id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,716 | OWR-7155451-006 | Positive Energy Conditions and Spaces of Initial Data | Do known results for nonnegative or positive scalar curvature generalize to initial data sets $(g,k)$ satisfying the strict dominant energy condition? In particular, do nontrivial homotopy classes detected for the space of positive-scalar-curvature metrics yield nontrivial classes in the corresponding space of initial ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-006",
"literature-status:open",
"owr-year:2021"
] | Dirac-Witten and index-theoretic results treat important spin and strict dominant-energy cases, but no theorem establishes the broad generalization requested for arbitrary initial data sets. | [
{
"url": "https://doi.org/10.4171/owr/2021/30",
"label": "Oberwolfach Reports 2022"
},
{
"url": "https://arxiv.org/abs/2103.11032",
"label": "Ammann and Glöckle, initial-data index theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Do known results for nonnegative or positive scalar curvature generalize to initial data sets $(g,k)$ satisfying the strict dominant energy condition? In particular, do nontrivial homotopy classes detected for the space of positive-scalar-curvature metrics yield nontrivial classes in the corresponding space of initial ... | Do known results for nonnegative or positive scalar curvature generalize to initial data sets (g,k) satisfying the strict dominant energy condition? In particular, do nontrivial homotopy classes detected for the space of positive-scalar-curvature metrics yield nontrivial classes in the corresponding space of initial da... | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,717 | OWR-7155451-007 | Sharp Width Bounds for Positive-Scalar-Curvature Bands | If $Y$ is a closed smooth $(n-1)$-manifold, with $n-1\neq4$, that admits no positive-scalar-curvature metric, and $g$ on $Y\times[-1,1]$ has scalar curvature at least $\sigma>0$, prove that $\operatorname{dist}_g(Y\times\{-1\},Y\times\{1\})\leq 2\pi\sqrt{(n-1)/(\sigma n)}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-007",
"literature-status:partially-solved",
"owr-year:2021"
] | The band-width inequality is established in important spin and index-theoretic cases, including orientable dimensions through seven, but no full all-dimension and all-topology solution is known. | [
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/topo.12303",
"label": "Cecchini, Rade and Zeidler, Journal of Topology"
},
{
"url": "https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/year/2023/docId/99573",
"label": "Rade, doctoral thesis on band width"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | If $Y$ is a closed smooth $(n-1)$-manifold, with $n-1\neq4$, that admits no positive-scalar-curvature metric, and $g$ on $Y\times[-1,1]$ has scalar curvature at least $\sigma>0$, prove that $\operatorname{dist}_g(Y\times\{-1\},Y\times\{1\})\leq 2\pi\sqrt{(n-1)/(\sigma n)}$. | Conjecture: if Y is a closed smooth (n−1)-manifold with n−1≠4 that admits no positive-scalar-curvature metric, and g on Y×[−1,1] has scalar curvature at least σ>0, then the band width dist_g(Y×{−1},Y×{1}) is at most 2π√((n−1)/(σn)). | corrected_verified | The band-width bound and its dimension and curvature hypotheses were normalized without changing the conjecture. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,718 | OWR-7155451-008 | Rigidity in Scalar-Curvature Band Width Inequalities | Let $Y$ be a closed $(n-1)$-manifold, with $n-1\neq4$, that admits no positive-scalar-curvature metric; set $X=Y\times[-1,1]$ and $c_n=\sqrt{(n-1)/n}$. Suppose $\operatorname{Sc}(X,g)\geq\sigma>0$, $-\pi c_n/\sqrt{\sigma}<\ell_-<\ell_+<\pi c_n/\sqrt{\sigma}$, $H(\partial_-X)\geq\sqrt{\sigma}c_n\tan(\sqrt{\sigma}\ell_-/... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-008",
"literature-status:partially-solved",
"owr-year:2021"
] | Rigidity is proved under spin, nonzero index, and related model hypotheses, but the conjectured rigidity statement in the extracted generality remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46909",
"label": "Oberwolfach Reports 2022"
},
{
"url": "https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/year/2023/docId/99573",
"label": "Rade, doctoral thesis on band rigidity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Let $Y$ be a closed $(n-1)$-manifold, with $n-1\neq4$, that admits no positive-scalar-curvature metric; set $X=Y\times[-1,1]$ and $c_n=\sqrt{(n-1)/n}$. Suppose $\operatorname{Sc}(X,g)\geq\sigma>0$, $-\pi c_n/\sqrt{\sigma}<\ell_-<\ell_+<\pi c_n/\sqrt{\sigma}$, $H(\partial_-X)\geq\sqrt{\sigma}c_n\tan(\sqrt{\sigma}\ell_-/... | Conjecture: under the stated scalar-curvature and boundary-mean-curvature lower bounds for a band X=Y×[−1,1], together with width(X,g)≥ℓ_+−ℓ_−, equality forces X to be the warped product (Y×[ℓ_−,ℓ_+],φ(t)^2g_Y+dt^2), where φ(t)=cos(√σ t/(2c_n))^{n/2} and g_Y is Ricci flat. | corrected_verified | The linked report was inspected and every scalar-curvature, boundary-mean-curvature, parameter-range, and width hypothesis of Conjecture 4 was restored. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,719 | OWR-7155451-009 | Fillability of Bartnik Boundary Data Under Scalar Curvature Bounds | Given a closed $(n-1)$-dimensional Riemannian manifold $(Y,h)$, a smooth function $\varphi$ on $Y$, and $\sigma$, find necessary and sufficient conditions for a complete $n$-dimensional manifold $(X,g)$ with boundary $Y$ and scalar curvature $R_g\geq\sigma$ to realize the Bartnik data $(g^\top,H_g)=(h,\varphi)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-009",
"literature-status:partially-solved",
"owr-year:2021"
] | Existence and nonexistence criteria are known in several regimes, notably for large mean curvature and in low-dimensional settings, but no general characterization of prescribed Bartnik data is known. | [
{
"url": "https://arxiv.org/abs/1907.12173",
"label": "Shi, Wang, Wei and Zhu, fill-ins with scalar bounds"
},
{
"url": "https://doi.org/10.1007/s00208-020-02087-1",
"label": "Mathematische Annalen 2021"
},
{
"url": "https://doi.org/10.1007/s10455-024-09956-x",
"label": "Fill-ins wit... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Given a closed $(n-1)$-dimensional Riemannian manifold $(Y,h)$, a smooth function $\varphi$ on $Y$, and $\sigma$, find necessary and sufficient conditions for a complete $n$-dimensional manifold $(X,g)$ with boundary $Y$ and scalar curvature $R_g\geq\sigma$ to realize the Bartnik data $(g^\top,H_g)=(h,\varphi)$. | Given a closed (n−1)-dimensional Riemannian manifold (Y,h), a smooth function φ on Y, and σ, find necessary and sufficient conditions for a complete n-dimensional manifold (X,g) with scalar curvature R_g≥σ and boundary Y to realize the Bartnik data (g^⊤,H_g)=(h,φ). | corrected_verified | The Bartnik boundary data and scalar-curvature notation were normalized without changing the existence problem. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,720 | OWR-7155451-010 | Equivalence of Weak Scalar-Curvature Notions for Continuous Metrics | Is the Ricci-flow-based $\beta$-weak notion of lower scalar-curvature bounds for $C^0$ metrics equivalent to Gromov's polyhedral formulation, locally or globally? For a metric near the origin in $\mathbb{R}^n$ of the form $g_{ij}(x)=\delta_{ij}+r^2G_{ij}(x/r)+O(|x|^{2+\eta})$, where $x^ix^jG_{ij}(x)=0$ on $S^{n-1}$, ch... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-010",
"literature-status:open",
"owr-year:2021"
] | The Ricci-flow and approximation formulations are identified, but equivalence with Gromov's polyhedral formulation and the requested explicit local characterization remain open. | [
{
"url": "https://arxiv.org/abs/1907.13116",
"label": "Burkhardt-Guim, pointwise scalar bounds"
},
{
"url": "https://arxiv.org/abs/1908.10612",
"label": "Gromov, scalar curvature lectures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Is the Ricci-flow-based $\beta$-weak notion of lower scalar-curvature bounds for $C^0$ metrics equivalent to Gromov's polyhedral formulation, locally or globally? For a metric near the origin in $\mathbb{R}^n$ of the form $g_{ij}(x)=\delta_{ij}+r^2G_{ij}(x/r)+O(|x|^{2+\eta})$, where $x^ix^jG_{ij}(x)=0$ on $S^{n-1}$, ch... | For the Ricci-flow-based weak lower-scalar-curvature notion for C^0 metrics, is it equivalent to Gromov's polyhedral formulation for global or local bounds, and can one explicitly characterize metrics with the stated asymptotic form that have nonnegative scalar curvature at the origin in this weak sense? | corrected_verified | The linked report was inspected; Questions 8 and 10 were combined while the full asymptotic metric and tangentiality condition were restored. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,721 | OWR-7155451-011 | Preservation of Positive-Scalar-Curvature Obstructions Under Surgery | If a smooth manifold $M$ admits no metric of positive scalar curvature, under what kinds of surgery does the resulting manifold also admit no positive-scalar-curvature metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-011",
"literature-status:open",
"owr-year:2021"
] | The forward codimension-three surgery theorem preserves existence of positive scalar curvature, but no general reverse or nonexistence surgery criterion answers the broad problem stated here. | [
{
"url": "https://doi.org/10.4171/owr/2021/30",
"label": "Oberwolfach Reports 2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | If a smooth manifold $M$ admits no metric of positive scalar curvature, under what kinds of surgery does the resulting manifold also admit no positive-scalar-curvature metric? | If a smooth manifold M admits no metric of positive scalar curvature, under what kinds of surgery does the resulting manifold also admit no positive-scalar-curvature metric? | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,722 | OWR-7155451-012 | Surgery Stability of Positive Ricci Curvature | Does a surgery theorem for positive Ricci curvature hold in the same generality as the Schoen–Yau and Gromov–Lawson surgery theorem for positive scalar curvature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-012",
"literature-status:open",
"owr-year:2021"
] | Current work explicitly still treats a surgery theorem for positive Ricci curvature in the Schoen--Yau and Gromov--Lawson generality as unknown; only restricted surgery results are available. | [
{
"url": "https://doi.org/10.1007/s00526-025-03211-2",
"label": "Reiser and Tripaldi, Calculus of Variations 2026"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC12795942/",
"label": "Open-access version of the surgery paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Does a surgery theorem for positive Ricci curvature hold in the same generality as the Schoen–Yau and Gromov–Lawson surgery theorem for positive scalar curvature? | Does a surgery theorem for positive Ricci curvature hold in the same generality as the Schoen–Yau and Gromov–Lawson surgery theorem for positive scalar curvature? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,723 | OWR-7155451-013 | Core Metrics and Positive Ricci Curvature on Simply Connected Manifolds | Does every closed simply connected manifold admitting a positive-Ricci-curvature metric admit a core metric, and does every closed simply connected 6-manifold admit a positive-Ricci-curvature metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-013",
"literature-status:open",
"owr-year:2021"
] | Many new families with positive Ricci curvature and core metrics are known, but the universal core-metric assertion and the assertion for every simply connected six-manifold remain open. | [
{
"url": "https://doi.org/10.1112/topo.70007",
"label": "Reiser, Journal of Topology 2024"
},
{
"url": "https://arxiv.org/abs/2401.06587",
"label": "Twisted suspensions and positive Ricci curvature"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Does every closed simply connected manifold admitting a positive-Ricci-curvature metric admit a core metric, and does every closed simply connected 6-manifold admit a positive-Ricci-curvature metric? | Does every closed simply connected manifold admitting a positive-Ricci-curvature metric admit a core metric, and does every closed simply connected 6-manifold admit a positive-Ricci-curvature metric? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,724 | OWR-7155451-014 | Negative-Mass Ends of Nonnegative-Scalar-Curvature Manifolds | Let $(M,g)$ be complete with nonnegative scalar curvature and let $E$ be an asymptotically flat end of $M$. Can $E$ have negative ADM mass? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-014",
"literature-status:partially-solved",
"owr-year:2021"
] | Negative mass is ruled out for spin ends in all dimensions and for asymptotically Schwarzschild ends in dimensions three through seven, but the unrestricted nonspin all-dimensional question remains unresolved. | [
{
"url": "https://arxiv.org/abs/2108.11972",
"label": "Cecchini and Zeidler, positive mass for ends"
},
{
"url": "https://arxiv.org/abs/2103.02744",
"label": "Lesourd, Unger and Yau, asymptotically Schwarzschild mass"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Let $(M,g)$ be complete with nonnegative scalar curvature and let $E$ be an asymptotically flat end of $M$. Can $E$ have negative ADM mass? | Let (M,g) be complete with nonnegative scalar curvature and let E be an asymptotically flat end of M. Can E have negative ADM mass? | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,725 | OWR-7155451-015 | Localized Scalar Curvature Conditions Forcing Nonnegative ADM Mass | For an asymptotically flat Riemannian manifold $X$ with compact boundary and nonnegative scalar curvature, can metric conditions involving a positive scalar-curvature lower bound in a region and the distance from that region to the boundary force the ADM mass of $X$ to be nonnegative? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-015",
"literature-status:partially-solved",
"owr-year:2021"
] | Explicit sufficient distance and scalar-curvature conditions are proved in the spin setting, but no general nonspin characterization of the requested type is known. | [
{
"url": "https://ems.press/content/serial-article-files/46909",
"label": "Oberwolfach Reports 2022"
},
{
"url": "https://arxiv.org/abs/2103.06833",
"label": "Cecchini and Zeidler, curvature comparison"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | For an asymptotically flat Riemannian manifold $X$ with compact boundary and nonnegative scalar curvature, can metric conditions involving a positive scalar-curvature lower bound in a region and the distance from that region to the boundary force the ADM mass of $X$ to be nonnegative? | For an asymptotically flat Riemannian manifold X with compact boundary and nonnegative scalar curvature, can metric conditions involving a positive scalar-curvature lower bound in a region and the distance from that region to the boundary force the ADM mass of X to be nonnegative? | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,726 | OWR-7155451-016 | Classification of Complete Positive-Scalar-Curvature Three-Manifolds | Can complete 3-manifolds admitting metrics of positive scalar curvature be classified up to diffeomorphism, extending the known classification of the closed orientable case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-016",
"literature-status:partially-solved",
"owr-year:2021"
] | Uniformly positive scalar curvature is topologically classified for open three-manifolds, and several decay-controlled cases are known, but the unrestricted complete pointwise-positive-scalar-curvature classification remains open. | [
{
"url": "https://arxiv.org/abs/2212.14383",
"label": "Wang, topology of three-manifolds with uniform positivity"
},
{
"url": "https://link.springer.com/article/10.1007/s00208-025-03192-9",
"label": "Complete three-manifolds with quadratic decay"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Can complete 3-manifolds admitting metrics of positive scalar curvature be classified up to diffeomorphism, extending the known classification of the closed orientable case? | Can complete 3-manifolds admitting metrics of positive scalar curvature be classified up to diffeomorphism, extending the known classification of the closed orientable case? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,727 | OWR-7155451-017 | Contractible Positive-Scalar-Curvature Three-Manifolds | Is every complete contractible $3$-manifold with positive scalar curvature homeomorphic to $\mathbb{R}^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-017",
"literature-status:open",
"owr-year:2021"
] | The assertion is proved with additional hypotheses such as trivial fundamental group at infinity, bounded geometry, or curvature decay, while current literature still identifies the unrestricted question as open. | [
{
"url": "https://ems.press/journals/jems/articles/11806807",
"label": "Wang, Contractible three-manifolds and positive scalar curvature II"
},
{
"url": "https://link.springer.com/article/10.1007/s00208-025-03192-9",
"label": "Complete three-manifolds with quadratic decay"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Is every complete contractible $3$-manifold with positive scalar curvature homeomorphic to $\mathbb{R}^3$? | Is every complete contractible 3-manifold with positive scalar curvature homeomorphic to R^3? | corrected_verified | The Euclidean-space notation was normalized without changing the topological question. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,728 | OWR-7155451-019 | Homotopy Invariance of Positive-Scalar-Curvature Metric Spaces | Let $M$ and $N$ be closed $d$-manifolds with $d\geq 5$ and the same normal $2$-type. If both admit metrics of positive scalar curvature, prove that the spaces $R^+(M)$ and $R^+(N)$ are homotopy equivalent. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649](https://doi.org/10.4171/owr/2021/30)
