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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,516 | OWR-13750328-023 | Tower-Equivalence for Irreducible Spetsial Groups | For every irreducible spetsial group except $G_{32}$, prove that the image of $\operatorname{Id}-f$ equals the space of class functions tower-equivalent to zero. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084](https://doi.org/10.4171/owr/2023/19)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750328-023",
"literature-status:open",
"owr-year:2023"
] | The inclusion of the image of Id-f in the kernel of tower equivalence is proved, but the proposed equality for irreducible spetsial groups other than G32 remains an explicit open question. | [
{
"url": "https://doi.org/10.1090/bproc/167",
"label": "Michel primary paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/19 | null | null | null | For every irreducible spetsial group except $G_{32}$, prove that the image of $\operatorname{Id}-f$ equals the space of class functions tower-equivalent to zero. | It follows from the first item that the image of Id − f is a vector space of class functions tower equivalent to 0. I call kernel of the tower equivalence the space of all class functions tower equivalent to 0. Many computations support the conjecture: Conjecture 1. For any irreducible spetsial group except G32 , the im... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Representations of Finite Groups (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/19, pp. 1031--1084 |
30,005,517 | OWR-13750331-001 | Energy Costs of Unspecified Molecular Mechanisms | What is the energy cost for implementing these molecular mechanisms? Collective problem solving in ants and humans Ofer Feinerman To try and understand how smarter a group of ants is compared to individuals, we presented them with geometrical puzzles that can be produced at different scales. The puzzles include a piece... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Foundations of Biological Organisation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/20, pp. 1085--1104](https://doi.org/10.4171/owr/2023/20)
## Literature review (checked... | 3 | open | null | 2,023 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extracted question introduces a talk's already-developed model of energetic cost in molecular-clock synchronization and is followed by i) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750331-001",
"literature-status:open",
"owr-year:2023"
] | General energy costs for implementing the reported molecular mechanisms have no established quantitative characterization; existing theory gives lower bounds for measurement or information acquisition. | [
{
"url": "https://doi.org/10.4171/owr/2023/20",
"label": "Oberwolfach problem report"
},
{
"url": "https://doi.org/10.1103/PhysRevE.95.062410",
"label": "free-energy lower bound"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/20 | null | null | null | null | What is the energy cost for implementing these molecular mechanisms? Collective problem solving in ants and humans Ofer Feinerman To try and understand how smarter a group of ants is compared to individuals, we presented them with geometrical puzzles that can be produced at different scales. The puzzles include a piece... | unrecoverable | The extracted question introduces a talk's already-developed model of energetic cost in molecular-clock synchronization and is followed by its application, rather than being posed as an open mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Foundations of Biological Organisation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/20, pp. 1085--1104 |
30,005,518 | OWR-13750331-002 | Reconstruction of Chromosome Structure from Contact Maps | What does a chromosome contact map look like? represent and analyze the structure of proteins. They are closely related to re- currence networks obtained from recurrence plots of dynamical systems, and the same reconstruction methods can be used. The main steps of the reconstruction are (i) to derive a complete distanc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Foundations of Biological Organisation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/20, pp. 1085--1104](https://doi.org/10.4171/owr/2023/20)
## Literature review (checked... | 3 | partially_solved | null | 2,023 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extracted phrase is a figure caption answered by the pictured contact map; the surrounding contribution describes established three-dime) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750331-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Contact maps are experimentally measurable as genome-wide matrices with compartments, domains and loops, but a universal complete three-dimensional chromosome structure is not determined by one map. | [
{
"url": "https://doi.org/10.1016/j.cell.2014.11.021",
"label": "Hi-C primary study"
},
{
"url": "https://doi.org/10.1016/j.celrep.2016.10.061",
"label": "multicell-type contact maps"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/20 | null | null | null | null | What does a chromosome contact map look like? represent and analyze the structure of proteins. They are closely related to re- currence networks obtained from recurrence plots of dynamical systems, and the same reconstruction methods can be used. The main steps of the reconstruction are (i) to derive a complete distanc... | unrecoverable | The extracted phrase is a figure caption answered by the pictured contact map; the surrounding contribution describes established three-dimensional reconstruction methods rather than an open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Foundations of Biological Organisation (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/20, pp. 1085--1104 |
30,005,519 | OWR-13750332-001 | Real Subspaces in Zeros of Elementary Symmetric Polynomials | If $r$ is even, does the zero set $e_r^{-1}(0)$ of the elementary symmetric polynomial contain no real vector subspace of dimension $r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | open | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23062557",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **Star Transforms Without Type 2 Singular Directions and Conflitti's Conjecture on Elementary Symmetric Polynomials** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23062557) | [
"owr",
"oberwolfach-reports",
"OWR-13750332-001",
"literature-status:open",
"owr-year:2023"
] | The stated all-dimensional extension remains conjectural: the cited real-subspace assertion for even r is still not established in general, despite results in special cases. | [
{
"url": "https://doi.org/10.4171/owr/2023/21",
"label": "Oberwolfach problem report"
},
{
"url": "https://www.math.nthu.edu.tw/~amen/2006/051014-3.pdf",
"label": "real symmetric polynomial paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | If $r$ is even, does the zero set $e_r^{-1}(0)$ of the elementary symmetric polynomial contain no real vector subspace of dimension $r$? | The generalization of Theorem 6 (b) to the case of m = 2k + 1 > 3 is technically more complicated and has not been proven yet. We finish with a result in algebraic geometry advertised at the beginning of this abstract. Let er (y1 , . . . , ym ) denote the elementary symmetric polynomial of degree r in Rm . In paper [5]... | 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 | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,520 | OWR-13750332-002 | Limits of Phase Retrieval and Tomographic Imaging | How much improvement in phase retrieval and tomographic imaging can be obtained by fully exploiting indirect measurements, sophisticated analysis, and high-performance algorithms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750332-002",
"literature-status:open",
"owr-year:2023"
] | Phase retrieval and tomographic algorithms exploit indirect measurements substantially, but there is no general theorem answering the report question about the ultimate room for improvement across mechanisms and noise regimes. | [
{
"url": "https://doi.org/10.4171/owr/2023/21",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | How much improvement in phase retrieval and tomographic imaging can be obtained by fully exploiting indirect measurements, sophisticated analysis, and high-performance algorithms? | How much more room for improvement is offered by full exploitation of indirect measurements, sophisticated analysis and high performance algorithms, and how far can this go? Phase Retrieval and Tomographic Reconstruction in X-ray Near-field Diffractive Imaging: Inverse Problems at Work Tim Salditt | 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 | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,521 | OWR-13750332-003 | Compton Transform Inversion with Spatially Unresolved Detectors | Can the three-stage Compton transform be inverted when the final detector records energy but not the spatial location of the detected photon? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750332-003",
"literature-status:open",
"owr-year:2023"
] | The spatially unresolved-detector extension of the Compton-camera transform remains open; exact inversion is available for spatially resolved data, while unresolved variants are presently modeled rather than generally inverted. | [
{
"url": "https://doi.org/10.1002/pamm.202300281",
"label": "unresolved-detector study"
},
{
"url": "https://doi.org/10.1117/1.JMI.7.3.032504",
"label": "resolved Compton inversion"
},
{
"url": "https://doi.org/10.4171/owr/2023/21",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | Can the three-stage Compton transform be inverted when the final detector records energy but not the spatial location of the detected photon? | transform has not been analyzed in the literature up to this point and is an open problem. The other extension that we propose to consider in the model is motivated by an imaging setup with a Compton camera with relatively large and spatially non- resolved detectors. P(2) (x2 , y, E ′′ ) = ZE0 Z Z C3 (x2 , y, E ′ , 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 | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,522 | OWR-13750332-004 | Unique Recovery of Continuous Motions | Classify the functions for which a continuous motion can be uniquely recovered from the tomographic data. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750332-004",
"literature-status:open",
"owr-year:2023"
] | Common-circle methods provide uniqueness and motion-recovery results under hypotheses, but a classification of functions permitting unique recovery for continuous motion remains open. | [
{
"url": "https://arxiv.org/abs/2209.08022",
"label": "common-circle primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2023/21",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | Classify the functions for which a continuous motion can be uniquely recovered from the tomographic data. | While some uniqueness results exist for the method of moments [7] and the common circle method [6], the classification of functions for which the unique recovery of a continuous motion is possible remains an open problem. Similar to the previous scenario, utilizing the fact that these hemispheres at two distinct time s... | 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 | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,523 | OWR-13750332-005 | Vanishing-Viscosity Limits for Transport Equations | Let $u_\varepsilon$ be the unique weak solution of the viscosity-regularized transport equation $$-\varepsilon\Delta u_\varepsilon+Hu_\varepsilon+\alpha u_\varepsilon=\langle f,\xi^m\rangle.$$ Does $u_\varepsilon$ converge as $\varepsilon\to0$ in a suitable topology, and if so, does its limit solve the corresponding un... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750332-005",
"literature-status:open",
"owr-year:2023"
] | The existence and topology of the singular limit u_epsilon, together with passage of that limit to the original transport equations, remain unresolved in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2023/21",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | Let $u_\varepsilon$ be the unique weak solution of the viscosity-regularized transport equation $$-\varepsilon\Delta u_\varepsilon+Hu_\varepsilon+\alpha u_\varepsilon=\langle f,\xi^m\rangle.$$ Does $u_\varepsilon$ converge as $\varepsilon\to0$ in a suitable topology, and if so, does its limit solve the corresponding un... | It is an (by now) open question whether lim\varepsilon\to0 u\varepsilon exists (and in which topology) and, if the answer is positive, whether the limit solves the original transport equations. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,524 | OWR-13750332-006 | Reliability of Bone Mineral Density Imaging | Are bone-mineral-density measurements obtained by DXA or CT reliable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194](https://doi.org/10.4171/owr/2023/21)
## L... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750332-006",
"literature-status:partially-solved",
"owr-year:2023"
] | DXA remains the clinical reference with established thresholds, while quantitative CT can be reliable after calibration and validation but is not generally interchangeable with DXA. | [
{
"url": "https://iscd.org/official-positions-2023/",
"label": "ISCD official positions"
},
{
"url": "https://doi.org/10.1038/s41598-024-79985-w",
"label": "CT and DXA validation study"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/21 | null | null | null | Are bone-mineral-density measurements obtained by DXA or CT reliable? | Is BMD by DXA or CT reliable? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tomographic Inverse Problems: Mathematical Challenges and Novel Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/21, pp. 1105--1194 |
30,005,525 | OWR-13750333-002 | Rational-Point Counting Near Immersed Manifolds | Determine the asymptotic behavior of the rational-point counting function $N(M;Q,\delta)$ as $Q\to\infty$ and $\delta\to 0$ for compact immersed manifolds $M$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Sharp counting asymptotics are proved for important curvature and non-flatness classes, but the full joint limit Q to infinity and delta to zero without those hypotheses remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2022.108358",
"label": "compact-manifold asymptotic"
},
{
"url": "https://arxiv.org/abs/2310.03867",
"label": "non-flat manifold asymptotic"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | Determine the asymptotic behavior of the rational-point counting function $N(M;Q,\delta)$ as $Q\to\infty$ and $\delta\to 0$ for compact immersed manifolds $M$. | What can we say about the counting function N (M; Q, \delta) for Q \to \infty and \delta \to 0? Density of rational points near/on compact manifolds Damaris Schindler (joint work with Shuntaro Yamagishi) Group Actions and Harmonic Analysis in Number Theory 1233 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,526 | OWR-13750333-003 | Asymptotic Counting Near Curved Submanifolds | Let $M\subset\mathbb R^m$ be a bounded immersed submanifold with boundary and codimension $R$, satisfying appropriate curvature conditions. Prove $N(M;Q,\delta)\sim c_M\delta^RQ^{\dim M+1}$ whenever $\delta\geq Q^{-1/R+\epsilon}$ and $Q\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-003",
"literature-status:partially-solved",
"owr-year:2023"
] | The conjectured rational-point asymptotic is established in strong curvature regimes and in broad nowhere-completely-flat settings, but not for all compact manifolds and all conjectured delta ranges. | [
{
"url": "https://doi.org/10.1016/j.aim.2022.108358",
"label": "Schindler--Yamagishi theorem"
},
{
"url": "https://arxiv.org/abs/2310.03867",
"label": "recent rational-point theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | Let $M\subset\mathbb R^m$ be a bounded immersed submanifold with boundary and codimension $R$, satisfying appropriate curvature conditions. Prove $N(M;Q,\delta)\sim c_M\delta^RQ^{\dim M+1}$ whenever $\delta\geq Q^{-1/R+\epsilon}$ and $Q\to\infty$. | conjecture: Let M be a bounded immersed submanifold of RM with boundary. As above, let R = M − dim M. Suppose M satisfies ‘proper’ curvature conditions. Then there exists a constant cM > 0 depending only on M such that N (M; Q, \delta) \sim cM \delta R Qdim M+1 1 when \delta \geq Q− R +ǫ for some ǫ > 0 and Q \to \infty.... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,527 | OWR-13750333-006 | Discrete Spectrum for Nonlattice Quotients | For a nonlattice subgroup $\Gamma<G$, determine whether $L^2(\Gamma\backslash X)$ can contain a Laplace eigenfunction and whether $L^2(\Gamma\backslash G)$ can be non-tempered. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-006",
"literature-status:partially-solved",
"owr-year:2023"
] | In higher-rank settings the existence question is settled negatively for nonlattices through the bottom-spectrum theorem, while temperedness is proved for important Anosov classes; the full nonlattice classification and possible non-tempered cases remain open. | [
