irrational covolume? 3. Ilaria Castellano Question 3. Let G, H be compactly generated TDLC groups, and suppose G is quasi-isometric to ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,707 | OWR-14298004-015 | Atiyah Conjectures and Irrational-Covolume Lattices for TDLC Groups | Does an Atiyah conjecture hold for totally disconnected locally compact groups, or do such groups have irrational $L^2$-Betti numbers? Do compactly generated totally disconnected locally compact groups admit lattices of irrational covolume? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-015",
"literature-status:open",
"owr-year:2023"
] | The Atiyah statement is known for important discrete and Coxeter subclasses, but the totally disconnected locally compact version and the irrational-covolume lattice question remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2505.08701",
"label": "Hughes--Moller--Varghese"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | Does an Atiyah conjecture hold for totally disconnected locally compact groups, or do such groups have irrational $L^2$-Betti numbers? Do compactly generated totally disconnected locally compact groups admit lattices of irrational covolume? | Does a version of the Atiyah conjecture hold for TDLC groups? Are there examples of compactly generated TDLC groups with lattices of irrational covolume? 6. Yuri Santos Rego Question 8. Under which conditions are Coxeter groups virtually residually finite rationally solvable (RFRS)? Remark 4. Kielak in [2] shows that f... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,708 | OWR-14298004-016 | Profinite Rigidity of Rational Euler Characteristics for Coxeter Groups | When are Coxeter groups virtually RFRS? Do there exist Coxeter groups $W_1,W_2$ with isomorphic profinite completions but $\chi(W_1)\neq\chi(W_2)$? For the Neretin group $N_q$, do $H^k(N_q,B_i(N_q))$ and $H_c^k(E_{\mathcal O}N_q,\mathbb Q)$ vanish for every $k$? Do non-good Coxeter groups exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138](https://doi.org/10.4171/owr/2023/55)
## Literature review (checked 2... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298004-016",
"literature-status:open",
"owr-year:2023"
] | Virtual RFRS is known for finite-rank Coxeter groups, but no Coxeter pair with isomorphic profinite completions and different rational Euler characteristics has been produced or ruled out. | [
{
"url": "https://ems.press/content/serial-article-files/48166",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2505.08701",
"label": "Hughes--Moller--Varghese"
},
{
"url": "https://arxiv.org/abs/1901.01227",
"label": "Kammeyer--Kionke--Wilkes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/55 | null | null | null | When are Coxeter groups virtually RFRS? Do there exist Coxeter groups $W_1,W_2$ with isomorphic profinite completions but $\chi(W_1)\neq\chi(W_2)$? For the Neretin group $N_q$, do $H^k(N_q,B_i(N_q))$ and $H_c^k(E_{\mathcal O}N_q,\mathbb Q)$ vanish for every $k$? Do non-good Coxeter groups exist? | 6. Yuri Santos Rego Question 8. Under which conditions are Coxeter groups virtually residually finite rationally solvable (RFRS)? Remark 4. Kielak in [2] shows that for a finitely generated virtually RFRS group G, virtual fibering is equivalent to the vanishing of the first L2 -Betti number, i.e. (2) b1 (G) = 0. Questi... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Homological aspects of TDLC-groups (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/55, pp. 3103--3138 |
30,005,709 | OWR-14298005-001 | Higher Associativity Structures on Mapping Cones | Develop the theory of $A_3^+$-structures encoding associativity for multiplicative structures on mapping cones, and more generally the theory of $A_\infty^+$-structures encoding associativity up to homotopy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Flavors of Rabinowitz Floer and Tate Homology (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/56, pp. 3139--3171](https://doi.org/10.4171/owr/2023/56)
## Literature review... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298005-001",
"literature-status:open",
"owr-year:2023"
] | The source presents development of the requested higher associativity structures and their A-infinity theory as an open problem; no complete resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/56",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/56 | null | null | null | Develop the theory of $A_3^+$-structures encoding associativity for multiplicative structures on mapping cones, and more generally the theory of $A_\infty^+$-structures encoding associativity up to homotopy. | It is an open problem to develop the theory of A+ 3 -structures (associativity), and indeed A+\infty -structures (associativity up to homotopy). Cone perspective on Rabinowitz Floer homology Alexandru Oancea (joint work with Kai Cieliebak, Nancy Hingston) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Flavors of Rabinowitz Floer and Tate Homology (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/56, pp. 3139--3171 |
30,005,710 | OWR-14298007-003 | Convex Equipartitions in Tautological Vector Bundles | Let $d,j,n,k\geq 1$, let $\mathcal C$ be a collection of $j$ proper convex bodies in $\mathbb R^d$ containing the origin in their interiors, and let $\mathcal P$ be a prescribed class of convex partitions of $\mathbb R^k$. Determine whether there are a $k$-dimensional linear subspace $L\subseteq\mathbb R^d$ and a parti... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-003",
"literature-status:partially-solved",
"owr-year:2023"
] | The vector-bundle partition question has positive theorems for important orthant and generalized-Voronoi settings, but the unrestricted formulation in the record is not resolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
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{
"url": "https://doi.org/10.4171/DM/980",
"label": "Blagojevic--Crabb, Many partitions of mass assignments"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Let $d,j,n,k\geq 1$, let $\mathcal C$ be a collection of $j$ proper convex bodies in $\mathbb R^d$ containing the origin in their interiors, and let $\mathcal P$ be a prescribed class of convex partitions of $\mathbb R^k$. Determine whether there are a $k$-dimensional linear subspace $L\subseteq\mathbb R^d$ and a parti... | Convex partitions of Euclidean vector bundles Motivated by the classical problems of convex partitions of a Euclidean space we ask whether a similar result can be obtained if instead of one (ambient) Euclidean space we consider a (parametrised) family of Euclidean spaces and look for a convex partition of at least one ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,711 | OWR-14298007-006 | Algebraic Connectivity of Complete Graphs | For $d\geq 3$ and $n\geq d+1$, prove the conjectured upper bound $a_d(K_n)\leq n/d$ for the $d$-dimensional algebraic connectivity of the complete graph. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 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-14298007-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The displayed lower bound for a_d(K_n) is proved, but its claimed essential sharpness remains a conjecture; later work does not establish the matching asymptotics. | [