## Literatur... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-7155451-019",
"literature-status:open",
"owr-year:2021"
] | The same-normal-two-type homotopy-equivalence conjecture remains open; existing results cover selected normal two-types and special fundamental groups rather than the stated generality. | [
{
"url": "https://ems.press/content/serial-article-files/31422",
"label": "Journal of the European Mathematical Society, positive scalar curvature spaces"
},
{
"url": "https://ems.press/content/serial-article-files/46909",
"label": "Oberwolfach Reports 2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/30 | null | null | null | Let $M$ and $N$ be closed $d$-manifolds with $d\geq 5$ and the same normal $2$-type. If both admit metrics of positive scalar curvature, prove that the spaces $R^+(M)$ and $R^+(N)$ are homotopy equivalent. | Conjecture: Let M and N be closed d-manifolds with d \geq 5 and the same normal 2-type. If both admit metrics of positive scalar curvature, then the spaces R^+(M) and R^+(N) are homotopy equivalent. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/30, pp. 1579--1649 |
30,004,729 | OWR-7155452-001 | Convergence of Far-Field Refractor Schemes | For the numerical scheme discretizing the general Monge–Ampère equation in the far-field refractor setting, do the solutions of the scheme converge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Numerical Methods for Fully Nonlinear and Related PDEs (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/31, pp. 1651--1674](https://doi.org/10.4171/owr/2021/31)
## Literature review (chec... | 3 | open | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-7155452-001",
"literature-status:open",
"owr-year:2021"
] | The exact record states that convergence of the numerical solutions remains an open problem; no general convergence theorem resolves this unspecified scheme. | [
{
"url": "https://ems.press/journals/owr/articles/7155452",
"label": "Oberwolfach Reports article 7155452"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/31 | null | null | null | For the numerical scheme discretizing the general Monge–Ampère equation in the far-field refractor setting, do the solutions of the scheme converge? | For the numerical scheme discretizing the general Monge--Ampere equation in the far-field refractor setting, do the solutions of the scheme converge? | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Numerical Methods for Fully Nonlinear and Related PDEs (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/31, pp. 1651--1674 |
30,004,730 | OWR-8415335-002 | Consistent Conical Bicombings in Metric Spaces | Does every metric space with a conical bicombing also admit a consistent conical bicombing? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734](https://doi.org/10.4171/owr/2021/32)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415335-002",
"literature-status:open",
"owr-year:2021"
] | The question is settled for proper spaces under weaker convexity assumptions, but the general assertion for complete metric spaces remains open and has no known counterexample. | [
{
"url": "https://ems.press/journals/lem/articles/14297776",
"label": "Basso, conical bicombings"
},
{
"url": "https://doi.org/10.1007/s00208-024-02905-w",
"label": "Metric geometry paper on consistent bicombings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/32 | null | null | null | Does every metric space with a conical bicombing also admit a consistent conical bicombing? | Does every metric space with a conical bicombing also admit a consistent conical bicombing? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734 |
30,004,731 | OWR-8415335-005 | Finite Euclidean Models of Compact Nonpositively Curved Surfaces | Is every compact two-dimensional nonpositively curved space homotopy equivalent to a finite two-dimensional nonpositively curved Euclidean complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734](https://doi.org/10.4171/owr/2021/32)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415335-005",
"literature-status:open",
"owr-year:2021"
] | The exact extraction is an incomplete contextual fragment and does not state the referenced Conjecture 2; its resolution is therefore unclear and classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2021/32",
"label": "Oberwolfach Reports, Differentialgeometrie im Grossen"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/32 | null | null | null | Is every compact two-dimensional nonpositively curved space homotopy equivalent to a finite two-dimensional nonpositively curved Euclidean complex? | Conjecture: Every compact two-dimensional non-positively curved space is homotopy equivalent to a finite two-dimensional non-positively curved Euclidean complex. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734 |
30,004,732 | OWR-8415335-007 | Critical-Exponent Geometry of Negatively Pinched Hadamard Quotients | Let $\Gamma$ be a finitely generated discrete isometry group of a Hadamard manifold $X$ with $-b^2\leq K_X\leq-1$ and critical exponent $\delta_\Gamma\leq2$. Must $X/\Gamma$ have finitely many cusps and bounded orders of torsion elements in $\Gamma$? Also, do there exist four-dimensional examples $(X_k,\Gamma_k)$ with ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734](https://doi.org/10.4171/owr/2021/32)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-8415335-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Orbifold geometrization is proved, but the extracted Conjecture 6 at critical exponent delta less than or equal to 2 is not settled; Liu--Wang prove only the cusp-finiteness subcase delta less than 1, leaving the full bounded-torsion and four-dimensional sequence claims unresolved. | [
{
"url": "https://annals.math.princeton.edu/2005/162-1/p04",
"label": "orbifold geometrization"
},
{
"url": "https://arxiv.org/abs/2008.12365",
"label": "small critical exponent subcase"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/32 | null | null | null | Let $\Gamma$ be a finitely generated discrete isometry group of a Hadamard manifold $X$ with $-b^2\leq K_X\leq-1$ and critical exponent $\delta_\Gamma\leq2$. Must $X/\Gamma$ have finitely many cusps and bounded orders of torsion elements in $\Gamma$? Also, do there exist four-dimensional examples $(X_k,\Gamma_k)$ with ... | Conjecture: If \Gamma is a finitely generated discrete isometry group of a negatively pinched Hadamard manifold X with -b^2 \leq K_X \leq -1 and critical exponent \delta_\Gamma \leq 2, then X/\Gamma has finitely many cusps and the orders of torsion elements of \Gamma are bounded. Also, there exists a sequence of four-d... | 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 | Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734 |
30,004,733 | OWR-8415335-008 | Special Lagrangian Fibrations in Calabi-Yau Degenerations | In a large-complex-structure degeneration of Calabi–Yau $n$-folds, does the Ricci-flat metric admit a special Lagrangian $T^n$-fibration on a generic region, as predicted by the Strominger–Yau–Zaslow conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734](https://doi.org/10.4171/owr/2021/32)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-8415335-008",
"literature-status:partially-solved",
"owr-year:2021"
] | The metric and SYZ large-complex-structure picture is proved in important cases such as K3 surfaces and has algebraic and symplectic partial realizations, but the general Calabi--Yau degeneration problem remains unresolved. | [
{
"url": "https://arxiv.org/abs/math/0008018",
"label": "Gross--Wilson K3 limits"
},
{
"url": "https://arxiv.org/abs/math/0211094",
"label": "Gross--Siebert program"
},
{
"url": "https://arxiv.org/abs/2206.01681",
"label": "later SYZ cases"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/32 | null | null | null | In a large-complex-structure degeneration of Calabi–Yau $n$-folds, does the Ricci-flat metric admit a special Lagrangian $T^n$-fibration on a generic region, as predicted by the Strominger–Yau–Zaslow conjecture? | In a large-complex-structure degeneration of Calabi--Yau n-folds, does the Ricci-flat metric admit a special Lagrangian T^n-fibration on a generic region of the manifold, as predicted by the Strominger--Yau--Zaslow conjecture? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Grossen (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/32, pp. 1685--1734 |
30,004,734 | OWR-8415336-003 | Periodic Billiards and the Wave Trace of Ellipses | Can a set of periodic billiard orbits, for example a positive-measure Cantor set of a fixed length, produce the wave-trace expansion of an ellipse? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Spectral rigidity is proved in analytic symmetry classes and 2025 work gives local uniqueness for almost every ellipse, but full rigidity of every ellipse without symmetry assumptions remains open. | [
{
"url": "https://annals.math.princeton.edu/2009/170-1/p06",
"label": "analytic symmetric rigidity"
},
{
"url": "https://doi.org/10.1007/s00222-025-01397-y",
"label": "local uniqueness of almost every ellipse"
},
{
"url": "https://msp.org/apde/2012/5-5/apde-v5-n5-p06-s.pdf",
"label":... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Can a set of periodic billiard orbits, for example a positive-measure Cantor set of a fixed length, produce the wave-trace expansion of an ellipse? | Can a set of periodic billiard orbits, for example a positive-measure Cantor set of a fixed length, produce the wave-trace expansion of an ellipse? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,735 | OWR-8415336-004 | Uniqueness of Fixed-Bounce Geodesic Loops in Billiards | For a billiard domain $\Omega$ and a boundary point $x$, is there a unique geodesic loop based at $x$ with winding number $1$ and $q$ reflections, so that the loop-length function $\psi_q$ is well defined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-004",
"literature-status:partially-solved",
"owr-year:2021"
] | Analytic symmetric and selected chaotic billiards admit marked-length or spectral determination results, but the general well-definedness of the loop-length data and spectral detection of convexity remain unresolved. | [
{
"url": "https://annals.math.princeton.edu/2009/170-1/p06",
"label": "analytic symmetric domains"
},
{
"url": "https://doi.org/10.1007/s00222-023-01191-8",
"label": "marked-length determination"
},
{
"url": "https://doi.org/10.4310/jdg/1214437138",
"label": "convex spectral invarian... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | For a billiard domain $\Omega$ and a boundary point $x$, is there a unique geodesic loop based at $x$ with winding number $1$ and $q$ reflections, so that the loop-length function $\psi_q$ is well defined? | For a billiard domain \Omega and a boundary point x, is there a unique geodesic loop at x with winding number 1 and q bounces, so that the loop-length function \psi_q is well-defined? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,736 | OWR-8415336-005 | Accumulation Points of Convex Billiard Length Spectra | For a real-analytic convex billiard domain $\Omega$, are the multiples of the perimeter $|\partial\Omega|$ the only accumulation points of its length spectrum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-005",
"literature-status:partially-solved",
"owr-year:2021"
] | Analytic symmetry classes have spectral rigidity and formal nonisometric Birkhoff-normal-form germs are known, but the general analytic realization and convexity-detection questions remain open. | [
{
"url": "https://msp.org/apde/2012/5-5/apde-v5-n5-p06-s.pdf",
"label": "formal Birkhoff-normal-form rigidity"
},
{
"url": "https://annals.math.princeton.edu/2009/170-1/p06",
"label": "analytic symmetric rigidity"
},
{
"url": "https://doi.org/10.1007/s00222-025-01397-y",
"label": "al... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | For a real-analytic convex billiard domain $\Omega$, are the multiples of the perimeter $|\partial\Omega|$ the only accumulation points of its length spectrum? | For a real-analytic convex billiard domain \Omega, are the multiples of the perimeter |\partial\Omega| the only accumulation points of its length spectrum? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,737 | OWR-8415336-006 | Smooth Rigidity of Diophantine Step-Two Affine Maps | For a Diophantine step-two affine map $a$, does every smooth perturbation that is $C^1$-conjugate to $a$ admit a smooth conjugacy to $a$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-006",
"literature-status:partially-solved",
"owr-year:2021"
] | The specific one-map C1-to-smooth conjugacy question is not settled in full generality, while 2026 work proves a locked--unlocked dichotomy and tame KAM rigidity for almost every translation in parabolic Z2 actions with a step-two generator; higher-step cases remain open. | [
{
"url": "https://doi.org/10.1007/s00222-026-01415-7",
"label": "parabolic KAM rigidity"
},
{
"url": "https://arxiv.org/abs/2106.01585",
"label": "higher-rank local rigidity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | For a Diophantine step-two affine map $a$, does every smooth perturbation that is $C^1$-conjugate to $a$ admit a smooth conjugacy to $a$? | For a Diophantine step-2 affine map a, does every smooth perturbation that is C^1-conjugate to a necessarily admit a smooth conjugacy to a? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,738 | OWR-8415336-007 | Ruelle Zeta Vanishing for Generic Negatively Curved Metrics | For a generic negatively curved metric on a closed connected oriented three-manifold $\Sigma$, does the order $m(0)$ of vanishing at zero of its Ruelle zeta function equal $4-b_1(\Sigma)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-007",
"literature-status:partially-solved",
"owr-year:2021"
] | The conjectured generic value of the Ruelle-zeta vanishing order is proved for generic conformal perturbations of compact hyperbolic three-manifolds, but this does not establish the stated claim for all generic negatively curved metrics. | [
{
"url": "https://doi.org/10.1007/s00222-022-01108-x",
"label": "Ruelle zeta near hyperbolic metrics"
},
{
"url": "https://arxiv.org/abs/2009.08558",
"label": "primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | For a generic negatively curved metric on a closed connected oriented three-manifold $\Sigma$, does the order $m(0)$ of vanishing at zero of its Ruelle zeta function equal $4-b_1(\Sigma)$? | Conjecture: For a generic negatively curved metric on a closed connected oriented three-manifold \Sigma, the order of vanishing m(0) of its Ruelle zeta function at 0 equals 4-b_1(\Sigma). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,739 | OWR-8415336-009 | Copreservation of Even and Odd Periodic Billiard Families | Can one-parameter families of $2$-periodic and $(2m+1)$-periodic billiard trajectories be preserved simultaneously under deformations of the billiard table? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-009",
"literature-status:partially-solved",
"owr-year:2021"
] | For deformations of a circle with analytic boundaries, preserving both the period-two and period-(2m+1) rational caustics forces the deformation to be trivial, but the corresponding global question for arbitrary convex domains remains open. | [
{
"url": "https://arxiv.org/abs/2107.03499",
"label": "non-co-preservation theorem"
},
{
"url": "https://arxiv.org/abs/1711.10541",
"label": "period-two and period-three rigidity"
},
{
"url": "https://doi.org/10.4171/owr/2021/33",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Can one-parameter families of $2$-periodic and $(2m+1)$-periodic billiard trajectories be preserved simultaneously under deformations of the billiard table? | Can one-parameter families of 2-periodic and (2m+1)-periodic billiard trajectories be co-preserved under deformations of the billiard table? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,740 | OWR-8415336-010 | Counting Rational Caustics in Convex Billiards | How many $(m,n)$-rational caustics should a sufficiently smooth strictly convex billiard domain have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-010",
"literature-status:open",
"owr-year:2021"
] | There is no general count of rational caustics for smooth strictly convex billiards; fixed-rotation caustics can be constructed densely and special integrable tables have many, but the expected number in general is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/33",
"label": "Oberwolfach problem report"
},
{
"url": "https://arxiv.org/abs/1706.07968",
"label": "density of rational caustics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | How many $(m,n)$-rational caustics should a sufficiently smooth strictly convex billiard domain have? | How many (m,n)-rational caustics should a sufficiently smooth strictly convex billiard domain have? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,741 | OWR-8415336-012 | Two-Term Weyl Asymptotics and Ivrii's Billiard Conjecture | For every smooth planar domain $\Omega$, does the eigenvalue counting function satisfy
$$
N(\lambda)=\frac{\operatorname{Area}(\Omega)}{4\pi}\lambda+C\ell(\partial\Omega)\lambda^{1/2}+o(\lambda^{1/2})?