{
"url": "https://arxiv.org/abs/2304.14565",
"label": "bottom-spectrum theorem"
},
{
"url": "https://arxiv.org/abs/2202.06203",
"label": "temperedness theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | For a nonlattice subgroup $\Gamma<G$, determine whether $L^2(\Gamma\backslash X)$ can contain a Laplace eigenfunction and whether $L^2(\Gamma\backslash G)$ can be non-tempered. | (1) When Γ < G is not a lattice, can there exist any Laplace eigenfunction in L2 (Γ\X)? (2) Is there an example of a non-lattice Γ such that L2 (Γ\G) is non-tempered? Group Actions and Harmonic Analysis in Number Theory 1247 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,528 | OWR-13750333-009 | Periodic Minimizers in Compact Linear Domino Games | For a linear domino game $(\Sigma,T,s)$ with infinite compact topological symbol space $\Sigma$ and continuous size function $s$, must an average-size minimizer be periodic? Equivalently, construct a game for which no periodic sequence minimizes average size, or prove none exists. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-009",
"literature-status:open",
"owr-year:2023"
] | The periodicity question for a maximizer in the infinite Sigma setting is still posed as an open problem; no general existence or nonexistence theorem was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/22",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | For a linear domino game $(\Sigma,T,s)$ with infinite compact topological symbol space $\Sigma$ and continuous size function $s$, must an average-size minimizer be periodic? Equivalently, construct a game for which no periodic sequence minimizes average size, or prove none exists. | What if Σ is infinite? Can a maximizer be periodic? . Chaired by Jens Marklof. Notes taken by Paul Nelson. 2. Javier Fresán, Pseudopolynomial permutation approximation problem Let f \in Z[T ] be an irreducible polynomial of degree n whose Galois group is the full symmetric group Sd . Let 0 \leq k \leq n. The Chebotarev... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,529 | OWR-13750333-010 | Compatible Geodesic and Horocycle Symbolic Codings | Construct a symbolic coding of the geodesic flow on $\operatorname{PSL}_2(\mathbb Z)\backslash\mathbb H$ that recovers the gap statistics obtained from the corresponding horocycle-flow coding. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-010",
"literature-status:open",
"owr-year:2023"
] | Classical symbolic codings of modular geodesic flow exist, but a coding that reproduces the report's specified gap statistics has not been established. | [
{
"url": "https://doi.org/10.4171/owr/2023/22",
"label": "Oberwolfach problem report"
},
{
"url": "https://arxiv.org/abs/math/9707215",
"label": "classical modular coding"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | Construct a symbolic coding of the geodesic flow on $\operatorname{PSL}_2(\mathbb Z)\backslash\mathbb H$ that recovers the gap statistics obtained from the corresponding horocycle-flow coding. | Is there also a coding for the geodesic flow on PSL2 (Z)\H that gives the same? Why might we want to have this? There remain open questions in the setting of Jens and Matthew’s talks, so maybe a coding of the geodesic flow would allow one to combine these two approaches to give a different view on the same problem. conver... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,530 | OWR-13750333-011 | Ramanujan Bounds for Siegel Cusp-Form Coefficients | Let $F$ be a holomorphic Siegel Hecke cusp form of weight $k$ for $\operatorname{Sp}_4(\mathbb Z)$. Prove that some fixed $\delta>0$ satisfies $a(F,S)\ll_F\det(S)^{(k-1)/2-\delta}$ for every fundamental-discriminant form $S$, and ultimately prove $a(F,S)\ll_{F,\epsilon}\det(S)^{k/2-3/4+\epsilon}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-011",
"literature-status:partially-solved",
"owr-year:2023"
] | Power-saving sup-norm bounds are proved on each fixed compact set for degree-two Hecke--Maass forms, but the stronger global uniform bound asked for in the report remains unresolved. | [
{
"url": "https://arxiv.org/abs/1402.4635",
"label": "Blomer--Pohl theorem"
},
{
"url": "https://doi.org/10.1353/ajm.2016.0032",
"label": "published sup-norm paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | Let $F$ be a holomorphic Siegel Hecke cusp form of weight $k$ for $\operatorname{Sp}_4(\mathbb Z)$. Prove that some fixed $\delta>0$ satisfies $a(F,S)\ll_F\det(S)^{(k-1)/2-\delta}$ for every fundamental-discriminant form $S$, and ultimately prove $a(F,S)\ll_{F,\epsilon}\det(S)^{k/2-3/4+\epsilon}$. | Question 3. Show that there exists a fixed \delta > 0 so that for all S \in Λ0 , k−1 a(F, S) ≪F det(S) 2 −\delta . Feel free to assume any standard conjecture on L-functions (e.g., GRH), as well as any expected period identities. The current best known unconditional bound is due to Kohnen. Theorem 6 (Kohnen). We have k ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,531 | OWR-13750333-012 | Gap Distribution of Prime Multiples Modulo One | For irrational $\alpha$, determine the limiting distribution and possible sizes of the gaps between the points $p\alpha\bmod 1$ as $p$ ranges over primes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262](https://doi.org/10.4171/owr/2023/22)
## Literature review (checke... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750333-012",
"literature-status:partially-solved",
"owr-year:2023"
] | Walker proved that the primes fail metric Poissonian pair correlation, but the requested complete gap-length laws for prime and square subsequences remain unresolved. | [
{
"url": "https://doi.org/10.1112/S002557931700050X",
"label": "Walker theorem"
},
{
"url": "https://doi.org/10.4171/owr/2023/22",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/22 | null | null | null | For irrational $\alpha$, determine the limiting distribution and possible sizes of the gaps between the points $p\alpha\bmod 1$ as $p$ ranges over primes. | What does the gap length distribution look like? How about the gap lengths? • Maksym Radziwill: does it have to be primes, or we could look at squares? • Jens Marklof: see the theorem of Aled Walker. The question posed challenges us to break the k2 − 12 barrier assuming any standard conjectures one wishes to. Maksym Ra... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Group Actions and Harmonic Analysis in Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/22, pp. 1195--1262 |
30,005,532 | OWR-13750334-001 | Galkin–Usnich Floer-Potential Conjecture Fragment | conjecture (establishing that the Newton polygons of the Floer potentials are as predicted). A direct tropical translation of the original con- struction of Galkin was suggested by Galkin and Mikhalkin. The talk by Grigory Mikhalkin surveyed symplectic developments in the last decade and introduced more recent construc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322](https://doi.org/10.4171/owr/2023/23)
## Literature review (checked 2026-08-22)
**Status:... | 3 | partially_solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this workshop-introduction fragment refers broadly to the Galkin–Usnich conjecture but does not state its ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750334-001",
"literature-status:partially-solved",
"owr-year:2023"
] | Vianna proved the predicted Newton-polygon distinction and infinitely many non-Hamiltonian-isotopic tori in key cases, but the full Galkin--Usnich Floer-potential conjecture is not established. | [
{
"url": "https://doi.org/10.1112/jtopol/jtw002",
"label": "Vianna primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2023/23",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/23 | null | null | null | null | conjecture (establishing that the Newton polygons of the Floer potentials are as predicted). A direct tropical translation of the original con- struction of Galkin was suggested by Galkin and Mikhalkin. The talk by Grigory Mikhalkin surveyed symplectic developments in the last decade and introduced more recent construc... | unrecoverable | The official report confirms that this workshop-introduction fragment refers broadly to the Galkin–Usnich conjecture but does not state its full mathematical claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322 |
30,005,533 | OWR-13750334-003 | Patchworking and Twisted Real Quintics | Does Viro patchworking of the Newton polytope of a quintic in $\mathbb P^4$, with the rays on its two-dimensional faces assigned the same sign as the interior point, produce a real quintic diffeomorphic to the connected $(M-2)$ real quintic obtained by twisting the corresponding real Lagrangian torus fibration? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322](https://doi.org/10.4171/owr/2023/23)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,023 | 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-13750334-003",
"literature-status:open",
"owr-year:2023"
] | Matessi constructs an M-2 real quintic by twisting a real Calabi-Yau; the OWR report presents equality with patchworking as an unanswered question. | [
{
"url": "https://ems.press/content/serial-article-files/47020",
"label": "OWR 2023 23"
},
{
"url": "https://arxiv.org/abs/2302.05357",
"label": "Matessi"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/23 | null | null | null | Does Viro patchworking of the Newton polytope of a quintic in $\mathbb P^4$, with the rays on its two-dimensional faces assigned the same sign as the interior point, produce a real quintic diffeomorphic to the connected $(M-2)$ real quintic obtained by twisting the corresponding real Lagrangian torus fibration? | Does patchworking give the same real quintic? Figure 3. A divisor giving an (M − 2) real quintic (a hint). | 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 | Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322 |
30,005,534 | OWR-13750334-004 | Quadratically Enriched Tropical Curve Invariants | For all integers $a,b\geq0$, do the quadratically enriched tropical invariants satisfy $$N^{\mathbb A^1}_{a,a+b}=\sum_{k\geq0}\binom{b+2k}{k}N^{\mathbb A^1}_{\triangle,a-k,b+2k}?$$ Establish or disprove this identity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322](https://doi.org/10.4171/owr/2023/23)
## Literature review (checked 2026-08-22)
**Status:... | 3 | solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-11",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **solved (yes; follows from published theorems)**. E. Brugallé, Oberwolfach Report 23/2023, p. 1299, Conjecture 1: for all integers a, b ≥ 0, N^{A¹}(□\_{a,a+b}) = Σ\_{k≥0} C(b+2k, k) · N^{A¹}(△\_{a−k,b+2k}) in GW(k), for the quadratically enriched tropical invariants of rat... | [
"owr",
"oberwolfach-reports",
"OWR-13750334-004",
"literature-status:open",
"owr-year:2023"
] | The displayed quadratically enriched tropical relation is still presented as a conjecture; later correspondence and algorithmic results do not establish this exact identity. | [
{
"url": "https://ems.press/content/serial-article-files/47020",
"label": "OWR 2023 23"
},
{
"url": "https://arxiv.org/abs/2502.02569",
"label": "Jaramillo Puentes Markwig Pauli Röhrle"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/23 | null | null | null | For all integers $a,b\geq0$, do the quadratically enriched tropical invariants satisfy $$N^{\mathbb A^1}_{a,a+b}=\sum_{k\geq0}\binom{b+2k}{k}N^{\mathbb A^1}_{\triangle,a-k,b+2k}?$$ Establish or disprove this identity. | ically enriched tropical invariant for the corresponding toric surface and ample A1 divisor, that we denote by N∆ . Conjecture 1. For any integers a, b \geq 0, the quadratically enriched tropical in- A1 A1 variants N and N△ satisfy the following relations: X b + 2k A1 A1 N a,a+b = N△ . k a−k,b+2k k\geq0 An analogous co... | 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 | Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322 |
30,005,535 | OWR-13750334-005 | Tropical Corrections to P equals W on Mumford Curves | Does a $P=W$ phenomenon with a tropical correction occur in other non-Archimedean settings, such as Mumford curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322](https://doi.org/10.4171/owr/2023/23)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,023 | 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-13750334-005",
"literature-status:open",
"owr-year:2023"
] | The OWR report asks whether a tropical correction to P equals W exists for Mumford curves; no proof of such a phenomenon was found. | [
{
"url": "https://ems.press/content/serial-article-files/47020",
"label": "OWR 2023 23"
},
{
"url": "https://arxiv.org/abs/2303.03734",
"label": "P equals W for abelian varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/23 | null | null | null | Does a $P=W$ phenomenon with a tropical correction occur in other non-Archimedean settings, such as Mumford curves? | This raises a natural question whether a similar P = W phenomenon with a tropical correction occurs in other non-Archimedean situations, e.g. on a Mumford curve. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322 |
30,005,536 | OWR-13750334-006 | Tropical Curve Counts for Smooth Cubic Log Divisors | For a smooth cubic plane curve $E\subset\mathbb P^2$, construct a tropical space whose curve counts agree with logarithmic Gromov–Witten invariants of the pair $\mathbb P^2(\log E)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322](https://doi.org/10.4171/owr/2023/23)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,023 | 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-13750334-006",
"literature-status:open",
"owr-year:2023"
] | The report notes that changing from the toric boundary to a smooth cubic changes the logarithmic space and asks for a general tropical correspondence; that extension remains unproved. | [
{
"url": "https://ems.press/content/serial-article-files/47020",
"label": "OWR 2023 23"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/23 | null | null | null | For a smooth cubic plane curve $E\subset\mathbb P^2$, construct a tropical space whose curve counts agree with logarithmic Gromov–Witten invariants of the pair $\mathbb P^2(\log E)$. | What if we change the log divisor? Meta-theorem 1. Counting tropical curves in Rn yields in the same non-negative number as counting algebraic curves in a projective toric variety (when matching constraints, genus and degree). Proof: [B17, CFPU16, CJMR17, GM07, GPS10, G10, G18, GS22, IKS03, LR18, M05, M07, MR09, MR20, ... | 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 | Tropical Methods in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/23, pp. 1263--1322 |
30,005,537 | OWR-13750335-002 | Classification of Critical CR Yamabe Solutions | Classify positive solutions of the critical CR Yamabe equation on the Heisenberg group without assuming finite volume; obtain analogous classifications for fourth-order CR $Q$-curvature equations and for the $p$-Laplace equation on $\mathbb H^n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396](https://doi.org/10.4171/owr/2023/24)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750335-002",
"literature-status:partially-solved",
"owr-year:2023"
] | Recent work classifies positive solutions of the critical CR Yamabe equation on the Heisenberg group without the finite volume assumption, but the fourth order CR Q curvature and p Laplace questions remain open. | [
{
"url": "https://ems.press/content/serial-article-files/47017",
"label": "OWR 2023 24"
},
{
"url": "https://arxiv.org/abs/2512.22458",
"label": "Liu"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/24 | null | null | null | Classify positive solutions of the critical CR Yamabe equation on the Heisenberg group without assuming finite volume; obtain analogous classifications for fourth-order CR $Q$-curvature equations and for the $p$-Laplace equation on $\mathbb H^n$. | Could we delete the condition on finite volume in Jerison-Lee [6] theorem? How about the fourth order equations which is related to CR Q-curvature? How about the p-Laplace equation in H n ? 2Q q ∗ + 1 = Q−2 is the CR Sobolev embedding exponent [2]. For the equation (1) Q+2 with q = q ∗ = Q−2 , by the splendid work [6] ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396 |
30,005,538 | OWR-13750335-004 | Bergman-Kernel Asymptotics at Curvature-Vanishing Points | Establish a full pointwise asymptotic expansion of the Bergman kernel at curvature-vanishing points for semipositive line bundles in complex dimension greater than one. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396](https://doi.org/10.4171/owr/2023/24)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750335-004",
"literature-status:open",
"owr-year:2023"
] | The Riemann surface case is proved, but the corresponding expansion for semipositive line bundles in higher dimensions remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/47017",
"label": "OWR 2023 24"
},
{
"url": "https://doi.org/10.1007/s00208-023-02750-3",