{
"url": "https://doi.org/10.1007/s00493-025-00149-z",
"label": "Lew--Nevo--Peled--Raz, Rigidity Expander Graphs"
},
{
"url": "https://arxiv.org/abs/2205.05530",
"label": "Lew--Nevo--Peled--Raz, algebraic connectivity of graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | For $d\geq 3$ and $n\geq d+1$, prove the conjectured upper bound $a_d(K_n)\leq n/d$ for the $d$-dimensional algebraic connectivity of the complete graph. | Second, we show that ad (Kn ) \geq 21 nd , which we conjecture to be essentially tight. Rigidity expander graphs Eran Nevo (joint work with Alan Lew, Yoval Peled, Orit Raz) Geometric, Algebraic and Topological Combinatorics 3283 rank(R(G, p)) \leq d|V |− d+1 2 ; see [1]. The framework (G, p) is called infinitesimally r... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,712 | OWR-14298007-007 | Generic Anisotropy of Simplicial Spheres | Is every simplicial sphere generically anisotropic over every field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 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-14298007-007",
"literature-status:partially-solved",
"owr-year:2023"
] | Generic anisotropy is proved in characteristic 2 and for several sphere classes and low dimensions, but the assertion for every simplicial sphere over every field remains open. | [
{
"url": "https://arxiv.org/abs/2012.09815",
"label": "Papadakis--Petrotou, characteristic 2 anisotropy"
},
{
"url": "https://arxiv.org/abs/2406.18989",
"label": "Fan, strongly edge decomposable spheres"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfac... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Is every simplicial sphere generically anisotropic over every field? | Is any simplicial sphere generically anisotropic over any field? Theorem 6 ([3]). Assume k is any field and D is a simplicial sphere. (1) If the suspension S(D) of D is generically anisotropic over k, then E[D] has the Weak Lefschetz property. (2) If both D and the suspension S(D) of D are generically anisotropic over ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,713 | OWR-14298007-008 | Generic Anisotropy of Gorenstein Graded Algebras | Identify classes of Gorenstein standard graded algebras that have the generic anisotropy property. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 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-14298007-008",
"literature-status:partially-solved",
"owr-year:2023"
] | Known classes include characteristic-2 spheres, cycles, and strongly edge decomposable spheres, but no classification of Gorenstein standard graded algebras with generic anisotropy is known. | [
{
"url": "https://arxiv.org/abs/2406.18989",
"label": "Fan, generic anisotropy of strongly edge decomposable spheres"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Identify classes of Gorenstein standard graded algebras that have the generic anisotropy property. | Question 8. Identify classes of Gorenstein standard graded algebras which have the generic anisotropy property. 4. Lefschetz properties for cycles As mentioned above, the paper [2] contains Lefschetz type theorems for pseudo- manifolds and simplicial cycles. An interesting application of them is the following: A simpli... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,714 | OWR-14298007-009 | Noncompact Casacuberta-Dicks Conjecture | Prove the Casacuberta-Dicks fixed-point conjecture without the compactness assumption: every action of a finite group on a contractible two-dimensional complex has a fixed point. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299915-017"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-009",
"literature-status:open",
"owr-year:2023"
] | The compact or finite case has recent positive results, but the cited current report explicitly states that the non-compact Casacuberta--Dicks case remains open. | [
{
"url": "https://ems.press/content/serial-article-files/53607",
"label": "Oberwolfach Report 9/2026"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Prove the Casacuberta-Dicks fixed-point conjecture without the compactness assumption: every action of a finite group on a contractible two-dimensional complex has a fixed point. | Finally, we mention that the non-compact case of the Casacuberta-Dicks con- jecture 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, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
30,005,715 | OWR-14298007-010 | Growth of Triangulated Homology Three-Spheres | Let $t_N$ be the number of combinatorial isomorphism classes of triangulations of three-dimensional homology spheres with $N$ facets. Determine whether $t_N$ grows exponentially or superexponentially in $N$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318](https://doi.org/10.4171/owr/2023/58)
## Literature review (checked ... | 3 | partially_solved | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14298007-010",
"literature-status:partially-solved",
"owr-year:2023"
] | The exponential-versus-superexponential question remains unanswered, although recent work constructs substantial families and transfers superexponential growth from higher-dimensional homology spheres to dimension three. | [
{
"url": "https://arxiv.org/abs/2509.06275",
"label": "Adiprasito--Lackenby--Souto--Yashfe, 2025"
},
{
"url": "https://doi.org/10.4171/owr/2023/58",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/58 | null | null | null | Let $t_N$ be the number of combinatorial isomorphism classes of triangulations of three-dimensional homology spheres with $N$ facets. Determine whether $t_N$ grows exponentially or superexponentially in $N$. | Is tN exponential or superexponential in N ? Counting triangulations of homology 3-spheres Geva Yashfe (joint work with Karim Adiprasito, Marc Lackenby, Juan Souto, and (separately) with Yuval Peled) Known results and related work. • For triangulations of S 2 Tutte [9] proved that there are exponentially many triangula... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric, Algebraic and Topological Combinatorics (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/58, pp. 3249--3318 |
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