$$
Also, does every smooth planar billiard domain have periodic trajectories of measure zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-012",
"literature-status:partially-solved",
"owr-year:2021"
] | Weyl's two-term formula follows under Ivrii's measure-zero hypothesis and is known in important analytic or generic classes, but Ivrii's conjecture for every smooth convex table remains open. | [
{
"url": "https://arxiv.org/abs/2406.16172",
"label": "current billiard Weyl-law results"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0001870825005729",
"label": "2025 algebraic billiards paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | For every smooth planar domain $\Omega$, does the eigenvalue counting function satisfy
$$
N(\lambda)=\frac{\operatorname{Area}(\Omega)}{4\pi}\lambda+C\ell(\partial\Omega)\lambda^{1/2}+o(\lambda^{1/2})?
$$
Also, does every smooth planar billiard domain have periodic trajectories of measure zero? | Conjectures: For every smooth planar domain \Omega, N(\lambda)=\frac{\operatorname{Area}(\Omega)}{4\pi}\lambda+C\ell(\partial\Omega)\lambda^{1/2}+o(\lambda^{1/2}); and the set of periodic billiards has measure zero for every smooth planar domain. | 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 | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,742 | OWR-8415336-013 | Absence of Absolutely Periodic Euclidean Billiard Orbits | Do Euclidean billiards have no absolutely periodic orbits? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-013",
"literature-status:partially-solved",
"owr-year:2021"
] | The no-absolutely-periodic-orbits conjecture remains unresolved: analytic convex cases and periods through four are ruled out, while arbitrarily high finite-order absolutely periodic degeneracies are constructed, not infinite-order examples. | [
{
"url": "https://arxiv.org/abs/2209.11721",
"label": "arbitrarily high finite-order orbits"
},
{
"url": "https://arxiv.org/abs/math/0110134",
"label": "analytic billiard result"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Do Euclidean billiards have no absolutely periodic orbits? | Conjecture: Euclidean billiards have no absolutely periodic orbits. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,743 | OWR-8415336-014 | Density of Finite-Order Absolutely Periodic Billiard Orbits | For every n \in \mathbb{N} and every strictly convex \Omega \in C^r(\mathbb{R}^2), there exists a strictly convex domain \widetilde{\Omega} \in C^{r-1}(\mathbb{R}^2), arbitrarily close to \Omega in the C^{r-1} topology, having an absolutely periodic orbit of order n. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report states this density construction as Theorem 1, not as an open problem. No separate clean statement is promoted, and the ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-014",
"literature-status:open",
"owr-year:2021"
] | Many special Lagrangian products are symplectomorphic to toric domains, including bidisks, lp sums, and symmetric polygonal examples, but no general characterization or equivalence with Minkowski-billiard integrability is known. | [
{
"url": "https://doi.org/10.4171/owr/2021/33",
"label": "Oberwolfach question"
},
{
"url": "https://www.intlpress.com/site/pub/files/_fulltext/journals/jsg/2019/0017/0005/JSG-2019-0017-0005-a007.pdf",
"label": "rigidity of Lagrangian products"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | null | For every n \in \mathbb{N} and every strictly convex \Omega \in C^r(\mathbb{R}^2), there exists a strictly convex domain \widetilde{\Omega} \in C^{r-1}(\mathbb{R}^2), arbitrarily close to \Omega in the C^{r-1} topology, having an absolutely periodic orbit of order n. | unrecoverable | The official report states this density construction as Theorem 1, not as an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,744 | OWR-8415336-016 | Local Typicality of the Newhouse Phenomenon | Is the Newhouse phenomenon locally typical in the space of smooth dynamical systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-016",
"literature-status:partially-solved",
"owr-year:2021"
] | Newhouse coexistence of infinitely many sinks is C r germ-typical near dissipative bicycles for finite r, but stronger local typicality notions such as Arnold prevalence and the smooth or analytic cases remain open. | [
{
"url": "https://doi.org/10.1016/j.aim.2022.108528",
"label": "germ-typicality theorem"
},
{
"url": "https://arxiv.org/abs/2103.16697",
"label": "primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Is the Newhouse phenomenon locally typical in the space of smooth dynamical systems? | Is the Newhouse phenomenon locally typical in the space of smooth dynamical systems? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,745 | OWR-8415336-017 | Displacement-Energy Bounds for Poisson Brackets of Open Covers | Let $(M,\omega)$ be a closed symplectic manifold and let $\mathcal U=\{U_i\}_{i\in I}$ be a finite open cover by displaceable sets. Is there a constant $C(M,\omega)>0$ such that
$$
pb(\mathcal U)e(\mathcal U)\geq C(M,\omega),
$$
where $e(\mathcal U)=\max_i e(U_i)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-017",
"literature-status:partially-solved",
"owr-year:2021"
] | Polterovich's dimension-free lower bound for Poisson brackets of partitions of unity is proved for closed symplectic surfaces, but the general closed-manifold statement remains unresolved. | [
{
"url": "https://doi.org/10.4171/CMH/487",
"label": "surface-case proof"
},
{
"url": "https://arxiv.org/abs/1705.02513",
"label": "primary preprint"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Let $(M,\omega)$ be a closed symplectic manifold and let $\mathcal U=\{U_i\}_{i\in I}$ be a finite open cover by displaceable sets. Is there a constant $C(M,\omega)>0$ such that
$$
pb(\mathcal U)e(\mathcal U)\geq C(M,\omega),
$$
where $e(\mathcal U)=\max_i e(U_i)$? | Conjecture: If (M,\omega) is a closed symplectic manifold and \mathcal{U} is a finite open cover of M by displaceable sets, then pb(\mathcal{U}) e(\mathcal{U}) \geq C(M,\omega)>0, where e(\mathcal{U}) is the largest displacement energy of a cover element. | 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 | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,746 | OWR-8415336-019 | $\gamma$-Topology Limits of Hamiltonians with Singular Sets | Let $H$ be a continuous Hamiltonian on $M\setminus V$, approximated uniformly on compact subsets by smooth Hamiltonians $H_k$ with time-one maps $\phi_k$. Does $\phi_k$ converge in the $\gamma$-topology to an element of the Humilière completion of $\operatorname{Ham}(M,\omega)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803](https://doi.org/10.4171/owr/2021/33)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,021 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415336-019",
"literature-status:partially-solved",
"owr-year:2021"
] | The gamma-topology convergence is proved when the singular set has dimension less than n and, more generally, when it is nowhere gamma-coisotropic, but the unrestricted claim for arbitrary compact singular sets remains open. | [
{
"url": "https://doi.org/10.24033/bsmf.2560",
"label": "Humiliere completion criterion"
},
{
"url": "https://doi.org/10.4171/owr/2021/33",
"label": "gamma-coisotropic extension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/33 | null | null | null | Let $H$ be a continuous Hamiltonian on $M\setminus V$, approximated uniformly on compact subsets by smooth Hamiltonians $H_k$ with time-one maps $\phi_k$. Does $\phi_k$ converge in the $\gamma$-topology to an element of the Humilière completion of $\operatorname{Ham}(M,\omega)$? | If H is a continuous Hamiltonian on M\setminus V, approximated uniformly on compact subsets by smooth Hamiltonians H_k with time-one maps \phi_k, does \phi_k converge in the \gamma-topology to an element of the Humiliere completion of Ham(M,\omega)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/33, pp. 1735--1803 |
30,004,747 | OWR-8415337-001 | Hardy-Littlewood Prime Tuple Conjecture | For every admissible finite set of distinct integer shifts $a_1,\ldots,a_k$, are there infinitely many integers $n$ for which $n+a_1,\ldots,n+a_k$ are all prime? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-001",
"literature-status:open",
"owr-year:2021"
] | The full Hardy--Littlewood prime k-tuples assertion remains open: sieve methods prove bounded-gap and other weaker substitutes, but not infinitely many simultaneous primes for every admissible tuple. | [
{
"url": "https://www.mathnet.ru/php/archive.phtml?jrnid=im&option_lang=eng&paperid=9544&wshow=paper",
"label": "2025 prime k-tuples survey"
},
{
"url": "https://arxiv.org/abs/2308.07205",
"label": "current work assuming the conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | For every admissible finite set of distinct integer shifts $a_1,\ldots,a_k$, are there infinitely many integers $n$ for which $n+a_1,\ldots,n+a_k$ are all prime? | Hardy--Littlewood's prime k-tuples conjecture: Every admissible finite set of distinct integer shifts a_1,\ldots,a_k, meaning one with no prime local obstruction, occurs infinitely often as n+a_1,\ldots,n+a_k all prime. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,748 | OWR-8415337-002 | Integral Points over Almost All Primitive Number Fields | Let $X/\mathbb Q$ be a hyperbolic curve with a model over $\mathbb Z$, and let $n\geq1$. When primitive degree-$n$ number fields $K$ are ordered by discriminant, does $X(\mathcal O_K)=X(\mathbb Z)$ for $100$ percent of them? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-002",
"literature-status:open",
"owr-year:2021"
] | No proof of the stated integral-point equality for one hundred percent of primitive number fields was found; recent work proves only special cases of related new-point conjectures. | [
{
"url": "https://ems.press/content/serial-article-files/46913",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2511.15635",
"label": "Khawaja--Siksek"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | Let $X/\mathbb Q$ be a hyperbolic curve with a model over $\mathbb Z$, and let $n\geq1$. When primitive degree-$n$ number fields $K$ are ordered by discriminant, does $X(\mathcal O_K)=X(\mathbb Z)$ for $100$ percent of them? | Conjecture: Let X/\mathbb{Q} be a hyperbolic curve with a model over \mathbb{Z}, and let n \geq 1. Then X(\mathcal{O}_K)=X(\mathbb{Z}) for 100 percent of primitive number fields K of degree n when ordered by discriminant. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,749 | OWR-8415337-003 | Degree-$d$ Points on Algebraic Curves | Given an integer $d$ and a smooth projective curve $X$ over a number field, is the set of degree-$d$ points on $X$ finite or infinite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-003",
"literature-status:open",
"owr-year:2021"
] | Results classify important low-degree configurations, especially in degrees two and three and selected higher degrees, but the stated extension of Mordell remains unresolved. | [
{
"url": "https://arxiv.org/abs/2208.01067",
"label": "Kadets--Vogt"
},
{
"url": "https://ems.press/content/serial-article-files/46913",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | Given an integer $d$ and a smooth projective curve $X$ over a number field, is the set of degree-$d$ points on $X$ finite or infinite? | Given an integer d and a nice curve X over a number field, is the number of points of degree d on X finite or infinite? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,750 | OWR-8415337-004 | Unified Selmer and Cohen-Lenstra-Martinet Heuristics | Can one formulate unified heuristics for $n$-Selmer groups of possibly nonproper algebraic groups that also imply the Cohen–Lenstra–Martinet heuristics for class groups of number fields? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-004",
"literature-status:open",
"owr-year:2021"
] | The proposed unified heuristics for Selmer groups of general algebraic groups and their implication of Cohen--Lenstra--Martinet heuristics remain a stated research question. | [
{
"url": "https://arxiv.org/abs/2106.10357",
"label": "Landesman"
},
{
"url": "https://ems.press/content/serial-article-files/46913",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | Can one formulate unified heuristics for $n$-Selmer groups of possibly nonproper algebraic groups that also imply the Cohen–Lenstra–Martinet heuristics for class groups of number fields? | Can one formulate unified heuristics for n-Selmer groups of possibly non-proper algebraic groups that also imply the Cohen--Lenstra--Martinet heuristics for class groups of number fields? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,751 | OWR-8415337-005 | Pairs of $p$-Congruent Elliptic Curves | Are the two known nontrivial $17$-congruent pairs, together with their simultaneous quadratic twists, the only nontrivial $17$-congruent pairs over $\mathbb Q$, and are there no nontrivial $p$-congruent pairs for primes $p>17$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-005",
"literature-status:open",
"owr-year:2021"
] | The classification conjecture for nontrivial pairs of p-congruent elliptic curves for p at least seventeen is not proved; the primary work leaves the conjectural list as the expected complete one. | [
{
"url": "https://www.dpmms.cam.ac.uk/~taf1000/papers/congr17.pdf",
"label": "Fisher"
},
{
"url": "https://ems.press/content/serial-article-files/46913",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | Are the two known nontrivial $17$-congruent pairs, together with their simultaneous quadratic twists, the only nontrivial $17$-congruent pairs over $\mathbb Q$, and are there no nontrivial $p$-congruent pairs for primes $p>17$? | The listed exceptional images of elliptic curves over Q are complete; equivalently, any counterexample must arise from an unexpected rational point on one of the specified normalizer nonsplit Cartan modular curves or on one of two level-49 modular curves of genus 9. | 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 | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,752 | OWR-8415337-006 | Exceptional Galois Images of Non-CM Elliptic Curves | For non-CM elliptic curves over $\mathbb Q$, is the known list of $22$ exceptional $\ell$-adic Galois images complete? Equivalently, must every counterexample arise from an unexpected rational point on $X_{\mathrm{ns}}^+(N)$ for $N\in\{33,5^2,7^2,11^2\}$ or a prime $\ell\geq17$, or on one of the two level-$49$ genus-$9... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-006",
"literature-status:open",
"owr-year:2021"
] | The exceptional-image list is not known to be complete; the remaining rational-point questions on several nonsplit Cartan modular curves and related levels are unresolved. | [
{
"url": "https://arxiv.org/abs/2106.11141",
"label": "Rouse--Sutherland--Zureick-Brown"
},
{
"url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D5BC92F9949B387570A7D764635B6AC8/S205050942200038Xa.pdf/dollarell-dollar-adic-images-of-galois-for-elliptic-curves-over-dollar... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | For non-CM elliptic curves over $\mathbb Q$, is the known list of $22$ exceptional $\ell$-adic Galois images complete? Equivalently, must every counterexample arise from an unexpected rational point on $X_{\mathrm{ns}}^+(N)$ for $N\in\{33,5^2,7^2,11^2\}$ or a prime $\ell\geq17$, or on one of the two level-$49$ genus-$9... | The list of exceptional Galois images of non-CM elliptic curves over Q is complete, and any counterexample must come from an unexpected rational point on Xns^+(N) for N=33, 52, 72, 112, or a prime ell at least 17, or on one of two level-49 modular curves of genus 9. | 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 | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,753 | OWR-8415337-007 | Rational Points on Nonsplit Cartan Modular Curves | Determine the rational points $X(\Gamma_{\mathrm{ns}}^+(p))(\mathbb Q)$ on the modular curve associated with the normalizer of a nonsplit Cartan subgroup. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858](https://doi.org/10.4171/owr/2021/34)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415337-007",
"literature-status:open",
"owr-year:2021"
] | The rational points on the plus nonsplit Cartan modular curves are known only in substantial special cases; a uniform determination for the prime levels in the question remains open. | [
{
"url": "https://arxiv.org/abs/2106.11141",
"label": "Rouse--Sutherland--Zureick-Brown"
},
{
"url": "https://annals.math.princeton.edu/2011/173-1/p13",
"label": "Bilu--Parent"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/34 | null | null | null | Determine the rational points $X(\Gamma_{\mathrm{ns}}^+(p))(\mathbb Q)$ on the modular curve associated with the normalizer of a nonsplit Cartan subgroup. | Determine the rational points X(Gamma^+_{ns}(p))(Q) on the modular curve associated with the normalizer of a nonsplit Cartan subgroup. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Explicit Methods in Number Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/34, pp. 1805--1858 |
30,004,754 | OWR-8415338-001 | Generic Singularities of Mean Curvature Flow | Huisken conjectured that spherical and generalized cylindrical singularities are generic singularity models for mean curvature flow. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 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-8415338-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Smooth surgery approximations are constructed for weak flows with spherical and neck-pinch singularities, but the broader generic-singularity conjecture remains unresolved. | [
{
"url": "https://arxiv.org/abs/2104.11647",
"label": "Daniels-Holgate"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Huisken conjectured that spherical and generalized cylindrical singularities are generic singularity models for mean curvature flow. | Huisken conjectured that spherical and generalized cylindrical singularities are generic singularity models for mean curvature flow. | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,755 | OWR-8415338-002 | Bogomolov–Miyaoka–Yau Inequality for Smooth Four-Manifolds | Let $X$ be a closed, oriented, smooth four-manifold with $b_1(X)=0$, odd $b^+(X)\geq3$, Seiberg–Witten simple type, and a nonzero Seiberg–Witten invariant. Must $$c_1(X)^2\leq3c_2(X)$$ hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415338-002",