"label": "Marinescu Savale"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/24 | null | null | null | Establish a full pointwise asymptotic expansion of the Bergman kernel at curvature-vanishing points for semipositive line bundles in complex dimension greater than one. | Here cj are sections of End(F ), and the leading term c0 (x) > 0 is given in terms of the Bergman kernel of a model Kodaira Laplacian on the tangent space at x. The problem of the expansion for semipositive line bundles is well known and largely unsolved, see [9, Problem 4.8]. Theorem 4 is the first instance where the ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396 |
30,005,539 | OWR-13750335-005 | Sharp Homogeneous Weights in Fractional Hardy Inequalities | In the sharp Hardy inequality for the fractional sub-Laplacian $\mathcal L_s$ on $\mathbb H^n$, replace the homogeneous weight $w_s(z,a)$ by $|(z,a)|^{2s}$ while retaining the sharp constant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396](https://doi.org/10.4171/owr/2023/24)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750335-005",
"literature-status:open",
"owr-year:2023"
] | The proposed replacement of the Heisenberg fractional Hardy weight by the homogeneous kernel weight is not proved in the cited report or the established fractional Hardy literature. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4050/OWR_2023_24.pdf?isAllowed=y&sequence=4",
"label": "OWR 2023 24"
},
{
"url": "https://arxiv.org/abs/1508.00714",
"label": "Roncal Thangavelu"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/24 | null | null | null | In the sharp Hardy inequality for the fractional sub-Laplacian $\mathcal L_s$ on $\mathbb H^n$, replace the homogeneous weight $w_s(z,a)$ by $|(z,a)|^{2s}$ while retaining the sharp constant. | We conjecture that in the above inequality we can replace ws (z, a) with |(z, a)|2s . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396 |
30,005,540 | OWR-13750335-006 | Singer’s Unobstructedness Conjecture for Anti-Self-Dual Four-Manifolds | Let $(M^4,g)$ be anti-self-dual. Prove that positivity of its Yamabe invariant implies $\ker D_g^*=\{0\}$, equivalently that $(M^4,g)$ is unobstructed. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396](https://doi.org/10.4171/owr/2023/24)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750335-006",
"literature-status:partially-solved",
"owr-year:2023"
] | Gover and Gursky prove unobstructedness under additional conformal and topological inequalities, but the full positive Yamabe Singer conjecture remains unproved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4050/OWR_2023_24.pdf?isAllowed=y&sequence=4",
"label": "OWR 2023 24"
},
{
"url": "https://doi.org/10.1515/crelle-2024-0028",
"label": "Gover Gursky"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/24 | null | null | null | Let $(M^4,g)$ be anti-self-dual. Prove that positivity of its Yamabe invariant implies $\ker D_g^*=\{0\}$, equivalently that $(M^4,g)$ is unobstructed. | The following conjecture is attributed to Singer: Conjecture 1. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Hypoelliptic Operators in Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/24, pp. 1323--1396 |
30,005,541 | OWR-13750336-001 | Fourier Restriction and Kakeya Incidence Conjectures | Many topics in contemporary Harmonic analysis, Geometric measure theory, and Ergodic theory are related to incidence problems. A prototypical example is the following: given a collection of narrow tubes in Euclidean space, or in some more exotic geometry, how often can the tubes come together to create “rich” intersec-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this is workshop-level motivation about incidence problems rather than a separately formulated conjecture.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-001",
"literature-status:open",
"owr-year:2023"
] | The extracted passage is an overview identifying Fourier restriction and Kakeya as outstanding incidence problems; their general conjectures remain open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | null | Many topics in contemporary Harmonic analysis, Geometric measure theory, and Ergodic theory are related to incidence problems. A prototypical example is the following: given a collection of narrow tubes in Euclidean space, or in some more exotic geometry, how often can the tubes come together to create “rich” intersec-... | unrecoverable | The official report confirms that this is workshop-level motivation about incidence problems rather than a separately formulated conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,542 | OWR-13750336-002 | Unspecified Harmonic Analysis Incidence Problem | problem . . . . . . . . . . . . . . . . . 1405 Balázs Bárány (joint with Roope Anttila and Antti Käenmäki) On the Assouad dimension of the Takagi function . . . . . . . . . . . . . . . . . . . 1407 Amir Algom (joint with Yuanyang Chang, Meng Wu and Yu-Liang Wu) Polynomial Fourier decay for smooth images of self-si... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extraction is a table-of-contents fragment and contains no mathematical problem. No separate clean statement is promoted, and the origin) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-002",
"literature-status:open",
"owr-year:2023"
] | The extracted value is a table of contents fragment rather than a well defined mathematical claim, so its resolution is unclear and is classified as open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | null | problem . . . . . . . . . . . . . . . . . 1405 Balázs Bárány (joint with Roope Anttila and Antti Käenmäki) On the Assouad dimension of the Takagi function . . . . . . . . . . . . . . . . . . . 1407 Amir Algom (joint with Yuanyang Chang, Meng Wu and Yu-Liang Wu) Polynomial Fourier decay for smooth images of self-si... | unrecoverable | The extraction is a table-of-contents fragment and contains no mathematical problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,543 | OWR-13750336-003 | Tomas–Stein Extremizers on the Circle | Are constant functions extremizers for the Tomas–Stein extension inequality $\lVert\widehat{f\sigma}\rVert_{L^6(\mathbb R^2)}\leq C\lVert f\rVert_{L^2(\sigma)}$ on the unit circle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-003",
"literature-status:partially-solved",
"owr-year:2023"
] | Becker proves the sharp inequality for functions localized near an antipodal pair, while the global constant extremizer conjecture remains open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://arxiv.org/abs/2304.02345",
"label": "Becker"
},
{
"url": "https://arxiv.org/abs/2002.05118",
"label": "Barker et al"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | Are constant functions extremizers for the Tomas–Stein extension inequality $\lVert\widehat{f\sigma}\rVert_{L^6(\mathbb R^2)}\leq C\lVert f\rVert_{L^2(\sigma)}$ on the unit circle? | on the space of antipodal functions in L2 (\sigma \times \sigma \times \sigma). Here we call a function on S 1 \times S 1 \times S 1 antipodal if it is even in each argument. Numerical computations of Barker, Thiele and Zorin-Kranich [1] verify that Q is positive semidefinite on the space of all antipodal functions wit... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,544 | OWR-13750336-004 | Favard Length and Lipschitz Graph Structure | Let $E\subset[0,1]^2$ be $1$-Ahlfors regular and define $\operatorname{Fav}(E)=\int_{S^1}\mathcal H^1(\pi_\theta(E))\,d\theta$. If $\operatorname{Fav}(E)\geq C>0$, must there exist a Lipschitz graph $\Gamma$ such that $\operatorname{Lip}(\Gamma)\lesssim_C1$ and $\mathcal H^1(E\cap\Gamma)\gtrsim_C1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-004",
"literature-status:partially-solved",
"owr-year:2023"
] | The full Favard length to Lipschitz graph statement remains conjectural; Dąbrowski proves a substantial special case for irregular direction sets. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://doi.org/10.1112/plms.70037",
"label": "Dąbrowski"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | Let $E\subset[0,1]^2$ be $1$-Ahlfors regular and define $\operatorname{Fav}(E)=\int_{S^1}\mathcal H^1(\pi_\theta(E))\,d\theta$. If $\operatorname{Fav}(E)\geq C>0$, must there exist a Lipschitz graph $\Gamma$ such that $\operatorname{Lip}(\Gamma)\lesssim_C1$ and $\mathcal H^1(E\cap\Gamma)\gtrsim_C1$? | Can this result be made quantitative? The following conjecture is wide open. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,545 | OWR-13750336-006 | General Kakeya Dimension Conjecture | Let $E\subset\mathbb R^n$, and let $D$ be the set of directions in which $E$ contains a unit line segment. If $D\neq\varnothing$, must $\dim_{\mathrm H}E\geq\dim_{\mathrm H}D+1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The conjecture is equivalent to the Kakeya conjecture and is known when the direction set has Hausdorff dimension at most one, but remains open in general. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://arxiv.org/abs/2203.15731",
"label": "Keleti Máthe"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | Let $E\subset\mathbb R^n$, and let $D$ be the set of directions in which $E$ contains a unit line segment. If $D\neq\varnothing$, must $\dim_{\mathrm H}E\geq\dim_{\mathrm H}D+1$? | conjecture: General Kakeya Conjecture. Let E be an arbitrary subset of Rn and let D be the set of directions in which E contains a line segment. If D 6= \varnothing then dimH E \geq dimH D + 1. By a result in [3] this conjecture holds if dimH D \leq 1. It is not hard to show using a projective transformation that the G... | 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 | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,546 | OWR-13750336-007 | Analytic Self-Maps and Automorphism Groups of Cantor Sets | For a Cantor set $X\subset\mathbb R$, characterize its real-analytic self-maps and the groups arising as subgroups of $\operatorname{Aut}_\omega(X)$. When is $\operatorname{Aut}_\omega(X)$ finitely generated? If $X\subset\mathbb R^d$ and every real-analytic submanifold $M$ has $M\cap X$ with empty interior in $X$, is t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-007",
"literature-status:open",
"owr-year:2023"
] | The listed extensions concerning maps and automorphism groups of Cantor sets are explicitly posed as open problems; the cited theorem proves only the basic countability result. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | For a Cantor set $X\subset\mathbb R$, characterize its real-analytic self-maps and the groups arising as subgroups of $\operatorname{Aut}_\omega(X)$. When is $\operatorname{Aut}_\omega(X)$ finitely generated? If $X\subset\mathbb R^d$ and every real-analytic submanifold $M$ has $M\cap X$ with empty interior in $X$, is t... | What can be said about the set of into (rather than onto) self- maps of a Cantor set X \subseteq R? The following related question was raised in [3], but remains open: Problem 3. What groups arise as [subgroups] if Aut\omega (X)? Is the analogue of Theorem 1 true for X \subseteq Rd and real-analytic maps, provided M \c... | 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 | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,547 | OWR-13750336-008 | Analytic Maps of Complex Cantor Sets | For Cantor sets $X,Y\subset\mathbb C$, is the set of analytic maps from a neighborhood of $X$ into $\mathbb C$ that send $X$ into $Y$ at most countable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-008",
"literature-status:open",
"owr-year:2023"
] | The analogue for complex Cantor sets and analytic maps is explicitly stated in the report to remain open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | For Cantor sets $X,Y\subset\mathbb C$, is the set of analytic maps from a neighborhood of $X$ into $\mathbb C$ that send $X$ into $Y$ at most countable? | Is the analogue of Theorem 1 true for Cantor sets X \subseteq C and analytic maps? It is possible that also the problem above becomes easier under the assumption that dim µ > 0 even this remains open. Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1425 | 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 | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,548 | OWR-13750336-009 | Equidistribution Rates for Semisimple Torus Random Walks | We ask whether νn converges in the weak-∗ topology to the Haar measure on Rd /Zd and how fast or how slow is that convergence. Semisimple linear random walks on the torus, II Weikun He (joint work with Nicolas de Saxcé) Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1431 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The motivating equidistribution question is answered immediately in the contribution by the two stated semisimple random-walk theorems. No s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-009",
"literature-status:partially-solved",
"owr-year:2023"
] | He and de Saxcé prove quantitative equidistribution for semisimple Zariski closure, but the broader random walk question with nondense orbits and general acting groups is not fully resolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://doi.org/10.1017/etds.2025.3",
"label": "He de Saxcé"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | null | We ask whether νn converges in the weak-∗ topology to the Haar measure on Rd /Zd and how fast or how slow is that convergence. Semisimple linear random walks on the torus, II Weikun He (joint work with Nicolas de Saxcé) Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1431 | unrecoverable | The motivating equidistribution question is answered immediately in the contribution by the two stated semisimple random-walk theorems. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,549 | OWR-13750336-010 | Rational Point Counts near Hypersurfaces | For a compact $C^1$ hypersurface $M\subset\mathbb R^n$, characterize the local obstructions to the uniform estimate $N_M(\delta,Q)\asymp\delta Q^n$ for $Q\geq1$ and $Q^{\varepsilon-1}<\delta<1/2$, where $N_M(\delta,Q)$ counts pairs $(q,p)\in\mathbb Z\times\mathbb Z^n$ with $Q\leq q<2Q$ and $\operatorname{dist}(p/q,M)\l... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-010",
"literature-status:partially-solved",
"owr-year:2023"
] | Sharp estimates are known for curved hypersurfaces and broad homogeneous classes, but arbitrary local obstructions and the general expected count remain unresolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://arxiv.org/abs/2305.01047",
"label": "Srivastava Technau"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | For a compact $C^1$ hypersurface $M\subset\mathbb R^n$, characterize the local obstructions to the uniform estimate $N_M(\delta,Q)\asymp\delta Q^n$ for $Q\geq1$ and $Q^{\varepsilon-1}<\delta<1/2$, where $N_M(\delta,Q)$ counts pairs $(q,p)\in\mathbb Z\times\mathbb Z^n$ with $Q\leq q<2Q$ and $\operatorname{dist}(p/q,M)\l... | How large should we expect Nf (\delta, Q) to be? Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1435 be the Hessian of f at x \in Rn−1 . If M is not locally flat, i.e. the Gaussian curvature det Hf (x) does not vanish for any x \in [−1, 1]n−1 , then (3) holds. In other words, uniform curvature i... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,550 | OWR-13750336-011 | $L^p$ Ranges for Radial Projection Estimates | Determine the optimal exponent range in mixed $L^p$ estimates for radial projections of Frostman measures, and find geometric applications in which that range improves the conclusion. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-011",
"literature-status:partially-solved",
"owr-year:2023"
] | The cited projection and mixed norm theorems establish important p ranges, but the proposed general improvement of radial projection estimates remains open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://arxiv.org/abs/2107.04471",
"label": "Dąbrowski Orponen Villa"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | Determine the optimal exponent range in mixed $L^p$ estimates for radial projections of Frostman measures, and find geometric applications in which that range improves the conclusion. | So a natural question is, does the range of p matter? Let \pie (x) = x \cdot e, x \in R2 , e \in S 1 , denote the orthogonal projection. One of the most classical results in geometric measure theory is the Marstrand projection theorem, which states that, for every Borel set E \subset R2 , dimH E > 1, the set \pie (E) \... | 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 | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,551 | OWR-13750336-012 | Pointwise Convergence of Multiple Ergodic Averages | For commuting invertible measure-preserving transformations $T_1,\ldots,T_d$ and bounded functions $f_1,\ldots,f_d$, do the averages $\frac1N\sum_{n=1}^N\prod_{k=1}^d f_k(T_k^n x)$ converge pointwise almost everywhere for every $d\geq2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-012",
"literature-status:open",
"owr-year:2023"
] | Norm convergence is known, including Tao's L2 theorem, but pointwise almost everywhere convergence for the stated multiple averages is still open for every d at least two. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
},
{
"url": "https://arxiv.org/abs/0707.1117",
"label": "Tao"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | For commuting invertible measure-preserving transformations $T_1,\ldots,T_d$ and bounded functions $f_1,\ldots,f_d$, do the averages $\frac1N\sum_{n=1}^N\prod_{k=1}^d f_k(T_k^n x)$ converge pointwise almost everywhere for every $d\geq2$? | Pointwise almost everywhere conver- gence of these multiple averages is not known for any d \geq 2 and remains a very interesting open question. For functions fk \in L (X), norm convergence in L2 (X) is known due to the work \infty | 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 | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,552 | OWR-13750336-013 | Endpoint Sparse Bounds for Planar Averaging Operators | conjecture. In our work we focus on the Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1445 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The extraction is a sentence fragment from the same Bochner–Riesz contribution whose complete open boundary-segment question is retained in ) | [
"OWR-13750336-014"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-013",
"literature-status:partially-solved",
"owr-year:2023"
] | Known results cover much of the planar sparse bound region and give conditional higher dimensional results, but the endpoint line segment identified in the report remains open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | null | conjecture. In our work we focus on the Incidence Problems in Harmon. Anal., Geom. Meas. Theory, Ergod. Theory 1445 | unrecoverable | The extraction is a sentence fragment from the same Bochner–Riesz contribution whose complete open boundary-segment question is retained in OWR-13750336-014. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,553 | OWR-13750336-014 | Boundary Sparse Bounds for Planar Bochner–Riesz Means | For $0<\lambda<1/2$, do the planar Bochner–Riesz means $R_t^\lambda$ satisfy every sparse bound $\operatorname{Sp}(p,q)$ whose reciprocal-exponent pair $(1/p,1/q)$ lies on the boundary segment $P_2P_3$ of the necessary-condition trapezoid $T_2(\lambda)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452](https://doi.org/10.4171/owr/2023/... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13750336-013"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750336-014",
"literature-status:open",
"owr-year:2023"
] | The report explicitly states that the sparse bound on the planar endpoint line segment remains open, and no later proof was found. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4055/OWR_2023_25.pdf?sequence=1",
"label": "OWR 2023 25"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/25 | null | null | null | For $0<\lambda<1/2$, do the planar Bochner–Riesz means $R_t^\lambda$ satisfy every sparse bound $\operatorname{Sp}(p,q)$ whose reciprocal-exponent pair $(1/p,1/q)$ lies on the boundary segment $P_2P_3$ of the necessary-condition trapezoid $T_2(\lambda)$? | This means that in two dimension we obtain the Sp(p, q) bound for Rt\lambda for all 1 1 ( p , q ) in T2 (\lambda)\ P2 P3 and it remains open what happens on the line segment P2 P3 . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Incidence Problems in Harmonic Analysis, Geometric Measure Theory, and Ergodic Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/25, pp. 1397--1452 |
30,005,554 | OWR-13750338-001 | Mathematical Conjecture Generation with Machine Intelligence | Develop machine-guided methods that discover useful bounds between hard matrix quantities and efficiently computable surrogates; characterize invariants of free-group actions on spaces of conjectures; and integrate conjecture-generation pipelines with formal proof assistants and natural-language representations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484](https://doi.org/10.... | 3 | open | null | 2,023 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750338-001",
"literature-status:open",
"owr-year:2023"
] | The paper establishes a conjecture space framework and toy generation experiments, but the extracted diameter conjecture and broader conjecture generation directions are not settled. | [
{
"url": "https://ems.press/content/serial-article-files/47019",
"label": "OWR 2023 26"
},
{
"url": "https://arxiv.org/abs/2306.07277",
"label": "Mishra Moulik Sarkar"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/26 | null | null | null | Develop machine-guided methods that discover useful bounds between hard matrix quantities and efficiently computable surrogates; characterize invariants of free-group actions on spaces of conjectures; and integrate conjecture-generation pipelines with formal proof assistants and natural-language representations. | conjecture (on diameters of Cayley graphs of non-abelian simple groups). We expect to study properties of Hermitian matrices such as Wigner matrices and local Hamiltonians (with applications to machine learning and quantum theory) in the future. One wishful application of such AI-driven inequality-discovery is to find ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484 |
30,005,555 | OWR-13750338-003 | Instance-Independent Drivers in Quantum Annealing | Extend the no-quantum-speedup theorem for the transverse-field driver to every instance-independent transverse Hamiltonian. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484](https://doi.org/10.... | 3 | open | null | 2,023 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750338-003",
"literature-status:open",
"owr-year:2023"
] | The cited work proves the negative result for the equal-superposition driver and explicitly leaves its extension to every instance-independent transverse Hamiltonian as a conjecture; no proof of that generalization was found. | [
{
"url": "https://doi.org/10.1088/1751-8121/ad0439",
"label": "Villanueva--Najafi--Kappen, Why adiabatic quantum annealing is unlikely to yield speed-up"
},
{
"url": "https://doi.org/10.4171/owr/2023/26",
"label": "Oberwolfach Report 26/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/26 | null | null | null | Extend the no-quantum-speedup theorem for the transverse-field driver to every instance-independent transverse Hamiltonian. | We conjecture that it is likely that this negative result also applies for any other instance independent transverse Hamiltonians. Why adiabatic quantum annealing is unlikely to yield quantum speed-up Bert Kappen | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484 |
30,005,556 | OWR-13750338-004 | Interoperable Virtual Laboratories for Scientific Simulation | Develop interoperable virtual laboratories that combine simulation methods across scientific fields and allow tools to be reused across distinct simulation environments. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484](https://doi.org/10.... | 3 | open | null | 2,023 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750338-004",
"literature-status:open",
"owr-year:2023"
] | This is a broad research-design question about combining tools across virtual laboratories, not a mathematically formulated theorem or conjecture with a demonstrated resolution in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2023/26",
"label": "Oberwolfach Report 26/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/26 | null | null | null | Develop interoperable virtual laboratories that combine simulation methods across scientific fields and allow tools to be reused across distinct simulation environments. | If we call the constellation of simulation tools a virtual laboratory, an important question is can we have better tools by combining strength across the different fields and developing tools usable across the different virtual laboratories. The report passage is retained verbatim as the relevant context for this extra... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Machine Learning for Science: Mathematics at the Interface of Data-driven and Mechanistic Modelling (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/26, pp. 1453--1484 |
30,005,557 | OWR-13750339-001 | Quasi-Modularity of Elliptic-Curve Stable-Map Classes | For the universal family $\pi:\mathcal E\to\overline{\mathcal M}_{1,1}$, prove the quasi-modularity of $\sum_{d=0}^\infty q^d[\overline{\mathcal M}_{g,n}(\pi,d)]^{\mathrm{vir}}$ as a cohomology-valued generating series. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,023 | 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-13750339-001",
"literature-status:open",
"owr-year:2023"
] | The moving-target analogue of the fixed-elliptic-target quasi-modularity theorem remains stated as a fundamental open question in the source report; only genus-two and genus-three calculations are cited as evidence. | [
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Pandharipande, Maps to a moving elliptic curve"
},
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Oberwolfach Report 27/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For the universal family $\pi:\mathcal E\to\overline{\mathcal M}_{1,1}$, prove the quasi-modularity of $\sum_{d=0}^\infty q^d[\overline{\mathcal M}_{g,n}(\pi,d)]^{\mathrm{vir}}$ as a cohomology-valued generating series. | A fundamental open question concerns the parallel claim for a moving elliptic target. Moduli spaces of genus g Hurwitz covers of CP1 yield cycles on the moduli space of genus g curves. The study of these classes is a very well-developed subject. Much less studied is the moduli space of Hurwitz covers of elliptic curves... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,558 | OWR-13750339-002 | Hodge Integrals over Genus-One Admissible Covers | For degree $d>2$, find a closed formula for the Hodge-integral generating series over admissible covers of a genus-one curve; identify the rational function of $q=-e^{iu}$ that it defines. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,023 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2506.12438",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (closed formula; unrefereed preprint)**. R. Pandharipande (OWR 27/2023, p. 1492, Question 2) asks for Σₙ u^{2n−1}/(2n−1)! ∫ λ_{n+1}λ_{n−1} over the admissible covers Adm₁^{n+1}((2)^{2n})_d of degree d > 2 of a genus-1 curve, as a rational function of q = −e^{iu} (d... | [
"owr",
"oberwolfach-reports",
"OWR-13750339-002",
"literature-status:open",
"owr-year:2023"
] | The higher-degree admissible-cover integral is known to be a rational function of q, but the source still asks for its closed form and no authoritative general formula resolving the extracted question was located. | [
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Pandharipande, Maps to a moving elliptic curve"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For degree $d>2$, find a closed formula for the Hodge-integral generating series over admissible covers of a genus-one curve; identify the rational function of $q=-e^{iu}$ that it defines. | Here, Admn+1 1 ((2)2n )d=2 is the moduli of admissible covers of degree 2 of a genus 1 curve with 2n simple branch points (so the domain has genus n + 1). Question 2: Can a closed form be found for the parallel integral over Admn+1 1 ((2)2n)d iu for higher d? The answer is known to be a rational function in q = −e , bu... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,559 | OWR-13750339-003 | Elliptic-Cover Cycles and the Gorenstein Kernel | Determine whether the cycles $\operatorname{Tor}^*[\operatorname{NL}_d]$ generated by elliptic-cover Noether–Lefschetz loci account for the entire Gorenstein kernel of $R^*(\mathcal M_g^{\mathrm{ct}})$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,023 | 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-13750339-003",
"literature-status:open",
"owr-year:2023"
] | The Gorenstein-kernel question is explicitly described as requiring a larger leap; the cited work proves that particular Torelli-pullback classes lie in the kernel but does not identify the whole kernel. | [
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Pandharipande, Maps to a moving elliptic curve"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | Determine whether the cycles $\operatorname{Tor}^*[\operatorname{NL}_d]$ generated by elliptic-cover Noether–Lefschetz loci account for the entire Gorenstein kernel of $R^*(\mathcal M_g^{\mathrm{ct}})$. | Question 3: Can we explain all of the Gorenstein kernel of R⋆ (Mgct ) using the cycles Tor∗ [NLd ]? While Questions 1 and 2 are likely solvable in some way using ideas not so far ahead of where we are in the field, Question 3 would require a larger leap. The moduli spaces of bi-elliptic curves determine non-tautologica... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,560 | OWR-13750339-004 | Vanishing Conjectures for Birational Cohomology of Projective Space | For every finite field $F$ of characteristic $p$ and every prime $\ell\neq p$, prove $H^{2i}(F_0\mathbb P_{\overline F}^n,\mathbb Q_\ell(i+1))^{G_F}=0$ and $H^{2i-1}(F_0\mathbb P_{\overline F}^n,\mathbb Q_\ell(i))^{G_F}=0$ for all $i,n\geq 2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,023 | 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-13750339-004",
"literature-status:open",
"owr-year:2023"
] | The primary 2026 paper proves equivalences reducing the Tate, Beilinson, and semisimplicity conjectures to vanishing of a birational invariant, but it does not prove that vanishing; the first open threefold cases therefore remain open. | [
{
"url": "https://doi.org/10.1007/s00029-026-01142-0",
"label": "Balkan--Schreieder, Cycle conjectures and birational invariants over finite fields"
},
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Oberwolfach Report 27/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For every finite field $F$ of characteristic $p$ and every prime $\ell\neq p$, prove $H^{2i}(F_0\mathbb P_{\overline F}^n,\mathbb Q_\ell(i+1))^{G_F}=0$ and $H^{2i-1}(F_0\mathbb P_{\overline F}^n,\mathbb Q_\ell(i))^{G_F}=0$ for all $i,n\geq 2$. | This corresponds to the first open cases of these conjectures, because the Beilinson conjecture is known for surfaces. 3. Results Our main results are as follows. Theorem 1. Let p be a prime. Then the following are equivalent: (1) Conjectures 1, 2, and 3 for all smooth projective varieties over finite fields of charact... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,561 | OWR-13750339-006 | Chow Vanishing for Lagrangian-Fibered Hyperkähler Varieties | Let $X$ be a projective hyperkähler variety of dimension $n$ with a Lagrangian fibration induced by $L$, and let $c_I(X)$ be a weighted polynomial of degree $2i$ in the even Chern classes. Prove $c_I(X)L^{n+1-k}=0$ in $\operatorname{CH}(X)_{\mathbb Q}$ whenever $i\geq k$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,023 | 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-13750339-006",
"literature-status:partially-solved",
"owr-year:2023"
] | Voisin proves the vanishing for individual even Chern classes and one additional LSV monomial, while the extracted conjecture asks for all weighted Chern-polynomial relations; the remaining monomial cases are not settled. | [
{
"url": "https://arxiv.org/abs/2305.09396",
"label": "Voisin, On Chern classes of Lagrangian fibered hyper-K\\\"ahler manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Oberwolfach Report 27/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | Let $X$ be a projective hyperkähler variety of dimension $n$ with a Lagrangian fibration induced by $L$, and let $c_I(X)$ be a weighted polynomial of degree $2i$ in the even Chern classes. Prove $c_I(X)L^{n+1-k}=0$ in $\operatorname{CH}(X)_{\mathbb Q}$ whenever $i\geq k$. | Conjecture 2. Let X, L be as above, with X projective hyper-Kähler of dimension n. Then for i \geq k, (2) cI (X)Ln+1−k = 0 in CH(X)Q ), where cI (X) \in CH(X) is any weighted polynomial of weighted degree 2i in the c2j (X) \in CH2j (X) (of degree 2j). We prove in [10] the following Theorem 2. Let X, L be as above, the... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,562 | OWR-13750339-007 | Cohomological Dimension of Stein Meromorphic Function Fields | For a Stein compact set $S$ of complex dimension $n$, prove that the meromorphic function field $\mathcal M(S)$ has cohomological dimension $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,023 | 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-13750339-007",
"literature-status:partially-solved",
"owr-year:2023"
] | The equality cd(M(S))=n is proved for connected normal Stein curves and, by Benoist's 2026 theorem, for Stein surfaces; the general n-dimensional question remains open for n\geq3. | [
{
"url": "https://doi.org/10.1515/crelle-2025-0071",
"label": "Benoist, On the field of meromorphic functions on a Stein surface"
},
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Benoist, On the field of meromorphic functions on a Stein compact set"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For a Stein compact set $S$ of complex dimension $n$, prove that the meromorphic function field $\mathcal M(S)$ has cohomological dimension $n$. | Is it true that cd(M(S)) = n? On the field of meromorphic functions on a Stein compact set Olivier Benoist | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,563 | OWR-13750339-008 | Chern and Degeneracy Classes of Coinvariant Bundles | For coinvariant bundles not arising from a cohomological field theory, compute their Chern classes; characterize when higher Chern classes are tautological or effective; realize extremal effective rays as first Chern classes; and determine degeneracy classes of natural maps between such bundles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,023 | 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-13750339-008",