"literature-status:open",
"owr-year:2021"
] | The stated Bogomolov--Miyaoka--Yau type inequality for the specified smooth four-manifolds with nonzero Seiberg--Witten invariants remains a conjectural target; later work develops the program without proving it in full. | [
{
"url": "https://arxiv.org/abs/2010.15789",
"label": "Feehan--Leness"
},
{
"url": "https://arxiv.org/abs/2410.13809",
"label": "Feehan--Leness sequel"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Let $X$ be a closed, oriented, smooth four-manifold with $b_1(X)=0$, odd $b^+(X)\geq3$, Seiberg–Witten simple type, and a nonzero Seiberg–Witten invariant. Must $$c_1(X)^2\leq3c_2(X)$$ hold? | If X is a closed, oriented, smooth four-manifold with b1(X)=0, odd b+(X) at least 3, Seiberg--Witten simple type, and a nonzero Seiberg--Witten invariant, then c1(X)^2 is at most 3c2(X). | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,756 | OWR-8415338-003 | Geometry of Singular Monge–Ampère Solution Loci | Let $n\geq5$ and consider convex solutions of $$\det D^2u=1+\sum_i a_i\delta_{p_i}.$$ Determine whether singular solutions analogous to the known lower-dimensional examples exist; whether their singularities persist under small perturbations of the locations $p_i$ and masses $a_i$; and the dimension, regularity, connec... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 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-8415338-003",
"literature-status:partially-solved",
"owr-year:2021"
] | Higher-dimensional polyhedral singular structures and stability under perturbation have been proved, but the extracted regularity and connectivity questions for the singular set are not settled in general. | [
{
"url": "https://arxiv.org/abs/2204.11365",
"label": "Mooney--Rakshit"
},
{
"url": "https://par.nsf.gov/servlets/purl/10213707",
"label": "Mooney"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Let $n\geq5$ and consider convex solutions of $$\det D^2u=1+\sum_i a_i\delta_{p_i}.$$ Determine whether singular solutions analogous to the known lower-dimensional examples exist; whether their singularities persist under small perturbations of the locations $p_i$ and masses $a_i$; and the dimension, regularity, connec... | For the singular Monge--Ampere solutions with Dirac masses described in the report, determine what happens in dimensions n at least 5; determine whether the singularities persist under small perturbations of the mass locations and sizes; and determine the dimension, regularity, connectivity, and other geometric propert... | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,757 | OWR-8415338-004 | Dirac-Mass Tangent Cones in Monge–Ampère Equations | For the singular convex solutions of $$\det D^2u=1+\sum_i a_i\delta_{p_i},$$ determine the precise tangent cones at the Dirac masses $p_i$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,021 | 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-8415338-004",
"literature-status:open",
"owr-year:2021"
] | The higher-dimensional constructions do not give a precise classification of tangent cones at the Dirac masses in the examples requested by this problem. | [
{
"url": "https://arxiv.org/abs/2204.11365",
"label": "Mooney--Rakshit"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | For the singular convex solutions of $$\det D^2u=1+\sum_i a_i\delta_{p_i},$$ determine the precise tangent cones at the Dirac masses $p_i$. | Find precise descriptions of the tangent cones at the Dirac masses for the Monge--Ampere examples, and investigate analogous questions when the obstacle graphs are not necessarily convex polytopes. | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,758 | OWR-8415338-005 | Monge–Ampère Singularities for Nonpolyhedral Obstacles | Develop singular solutions for Monge–Ampère equations with obstacles whose graphs need not be convex polytopes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,021 | 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-8415338-005",
"literature-status:open",
"owr-year:2021"
] | The subsequent theory treats broad polyhedral and dual-obstacle settings, but a comparable theory for obstacles whose graphs are not convex polytopes remains unavailable. | [
{
"url": "https://arxiv.org/abs/2204.11365",
"label": "Mooney--Rakshit"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Develop singular solutions for Monge–Ampère equations with obstacles whose graphs need not be convex polytopes. | Investigate the Monge--Ampere singularity questions for obstacles whose graphs are not necessarily convex polytopes. | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,759 | OWR-8415338-009 | Positive Scalar Curvature Obstruction for Aspherical Manifolds | For every closed smooth aspherical manifold $M$ of dimension $n\geq 4$, $M$ admits no Riemannian metric of positive scalar curvature. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415338-009",
"literature-status:partially-solved",
"owr-year:2021"
] | The aspherical positive-scalar-curvature conjecture is proved in dimensions four and five, while the stated all-dimensional result for n at least four remains open. | [
{
"url": "https://annals.math.princeton.edu/2024/199-2/p03",
"label": "Chodosh--Li"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | For every closed smooth aspherical manifold $M$ of dimension $n\geq 4$, $M$ admits no Riemannian metric of positive scalar curvature. | For every closed smooth aspherical manifold M of dimension n at least 4, M admits no Riemannian metric of positive scalar curvature. | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,760 | OWR-8415338-010 | Regularity of Varifolds for Anisotropic Energies | Does the regularity theorem for rectifiable varifolds with generalized mean curvature bounded in $L^p$, where $p$ is greater than the varifold dimension, extend to anisotropic energies $\Sigma_\Psi(V)=\int\Psi(T_z\Gamma)\theta(z)\,d\mathcal{H}^m(z)$, under the corresponding density-ratio hypothesis? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 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-8415338-010",
"literature-status:partially-solved",
"owr-year:2021"
] | Regularity is established for important graph classes and selected anisotropies, but the general anisotropic varifold regularity problem described in the record remains open. | [
{
"url": "https://arxiv.org/abs/2011.09922",
"label": "De Rosa--Tione"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Does the regularity theorem for rectifiable varifolds with generalized mean curvature bounded in $L^p$, where $p$ is greater than the varifold dimension, extend to anisotropic energies $\Sigma_\Psi(V)=\int\Psi(T_z\Gamma)\theta(z)\,d\mathcal{H}^m(z)$, under the corresponding density-ratio hypothesis? | Does the regularity theorem for rectifiable varifolds with generalized mean curvature bounded in Lp, p greater than the varifold dimension, extend to anisotropic energies Sigma_Psi(V)=integral Psi(T_z Gamma) theta(z) dH^m(z), under the corresponding density-ratio hypothesis? | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,761 | OWR-8415338-011 | Rank-One Convex Energies Excluding Nontrivial Young Measures | Find rank-one convex functions whose differential inclusion for critical points under outer variations only supports exclusively trivial Young measures. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914](https://doi.org/10.4171/owr/2021/35)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415338-011",
"literature-status:partially-solved",
"owr-year:2021"
] | The atomic-condition results exclude nontrivial Young measures for broad classes of stationary graphs, giving a partial answer, but the outer-variation-only question in full generality remains unresolved. | [
{
"url": "https://arxiv.org/abs/2011.09922",
"label": "De Rosa--Tione"
},
{
"url": "https://ems.press/content/serial-article-files/46911",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/35 | null | null | null | Find rank-one convex functions whose differential inclusion for critical points under outer variations only supports exclusively trivial Young measures. | Find rank-one convex functions whose differential inclusion for critical points under outer variations only supports exclusively trivial Young measures. | 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 | Partial Differential Equations (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/35, pp. 1859--1914 |
30,004,762 | OWR-8415340-004 | Uniform Low-Regularity Schemes for Coupled Klein–Gordon Systems | Extend uniformly accurate low-regularity numerical approximations from the Klein–Gordon equation to systems such as coupled Klein–Gordon equations and Klein–Gordon–Schrödinger systems. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamics of Waves and Patterns (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/37, pp. 1965--2026](https://doi.org/10.4171/owr/2021/37)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,021 | 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-8415340-004",
"literature-status:partially-solved",
"owr-year:2021"
] | Uniformly accurate low-regularity schemes have been extended to Klein--Gordon--Schrödinger systems, but the broader class of coupled Klein--Gordon-type systems in the question is not covered in full. | [
{
"url": "https://doi.org/10.1016/j.cam.2022.114756",
"label": "Cabrera Calvo--Schratz"
},
{
"url": "https://ems.press/content/serial-article-files/46915",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/37 | null | null | null | Extend uniformly accurate low-regularity numerical approximations from the Klein–Gordon equation to systems such as coupled Klein–Gordon equations and Klein–Gordon–Schrödinger systems. | Extend low-regularity approximations with uniform accuracy from the Klein--Gordon equation to more general Klein--Gordon-type systems, such as coupled Klein--Gordon equations and Klein--Gordon--Schrodinger systems. | 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 | Dynamics of Waves and Patterns (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/37, pp. 1965--2026 |
30,004,763 | OWR-8415340-005 | Solitary-Wave Stability for the Lugiato–Lefever Equation | For the Lugiato–Lefever equation $$\partial_t\psi=-i\beta\,\partial_x^2\psi-(1+i\alpha)\psi+i|\psi|^2\psi+F,$$ determine the stability or instability of its solitary-wave solutions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamics of Waves and Patterns (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/37, pp. 1965--2026](https://doi.org/10.4171/owr/2021/37)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,021 | 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-8415340-005",
"literature-status:open",
"owr-year:2021"
] | Existence and criteria for several periodic and solitary waves are known, but stability of solitary waves in the general family described by the problem remains largely unresolved. | [
{
"url": "https://doi.org/10.1016/j.physd.2022.133477",
"label": "Lafortune--Pelinovsky"
},
{
"url": "https://ems.press/content/serial-article-files/46915",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/37 | null | null | null | For the Lugiato–Lefever equation $$\partial_t\psi=-i\beta\,\partial_x^2\psi-(1+i\alpha)\psi+i|\psi|^2\psi+F,$$ determine the stability or instability of its solitary-wave solutions. | Determine the stability of solitary waves for the considered nonlinear wave equation. | 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 | Dynamics of Waves and Patterns (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/37, pp. 1965--2026 |
30,004,764 | OWR-8415341-002 | Modular Structure of Exceptional Finite Lie-Type Groups | Determine the radical subgroups of exceptional groups of Lie type in bad characteristic; determine $p$-modular decomposition matrices for finite groups of Lie type, including basic sets, unitriangularity, and complete results for exceptional families; and determine the modular Harish–Chandra series for groups of Lie ty... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-002",
"literature-status:open",
"owr-year:2021"
] | The report identifies the determination of radical subgroups in bad characteristic, exceptional-group decomposition matrices, and complete modular Harish-Chandra series as open; later work gives important partial classifications but explicitly leaves major exceptional cases unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://arxiv.org/abs/2401.00156",
"label": "Radical subgroups of finite reductive groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Determine the radical subgroups of exceptional groups of Lie type in bad characteristic; determine $p$-modular decomposition matrices for finite groups of Lie type, including basic sets, unitriangularity, and complete results for exceptional families; and determine the modular Harish–Chandra series for groups of Lie ty... | Determine the radical subgroups of exceptional groups of Lie type in bad characteristic; determine p-modular decomposition matrices for finite groups of Lie type, including basic sets, unitriangularity, and complete determination for exceptional families; and completely determine the modular Harish--Chandra series for ... | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,765 | OWR-8415341-003 | Conjectural Schur-Multiplier Exponents | Is the exponent of the Schur multiplier of $H(8,12)$ equal to $32$, and is the exponent of the Schur multiplier of $H(7,13)$ equal to $49$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-003",
"literature-status:open",
"owr-year:2021"
] | The exponent claims for the Schur multipliers of H(8,12) and H(7,13) are still posed as questions in the available primary literature, with the stated obstruction that the groups are too large for the cited computations. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://alglog.org/21tkt.pdf",
"label": "Twenty-first Issue of the Kourovka Notebook"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Is the exponent of the Schur multiplier of $H(8,12)$ equal to $32$, and is the exponent of the Schur multiplier of $H(7,13)$ equal to $49$? | The Schur multiplier of H(8,12) has exponent 32, and the Schur multiplier of H(7,13) has exponent 49. | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,766 | OWR-8415341-004 | Efficient Normalizers of Non-Chevalley Derivation Lie Algebras | Can normalizers of the non-Chevalley simple Lie algebras that arise as derivation algebras be constructed efficiently? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-004",
"literature-status:open",
"owr-year:2021"
] | The cited work gives efficient normalizer constructions for important Chevalley-type cases but leaves the requested construction for non-Chevalley simple Lie algebras arising as derivation algebras as a future problem. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://arxiv.org/abs/2005.04046",
"label": "Tensor Isomorphism by Derivations and Densors"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Can normalizers of the non-Chevalley simple Lie algebras that arise as derivation algebras be constructed efficiently? | Can normalizers of the non-Chevalley simple Lie algebras that arise as derivation algebras be constructed efficiently? | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,767 | OWR-8415341-006 | Post Correspondence and Matrix Commutators in Infinite Groups | Determine whether the Post correspondence problem is decidable for free groups, even in rank $2$, and for an infinite linear group $G$ such as $\operatorname{SL}(n,\mathbb{Z})$ or $\operatorname{GL}(n,\mathbb{Z})$, determine whether a given matrix $M\in G$ can be written as a commutator $M=[A,B]$ with $A,B\in G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-006",
"literature-status:open",
"owr-year:2021"
] | The report states that the Post Correspondence Problem remains open for free groups even in rank two; the accompanying matrix-commutator decision questions are likewise presented without a general solution. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://researchportal.hw.ac.uk/files/50837506/GPCP_and_injectivity.pdf",
"label": "GPCP and injectivity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Determine whether the Post correspondence problem is decidable for free groups, even in rank $2$, and for an infinite linear group $G$ such as $\operatorname{SL}(n,\mathbb{Z})$ or $\operatorname{GL}(n,\mathbb{Z})$, determine whether a given matrix $M\in G$ can be written as a commutator $M=[A,B]$ with $A,B\in G$. | Determine whether the post correspondence problem is decidable for free groups, even in rank 2, and for an infinite linear group G such as SL(n,Z) or GL(n,Z), determine whether a given matrix M in G can be written as a commutator M=[A,B] with A,B in 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,768 | OWR-8415341-007 | Finding Free Subgroups Containing a Given Matrix | Given a linear group $G$ and a matrix $M\in G$, determine whether $M$ belongs to a nontrivial free subgroup of $G$ and, if so, find a basis for that free subgroup. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-007",
"literature-status:open",
"owr-year:2021"
] | The known virtually-free rank-two cases do not resolve the stated matrix-input problem in dimensions at least three; the source report explicitly says that nothing appears to be known there. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://www.math.auckland.ac.nz/~obrien/research/Tits.pdf",
"label": "Algorithms for the Tits Alternative and Related Problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Given a linear group $G$ and a matrix $M\in G$, determine whether $M$ belongs to a nontrivial free subgroup of $G$ and, if so, find a basis for that free subgroup. | Given a linear group G and a matrix M in G, determine whether M belongs to a nontrivial free subgroup of G and, if so, find a basis for that free subgroup. | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,769 | OWR-8415341-008 | Orbit Computation for Constructible Maximal-Class p-Groups | For the infinite group $G$ acting on the finite quotients $(\theta-1)^n\Gamma/(\theta-1)^{n+e}\Gamma$ arising from constructible $p$-groups of maximal class, develop computational methods to determine its orbits as $n$ and $e$ vary. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-008",