"literature-status:open",
"owr-year:2023"
] | Primary work establishes coherence, factorization, vector-bundle cases, and tautological Chern classes under strong finiteness hypotheses, but the broader questions for non-CohFT-type coinvariant sheaves and effective or extremal classes remain open. | [
{
"url": "https://arxiv.org/abs/2307.03767",
"label": "Damiolini--Gibney--Krashen, Conformal blocks on smoothings via mode transition algebras"
},
{
"url": "https://arxiv.org/abs/1910.01658",
"label": "Damiolini--Gibney--Tarasca, Vertex algebras of CohFT-type"
},
{
"url": "https://doi.or... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For coinvariant bundles not arising from a cohomological field theory, compute their Chern classes; characterize when higher Chern classes are tautological or effective; realize extremal effective rays as first Chern classes; and determine degeneracy classes of natural maps between such bundles. | One may also ask: Can one find Chern classes of associated bundles (in this more general setting where V is not of CohFT-type) and determine when the higher Chern classes are tautological? What are sufficient conditions ensuring the Chern classes are effective? Can one realize the infinitely many extremal rays of the e... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,564 | OWR-13750339-011 | Stability of Brill–Noether Triples | Prove that all but finitely many Brill–Noether triples $(d,g,r)$ with $g\geq 2$ are stable; more strongly, classify the exceptional triples and prove stability for every other triple in characteristic zero. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,023 | 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-13750339-011",
"literature-status:partially-solved",
"owr-year:2023"
] | The stability conjecture remains open, but current primary work proves stability outside finitely many triples for each r and substantially enlarges the known stable and semistable ranges. | [
{
"url": "https://arxiv.org/abs/2602.03944",
"label": "Coskun--Larson--Vogt, Stability of natural bundles on curves"
},
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Coskun--Larson--Vogt, Stability of normal bundles of curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | Prove that all but finitely many Brill–Noether triples $(d,g,r)$ with $g\geq 2$ are stable; more strongly, classify the exceptional triples and prove stability for every other triple in characteristic zero. | Conjecture 1. [CLV22, Conjecture 1.1] All but finitely many BN triples (d, g, r) with g \geq 2 are stable. In fact, one may conjecture that except for the triples in Examples 1 and 2, every BN triple with g \geq 2 is stable (at least in characteristic 0). The following two theorems provide evidence for the conjecture. ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,565 | OWR-13750339-012 | Manin Components of Section Spaces of Fano Fibrations | For a Fano fibration $\pi:X\to B$, prove uniqueness of the nonpathological component of $\operatorname{Sec}(X/B,\alpha)$ for every sufficiently positive section class $\alpha$, and prove homological or motivic stability of these Manin components as degree grows. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | open | null | 2,023 | 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-13750339-012",
"literature-status:open",
"owr-year:2023"
] | The extracted entry is a description of Manin's conjecture rather than a proof claim; the conjecture has many verified special families but remains open in general for Fano varieties over number fields. | [
{
"url": "https://doi.org/10.4171/owr/2023/27",
"label": "Tanimoto, From exceptional sets to non-free sections"
},
{
"url": "https://doi.org/10.1007/s00208-024-02854-4",
"label": "Frei--Loughran--Sofos, Density of rational points on some quadric bundle threefolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For a Fano fibration $\pi:X\to B$, prove uniqueness of the nonpathological component of $\operatorname{Sec}(X/B,\alpha)$ for every sufficiently positive section class $\alpha$, and prove homological or motivic stability of these Manin components as degree grows. | Manin’s conjecture is a conjetural asymptotic formula for the counting function of rational points of bounded height on a smooth Fano variety defined over a number field. Next let us explain what we mean by pathological components in GMC (1). A key definition to this is freeness of sections: Definition 2. Let \pi : X \... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,566 | OWR-13750339-013 | Logarithmic Hilbert Schemes for Divisor-Stratified Varieties | For a smooth projective variety $Y$ with a simple-normal-crossings divisor $D$, construct and characterize a logarithmic Hilbert scheme encoding how subschemes meet $D$ and its strata. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542](https://doi.org/10.4171/owr/2023/27)
## Literature review (checked 2026-08-22)
**... | 3 | partially_solved | null | 2,023 | 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-13750339-013",
"literature-status:partially-solved",
"owr-year:2023"
] | Kennedy-Hunt constructs the logarithmic Hilbert/Quot moduli problem and proves foundational separatedness, properness, boundedness, and tropicalization results, but the broad effect of D on the classical Hilbert scheme is not a single fully settled classification. | [
{
"url": "https://arxiv.org/abs/2308.14470",
"label": "Kennedy-Hunt, The logarithmic Quot space: foundations and tropicalisation"
},
{
"url": "https://arxiv.org/abs/2508.08175",
"label": "Kennedy-Hunt--Ranganathan, Logarithmic Quot spaces, boundedness, and K-tropicalizations"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/27 | null | null | null | For a smooth projective variety $Y$ with a simple-normal-crossings divisor $D$, construct and characterize a logarithmic Hilbert scheme encoding how subschemes meet $D$ and its strata. | How does the presence of D affect the Hilbert scheme Hilb(Y )? The Hilbert scheme in logarithmic geometry, after Kennedy-Hunt Dhruv Ranganathan | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Recent Trends in Algebraic Geometry (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/27, pp. 1485--1542 |
30,005,567 | OWR-13750341-001 | Unspecified P-Adic Euler System Conjecture | conjecture. Note that the case k2 = 2 is allowed here, unlike the previous theorem. When k2 \geq 3 we have a relation between Euler systems and p-adic L-functions: Theorem 3 (L.–Zerbes). If k2 \geq 3, then for every 1 \leq j \leq k2 − 2, the value Lp (F )(j) is related to the Euler system for VF∗ (1−j) via a p-adic reg... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extraction begins with the trailing word of a Bloch–Kato reference and then states proved Euler-system and regulator theorems; it contai) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-001",
"literature-status:open",
"owr-year:2023"
] | The extracted statement is only the word `conjecture' and does not identify a mathematical assertion; under the required uncertainty rule it cannot be classified as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Oberwolfach Report 28/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | null | conjecture. Note that the case k2 = 2 is allowed here, unlike the previous theorem. When k2 \geq 3 we have a relation between Euler systems and p-adic L-functions: Theorem 3 (L.–Zerbes). If k2 \geq 3, then for every 1 \leq j \leq k2 − 2, the value Lp (F )(j) is related to the Euler system for VF∗ (1−j) via a p-adic reg... | unrecoverable | The extraction begins with the trailing word of a Bloch–Kato reference and then states proved Euler-system and regulator theorems; it contains no new standalone conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,568 | OWR-13750341-002 | Unspecified Abelian Surface BSD Conjecture | conjecture. In the CM case, Rubin proved this converse theorem in the p-ordinary case (i.e. p is split in the quadratic imaginary field K) under the assumption that the p-part of the Shafarevich-Tate is finite. Recently Burungale-Tian removed 5. Applications to BSD Perhaps the most interesting weight is (2, 2), since thi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extraction joins the end of a proved Gross–Zagier converse discussion to an abelian-surface BSD application theorem, without stating a s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-002",
"literature-status:open",
"owr-year:2023"
] | The extracted fragment does not identify which conjecture is being discussed; the surrounding report records several conditional and case-specific results, so the exact incomplete claim remains unresolved for triage. | [
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Oberwolfach Report 28/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | null | conjecture. In the CM case, Rubin proved this converse theorem in the p-ordinary case (i.e. p is split in the quadratic imaginary field K) under the assumption that the p-part of the Shafarevich-Tate is finite. Recently Burungale-Tian removed 5. Applications to BSD Perhaps the most interesting weight is (2, 2), since thi... | unrecoverable | The extraction joins the end of a proved Gross–Zagier converse discussion to an abelian-surface BSD application theorem, without stating a separate open conjecture. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,569 | OWR-13750341-003 | Algebraicity of Endoscopic Tate Classes | Do all endoscopic Tate classes in the middle-degree cohomology of products $S_K(\operatorname{GSp}_4)\times X_0(N)$ arise from algebraic cycles, including the classes attached to non-generic members of endoscopic $L$-packets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 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-13750341-003",
"literature-status:partially-solved",
"owr-year:2023"
] | Sweeting proves that a natural algebraic cycle gives exactly the generic endoscopic Tate classes and constructs Hodge-cycle realizations in the non-generic case, but algebraicity of those non-generic classes remains open. | [
{
"url": "https://arxiv.org/abs/2211.10838",
"label": "Sweeting, Tate classes and endoscopy for GSp(4) over totally real fields"
},
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Sweeting, Tate classes and endoscopy for GSp4"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Do all endoscopic Tate classes in the middle-degree cohomology of products $S_K(\operatorname{GSp}_4)\times X_0(N)$ arise from algebraic cycles, including the classes attached to non-generic members of endoscopic $L$-packets? | The main question of this talk is when these classes arise from algebraic cycles, as predicted by the Tate conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,570 | OWR-13750341-004 | Nonvanishing Statistics of Twisted Central L-Values | Fix a modular form $f$ of weight $k\geq2$ and an integer $d\geq1$. If $K_d(X)$ is the set of primitive Dirichlet characters of order $d$ and conductor at most $X$, what is the asymptotic behavior of $\#\{\chi\in K_d(X):L(f,\chi,k/2)\neq0\}$ as $X\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-004",
"literature-status:open",
"owr-year:2023"
] | The requested asymptotic for nonvanishing twists is not known in general; Goldfeld's 50-percent prediction is still conjectural, although recent horizontal p-adic methods give strong lower bounds and special-case progress. | [
{
"url": "https://arxiv.org/abs/2310.20678",
"label": "Kriz--Nordentoft, Horizontal p-adic L-functions"
},
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Kriz, Horizontal p-adic L-functions with applications to L-values"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Fix a modular form $f$ of weight $k\geq2$ and an integer $d\geq1$. If $K_d(X)$ is the set of primitive Dirichlet characters of order $d$ and conductor at most $X$, what is the asymptotic behavior of $\#\{\chi\in K_d(X):L(f,\chi,k/2)\neq0\}$ as $X\to\infty$? | One version of this question is the following. What is the asymptotic behavior of \#\{χ \in Kd (X) : L(f, χ, k/2) 6= 0\} as X \to \infty? L(f, s) = L(E, s)), this question is addressed by Goldfeld’s conjecture [3]: when ordering quadratic χ by conductor, the order of vanishing ords=1 L(f, χ, s) is 0 for 50\% of such χ ... | 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 | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,571 | OWR-13750341-005 | Eisenstein Maps and Modular Symbols in Cyclotomic K-Theory | Let $I$ be the Eisenstein ideal and let $\widetilde\Pi$ and $\Pi$ be the modular-symbol maps in the cyclotomic K-theory construction. Is $\widetilde\Pi$ Eisenstein, meaning $\widetilde\Pi\circ T=0$ for every $T\in I$? Is $\Pi\bmod I$ an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-005",
"literature-status:partially-solved",
"owr-year:2023"
] | The Eisenstein property is proved in substantial ranges, including away from the level and, after inverting 3, for the cyclotomic map, while the asserted isomorphism modulo the Eisenstein ideal remains conjectural. | [
{
"url": "https://doi.org/10.1112/S0010437X24007322",
"label": "Sharifi--Venkatesh, Eisenstein cocycles in motivic cohomology"
},
{
"url": "https://arxiv.org/abs/2504.19125",
"label": "Lecouturier--Sharifi--Shih--Wang, Eisenstein cocycles for imaginary quadratic fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Let $I$ be the Eisenstein ideal and let $\widetilde\Pi$ and $\Pi$ be the modular-symbol maps in the cyclotomic K-theory construction. Is $\widetilde\Pi$ Eisenstein, meaning $\widetilde\Pi\circ T=0$ for every $T\in I$? Is $\Pi\bmod I$ an isomorphism? | conjecture: Conjecture 1. The map Π̃ is Eisenstein, i.e., Π̃ ◦ T = 0 for all T \in I. Moreover, I expect that Π mod I is an isomorphism. In a 2012 preprint [2], Fukaya and Kato proved an earlier form of the conjecture (see [5]), as well a result towards the latter statement. Theorem 1 (Fukaya-Kato). The conjecture hold... | 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 | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,572 | OWR-13750341-006 | Eisenstein Maps from Bianchi Homology to K2 | Does there exist an Eisenstein map $\Pi:H_1(\widetilde X_1(N),\mathbb Z')\to K_2(\mathcal O(N))\otimes\mathbb Z'$ that extends from homology relative to the non-infinity cusps and sends each Cremona symbol $[u:v]$ to the corresponding Steinberg symbol? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-006",
"literature-status:partially-solved",
"owr-year:2023"
] | The 2025 primary paper constructs the Bianchi-space to K\_2 map and proves its Eisenstein property away from the level after controlled localization, but the exact integral all-level formulation in the extracted question is not fully established. | [
{
"url": "https://arxiv.org/abs/2504.19125",
"label": "Lecouturier--Sharifi--Shih--Wang, Eisenstein cocycles for imaginary quadratic fields"
},
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Sharifi, Eisenstein cocycles for imaginary quadratic fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Does there exist an Eisenstein map $\Pi:H_1(\widetilde X_1(N),\mathbb Z')\to K_2(\mathcal O(N))\otimes\mathbb Z'$ that extends from homology relative to the non-infinity cusps and sends each Cremona symbol $[u:v]$ to the corresponding Steinberg symbol? | Does there exist an Eisenstein map Π : H1 (X̃1 (N ), Z′ ) \to K2 (O(N )) ⊗ Z′ that is the restriction of a map Π̃ on homology relative to non-infinty cusps that takes the Cremona symbol [u : v] to the Steinberg symbol \{\thetaE (cP ), \thetaE (dP )\}? In work in progress, we nevertheless show that the answer to our ques... | 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 | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,573 | OWR-13750341-007 | Nontriviality of Heegner-Point Kolyvagin Systems | For an elliptic curve $E/\mathbb Q$, an odd prime $p$ of good ordinary reduction, and an admissible imaginary quadratic field $K$, is the Kolyvagin system $\{\kappa_n\}_{n\in\mathcal N}$ derived from Heegner points nontrivial; equivalently, does $\kappa_n\neq0$ for some square-free product $n$ of admissible inert prime... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-007",
"literature-status:open",
"owr-year:2023"
] | The fragment `the first major progress towards this conjecture is due to W.' does not identify the conjecture or a complete claim, so no determinate solved or disproved status can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "Oberwolfach Report 28/2023"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | For an elliptic curve $E/\mathbb Q$, an odd prime $p$ of good ordinary reduction, and an admissible imaginary quadratic field $K$, is the Kolyvagin system $\{\kappa_n\}_{n\in\mathcal N}$ derived from Heegner points nontrivial; equivalently, does $\kappa_n\neq0$ for some square-free product $n$ of admissible inert prime... | The first major progress towards this conjecture is due to W. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,574 | OWR-13750341-010 | Steinness of Local Shimura Varieties | Is every local Shimura variety a Stein space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-010",
"literature-status:open",
"owr-year:2023"
] | Hansen's Steinness conjecture for arbitrary local Shimura varieties remains unresolved; the literature establishes special cases such as Lubin--Tate, Drinfeld, and selected ordinary or reducible settings, not the general assertion. | [
{
"url": "https://www.davidrenshawhansen.net/middlev2.pdf",
"label": "Hansen"
},
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Is every local Shimura variety a Stein space? | A recent conjecture of Hansen, [10, Conjecture 1.10], suggests that any local Shimura variety is a Stein space, therefore Theorem 3 potentially applies to any such variety. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,575 | OWR-13750341-011 | Poincaré Duality for Pro-Étale Cohomology of Stein Varieties | Let $X$ be a smooth geometrically irreducible Stein variety over $K$. Are $H^i_{\mathrm{pro\acute et}}(X,\mathbb{Q}_p(j))$ nuclear Fréchet spaces and $H^i_{\mathrm{pro\acute et},c}(X,\mathbb{Q}_p(j))$ spaces of compact type? Does the cup-product pairing give perfect duality between ordinary and compactly supported pro-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606](https://doi.org/10.4171/owr/2023/28)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,023 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13750341-011",
"literature-status:partially-solved",
"owr-year:2023"
] | The higher-dimensional pro-etale cohomology conjecture is not proved in full generality, but recent work establishes comparison and duality results in stable ranges and conditional forms, extending the known curve cases. | [
{
"url": "https://arxiv.org/abs/2501.13651",
"label": "Achinger--Gilles--Nizioł"
},
{
"url": "https://arxiv.org/abs/2412.11786",
"label": "arithmetic duality"
},
{
"url": "https://doi.org/10.4171/owr/2023/28",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/28 | null | null | null | Let $X$ be a smooth geometrically irreducible Stein variety over $K$. Are $H^i_{\mathrm{pro\acute et}}(X,\mathbb{Q}_p(j))$ nuclear Fréchet spaces and $H^i_{\mathrm{pro\acute et},c}(X,\mathbb{Q}_p(j))$ spaces of compact type? Does the cup-product pairing give perfect duality between ordinary and compactly supported pro-... | where D(−, Qp ) := RHomQp (−, Qp ). Having that, we get the quasi-isomorphism \gammaX,i above by taking cohomol- ogy and using the fact that Exts (Hproét,c i (X, Qp (j)), Qp ) = 0, s \geq 1, because i Hproét,c (X, Qp (j)) is of compact type (hence a colimit of Smith spaces, which are c i projective solid objects). Th... | 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 | Algebraische Zahlentheorie (2023), Oberwolfach Reports, DOI 10.4171/owr/2023/28, pp. 1543--1606 |
30,005,576 | OWR-14297732-001 | Geometric Analysis Table-of-Contents Fragment | Conjecture . . . . . 1627 Ronan J. Conlon (joint with Richard Bamler, Charles Cifarelli, and Alix Deruelle) Two-dimensional shrinking gradient Kähler-Ricci solitons . . . . . . . . . . . . 1628 Hokuto Konno (joint with Jianfeng Lin) Seiberg-Witten theory and moduli spaces of 4-manifolds and metrics . . . 1631 Christos... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this record is a table-of-contents fragment rather than a mathematical question. No separate clean stateme) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-001",
"literature-status:open",
"owr-year:2023"
] | The extracted record is a table-of-contents fragment and does not state a determinate mathematical conjecture, so no resolution can be established from the record; it is conservatively classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | null | Conjecture . . . . . 1627 Ronan J. Conlon (joint with Richard Bamler, Charles Cifarelli, and Alix Deruelle) Two-dimensional shrinking gradient Kähler-Ricci solitons . . . . . . . . . . . . 1628 Hokuto Konno (joint with Jianfeng Lin) Seiberg-Witten theory and moduli spaces of 4-manifolds and metrics . . . 1631 Christos... | unrecoverable | The official report confirms that this record is a table-of-contents fragment rather than a mathematical question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,577 | OWR-14297732-002 | Einstein Metrics Table-of-Contents Fragment | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1653 Tristan Ozuch (joint with Claude LeBrun) Holonomy of limits of Einstein 4-manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 1656 Shuli Chen Morse index of minimal surfaces in R3 and the half-space . . . . . . . . . . . . 1657 ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this record is a continuation of the table of contents rather than a mathematical question. No separate cl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-002",
"literature-status:open",
"owr-year:2023"
] | The extracted record is only a conjecture heading followed by table-of-contents material and does not identify a mathematical claim whose status can be checked; it is therefore conservatively open. | [
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1653 Tristan Ozuch (joint with Claude LeBrun) Holonomy of limits of Einstein 4-manifolds . . . . . . . . . . . . . . . . . . . . . . . . . 1656 Shuli Chen Morse index of minimal surfaces in R3 and the half-space . . . . . . . . . . . . 1657 ... | unrecoverable | The official report confirms that this record is a continuation of the table of contents rather than a mathematical question. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,578 | OWR-14297732-004 | Finite Generation of Fundamental Groups Under Nonnegative Ricci Curvature | Let $(M^n,g)$ be a smooth complete Riemannian manifold with $\operatorname{Ric}_g\geq0$. Must $\pi_1(M)$ be finitely generated when $n\in\{4,5,6\}$? In arbitrary dimension, must $\pi_1(M)$ be finitely generated if one additionally assumes, respectively, that $g$ is Ricci-flat, that $(M,g)$ is Kähler, or that the univer... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-004",
"literature-status:open",
"owr-year:2023"
] | The unrestricted Milnor conjecture is disproved, but the extracted Ricci-flat, Kahler, and Euclidean-volume-growth questions are not fully resolved; known results require additional tangent-cone or geometric hypotheses. | [
{
"url": "https://annals.math.princeton.edu/2025/201-1/p04",
"label": "Bruè--Naber--Semola"
},
{
"url": "https://arxiv.org/abs/1710.05498",
"label": "Ricci curvature stability"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | Let $(M^n,g)$ be a smooth complete Riemannian manifold with $\operatorname{Ric}_g\geq0$. Must $\pi_1(M)$ be finitely generated when $n\in\{4,5,6\}$? In arbitrary dimension, must $\pi_1(M)$ be finitely generated if one additionally assumes, respectively, that $g$ is Ricci-flat, that $(M,g)$ is Kähler, or that the univer... | Apart from the obvious open question about the validity of Milnor’s conjecture in dimensions 4, 5, and 6, the following remain open: Question 1. Does Milnor’s conjecture hold for Ricci flat manifolds? Does Milnor’s conjecture hold for Kähler manifolds with Ric \geq 0? Does Milnor’s conjecture hold under the additional... | 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 | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,579 | OWR-14297732-006 | Symplectic Structures and Einstein Metrics | For which additional four-manifolds can a symplectic structure reveal information about the existence or structure of Einstein metrics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-006",
"literature-status:open",
"owr-year:2023"
] | This is a broad exploratory question about whether symplectic structures expose further information about Einstein metrics; no general theorem resolving it was identified. | [
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | For which additional four-manifolds can a symplectic structure reveal information about the existence or structure of Einstein metrics? | Are there other 4-manifolds where a symplectic structure helps reveal something about Einstein metrics? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,580 | OWR-14297732-007 | Flow Limits of Local Mass Invariants | How does $\lim_{r\to\infty}M_C^0(g,\Phi,\varphi_r,r)$ relate to Huisken's isoperimetric mass and Jauregui's isocapacitary mass? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-007",
"literature-status:partially-solved",
"owr-year:2023"
] | The C0 local mass is identified with ADM mass in the smooth asymptotically flat setting, and recent work relates the isoperimetric and isocapacitary masses, but a general direct identification with the C0 flow limit remains open. | [
{
"url": "https://arxiv.org/abs/2208.14550",
"label": "Burkhardt--Guim"
},
{
"url": "https://arxiv.org/abs/2511.11155",
"label": "Benatti"
},
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | How does $\lim_{r\to\infty}M_C^0(g,\Phi,\varphi_r,r)$ relate to Huisken's isoperimetric mass and Jauregui's isocapacitary mass? | How does limr\to\infty MC 0 (g, Φ, ϕr , r) relate to Huisken’s isoperimetric mass [7, Definition 11] and Jauregui’s isocapacitary mass [8, Definition 4]? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,581 | OWR-14297732-008 | Doubling and Homotopy of Positive Scalar Curvature Metrics | Is the Doubling Conjecture always true? What is the homotopy type of the space of positive-scalar-curvature metrics on a compact manifold with boundary when one imposes either product-type boundary behavior or the corresponding mean-convex boundary condition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-008",
"literature-status:open",
"owr-year:2023"
] | The doubling conjecture is proved in dimension three and under a split fundamental-group condition, but the general conjecture and the accompanying homotopy-type question remain unresolved. | [
{
"url": "https://arxiv.org/abs/2201.01263",
"label": "Rosenberg--Weinberger"
},
{
"url": "https://arxiv.org/abs/2604.12901",
"label": "Frenck"
},
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | Is the Doubling Conjecture always true? What is the homotopy type of the space of positive-scalar-curvature metrics on a compact manifold with boundary when one imposes either product-type boundary behavior or the corresponding mean-convex boundary condition? | Open Problems (1) Is the Doubling Conjecture always true? Note that in this case, M = Dbl(X, \partialX) = Y \times S 1 does admit a psc metric, so our Theorem 1 about obstructions to product-type boundary conditions definitely fails in this case. (2) What can one say about the homotopy type of the space of psc metrics ... | 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 | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,582 | OWR-14297732-009 | Ricci Flow Uniqueness from Metric Space Initial Data | For two Ricci flows converging locally to the same metric space as $t\to0$, what regularity assumptions on the limiting metric ensure a common gauge in which the flows can be effectively compared and remain close for small time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | partially_solved | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-009",
"literature-status:partially-solved",
"owr-year:2023"
] | Stability results now give effective comparison for Ricci flows from Reifenberg and locally bi-Lipschitz initial spaces under additional curvature hypotheses, but the broader regularity-and-uniqueness problem in the record remains open. | [
{
"url": "https://wrap.warwick.ac.uk/id/eprint/190769/",
"label": "Deruelle--Schulze--Simon"
},
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | For two Ricci flows converging locally to the same metric space as $t\to0$, what regularity assumptions on the limiting metric ensure a common gauge in which the flows can be effectively compared and remain close for small time? | problem: Problem 1. Let (Min , gi (t))t\in(0,T ) , i = 1, 2 be two smooth, connected (possibly incomplete) Ricci flows satisfying (1) and (2) and converging locally to the same metric space, up to an isometry as t tends to 0, that is: limt\to0 d(g1 (t)) = d0,1 on Up,1 limt\to0 d(g2 (t)) = d0,2 , on Up,2 and \psi0 (Up,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 | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,583 | OWR-14297732-011 | Desingularization of Kähler–Einstein Metrics | Can every singular Kähler–Einstein metric be desingularized by Einstein four-manifolds, possibly using Einstein metrics that are not Kähler? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-011",
"literature-status:open",
"owr-year:2023"
] | General desingularization of Kahler--Einstein orbifolds by Einstein four-manifolds is not settled; known obstruction results and conditional Hermitian or anti-self-dual gluing theorems do not prove the asserted universal statement. | [
{
"url": "https://doi.org/10.1002/cpa.22129",
"label": "Ozuch"
},
{
"url": "https://arxiv.org/abs/2601.19215",
"label": "LeBrun--Ozuch"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | Can every singular Kähler–Einstein metric be desingularized by Einstein four-manifolds, possibly using Einstein metrics that are not Kähler? | The natural question is then: Can any Kähler-Einstein singular metric be desingularized by Einstein 4-manifolds? Can this still be achieved by Einstein metrics that are not necessarily Kähler, [And10]? Holonomy of limits of Einstein 4-manifolds Tristan Ozuch (joint work with Claude LeBrun) | 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 | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,584 | OWR-14297732-013 | Degrees of Asymptotically Conical Expanders Under Connected Sum | How are $\deg_{\exp}(X_1)$, $\deg_{\exp}(X_2)$, and $\deg_{\exp}(X_1\#_\partial X_2)$ related, and what is $\deg_{\exp}(D^3\times S^1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670](https://doi.org/10.4171/owr/2023/29)
## Literature review (checked 2026-08-22)
**Sta... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297732-013",
"literature-status:open",
"owr-year:2023"
] | The degree of asymptotically conical expanders under connected sum remains posed as an open question in later reports, and no computation of degexp of D3 times S1 or general connected-sum law was identified. | [
{
"url": "https://doi.org/10.4171/owr/2023/29",
"label": "original OWR report"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/0157a756-a5e7-48ad-abe4-dcc06bc0796f/download",
"label": "later OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/29 | null | null | null | How are $\deg_{\exp}(X_1)$, $\deg_{\exp}(X_2)$, and $\deg_{\exp}(X_1\#_\partial X_2)$ related, and what is $\deg_{\exp}(D^3\times S^1)$? | Is there any relation between the degrees degexp (X1 ), degexp (X2 ), and degexp (X1 \#\partial X2 )? What is degexp (D3 \times S 1 )? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Differentialgeometrie im Grossen (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/29, pp. 1617--1670 |
30,005,585 | OWR-14297733-002 | Abundance of Zoll Flows in Hamiltonian Systems | Characterize how abundant Zoll flows are within natural classes of Hamiltonian systems, including geodesic and magnetic flows on the two-torus. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730](https://doi.org/10.4171/owr/2023/30)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297733-002",
"literature-status:partially-solved",
"owr-year:2023"
] | An infinite-dimensional family of Zoll magnetic systems on the two-torus has been constructed near the flat or constant-field examples, substantially answering abundance in that class, while the broader Hamiltonian and geodesic-flow question remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2024.109826",
"label": "Asselle--Benedetti--Berti"
},
{
"url": "https://arxiv.org/abs/1909.13821",
"label": "Asselle--Benedetti"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/30 | null | null | null | Characterize how abundant Zoll flows are within natural classes of Hamiltonian systems, including geodesic and magnetic flows on the two-torus. | For this reason, a natural question is to understand how abundant Zoll flows are within a given class of Hamiltonian systems, e.g., among geodesic flows, magnetic Zoll magnetic systems on the two-torus: a Nash–Moser approach Gabriele Benedetti (joint work with Luca Asselle, Massimiliano Berti) | 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 (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730 |
30,005,586 | OWR-14297733-003 | Birkhoff Sections for Three-Dimensional Reeb Flows | Does every three-dimensional Reeb vector field admit a Birkhoff section? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730](https://doi.org/10.4171/owr/2023/30)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297733-003",
"literature-status:open",
"owr-year:2023"