"literature-status:open",
"owr-year:2021"
] | The extracted question asks for computational investigation of the orbit problem for varying parameters n and e; the primary report presents this as an open direction and no general algorithmic resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | For the infinite group $G$ acting on the finite quotients $(\theta-1)^n\Gamma/(\theta-1)^{n+e}\Gamma$ arising from constructible $p$-groups of maximal class, develop computational methods to determine its orbits as $n$ and $e$ vary. | For the infinite group G acting on the finite quotients (theta-1)^n Gamma over (theta-1)^{n+e} Gamma arising from constructible p-groups of maximal class, develop computational methods to determine its orbits as n and e vary. | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,770 | OWR-8415341-009 | Extending Generator Maps to Finite Group Homomorphisms | Given $G=\langle g_1,\ldots,g_k\rangle\leq\operatorname{SL}(n,\mathbb{Z})$ and a map on the generators sending them to a generating set of a finite group $H$, determine whether the map extends to a homomorphism $G\to H$, including the case where it does not factor through a congruence homomorphism. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-009",
"literature-status:open",
"owr-year:2021"
] | For an arbitrary generator map from a permutation group to a small finite group, especially outside congruence quotients, the report formulates extension to a homomorphism as an unresolved verification problem. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | Given $G=\langle g_1,\ldots,g_k\rangle\leq\operatorname{SL}(n,\mathbb{Z})$ and a map on the generators sending them to a generating set of a finite group $H$, determine whether the map extends to a homomorphism $G\to H$, including the case where it does not factor through a congruence homomorphism. | Given G=<g1,...,gk> less than or equal to SL(n,Z) and a map on the generators sending them to a generating set of a finite group H, determine whether the map extends to a homomorphism G to H, including the case where it does not factor through a congruence homomorphism. | 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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,771 | OWR-8415341-010 | Smallest Colored Graph Representations of Permutation Groups | For $G\leq\operatorname{Sym}(\Omega)$, determine the smallest vertex-colored and edge-colored graph $\Gamma$ representing $G$, where size is measured by $|V|+|E|$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-010",
"literature-status:open",
"owr-year:2021"
] | General graph representations of permutation groups exist, but the minimum of |V|+|E| for a prescribed group is not characterized; the source report records this optimization problem as open. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2021.06.015",
"label": "Permutation group algorithms based on directed graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | For $G\leq\operatorname{Sym}(\Omega)$, determine the smallest vertex-colored and edge-colored graph $\Gamma$ representing $G$, where size is measured by $|V|+|E|$. | For G less than or equal to Sym(Omega), determine the smallest vertex- and edge-coloured graph Gamma representing G, where size is measured by |V|+|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 | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,772 | OWR-8415341-011 | Compact Graph Representations of Permutation Groups | For permutation groups represented by graphs, determine which classes admit representations with $|V|+|E|$ of order $|\Omega|$, $|\Omega|\log|\Omega|$, or a low-order polynomial in $|\Omega|$; develop construction methods and fast algorithms; and determine whether low-index supergroups can be represented when the group... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-011",
"literature-status:open",
"owr-year:2021"
] | Only general constructions and selected lower bounds are available; the requested classification of compact graph representations, construction methods, algorithms, and low-index supergroups remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2021.06.015",
"label": "Permutation group algorithms based on directed graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | For permutation groups represented by graphs, determine which classes admit representations with $|V|+|E|$ of order $|\Omega|$, $|\Omega|\log|\Omega|$, or a low-order polynomial in $|\Omega|$; develop construction methods and fast algorithms; and determine whether low-index supergroups can be represented when the group... | For permutation groups represented by graphs, determine which classes admit representations with |V|+|E| of order |Omega|, |Omega| log |Omega|, or a low-order polynomial in |Omega|; develop construction methods and fast algorithms; and determine whether low-index supergroups can be represented when the group itself can... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,773 | OWR-8415341-012 | Character Degrees of Graph-Defined Exponent-$p$ Groups | For a finite simple graph $\Gamma$ and an odd prime $p$, determine the ordinary representation theory of the exponent-$p$, nilpotency-class-two group $G_\Gamma(\mathbb F_p)$. For each $i\geq1$, how does the number of its irreducible characters of degree $p^i$ depend on $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087](https://doi.org/10.4171/owr/2021/38)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,021 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415341-012",
"literature-status:open",
"owr-year:2021"
] | Polynomial character-count formulas are known for special graph families such as edgeless, path, and complete graphs, but the general dependence of the number of irreducible characters of each degree on p remains explicitly open. | [
{
"url": "https://doi.org/10.1112/blms.12665",
"label": "Rossmann, Enumerating conjugacy classes of graphical groups"
},
{
"url": "https://doi.org/10.4171/owr/2021/38",
"label": "Oberwolfach Report 38/2021"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/38 | null | null | null | For a finite simple graph $\Gamma$ and an odd prime $p$, determine the ordinary representation theory of the exponent-$p$, nilpotency-class-two group $G_\Gamma(\mathbb F_p)$. For each $i\geq1$, how does the number of its irreducible characters of degree $p^i$ depend on $p$? | For a finite simple graph Gamma and odd prime p, determine the ordinary representation theory of the class-two exponent-p group G_Gamma(Fp), in particular how the number of irreducible characters of degree p^i depends on p for each i at least 1. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Computational Group Theory (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/38, pp. 2027--2087 |
30,004,774 | OWR-8415342-002 | Hiraga–Ichino–Ikeda–Langlands Plancherel Density Conjecture | For almost every tempered representation $\sigma$ of a reductive group $H$, prove the Hiraga–Ichino–Ikeda–Langlands formula $d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}\lvert\gamma^*(0,\sigma,\operatorname{Ad}_H)\rvert$, where $\gamma^*$ is the suitably normalized first nonzero Laurent coefficient at $s=0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-8415342-004"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The Hiraga--Ichino--Ikeda and Langlands prediction is proved in the Archimedean case and in substantial p-adic families, but the extracted general Plancherel-density statement is not established for all reductive groups. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2508.08470",
"label": "Hiraga--Ichino--Ikeda conjecture for classical groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For almost every tempered representation $\sigma$ of a reductive group $H$, prove the Hiraga–Ichino–Ikeda–Langlands formula $d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}\lvert\gamma^*(0,\sigma,\operatorname{Ad}_H)\rvert$, where $\gamma^*$ is the suitably normalized first nonzero Laurent coefficient at $s=0$. | Conjecture (Hiraga--Ichino--Ikeda--Langlands): for almost every tempered representation \sigma of a reductive group H, the Plancherel density satisfies d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}|\gamma^*(0,\sigma,\operatorname{Ad}_H)|, where \gamma^* is the suitably normalized first nonzero Laurent coefficient at... | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,775 | OWR-8415342-003 | Hiraga–Ichino–Ikeda Formal Degree Conjecture | For every discrete-series representation $\sigma$ of $H$, prove the Hiraga–Ichino–Ikeda formula $d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}\lvert\gamma(0,\sigma,\operatorname{Ad}_H)\rvert$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-003",
"literature-status:partially-solved",
"owr-year:2021"
] | The formal-degree conjecture is known for Archimedean groups and many p-adic cases including general linear, unitary, odd orthogonal, regular, and unipotent families, while the general tempered extension remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2508.08470",
"label": "Hiraga--Ichino--Ikeda conjecture for classical groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For every discrete-series representation $\sigma$ of $H$, prove the Hiraga–Ichino–Ikeda formula $d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}\lvert\gamma(0,\sigma,\operatorname{Ad}_H)\rvert$. | Conjecture (Hiraga--Ichino--Ikeda): for every discrete-series representation \sigma of H, d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}|\gamma(0,\sigma,\operatorname{Ad}_H)|. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,776 | OWR-8415342-004 | Duplicate Hiraga–Ichino–Ikeda–Langlands Conjecture | Conjecture (Hiraga--Ichino--Ikeda--Langlands): for almost every tempered representation \sigma of H, the Plancherel density is d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}|\gamma^*(0,\sigma,\operatorname{Ad}_H)|, with \gamma^* the suitably normalized first nonzero Laurent coefficient at s=0. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 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 | Duplicate/merged OWR extraction (The official Oberwolfach report confirms that this extraction repeats the Hiraga–Ichino–Ikeda–Langlands Plancherel-density conjecture alread) | [
"OWR-8415342-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-004",
"literature-status:partially-solved",
"owr-year:2021"
] | The extracted fragment records the established GLn case and other partial formal-degree results, but the local Langlands and formal-degree assertions for arbitrary p-adic reductive groups remain open. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://doi.org/10.5802/jep.138",
"label": "Supercuspidal unipotent representations and formal degrees"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | null | Conjecture (Hiraga--Ichino--Ikeda--Langlands): for almost every tempered representation \sigma of H, the Plancherel density is d_H(\sigma)=\frac{\dim(\rho_\sigma)}{|S_\sigma|}|\gamma^*(0,\sigma,\operatorname{Ad}_H)|, with \gamma^* the suitably normalized first nonzero Laurent coefficient at s=0. | unrecoverable | The official Oberwolfach report confirms that this extraction repeats the Hiraga–Ichino–Ikeda–Langlands Plancherel-density conjecture already preserved as OWR-8415342-002. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,777 | OWR-8415342-005 | Formal Degrees for Symplectic and Even Orthogonal Groups | The formal-degree and Plancherel-density conjectures hold whenever H is a symplectic group or an even special orthogonal group, subject to the stated local Langlands framework. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | solved | null | 2,021 | 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 | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | Unrecoverable OWR statement (The official report labels the extracted assertion Theorem 1.3 and states it as a proved special case, not an open problem.) | null | null | [Discussion #4 literature review, 2026-09-29] **solved**. | [
"owr",
"oberwolfach-reports",
"OWR-8415342-005",
"literature-status:partially-solved",
"owr-year:2021"
] | The listed theorem for symplectic and even special orthogonal groups is a substantial established case, alongside unitary, odd orthogonal, regular, and unipotent cases; it does not settle the general formal-degree conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2508.08470",
"label": "Hiraga--Ichino--Ikeda conjecture for classical groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | null | The formal-degree and Plancherel-density conjectures hold whenever H is a symplectic group or an even special orthogonal group, subject to the stated local Langlands framework. | unrecoverable | The official report labels the extracted assertion Theorem 1.3 and states it as a proved special case, not an open problem. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,778 | OWR-8415342-006 | Spectral Expansion of Twisted Orbital Integrals | For split H equal to \operatorname{Sp}(2n) or \operatorname{SO}(2n), the twisted orbital integral of the relevant bilinear-form element in \operatorname{GL}(V) admits the spectral expansion of Theorem 1.4, whose terms are twisted characters of functorial lifts weighted by the formal-degree gamma factors and the element... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a theorem-level spectral-expansion result used in the proof of Theorem 1.3, not an open ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-006",
"literature-status:open",
"owr-year:2021"
] | The extracted passage is an incomplete continuation of the proof setup and does not state a complete theorem; the associated general formal-degree and twisted-orbital-integral claim therefore remains unresolved as extracted. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2508.08470",
"label": "Hiraga--Ichino--Ikeda conjecture for classical groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | null | For split H equal to \operatorname{Sp}(2n) or \operatorname{SO}(2n), the twisted orbital integral of the relevant bilinear-form element in \operatorname{GL}(V) admits the spectral expansion of Theorem 1.4, whose terms are twisted characters of functorial lifts weighted by the formal-degree gamma factors and the element... | unrecoverable | The official report confirms that the extraction is a theorem-level spectral-expansion result used in the proof of Theorem 1.3, not an open problem. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,779 | OWR-8415342-007 | Component-Group Factorization on Dualizing Cohomology | For every algebraically closed field $K$ and every $\gamma\in C^{\bullet}(K)$, does the action of the stabilizer group $P_\gamma$ on $R\Gamma(f^{-1}(\gamma),\omega_{f^{-1}(\gamma)})$ factor through the component group $\pi_0(P_\gamma)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-007",
"literature-status:open",
"owr-year:2021"
] | The conjecture that the component-group action factors through pi_0(P_gamma) is used as an assumption for the stated perversity theorem in the report, and no general proof of that conjecture was found. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2108.12663",
"label": "Bouthier, Faisceaux caracteres"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For every algebraically closed field $K$ and every $\gamma\in C^{\bullet}(K)$, does the action of the stabilizer group $P_\gamma$ on $R\Gamma(f^{-1}(\gamma),\omega_{f^{-1}(\gamma)})$ factor through the component group $\pi_0(P_\gamma)$? | For every algebraically closed field K and every \gamma\in C^{\bullet}(K), the action of the stabilizer group P_\gamma on R\Gamma(f^{-1}(\gamma),\omega_{f^{-1}(\gamma)}) factors through the component group \pi_0(P_\gamma). | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,780 | OWR-8415342-008 | The Twisted Fourier–Jacobi Gan–Gross–Prasad Conjecture | For étale quadratic algebras $E$ and $K$ over a local or global field $F$, a skew-Hermitian $E$-space $V$, an irreducible representation $\Pi$ of $U(V_K)$, and the Weil representation $\omega_{V,\psi,\mu}$ of $U(V)$, determine the local branching multiplicity $\operatorname{Hom}_{U(V)}(\Pi,\omega_{V,\psi,\mu})$ and the... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-008",
"literature-status:partially-solved",
"owr-year:2021"
] | The twisted Fourier--Jacobi branching and period conjectures have precise formulations and verified low-rank and principal-series evidence, but the general local and global conjectures remain open. | [
{
"url": "https://arxiv.org/abs/2204.10108",
"label": "Twisted GGP Problems and Conjectures"
},
{
"url": "https://arxiv.org/abs/2511.01301",
"label": "Local twisted GGP for U(V_K)/U(V)"
},
{
"url": "https://arxiv.org/abs/2307.15234",
"label": "Twisted GGP for unramified quadratic ext... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For étale quadratic algebras $E$ and $K$ over a local or global field $F$, a skew-Hermitian $E$-space $V$, an irreducible representation $\Pi$ of $U(V_K)$, and the Weil representation $\omega_{V,\psi,\mu}$ of $U(V)$, determine the local branching multiplicity $\operatorname{Hom}_{U(V)}(\Pi,\omega_{V,\psi,\mu})$ and the... | Twisted Fourier--Jacobi GGP conjecture: for etale quadratic algebras E and K over a local or global field F, a skew-Hermitian E-space V, an irreducible representation \Pi of U(V_K), and the Weil representation \omega_{V,\psi,\mu} of \ U(V), the local branching multiplicity \operatorname{Hom}_{U(V)}(\Pi,\omega_{V,\psi,\... | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,781 | OWR-8415342-009 | The Local Langlands Correspondence for Reductive Groups | For a connected reductive group $G$ over a non-Archimedean local field $F$, construct the canonical local Langlands map $L_{G/F}:\Pi(G/F)\to\Phi(G/F)$ and prove that every parameter has a finite, nonempty $L$-packet. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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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-8415342-009",
"literature-status:partially-solved",
"owr-year:2021"
] | The local Langlands conjecture is proved for GLn and has major established versions for p-adic classical groups and other families, but the canonical finite nonempty parametrization for general reductive groups is not known. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2510.00632",