] | An open dense set of three-dimensional contact forms admits Birkhoff sections, but whether every three-dimensional Reeb vector field admits one remains unanswered and no counterexample is known. | [
{
"url": "https://arxiv.org/abs/2202.01506",
"label": "Colin--Dehornoy--Hryniewicz--Rechtman"
},
{
"url": "https://arxiv.org/abs/2501.11725",
"label": "generic Reeb-flow sections"
},
{
"url": "https://doi.org/10.4171/owr/2023/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/30 | null | null | null | Does every three-dimensional Reeb vector field admit a Birkhoff section? | The obvious open question is: are there 3D Reeb vector fields that do not admit a Birkhoff section? 3. Comments on Theorem 2. A Birkhoff section allows to change the study of a 3D flow, to the study of the dynamics of a 2D diffeomorphism or homeomorphism, that is a priory a simpler problem. In [3], we used the existenc... | 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 (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730 |
30,005,587 | OWR-14297733-004 | Uniform Long-Time Sobolev Bounds for Nonlinear Beam Equations | Are we able to prove that f (t) = cǫ, for some absolute constant c? \psitt + \psixxxx + m\psi + f (\psi) = 0, x \in T = R/2\piZ (beam) \psi = \psi(x, t), m \in [1, 2] where the nonlinearity is given by f (\psi) := \partial\psi F (\psi), F being real analytic in the neighborhood of the origin and such that F (0) = 0, an... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730](https://doi.org/10.4171/owr/2023/30)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The long-time Sobolev-bound question is followed immediately by the contribution's stability theorem, which supplies the requested constant ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297733-004",
"literature-status:partially-solved",
"owr-year:2023"
] | Feola and Massetti prove a uniform O epsilon Sobolev bound, with constant 8, for a long sub-exponential time interval and almost every mass parameter, but the unrestricted absolute-constant bound asked in the record is not established. | [
{
"url": "https://doi.org/10.1016/j.jde.2023.01.038",
"label": "Feola--Massetti"
},
{
"url": "https://doi.org/10.4171/owr/2023/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/30 | null | null | null | null | Are we able to prove that f (t) = cǫ, for some absolute constant c? \psitt + \psixxxx + m\psi + f (\psi) = 0, x \in T = R/2\piZ (beam) \psi = \psi(x, t), m \in [1, 2] where the nonlinearity is given by f (\psi) := \partial\psi F (\psi), F being real analytic in the neighborhood of the origin and such that F (0) = 0, an... | unrecoverable | The long-time Sobolev-bound question is followed immediately by the contribution's stability theorem, which supplies the requested constant multiple of the initial norm on the stated time scale. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Dynamische Systeme (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730 |
30,005,588 | OWR-14297733-005 | Spatially Periodic Reaction-Diffusion Patterns and Homoclinic Entropy | For reaction–diffusion systems on $\mathbb R^m$ with $m>1$, can the complexity theorem for stationary, asymptotically spatially periodic solutions with localized defects be extended from one spatial dimension? Do symmetric homoclinic tangles involving multi-parameter families of periodic orbits always have positive top... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730](https://doi.org/10.4171/owr/2023/30)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297733-005",
"literature-status:open",
"owr-year:2023"
] | The record itself states that the higher-dimensional stationary spatially periodic reaction-diffusion question and the associated entropy question remain open, with no later resolution identified. | [
{
"url": "https://doi.org/10.4171/owr/2023/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/30 | null | null | null | For reaction–diffusion systems on $\mathbb R^m$ with $m>1$, can the complexity theorem for stationary, asymptotically spatially periodic solutions with localized defects be extended from one spatial dimension? Do symmetric homoclinic tangles involving multi-parameter families of periodic orbits always have positive top... | Can a similar result be obtained for stationary in time and asymptotically spatially-periodic solutions of reaction-diffusion systems defined for x \in Rm with m > 1? This question is open. The question of whether symmetric homoclinic tangles involving such families of periodic orbits always yield positive topological ... | 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 (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/30, pp. 1671--1730 |
30,005,589 | OWR-14297734-001 | Wave Amplification of Upper Ocean Currents | Can waves amplify upper-ocean currents? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Transport and Scale Interactions in Geophysical Flows (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/31, pp. 1731--1788](https://doi.org/10.4171/owr/2023/31)
## Literature review (check... | 3 | open | null | 2,023 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297734-001",
"literature-status:open",
"owr-year:2023"
] | Whether waves amplify currents in the broad upper-ocean setting is an active research question; the extracted record gives a motivating physical problem rather than a resolved mathematical claim. | [
{
"url": "https://doi.org/10.4171/owr/2023/31",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/31 | null | null | null | Can waves amplify upper-ocean currents? | Can waves amplify currents? SWOT: A wonderful new era of upper ocean physics Darryl Holm (joint work with Albert Dombret, Ruiao Hu and Oliver D. Street) Transport and Scale Interactions in Geophysical Flows 1753 | 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 | Transport and Scale Interactions in Geophysical Flows (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/31, pp. 1731--1788 |
30,005,590 | OWR-14297735-001 | Regularity of Weak Hamiltonian-Minimal Legendrian Surfaces | Prove that every weak solution of the Hamiltonian-minimal equation arising from Legendrian area variation is a smooth branched Legendrian immersion away from isolated Schoen–Wolfson conical singularities of nonzero Maslov class. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842](https://doi.org/10.4171/owr/2023/32)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297735-001",
"literature-status:open",
"owr-year:2023"
] | The conjecture remains explicitly stated in the primary paper: recent variational and partial-regularity results establish important special cases, but do not prove the asserted regularity for every weak Hamiltonian-minimal solution. | [
{
"url": "https://doi.org/10.1007/s42543-024-00090-y",
"label": "Riviere"
},
{
"url": "https://arxiv.org/abs/2405.06955",
"label": "variational theory"
},
{
"url": "https://doi.org/10.4171/owr/2023/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/32 | null | null | null | Prove that every weak solution of the Hamiltonian-minimal equation arising from Legendrian area variation is a smooth branched Legendrian immersion away from isolated Schoen–Wolfson conical singularities of nonzero Maslov class. | We conjecture that any solution to this equation is a smooth branched Legendrian immersion away from isolated Schoen-Wolfson conical singularities with non zero Maslov class. On the fine structure of the two-phase free boundaries Bozhidar Velichkov (joint work with Guido De Philippis, Luca Spolaor) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842 |
30,005,591 | OWR-14297735-005 | Rigidity and Symmetry of Steady Ricci Solitons | Prove that two three-dimensional flying-wing steady gradient Ricci solitons with the same asymptotic cone angle are isometric up to rescaling; determine whether $O(2)$-symmetry holds for three-dimensional ancient Ricci flows and higher-dimensional positive-curvature steady solitons, and whether all noncollapsed four-di... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842](https://doi.org/10.4171/owr/2023/32)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297735-005",
"literature-status:open",
"owr-year:2023"
] | Lai proved existence of three-dimensional flying wings for every cone angle and established their symmetry, but uniqueness for a fixed angle modulo rescaling remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2023/32",
"label": "Oberwolfach Report 32"
},
{
"url": "https://arxiv.org/abs/2207.02714",
"label": "Lai primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/32 | null | null | null | Prove that two three-dimensional flying-wing steady gradient Ricci solitons with the same asymptotic cone angle are isometric up to rescaling; determine whether $O(2)$-symmetry holds for three-dimensional ancient Ricci flows and higher-dimensional positive-curvature steady solitons, and whether all noncollapsed four-di... | Conjecture 1. If two 3D flying wings have the same asymptotic cone angle, then they are isometric modulo rescalings. It is also interesting to see whether the O(2)-symmetry holds for 3D ancient Ricci flows, as well as higher dimensional steady gradient solitons with positive curvature operator. In dimension 4, one can a... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842 |
30,005,592 | OWR-14297735-006 | Classification of Noncollapsed Four-Dimensional Steady Solitons | Prove that the only noncollapsed four-dimensional steady gradient Ricci solitons with nonnegative curvature operator are the Bryant soliton and the $\mathbb Z_2\times O(3)$-symmetric family, and that every soliton in the latter family has a ray as its blow-down. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842](https://doi.org/10.4171/owr/2023/32)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297735-006",
"literature-status:open",
"owr-year:2023"
] | The Bryant and constructed Z2 times O3 families are known, and several four-dimensional classifications hold under extra asymptotic or curvature-decay hypotheses, but the stated unrestricted noncollapsed classification and blow-down assertion remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2023/32",
"label": "Oberwolfach Report 32"
},
{
"url": "https://arxiv.org/abs/2403.19627",
"label": "Four-dimensional partial classification"
},
{
"url": "https://arxiv.org/abs/2505.20576",
"label": "Law uniqueness theorem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/32 | null | null | null | Prove that the only noncollapsed four-dimensional steady gradient Ricci solitons with nonnegative curvature operator are the Bryant soliton and the $\mathbb Z_2\times O(3)$-symmetric family, and that every soliton in the latter family has a ray as its blow-down. | Conjecture 2. The only non-collapsed steady gradient solitons with non-negative curvature operator are the 4D Bryant soliton, and the family of Z2 \timesO(3)-symmetric solitons I constructed in [5]. Moreover, the blow-down of each of the Z2 \times O(3)- symmetric soliton is a ray. It is also interesting to see whether ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842 |
30,005,593 | OWR-14297735-007 | Genus Monotonicity and Klein-Bottle Willmore Minimizers | Is the minimum of the Willmore functional among orientable surfaces of fixed genus monotone in the genus? Also prove that $\widetilde\tau_{3,1}$ is the unique Willmore minimizer among all Klein bottles. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842](https://doi.org/10.4171/owr/2023/32)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297735-007",
"literature-status:open",
"owr-year:2023"
] | Existence of fixed-genus minimizers is known, but monotonicity of the minimum with genus and uniqueness of the Lawson bipolar Klein bottle among all competitors remain conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2023/32",
"label": "Oberwolfach Report 32"
},
{
"url": "https://arxiv.org/abs/1606.04745",
"label": "Klein-bottle primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/32 | null | null | null | Is the minimum of the Willmore functional among orientable surfaces of fixed genus monotone in the genus? Also prove that $\widetilde\tau_{3,1}$ is the unique Willmore minimizer among all Klein bottles. | Further results and open problems are: • For every (orientable) genus g \geq 1 and every n \geq 3 there is a smooth minimizer fgn : Σg \to Rn which attains the infimum of the Willmore functional among all competitors of the same genus [15, 1]. A weaker, but still open questions is: Is the minimum of W among surfaces wit... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842 |
30,005,594 | OWR-14297735-008 | Vectorial Allen–Cahn Limits Without Energy Convergence | Prove convergence of the vectorial Allen–Cahn equation to a De Giorgi solution of multiphase mean-curvature flow without assuming convergence of the energies. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842](https://doi.org/10.4171/owr/2023/32)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,023 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297735-008",
"literature-status:open",
"owr-year:2023"
] | The report explicitly identifies unconditional convergence as open; later special-purpose numerical convergence results do not establish the general statement represented by this extracted record. | [
{
"url": "https://doi.org/10.4171/owr/2023/32",
"label": "Oberwolfach Report 32"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/32 | null | null | null | Prove convergence of the vectorial Allen–Cahn equation to a De Giorgi solution of multiphase mean-curvature flow without assuming convergence of the energies. | Unconditional convergence, however, remains a challenging open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Partial Differential Equations (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/32, pp. 1789--1842 |
30,005,595 | OWR-14297736-001 | Spectral-Geometry Workshop Overview | Last but not least, there were three open problem sessions: on emerging topics (orga- nized by Pavel Exner), on spectral optimization (organized by Pedro Freitas) and on eigenfunctions (organized by Dan Mangoubi). A summary of most important open problems that were presented at this conference is included in the presen... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a workshop summary and open-session introduction, not a standalone mathematical problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-001",
"literature-status:open",
"owr-year:2023"
] | This record is a conference-level statement that an open-problem summary exists, not a resolved mathematical assertion; the associated problem list remains unresolved as a whole. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | null | Last but not least, there were three open problem sessions: on emerging topics (orga- nized by Pavel Exner), on spectral optimization (organized by Pedro Freitas) and on eigenfunctions (organized by Dan Mangoubi). A summary of most important open problems that were presented at this conference is included in the presen... | unrecoverable | The official report confirms that this extraction is a workshop summary and open-session introduction, not a standalone mathematical problem. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,596 | OWR-14297736-002 | Geometric Bounds for Magnetic-Laplacian Ground States | Determine sharp relationships between the first magnetic Neumann eigenvalue and planar-domain geometry for constant magnetic fields and Aharonov–Bohm potentials. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-002",
"literature-status:open",
"owr-year:2023"
] | The relation between the first magnetic-Laplacian eigenvalue and domain geometry is posed as a natural research question in the source report, with no general resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Determine sharp relationships between the first magnetic Neumann eigenvalue and planar-domain geometry for constant magnetic fields and Aharonov–Bohm potentials. | As in the case of the Laplacian, a natural question is to study the relation be- tween the first eigenvalue and the geometry of the domain. Geometric aspects of the ground state of magnetic Laplacians on domains of the plane Bruno Colbois (joint work with C. Léna, L. Provenzano and A. Savo) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,597 | OWR-14297736-003 | Three Magnetic-Laplacian Optimization Problems | Determine the maximal domain for the second magnetic Neumann eigenvalue with Aharonov–Bohm flux; prove that a disk maximizes the constant-field ground state among simply connected domains of fixed area; and determine the ground-state asymptotics as an Aharonov–Bohm pole approaches the boundary. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-003",
"literature-status:open",
"owr-year:2023"