"label": "The local Langlands conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For a connected reductive group $G$ over a non-Archimedean local field $F$, construct the canonical local Langlands map $L_{G/F}:\Pi(G/F)\to\Phi(G/F)$ and prove that every parameter has a finite, nonempty $L$-packet. | Local Langlands conjecture: for a connected reductive group G over a nonarchimedean local field F, there is a canonical map L_{G/F}:\Pi(G/F)\to\Phi(G/F) such that every parameter has a finite, nonempty L-packet. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,782 | OWR-8415342-010 | Analytic Continuation and Functional Equations of Automorphic L-Functions | For a number field $k$, a split reductive group $G$, a cuspidal automorphic representation $\sigma$ of $G(\mathbb A)$, and a finite-dimensional dual-group representation $\rho$, prove that the automorphic $L$-function $L(s,\sigma,\rho)$ has meromorphic continuation and satisfies $L(s,\sigma,\rho)=\epsilon(s,\sigma,\rho... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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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-8415342-010",
"literature-status:partially-solved",
"owr-year:2021"
] | Meromorphic continuation and functional equations are established for GLn and many further families by Langlands--Shahidi, Rankin--Selberg, and functorial methods, but the extracted general automorphic L-function conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/math/9912208",
"label": "Braverman--Kazhdan, Gamma-functions of representations and lifting"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For a number field $k$, a split reductive group $G$, a cuspidal automorphic representation $\sigma$ of $G(\mathbb A)$, and a finite-dimensional dual-group representation $\rho$, prove that the automorphic $L$-function $L(s,\sigma,\rho)$ has meromorphic continuation and satisfies $L(s,\sigma,\rho)=\epsilon(s,\sigma,\rho... | For a number field k, a split reductive group G, a cuspidal automorphic representation \sigma of G(\mathbb A), and a finite-dimensional dual-group representation \rho, the automorphic L-function L(s,\sigma,\rho) has meromorphic continuation and satisfies L(s,\sigma,\rho)=\epsilon(s,\sigma,\rho)L(1-s,\widetilde{\sigma},... | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,783 | OWR-8415342-011 | Invariant Functionals and Automorphic Fourier Transforms | For a pair $(G,\rho)$ and a cuspidal automorphic representation $\sigma$, do there exist nonzero $k^\times$-invariant linear functionals $E_{\sigma,\rho}$ and $E_{\widetilde{\sigma},\rho}$ such that $E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi)$ for every $\phi\in S_{\sigma,\rho}(\mathbb{... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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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-8415342-011",
"literature-status:open",
"owr-year:2021"
] | The proposed generalized Fourier-transform framework is a research direction intended to address the broad Langlands functoriality problem; the extracted statement records a suggestion, not a completed general construction or proof. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/2103.10261",
"label": "Harmonic analysis on certain spherical varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For a pair $(G,\rho)$ and a cuspidal automorphic representation $\sigma$, do there exist nonzero $k^\times$-invariant linear functionals $E_{\sigma,\rho}$ and $E_{\widetilde{\sigma},\rho}$ such that $E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi)$ for every $\phi\in S_{\sigma,\rho}(\mathbb{... | For a pair (G,\rho) and a cuspidal automorphic representation \sigma, there exist nonzero k^\times-invariant linear functionals E_{\sigma,\rho} and E_{\widetilde{\sigma},\rho} such that E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi) for every \phi\in S_{\sigma,\rho}(\mathbb A^\times). | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,784 | OWR-8415342-012 | The Sigma–Rho Poisson Summation Conjecture | The $(\sigma,\rho)$-Poisson summation conjecture asserts that the nonzero invariant functionals on the Schwartz spaces attached to $\sigma$ and its contragredient satisfy $E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi)$ for every test function $\phi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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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-8415342-012",
"literature-status:open",
"owr-year:2021"
] | The general Braverman--Kazhdan (sigma,rho)-Poisson summation formula is still conjectural; established GL1, GLn, and selected spherical or doubling-type analogues do not prove the statement for arbitrary G and rho. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/math/9912208",
"label": "Braverman--Kazhdan, Gamma-functions of representations and lifting"
},
{
"url": "https://arxiv.org/abs/1707.06091",
"label": "A refined Po... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | The $(\sigma,\rho)$-Poisson summation conjecture asserts that the nonzero invariant functionals on the Schwartz spaces attached to $\sigma$ and its contragredient satisfy $E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi)$ for every test function $\phi$. | Conjecture ((\sigma,\rho)-Poisson summation): the nonzero invariant functionals on the Schwartz spaces attached to \sigma and its contragredient satisfy E_{\sigma,\rho}(\phi)=E_{\widetilde{\sigma},\rho}(F_{\sigma,\rho,\psi}\phi) for all test functions \phi. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,785 | OWR-8415342-013 | Direct Poisson Summation for Split Classical Groups | Prove the $(\sigma,\rho)$-Poisson summation formula directly for split classical groups $G$, with $\rho$ the standard representation of the complex dual group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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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-8415342-013",
"literature-status:partially-solved",
"owr-year:2021"
] | The formula is proved when the relevant global functorial transfer to GLn is known and cuspidal, and GLn has a direct theorem, but the conditional mechanism does not establish the conjecture for all pairs (G,rho). | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/1707.06091",
"label": "A refined Poisson summation formula"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Prove the $(\sigma,\rho)$-Poisson summation formula directly for split classical groups $G$, with $\rho$ the standard representation of the complex dual group. | It is an open problem to prove the (\sigma,\rho)-Poisson summation formula directly for split classical groups G with \rho the standard representation of the complex dual group. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,786 | OWR-8415342-014 | Automorphic L-Functions from Sigma–Rho Poisson Summation | Prove that the conjectural $(\sigma,\rho)$-Poisson summation formula implies meromorphic continuation and the functional equation of the automorphic $L$-function $L(s,\sigma,\rho)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-014",
"literature-status:open",
"owr-year:2021"
] | The GLn identity is established, and refined Poisson formulas are known for selected Braverman--Kazhdan spaces, but the proposed direct proof for all split classical groups with the standard representation remains an expected extension rather than a general theorem. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "Oberwolfach Report 39/2021"
},
{
"url": "https://arxiv.org/abs/1707.06091",
"label": "A refined Poisson summation formula"
},
{
"url": "https://arxiv.org/abs/2103.10261",
"label": "Harmonic analysis on certain spherical variet... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Prove that the conjectural $(\sigma,\rho)$-Poisson summation formula implies meromorphic continuation and the functional equation of the automorphic $L$-function $L(s,\sigma,\rho)$. | The conjectural (\sigma,\rho)-Poisson summation formula is expected to imply the meromorphic continuation and functional equation of the automorphic L-function L(s,\sigma,\rho). | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,787 | OWR-8415342-015 | Kernels and Involutivity of Exotic Fourier Transforms | Compute explicitly the kernel $\phi^G_\rho$ defining the exotic Fourier transform $F^G_\rho$ on functions on $G^F$, and extend $F^G_\rho$ to an involutive operator. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-015",
"literature-status:open",
"owr-year:2021"
] | The extracted passage is an incomplete computational problem: it does not define the operator or specify the requested formula, and no identifiable resolution can therefore be verified. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Compute explicitly the kernel $\phi^G_\rho$ defining the exotic Fourier transform $F^G_\rho$ on functions on $G^F$, and extend $F^G_\rho$ to an involutive operator. | Problem: compute explicitly the kernel \phi^G_\rho defining the exotic Fourier transform F^G_\rho on functions on G^F, and extend F^G_\rho to an involutive operator. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,788 | OWR-8415342-016 | Restriction of Unramified GL Representations to Iwahori Blocks | For an unramified generic representation $\pi$ of $\operatorname{GL}_{n+1}(F)$, determine and model its restriction to the Iwahori block of $\operatorname{GL}_n(F)$, including whether the isomorphism class is independent of $\pi$ and how products of Steinberg representations behave. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-016",
"literature-status:partially-solved",
"owr-year:2021"
] | Chan and Savin proved important homological branching and projectivity results, but the full tempered-representation restriction conjecture for the Iwahori component remains unproved in general. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1905.01668",
"label": "Chan, homological branching law"
},
{
"url": "https://arxiv.org/abs/1605.05130",
"label": "Chan--Savin, branching rules and Hecke algebras"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For an unramified generic representation $\pi$ of $\operatorname{GL}_{n+1}(F)$, determine and model its restriction to the Iwahori block of $\operatorname{GL}_n(F)$, including whether the isomorphism class is independent of $\pi$ and how products of Steinberg representations behave. | For an unramified generic representation \pi of \operatorname{GL}_{n+1}(F), determine and model its restriction to the Iwahori block of \operatorname{GL}_n(F), including whether the isomorphism class is independent of \pi and how products of Steinberg representations behave. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,789 | OWR-8415342-017 | Integral Shimura Models with Universal Shtukas | Let $\mathcal G$ be a parahoric group scheme. Construct a pro-system of normal flat integral Shimura-variety models $\mathcal S_K$ over the reflex integers, with finite étale transition maps, such that the valuative extension property holds, the generic-fiber $\mathcal G$-shtuka extends to $\mathcal S_K$, and every for... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-017",
"literature-status:partially-solved",
"owr-year:2021"
] | The representability and local-model assertions are proved for abelian-type data under the stated prime and group hypotheses, extending the PEL cases, but the conjecture for arbitrary parahoric data is not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1017/S1474748025101345",
"label": "Pappas--Rapoport, integral local Shimura varieties"
},
{
"url": "https://arxiv.org/abs/2204.02829",
"label": "Pappas--Rapoport, pr... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Let $\mathcal G$ be a parahoric group scheme. Construct a pro-system of normal flat integral Shimura-variety models $\mathcal S_K$ over the reflex integers, with finite étale transition maps, such that the valuative extension property holds, the generic-fiber $\mathcal G$-shtuka extends to $\mathcal S_K$, and every for... | Conjecture: for a parahoric group scheme G, there is a pro-system of normal flat integral models of the associated Shimura varieties over the reflex integers, with finite etale transition maps, extending the universal G-shtuka and satisfying the stated integral and local-model uniformization properties. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,790 | OWR-8415342-018 | The Restricted Geometric Langlands Conjecture | Let $k$ be algebraically closed, let $X/k$ be a smooth projective geometrically connected curve, and let $G$ be reductive, with $\operatorname{char}(k)$ greater than the Coxeter number of $G$. In the corresponding derived $\ell$-adic setting, prove the canonical equivalence $\operatorname{Shv}_{\operatorname{Nilp}}(\op... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-018",
"literature-status:partially-solved",
"owr-year:2021"
] | The restricted geometric Langlands equivalence has been established in important characteristic-zero and selected positive-characteristic settings, but the general sheaf-theoretic equivalence stated here remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2010.01906",
"label": "Arinkin--Gaitsgory and collaborators, restricted formulation"
},
{
"url": "https://arxiv.org/abs/2508.02237",
"label": "Gaitsgory--Raskin, ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Let $k$ be algebraically closed, let $X/k$ be a smooth projective geometrically connected curve, and let $G$ be reductive, with $\operatorname{char}(k)$ greater than the Coxeter number of $G$. In the corresponding derived $\ell$-adic setting, prove the canonical equivalence $\operatorname{Shv}_{\operatorname{Nilp}}(\op... | Restricted geometric Langlands conjecture: in the stated setting, there is a canonical equivalence of DG categories \operatorname{Shv}_{\operatorname{Nilp}}(\operatorname{Bun}_G)\simeq\operatorname{IndCoh}_{\operatorname{Nilp}}(\operatorname{LocSys}^{\operatorname{restr}}_{\widehat G}). | corrected_verified | The linked report was inspected; the hypotheses immediately preceding the restricted geometric Langlands conjecture were restored. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,791 | OWR-8415342-019 | Beilinson–Drinfeld Equivalence and Restricted Geometric Langlands | The restricted geometric Langlands equivalence is known for tori and for arbitrary G when the curve is \mathbb P^1; in characteristic zero, its validity is equivalent to the Beilinson--Drinfeld conjecture, and it carries a canonical spectral action of \operatorname{QCoh}(\operatorname{LocSys}^{\operatorname{restr}}_{\w... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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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 official report confirms that this extraction is the evidence paragraph following the restricted geometric Langlands conjecture, which i) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-019",
"literature-status:partially-solved",
"owr-year:2021"
] | The excerpt records proofs for tori and for the projective line, together with a characteristic-zero reduction to the Beilinson--Drinfeld conjecture; these are substantial special cases, not a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2010.01906",
"label": "restricted geometric Langlands formulation"
},
{
"url": "https://arxiv.org/abs/2508.02237",
"label": "positive-characteristic progress"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | null | The restricted geometric Langlands equivalence is known for tori and for arbitrary G when the curve is \mathbb P^1; in characteristic zero, its validity is equivalent to the Beilinson--Drinfeld conjecture, and it carries a canonical spectral action of \operatorname{QCoh}(\operatorname{LocSys}^{\operatorname{restr}}_{\w... | unrecoverable | The official report confirms that this extraction is the evidence paragraph following the restricted geometric Langlands conjecture, which is already preserved in the preceding record. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,792 | OWR-8415342-021 | Automorphic Functions as Sections on Arithmetic Local Systems | Prove that there is an isomorphism $\operatorname{Func}(\operatorname{Bun}_G(\mathbb{F}_q))\simeq\Gamma(\operatorname{LocSys}^{\operatorname{arithm}}_{\widehat G},\omega)$ compatible with Hecke operators; equivalently, prove that Frobenius traces of nilpotent $\operatorname{IndCoh}$ recover the dualizing global section... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-021",
"literature-status:open",
"owr-year:2021"
] | The proposed identification of unramified automorphic functions with spectral global sections is verified in elementary examples such as the projective line and a torus, but no general proof for reductive groups is established. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2010.01906",
"label": "restricted geometric Langlands formulation"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Prove that there is an isomorphism $\operatorname{Func}(\operatorname{Bun}_G(\mathbb{F}_q))\simeq\Gamma(\operatorname{LocSys}^{\operatorname{arithm}}_{\widehat G},\omega)$ compatible with Hecke operators; equivalently, prove that Frobenius traces of nilpotent $\operatorname{IndCoh}$ recover the dualizing global section... | Conjecture: there is an isomorphism \operatorname{Func}(\operatorname{Bun}_G(\mathbb F_q))\simeq\Gamma(\operatorname{LocSys}^{\operatorname{arithm}}_{\widehat G},\omega), compatible with Hecke operators; equivalently, the relevant Frobenius traces of nilpotent IndCoh recover the dualizing global sections. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,793 | OWR-8415342-022 | Geometric Supercuspidals, Base Change, and Ramified Temperedness | Determine which Yu representations are monomial geometric supercuspidals; extend the proof beyond monomial representations; remove or replace the cyclic-base-change assumption; and determine when ramified Hecke operators establish temperedness at ramified places. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-022",
"literature-status:partially-solved",
"owr-year:2021"
] | Geometric and monomial supercuspidals yield proven automorphic applications and temperedness results at unramified places, but the extent of monomiality, generalization to other representations, and ramified temperedness remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://preprints.ihes.fr/storage/OnRamanujan.pdf",
"label": "Lafforgue, Ramanujan conjecture for automorphic forms"
},
{
"url": "https://arxiv.org/abs/1605.08820",
"label": "geometric... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Determine which Yu representations are monomial geometric supercuspidals; extend the proof beyond monomial representations; remove or replace the cyclic-base-change assumption; and determine when ramified Hecke operators establish temperedness at ramified places. | Open questions: how many Yu-constructed representations are monomial geometric supercuspidals; how far the proof extends beyond monomial representations; whether cyclic base change assumptions can be removed or replaced; and when Hecke operators at ramified places prove temperedness by this method. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,794 | OWR-8415342-023 | Hiraga–Ichino–Ikeda Degrees for Essentially Discrete Series | For an essentially discrete-series representation $\pi$ of $G$ with extended parameter $(\phi,\rho)$, prove the Hiraga–Ichino–Ikeda formula $d(\pi,\nu_G)=\frac{\dim\rho}{|S_\phi|}\lvert\gamma(0,\phi,\operatorname{Ad}_G)\rvert$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-023",
"literature-status:open",
"owr-year:2021"
] | The record is only an introduction to the Hiraga--Ichino--Ikeda conjecture and omits a complete mathematical claim; its resolution cannot be inferred from this fragment, so it is conservatively classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For an essentially discrete-series representation $\pi$ of $G$ with extended parameter $(\phi,\rho)$, prove the Hiraga–Ichino–Ikeda formula $d(\pi,\nu_G)=\frac{\dim\rho}{|S_\phi|}\lvert\gamma(0,\phi,\operatorname{Ad}_G)\rvert$. | Hiraga--Ichino--Ikeda conjecture: for an essentially discrete-series representation \pi of G with extended parameter (\phi,\rho), d(\pi,\nu_G)=\frac{\dim\rho}{|S_\phi|}|\gamma(0,\phi,\operatorname{Ad}_G)|. | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,795 | OWR-8415342-024 | Root Numbers and Central Characters of Langlands Parameters | Let $k$ be a non-Archimedean local field, let $G$ be a reductive $k$-group, and let $\phi$ be the Langlands parameter of an essentially discrete-series representation of $G(k)$. Prove that $\frac{\omega(\operatorname{Ad}_G\circ\phi)}{\omega(\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}=\chi_\phi(z_{\operatorname... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-024",
"literature-status:partially-solved",
"owr-year:2021"
] | The formal-degree formula is proved for broad families including classical groups, regular Yu supercuspidals, and principal-series discrete series, but it is not established for all reductive p-adic groups and discrete-series parameters. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2508.08470",
"label": "Beuzart-Plessis, classical groups"
},
{
"url": "https://doi.org/10.4171/JEMS/1412",
"label": "formal degree of regular supercuspidals"
}
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Let $k$ be a non-Archimedean local field, let $G$ be a reductive $k$-group, and let $\phi$ be the Langlands parameter of an essentially discrete-series representation of $G(k)$. Prove that $\frac{\omega(\operatorname{Ad}_G\circ\phi)}{\omega(\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}=\chi_\phi(z_{\operatorname... | Conjecture: in the preceding formal-degree setting, the orthogonal root-number ratio satisfies \frac{\omega(\operatorname{Ad}_G\circ\phi)}{\omega(\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}=\chi_\phi(z_{\operatorname{Ad}_G}), where z_{\operatorname{Ad}_G} is the specified central involution and \chi_\phi is th... | corrected_verified | The linked report was inspected; the local-field, reductive-group, representation, and principal-parameter context was restored around its Conjecture 1.2. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,796 | OWR-8415342-025 | The Refined Formal-Degree Conjecture | Refined formal-degree conjecture: if the split center $A_G$ is trivial, then $(-1)^{r(G)}\deg(\pi,\mu_G)=\pm\frac{\dim\rho}{|S_\phi|}\frac{\gamma(0,\operatorname{Ad}_G\circ\phi)}{\gamma(0,\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}$, with sign given by the quotient of the corresponding root numbers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-025",
"literature-status:partially-solved",
"owr-year:2021"
] | The refined central-character identity for orthogonal root numbers is proved for tempered parameters, while the accompanying refined formal-degree statement and its full generality remain only partly resolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2107.02360",
"label": "Schwein, orthogonal root numbers"
},
{
"url": "https://doi.org/10.1007/s00208-022-02416-6",
"label": "published orthogonal-root-number theo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Refined formal-degree conjecture: if the split center $A_G$ is trivial, then $(-1)^{r(G)}\deg(\pi,\mu_G)=\pm\frac{\dim\rho}{|S_\phi|}\frac{\gamma(0,\operatorname{Ad}_G\circ\phi)}{\gamma(0,\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}$, with sign given by the quotient of the corresponding root numbers. | Refined formal-degree conjecture: if the split center A_G is trivial, then }(-1)^{r(G)}\deg(\pi,\mu_G)=\pm\frac{\dim\rho}{|S_\phi|}\frac{\gamma(0,\operatorname{Ad}_G\circ\phi)}{\gamma(0,\operatorname{Ad}_G\circ\phi_{\operatorname{prin}})}, with sign given by the quotient of the corresponding root numbers.} | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,797 | OWR-8415342-028 | Plancherel Densities on Yu-Induced Tempered Components | Verify the Hiraga–Ichino–Ikeda Plancherel-measure conjecture on the nondiscrete tempered-dual components arising by parabolic induction from nonsingular Yu supercuspidal representations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-028",
"literature-status:open",
"owr-year:2021"
] | The proposed Plancherel-measure formula for components induced from nonsingular Yu supercuspidals remains an open target; recent work treats only narrower generic or otherwise special parabolic-induction cases. | [
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00229-025-01632-z",
"label": "formal degrees and parabolic induction"
},
{
"url": "https://arxiv.org/abs/1807.10232",
"label": "affine Hecke algebras and HII P... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Verify the Hiraga–Ichino–Ikeda Plancherel-measure conjecture on the nondiscrete tempered-dual components arising by parabolic induction from nonsingular Yu supercuspidal representations. | Open problem: verify the Hiraga--Ichino--Ikeda Plancherel-measure conjecture on the nondiscrete tempered-dual components arising by parabolic induction from nonsingular Yu supercuspidal representations. | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,798 | OWR-8415342-030 | Equality of Discrete and Automorphic Multiplicities | Let $F$ be a number field, let $G$ be an even orthogonal or unitary group over $F$, let $\psi$ be an elliptic Arthur parameter of $G$, and let $\pi$ be an automorphic representation in the near-equivalence class represented by $\psi$. Prove $m_{\mathrm{disc}}(\pi)=m_{\mathrm{aut}}(\pi)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-030",
"literature-status:partially-solved",
"owr-year:2021"
] | Chen and Zou proved the multiplicity formula in the stated broad families of even orthogonal and unitary groups, including the low-Witt-index case, but the extracted conjecture is not resolved for every group and parameter. | [
{
"url": "https://ems.press/journals/jems/articles/14298407",
"label": "Chen--Zou, Arthur multiplicity formula"
},
{
"url": "https://arxiv.org/abs/2104.12354",
"label": "Chen--Zou, theta correspondence and Arthur packets"
},
{
"url": "https://doi.org/10.4171/owr/2021/39",
"label": "o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | Let $F$ be a number field, let $G$ be an even orthogonal or unitary group over $F$, let $\psi$ be an elliptic Arthur parameter of $G$, and let $\pi$ be an automorphic representation in the near-equivalence class represented by $\psi$. Prove $m_{\mathrm{disc}}(\pi)=m_{\mathrm{aut}}(\pi)$. | Conjecture: Let G be an even orthogonal or unitary group over a number field, let \psi be an elliptic A-parameter of G, and let \pi be an automorphic representation in the near-equivalence class represented by \psi. Then the discrete and automorphic multiplicities coincide: m_{\mathrm{disc}}(\pi)=m_{\mathrm{aut}}(\pi). | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,799 | OWR-8415342-031 | Endoscopic Identities and Archimedean Independence of Local Packets | For the local packet $\Pi^{\theta(\psi)}_v(G_v)$ attached to an Arthur parameter, prove the endoscopic character identities. At Archimedean places $v$, is the packet independent of the auxiliary group, and does it agree with Arthur's packet in the quasi-split case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156](https://doi.org/10.4171/owr/2021/39)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415342-031",
"literature-status:partially-solved",
"owr-year:2021"
] | Endoscopic character identities are available in important non-Archimedean cases, including recent results for bounded packets of non-quasi-split even orthogonal groups, but the extracted Archimedean and full local questions remain unresolved. | [
{
"url": "https://arxiv.org/abs/2506.17907",
"label": "endoscopic character identity for even special orthogonal groups"
},
{
"url": "https://arxiv.org/abs/2104.12354",
"label": "Chen--Zou, theta correspondence and Arthur packets"
},
{
"url": "https://doi.org/10.4171/owr/2021/39",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/39 | null | null | null | For the local packet $\Pi^{\theta(\psi)}_v(G_v)$ attached to an Arthur parameter, prove the endoscopic character identities. At Archimedean places $v$, is the packet independent of the auxiliary group, and does it agree with Arthur's packet in the quasi-split case? | For the local packet \Pi^{\theta(\psi)}_v(G_v) attached to an A-parameter, can one prove that it satisfies the endoscopic character identities, and can one extend Theorem 1.5(2)—independence of the auxiliary group and agreement with Arthur's packet in the quasi-split case—to Archimedean places v? | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | Automorphic Forms, Geometry and Arithmetic (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/39, pp. 2089--2156 |
30,004,800 | OWR-8415343-001 | Weighted Sobolev Stability Under Nonlinear Composition | Let $G$ be smooth with a first-order zero at the origin, and let $s>1$. Does there exist $C_2=C_2(G,s)$ such that every coefficient family $\{\phi_{\widetilde{\ell}}(t)\}_{\widetilde{\ell}\in\mathbb{N}^2}$ on $[t_-,t_+]$ satisfying $\sum_{\widetilde{\ell}}(1+|\widetilde{\ell}|)^{2s}\sup_{t\in[t_-,t_+]}|\phi_{\widetilde... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23272241",
"checked_at": "2026-10-10",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **A Composition Estimate for Fourier Series with the Supremum in Time Inside the Sum, and a Question of Chruściel** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23272241) | [
"owr",
"oberwolfach-reports",
"OWR-8415343-001",
"literature-status:open",
"owr-year:2021"
] | The extracted question asks for a nonlinear Sobolev estimate for a composition operator near a first-order zero; the source gives the question but no proof, and no authoritative general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Let $G$ be smooth with a first-order zero at the origin, and let $s>1$. Does there exist $C_2=C_2(G,s)$ such that every coefficient family $\{\phi_{\widetilde{\ell}}(t)\}_{\widetilde{\ell}\in\mathbb{N}^2}$ on $[t_-,t_+]$ satisfying $\sum_{\widetilde{\ell}}(1+|\widetilde{\ell}|)^{2s}\sup_{t\in[t_-,t_+]}|\phi_{\widetilde... | Let G be smooth with a first-order zero at the origin and let s>1. Does there exist C_2=C_2(G,s) such that every coefficient family \{\phi_{\widetilde{\ell}}(t)\}_{\widetilde{\ell}\in\mathbb N^2} on [t_-,t_+] satisfying \sum_{\widetilde{\ell}}(1+|\widetilde{\ell}|)^{2s}\sup_{t\in[t_-,t_+]}|\phi_{\widetilde{\ell}}(t)|^2... | corrected_verified | The explicit question or conjecture was isolated from surrounding report prose and its mathematical notation was normalized. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,801 | OWR-8415343-003 | Emergence of Isotropic Big-Bang Singularities | Within mathematical models of cosmological singularity formation, what mechanism or initial-data principle explains the emergence of a homogeneous, isotropic Big-Bang singularity with vanishing Weyl curvature from more general initial conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415343-003",
"literature-status:open",
"owr-year:2021"
] | The origin question is a broad cosmological problem rather than a precise theorem; existing work constrains initial singularities and inflationary past completeness but does not determine a unique mathematical account of the universe's beginning. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/gr-qc/0110012",
"label": "Borde--Guth--Vilenkin, inflationary incompleteness"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Within mathematical models of cosmological singularity formation, what mechanism or initial-data principle explains the emergence of a homogeneous, isotropic Big-Bang singularity with vanishing Weyl curvature from more general initial conditions? | Within mathematical models of cosmological singularity formation, what mechanism or initial-data principle explains the emergence of a homogeneous, isotropic Big-Bang singularity with vanishing Weyl curvature from more general initial conditions? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,802 | OWR-8415343-005 | Bartnik’s Stationary Vacuum Extension Conjecture | Bartnik's stationary vacuum extension conjecture: let $(B^3,g_0,k_0)$ satisfy the dominant energy condition, with boundary $S^2$ whose expansion $\theta=H_{g_0}+\operatorname{tr}_{S^2}k_0$ is not everywhere nonpositive. Does there exist a unique asymptotically flat stationary vacuum initial-data set $(\mathbb{R}^3\setm... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415343-005",
"literature-status:open",
"owr-year:2021"
] | The extracted record is only a lead-in to a Bartnik conjecture and omits the conjecture's mathematical statement; its resolution is consequently unclear and is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
},
{
"url": "https://par.nsf.gov/servlets/purl/10552859",
"label": "Huang--Lee, Bartnik mass minimizers"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Bartnik's stationary vacuum extension conjecture: let $(B^3,g_0,k_0)$ satisfy the dominant energy condition, with boundary $S^2$ whose expansion $\theta=H_{g_0}+\operatorname{tr}_{S^2}k_0$ is not everywhere nonpositive. Does there exist a unique asymptotically flat stationary vacuum initial-data set $(\mathbb{R}^3\setm... | Bartnik's stationary vacuum extension conjecture: Let (B^3,g_0,k_0) satisfy the dominant energy condition, with boundary S^2 whose expansion \theta=H_{g_0}+\operatorname{tr}_{S^2}k_0 is not everywhere nonpositive. Does there exist a unique asymptotically flat stationary vacuum initial-data set (\mathbb R^3\setminus B^3... | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,803 | OWR-8415343-006 | Asymptotics of Expanding Vacuum Spacetimes Near Singularities | For a globally hyperbolic expanding vacuum spacetime with compact Cauchy hypersurfaces and a CMC foliation, what is the asymptotic behavior as the past singularity is approached, and what is the future behavior of the spacetime? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-8415343-006",
"literature-status:open",
"owr-year:2021"
] | Rigorous asymptotics are known for symmetric and selected Kasner-like families, but the general past and future behavior asked for in the excerpt remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1908.02185",
"label": "Lott, initial geometry of vacuum cosmological spacetimes"
},
{
"url": "https://arxiv.org/abs/1709.03952",
"label": "Lott, future behavior o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | For a globally hyperbolic expanding vacuum spacetime with compact Cauchy hypersurfaces and a CMC foliation, what is the asymptotic behavior as the past singularity is approached, and what is the future behavior of the spacetime? | For a globally hyperbolic expanding vacuum spacetime with compact Cauchy hypersurfaces and a CMC foliation, what is the asymptotic behavior as the past singularity is approached, and what is the future behavior of the spacetime? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,804 | OWR-8415343-007 | Weak Cosmic Censorship for Vacuum Spacetimes | Weak Cosmic Censorship for the Einstein vacuum equations: for generic complete, regular, asymptotically flat Cauchy data, are all singularities in the corresponding maximal development hidden inside a black hole (so that naked singularities do not occur)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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-8415343-007",
"literature-status:partially-solved",
"owr-year:2021"
] | Christodoulou proved the weak cosmic censorship analogue in spherical Einstein--scalar collapse, and later work treats further symmetric systems, but the general asymptotically flat formulation with precise genericity and regularity remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2402.16250",
"label": "spherically symmetric charged-scalar WCC proof"
},
{
"url": "https://doi.org/10.1007/s10714-022-02973-w",
"label": "Penrose singularity the... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Weak Cosmic Censorship for the Einstein vacuum equations: for generic complete, regular, asymptotically flat Cauchy data, are all singularities in the corresponding maximal development hidden inside a black hole (so that naked singularities do not occur)? | Weak Cosmic Censorship for the Einstein vacuum equations: for generic complete, regular, asymptotically flat Cauchy data, are all singularities in the corresponding maximal development hidden inside a black hole (so that naked singularities do not occur)? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,805 | OWR-8415343-008 | Kasner Singularities Beyond the Subcritical Regime | For general sufficiently small perturbations, possibly without symmetry, of generalized Kasner solutions of the Einstein equations, what behavior occurs near the singularity when the sub-criticality condition $\max_{I<J,B}(\widetilde q_I+\widetilde q_J-\widetilde q_B)<1$ fails? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415343-008",
"literature-status:open",
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] | The complete sub-critical regime has rigorous stability theorems, including nonsymmetric high-dimensional cases, but the behavior of general small perturbations when sub-criticality fails remains an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "original Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2012.05888",
"label": "Fournodavlos--Rodnianski--Speck, stable Big Bang"
},
{
"url": "https://arxiv.org/abs/2003.13591",
"label": "asymptotically Kasner-like sing... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | For general sufficiently small perturbations, possibly without symmetry, of generalized Kasner solutions of the Einstein equations, what behavior occurs near the singularity when the sub-criticality condition $\max_{I<J,B}(\widetilde q_I+\widetilde q_J-\widetilde q_B)<1$ fails? | For general sufficiently small perturbations, possibly without symmetry, of generalized Kasner solutions of the Einstein equations, what behavior occurs near the singularity when the sub-criticality condition max_{I<J,B}(\widetilde q_I+\widetilde q_J-\widetilde q_B)<1 fails? | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,806 | OWR-8415343-009 | Self-Consistent Motion of Massive Charged Particles in Relativity | How can one rigorously model the motion of massive and charged particles in general relativity, including their coupled electromagnetic and gravitational fields and the timelike singularities they generate? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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-8415343-009",
"literature-status:open",
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] | This is a broad modeling question rather than a definite theorem; no general mathematically canonical model for massive charged particles and their self-generated gravitational and electromagnetic fields has been established. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | How can one rigorously model the motion of massive and charged particles in general relativity, including their coupled electromagnetic and gravitational fields and the timelike singularities they generate? | How can one rigorously model the motion of massive and charged particles in general relativity, including their coupled electromagnetic and gravitational fields and the timelike singularities they generate? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,807 | OWR-8415343-010 | Weak Bianchi Identities Across Timelike Singularities | Does the weak contracted second Bianchi identity $\int_M(R_{\mu\nu}-\tfrac12R g_{\mu\nu})\nabla^\mu\psi^\nu\,dV_g=0$ hold for every spacetime whose timelike singularity restricts on spacelike slices to a regular zero-area singularity with negative ZAS mass in the sense of Bray and Jauregui, and for every compactly supp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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-8415343-010",
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] | The cited work proves the weak twice-contracted second Bianchi identity only for a restricted static spherically symmetric class; the extension to all admissible timelike singularities remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
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{
"url": "https://arxiv.org/abs/1901.00813",
"label": "Burtscher--Kiessling--Tahvildar-Zadeh"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Does the weak contracted second Bianchi identity $\int_M(R_{\mu\nu}-\tfrac12R g_{\mu\nu})\nabla^\mu\psi^\nu\,dV_g=0$ hold for every spacetime whose timelike singularity restricts on spacelike slices to a regular zero-area singularity with negative ZAS mass in the sense of Bray and Jauregui, and for every compactly supp... | Does the weak contracted second Bianchi identity \int_M(R_{\mu\nu}-\tfrac12R g_{\mu\nu})\nabla^\mu\psi^\nu dV_g=0 hold for every spacetime with an admissible timelike singularity of the specified zero-area, regular-boundary type, for every compactly supported vector field \psi? | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,808 | OWR-8415343-011 | Initial Data for Physical Late-Time Schwarzschild Wave Tails | For solutions of the scalar wave equation $\Box_g\phi=0$ on a Schwarzschild background arising from physically realistic isolated-system data, how should one choose or characterize the data on an asymptotically hyperboloidal hypersurface $\Sigma$ so as to obtain physically meaningful predictions for the late-time asymp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
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"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415343-011",
"literature-status:open",
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] | Sharp Price-law asymptotics are proved for important compact-support and related data classes, but the physically relevant choice of asymptotically hyperboloidal data and the resulting general predictions along future null infinity remain unresolved. | [
{
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"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/gr-qc/0401121",
"label": "Dafermos--Rodnianski"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | For solutions of the scalar wave equation $\Box_g\phi=0$ on a Schwarzschild background arising from physically realistic isolated-system data, how should one choose or characterize the data on an asymptotically hyperboloidal hypersurface $\Sigma$ so as to obtain physically meaningful predictions for the late-time asymp... | For solutions of the scalar wave equation \Box_g\phi=0 on a Schwarzschild background arising from physically realistic isolated-system data, how should one choose or characterize the data on an asymptotically hyperboloidal hypersurface \Sigma so as to obtain physically meaningful predictions for the late-time asymptoti... | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,809 | OWR-8415343-012 | Interior Singularity Structure of Dynamically Formed Black Holes | What is the global singularity structure inside a black hole formed by gravitational collapse, in particular the relationship between a weakly singular Cauchy horizon, stronger terminal singularities, and the center? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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-8415343-012",
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] | The literature establishes detailed interior structures in symmetric models and C0 stability results for dynamical Kerr interiors, but no general classification of singularities formed in gravitational collapse is known. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "OWR report"
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{
"url": "https://annals.math.princeton.edu/2025/202-2/p01",
"label": "Dafermos--Luk"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | What is the global singularity structure inside a black hole formed by gravitational collapse, in particular the relationship between a weakly singular Cauchy horizon, stronger terminal singularities, and the center? | What is the global singularity structure inside a black hole formed by gravitational collapse, in particular the relationship between a weakly singular Cauchy horizon, stronger terminal singularities, and the center? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,810 | OWR-8415343-013 | Local Weak Cosmic Censorship in Charged Spherical Collapse | Local Weak Cosmic Censorship Conjecture: for generic spacetimes arising from charged spherical collapse, the center endpoint $\widehat{\Gamma}$ is not a locally naked singularity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | open | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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-8415343-013",
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] | The exact local conjecture that the charged-collapse center endpoint is generically not locally naked remains unresolved; existing charged-collapse results do not prove this local statement. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "OWR report"
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{
"url": "https://arxiv.org/abs/2402.16250",
"label": "An--Tan"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | Local Weak Cosmic Censorship Conjecture: for generic spacetimes arising from charged spherical collapse, the center endpoint $\widehat{\Gamma}$ is not a locally naked singularity. | Local Weak Cosmic Censorship Conjecture: for generic spacetimes arising from charged spherical collapse, the center endpoint \widehat{\Gamma} is not a locally naked singularity. | corrected_verified | All explicit formulas were dollar-delimited and the supplied mathematical content was preserved. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,811 | OWR-8415343-014 | Equality of Capacity–Volume and ADM Mass | For every asymptotically flat Riemannian three-manifold $(M^3,g)$, does the capacity–volume mass equal the ADM mass, $m_{\mathrm{CV}}(M,g)=m_{\mathrm{ADM}}(M,g)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267](https://doi.org/10.4171/owr/2021/40)
## Literature review (checked 2026-08-... | 3 | solved | null | 2,021 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.3842/SIGMA.2023.091",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, for C¹\_τ-asymptotically flat metrics with R ≥ 0)**. J. Jauregui (OWR 40/2021, p. 2257) conjectures that his capacity–volume mass equals the ADM mass for general asymptotically flat 3-manifolds; he had proved the inequality ≥ (for R ≥ 0 outside a compact set)... | [
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"literature-status:open",
"owr-year:2021"
] | The capacity-volume mass is known to satisfy an upper bound by ADM mass and agrees with it in Schwarzschild, but equality for general asymptotically flat metrics remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2021/40",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2002.08941",
"label": "Jauregui"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/40 | null | null | null | For every asymptotically flat Riemannian three-manifold $(M^3,g)$, does the capacity–volume mass equal the ADM mass, $m_{\mathrm{CV}}(M,g)=m_{\mathrm{ADM}}(M,g)$? | For every asymptotically flat metric (M,g) in the relevant three-dimensional class, does the capacity-volume mass equal the ADM mass, m_{\mathrm{CV}}(M,g)=m_{\mathrm{ADM}}(M,g)? | corrected_verified | The official Oberwolfach report was checked directly; the conjecture's full class of general asymptotically flat three-dimensional metrics and its equality were restored. | null | null | null | null | null | Mathematical Aspects of General Relativity (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/40, pp. 2157--2267 |
30,004,812 | OWR-8415345-001 | Polynomial Knot Invariants and Projections in General Three-Manifolds | For knots in general 3-manifolds, do Jones/HOMFLYPT-type polynomial invariants exist; what knot projections have useful computational and invariant-theoretic properties; and is there a Reidemeister theorem for such projections? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | partially_solved | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-001",
"literature-status:partially-solved",
"owr-year:2021"
] | Kauffman-bracket and related skein modules provide established Jones-type generalizations, but a single canonical Jones/HOMFLYPT polynomial with the full classical role for arbitrary 3-manifolds is not established. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1112/jlms.12410",
"label": "Detcherry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | For knots in general 3-manifolds, do Jones/HOMFLYPT-type polynomial invariants exist; what knot projections have useful computational and invariant-theoretic properties; and is there a Reidemeister theorem for such projections? | For knots in general 3-manifolds, do Jones/HOMFLYPT-type polynomial invariants exist; what knot projections have useful computational and invariant-theoretic properties; and is there a Reidemeister theorem for such projections? | exact | The supplied statement is retained byte-for-byte; it is a genuine research question requiring no statement-level reconstruction. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,813 | OWR-8415345-002 | Knot Complements and Prime Decomposition in General Three-Manifolds | For knots in general 3-manifolds, what is the correct Gordon–Luecke analogue and is it true—for example, does an orientation-preserving homeomorphism of complements imply equivalence of knots in closed oriented irreducible 3-manifolds outside the rational-unknot lens-space exceptions—and does a prime decomposition theo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | partially_solved | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-002",
"literature-status:partially-solved",
"owr-year:2021"
] | The strong Gordon-Luecke analogue is false, while the weak analogue remains open in the stated generality; the separate prime-decomposition question was answered by Miyazaki, with nonterminating decompositions possible. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1112/jlms.70600",
"label": "Aceto et al."
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | For knots in general 3-manifolds, what is the correct Gordon–Luecke analogue and is it true—for example, does an orientation-preserving homeomorphism of complements imply equivalence of knots in closed oriented irreducible 3-manifolds outside the rational-unknot lens-space exceptions—and does a prime decomposition theo... | For knots in general 3-manifolds, what is the correct Gordon--Luecke analogue and is it true—for example, does an orientation-preserving homeomorphism of complements imply equivalence of knots in closed oriented irreducible 3-manifolds outside the rational-unknot lens-space exceptions—and does a prime decomposition the... | corrected_verified | A publication-format audit preserved the mathematical content while repairing notation or typography. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,814 | OWR-8415345-003 | The Weak Gordon–Luecke Conjecture | Let $K_1$ and $K_2$ be knots in a closed oriented irreducible $3$-manifold $Y$, neither a rational unknot in a lens space. Prove that $Y\setminus K_1$ and $Y\setminus K_2$ are orientation-preservingly homeomorphic if and only if an orientation-preserving self-homeomorphism of $Y$ takes $K_1$ to $K_2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-8415345-003",
"literature-status:open",
"owr-year:2021"
] | For knots in general 3-manifolds the complement-determines-knot statement is not proved; the weak Gordon-Luecke formulation is tied to still-open cosmetic-surgery questions. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1112/jlms.70600",
"label": "Aceto et al."
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | Let $K_1$ and $K_2$ be knots in a closed oriented irreducible $3$-manifold $Y$, neither a rational unknot in a lens space. Prove that $Y\setminus K_1$ and $Y\setminus K_2$ are orientation-preservingly homeomorphic if and only if an orientation-preserving self-homeomorphism of $Y$ takes $K_1$ to $K_2$. | Weak Gordon--Luecke conjecture: if K_1 and K_2 are knots in a closed oriented irreducible 3-manifold Y, under the usual nonexceptional hypotheses, then Y\setminus K_1\cong Y\setminus K_2 by an orientation-preserving homeomorphism if and only if K_1 and K_2 are equivalent under an orientation-preserving self-homeomorphi... | corrected_verified | The standalone statement and its hypotheses were checked against the official Oberwolfach report. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
30,004,815 | OWR-8415345-005 | Bridge Position for Surfaces in Trisected Four-Manifolds | Any smoothly embedded surface S in a trisected 4-manifold X=X_1\cup X_2\cup X_3 can be isotoped into bridge position: S meets the central surface transversely in an even number of points, each S\cap X_i\cap X_j is a boundary-parallel tangle, and each S\cap X_i is a boundary-parallel disk tangle. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364](https://doi.org/10.4171/owr/2021/42)
... | 3 | open | null | 2,021 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (a theorem, not a problem)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (a theorem, not a problem)**. The record is Theorem 5 of D. Moussard's survey abstract (OWR 42/2021, p. 2349), the bridge-position theorem of Meier–Zupan, [PNAS 115 (2018)](https://doi.org/10.1073/pnas.1717171115). **Mark solved, or retire it.** If a replacement is... | [
"owr",
"oberwolfach-reports",
"OWR-8415345-005",
"literature-status:open",
"owr-year:2021"
] | The extracted record contains only the word conjecture and a theorem about bridge position, so the intended conjectural claim cannot be identified; under the triage rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2021/42",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2021/42 | null | null | null | null | Any smoothly embedded surface S in a trisected 4-manifold X=X_1\cup X_2\cup X_3 can be isotoped into bridge position: S meets the central surface transversely in an even number of points, each S\cap X_i\cap X_j is a boundary-parallel tangle, and each S\cap X_i is a boundary-parallel disk tangle. | unrecoverable | The official report labels the bridge-position assertion Theorem 5; the extraction is a proved theorem, not the neighboring open conjecture. | null | null | null | null | null | MATRIX-MFO Tandem Workshop: Invariants and Structures in Low-Dimensional Topology (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/42, pp. 2327--2364 |
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