] | The second-eigenvalue problem, the simply connected constant-curvature ground-state comparison, and the punctured-domain asymptotic are explicitly left open in the primary report; no later complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Determine the maximal domain for the second magnetic Neumann eigenvalue with Aharonov–Bohm flux; prove that a disk maximizes the constant-field ground state among simply connected domains of fixed area; and determine the ground-state asymptotics as an Aharonov–Bohm pole approaches the boundary. | If ν 6\in Z, the equality holds if and only if Ω = Ω∗ This result leads to natural questions: Open question: what about the second eigenvalue? Regarding the isoperimetric inequality for the ground state \lambdaN 1 (Ω, \beta), the natural question is to compare with the ground state \lambdaN1 (Ω ∗ , \beta) of the disk Ω... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,598 | OWR-14297736-004 | de Gennes Bound for Magnetic Neumann Eigenvalues | For every bounded smooth planar domain $\Omega$ and constant magnetic field $\beta$, prove $\lambda_1^N(\Omega,\beta)\leq\Theta_0\beta$, where $\Theta_0$ is the de Gennes constant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-004",
"literature-status:open",
"owr-year:2023"
] | The proposed De Gennes upper bound for the magnetic Neumann ground state is still open even for the disk according to the primary report, and no proof or counterexample resolving that exact claim was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://doi.org/10.1016/j.jmaa.2025.129261",
"label": "Magnetic Laplacian on the disc"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For every bounded smooth planar domain $\Omega$ and constant magnetic field $\beta$, prove $\lambda_1^N(\Omega,\beta)\leq\Theta_0\beta$, where $\Theta_0$ is the de Gennes constant. | However Open question: do we have \lambdaN 1 (Ω, \beta) \leq Θ0 \beta where Θ0 is the De Gennes constant (Θ0 \sim 0, 590106.) Even for the disc, the question is open. and if \beta\delta 2 \geq 1, \lambdaN 1 (Ω, \beta) \geq C\beta. with C universal. Note that the estimate is good in terms of \beta: s \beta \to 0, the as... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,599 | OWR-14297736-005 | Heat-Content Asymptotics for Polyhedra and Other Planar Domains | Determine small-time heat-content asymptotics for broader classes of planar domains and for polyhedra in $\mathbb R^3$, including the exact angle contributions, and determine how much the first three asymptotic terms distinguish planar domains. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-005",
"literature-status:open",
"owr-year:2023"
] | The precise angular contribution is posed as an unresolved spectral-geometric question in the report, and the checked literature does not supply a general answer. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Determine small-time heat-content asymptotics for broader classes of planar domains and for polyhedra in $\mathbb R^3$, including the exact angle contributions, and determine how much the first three asymptotic terms distinguish planar domains. | What is the precise contribution from the angles? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,600 | OWR-14297736-006 | Conformal Spinorial Eigenvalue Infimum on the Torus | For the trivial spin structure on the torus $T$, prove $\inf_{g\in[g_{a,b}]}\overline\mu_1(g)=2\pi/\sqrt b$ when $b>\pi$ and equals $2\sqrt\pi$ when $b\leq\pi$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-006",
"literature-status:open",
"owr-year:2023"
] | The stated threshold conjecture for minimizers in the trivial spin structure is presented as Conjecture 3; the existence and bubbling dichotomy at the threshold remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For the trivial spin structure on the torus $T$, prove $\inf_{g\in[g_{a,b}]}\overline\mu_1(g)=2\pi/\sqrt b$ when $b>\pi$ and equals $2\sqrt\pi$ when $b\leq\pi$. | We conjecture that for the trivial spin structure, the bound b \geq \pi is the best possible for the existence of minimisers, and if b < \pi then we have no minimal metric and the formation of a bubble. Considering Ammann’s existence result, our conjecture is Conjecture 3. The report passage is retained verbatim as the... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,601 | OWR-14297736-007 | Dimension-Free Neumann Eigenvalue-Ratio Bounds | For every bounded convex domain $\Omega$ and every $k$, prove a dimension-free bound $\mu_{k+1}(\Omega)\lesssim\mu_k(\Omega)$; find an analytic proof; and extend the universal eigenvalue-ratio bound to convex domains in manifolds of nonnegative Ricci curvature. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-007",
"literature-status:open",
"owr-year:2023"
] | Known quantitative Neumann eigenvalue inequalities for convex domains do not prove the conjectured adjacent-eigenvalue bound, and the requested analytic proof remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://nms.kcl.ac.uk/jean.lagace/papers/Hom_Control.pdf",
"label": "Lagace primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For every bounded convex domain $\Omega$ and every $k$, prove a dimension-free bound $\mu_{k+1}(\Omega)\lesssim\mu_k(\Omega)$; find an analytic proof; and extend the universal eigenvalue-ratio bound to convex domains in manifolds of nonnegative Ricci curvature. | How about the opposite of the inequality (1)? In [7, 8] I conjectured that (3) µk+1 (Ω) . µk (Ω) for any bounded convex domain Ω and any k. Is there analytic proof for (4) or (3)? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,602 | OWR-14297736-008 | Exact Bases with Exponential-Polyhomogeneous Asymptotics | For generalized semiclassical ordinary differential operators $P_h=\sum_{k=0}^mC_k(x,h)\partial_x^k$, prove that $\ker P_h$ has a basis of exact solutions with the same exponential-polyhomogeneous asymptotics as the corresponding quasimodes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-008",
"literature-status:open",
"owr-year:2023"
] | The existence of an actual solution basis with the prescribed quasimode asymptotics is stated as a conjecture; the checked source provides no proof. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For generalized semiclassical ordinary differential operators $P_h=\sum_{k=0}^mC_k(x,h)\partial_x^k$, prove that $\ker P_h$ has a basis of exact solutions with the same exponential-polyhomogeneous asymptotics as the corresponding quasimodes. | We conjecture that there is a basis of actual solutions of P u = 0 having the same asymptotic behavior as the quasimodes that we construct. however. We call a function u on the interior of the manifold with boundary I \times [0, h0 ) exponential-polyhomogeneous if it is smooth and \infty X \delta h\to0 (4) u = eϕ(x)/h ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,603 | OWR-14297736-009 | Fourier Coefficients of Inhomogeneous Automorphic Laplace Equations | For solutions of $(\Delta-r(r+1))f=E_aE_b$ on $\operatorname{PSL}_2(\mathbb Z)\backslash\mathbb H$, compute all Fourier coefficients and evaluate the divisor-correlation sums occurring in them. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-009",
"literature-status:open",
"owr-year:2023"
] | The record asks for exact Fourier coefficients and arithmetic information about the displayed divisor-sum expressions; the primary report leaves this as an open question. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For solutions of $(\Delta-r(r+1))f=E_aE_b$ on $\operatorname{PSL}_2(\mathbb Z)\backslash\mathbb H$, compute all Fourier coefficients and evaluate the divisor-correlation sums occurring in them. | Can we recover its Fourier coefficients? • It turns out that Fourier coefficients of f include sums of the type X hn − n n1 i 2 1 (3) \sigma0 (n1 )\sigma0 (n2 ) log +2 n n2 n1 ,n2 \inZ\\{0\} n1 +n2 =n for any given n \in N. That leads to the second question: what can we say about values of the sums? | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,604 | OWR-14297736-010 | Bessel-Function Solutions of Inhomogeneous Laplace Equations | For every admissible tuple $(r,a,b)$, prove existence of Fourier-mode solutions expressed through modified Bessel functions, find closed formulas for their Laurent-polynomial coefficients, and relate the solution space to differential Galois theory. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-010",
"literature-status:open",
"owr-year:2023"
] | The proposed link between the constructed Bessel-type equations and differential Galois theory is explicitly described as an open problem, with no complete treatment located. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For every admissible tuple $(r,a,b)$, prove existence of Fourier-mode solutions expressed through modified Bessel functions, find closed formulas for their Laurent-polynomial coefficients, and relate the solution space to differential Galois theory. | Additionally, establishing a connection to the differential Galois theory would be an interesting open problem. where for η \in C, Iη and Kη denote the modified Bessel function of the first and second kind of index η, respectively, and where q i,j = qni,j1 ,n2 ,\lambda,\alpha,\beta and µi,j = µi,j n1 ,n2 ,\lambda,\alph... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,605 | OWR-14297736-011 | Removing Complementary-Cap Restrictions for Spherical Neumann Eigenvalues | For domains in $S^2$ of area at most half the sphere, prove that a spherical cap maximizes the second Neumann eigenvalue without assuming that the competing domain lies outside a complementary cap. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-011",
"literature-status:partially-solved",
"owr-year:2023"
] | Spherical caps maximize the first positive Neumann eigenvalue for simply connected domains through 94 percent of the sphere, but the extension beyond 94 percent remains open; rigorous counterexamples are known only for multiply connected domains. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://arxiv.org/abs/2305.11090",
"label": "Langford and Laugesen primary article"
},
{
"url": "https://arxiv.org/abs/2503.15385",
"label": "Bucur et al. counterexample"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | For domains in $S^2$ of area at most half the sphere, prove that a spherical cap maximizes the second Neumann eigenvalue without assuming that the competing domain lies outside a complementary cap. | Is the second Neumann eigenvalue maximal for a spherical cap, among subdo- mains of the 2-sphere with specified area? Yes for simply connected subdomains with area up to 94\% of the the sphere (it is an open problem to try to get up to 100\%), and also yes for arbitrary subdomains with area at most half that of the sph... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,606 | OWR-14297736-012 | Spherical Neumann-Eigenvalue Context | What shape maximizes µ2 (Ω)? We fix the area of Ω and ask: 1. For which free membrane is the ground tone highest? 2. For which insulated shape does heat equilibrate fastest? Both questions are in fact asking: what shape maximizes µ2 (Ω)? The answer is the domain with maximal symmetry, that is, a disk, by the Szegő–Wei... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is explanatory material duplicated by the adjacent complete open problems.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-012",
"literature-status:partially-solved",
"owr-year:2023"
] | The disk is the Euclidean simply connected optimizer by the Szego-Weinberger theorem and spherical-cap results hold under restrictions, but the unrestricted curved or multiply connected shape-optimization problem has no single resolved optimizer. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://arxiv.org/abs/2503.15385",
"label": "Bucur et al. counterexample"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | null | What shape maximizes µ2 (Ω)? We fix the area of Ω and ask: 1. For which free membrane is the ground tone highest? 2. For which insulated shape does heat equilibrate fastest? Both questions are in fact asking: what shape maximizes µ2 (Ω)? The answer is the domain with maximal symmetry, that is, a disk, by the Szegő–Wei... | unrecoverable | The official report confirms that this extraction is explanatory material duplicated by the adjacent complete open problems. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,607 | OWR-14297736-013 | Unrestricted Spherical-Cap Maximization of the Second Neumann Eigenvalue | Prove that among all simply connected domains of any prescribed area in $S^2$, a spherical cap maximizes the second Neumann eigenvalue. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-013",
"literature-status:open",
"owr-year:2023"
] | The 94-percent theorem is known, but the conjectured improvement to all simply connected domains remains open; the 2025 counterexample paper explicitly leaves the simply connected range above 94 percent unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://arxiv.org/abs/2503.15385",
"label": "Bucur et al. counterexample and open problems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Prove that among all simply connected domains of any prescribed area in $S^2$, a spherical cap maximizes the second Neumann eigenvalue. | Conjecture 1. The previous theorem can be improved from 0.94 to 1.00, so that the spherical cap maximizes µ2 among simply connected domains of any given area. One approach would be to find a way to use certain qualitative information that is currently discarded in the proof. 2066 Oberwolfach Report 36/2023 Figure 1. Co... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,608 | OWR-14297736-015 | Spherical Robin-Eigenvalue Maximization Beyond Known Regimes | Prove spherical-cap maximality of the second Robin eigenvalue for hyperbolic domains with positive Robin parameter and in the regime where the cap's second eigenfunction is radial. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-015",
"literature-status:open",
"owr-year:2023"
] | The source identifies parameter regions where the existing method does not apply and treats the corresponding maximality question as open; no general replacement argument was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Prove spherical-cap maximality of the second Robin eigenvalue for hyperbolic domains with positive Robin parameter and in the regime where the cap's second eigenfunction is radial. | Open problem: the method is Not Applicable for hyperbolic do- mains with positive Robin parameter (2nd quadrant) or where the 2nd eigenfunction of the cap is radial (red region). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,609 | OWR-14297736-016 | Duplicate Spherical Robin-Eigenvalue Question | Is the cap (geodesic disk) still maximal in those situations? simply connected Ω \lambda2 (Ω, \beta/L(Ω)) (area(Ω), \beta) \in =\Rightarrow \leq \lambda2 (C, \beta/L(C)) shaded region in Figure 2 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | partially_solved | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction duplicates the complete open problem preserved in the preceding record.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-016",
"literature-status:partially-solved",
"owr-year:2023"
] | The cap is proved maximal for substantial intervals of Robin parameters and areas on simply connected spherical domains, while the shaded parameter regimes represented by this question remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://doi.org/10.1007/s40315-023-00516-1",
"label": "Langford and Laugesen primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | null | Is the cap (geodesic disk) still maximal in those situations? simply connected Ω \lambda2 (Ω, \beta/L(Ω)) (area(Ω), \beta) \in =\Rightarrow \leq \lambda2 (C, \beta/L(C)) shaded region in Figure 2 | unrecoverable | The official report confirms that this extraction duplicates the complete open problem preserved in the preceding record. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,610 | OWR-14297736-018 | Pleijel Constants and Steklov–Robin Duality | Determine whether the Robin and Dirichlet Pleijel constants always coincide on a fixed domain; bound nodal counts for Dirichlet-to-Neumann eigenfunctions; and find further consequences of Steklov–Robin duality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-018",
"literature-status:open",
"owr-year:2023"
] | The Robin Pleijel-constant equality is proved generically for balls but remains open for general domains; general Dirichlet-to-Neumann nodal counts and further Steklov-Robin consequences likewise remain unresolved. | [
{
"url": "https://doi.org/10.1112/blms.13005",
"label": "Hassannezhad primary article"
},
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Determine whether the Robin and Dirichlet Pleijel constants always coincide on a fixed domain; bound nodal counts for Dirichlet-to-Neumann eigenfunctions; and find further consequences of Steklov–Robin duality. | We have a number of open questions on which progress or thoughts would be more than welcome! (1) For any boundary condition, we can define the Pleijel constant to be the true value of lim sup Nkk . This leads to the natural question: is it always true that the Pleijel constant for a Robin problem is equal to the Pleije... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,611 | OWR-14297736-019 | Genus-Free Steklov-Eigenvalue Bound | What about the genus \gamma of the surface Ω? Could we remove it from (3)? Let (Ω, g) be a compact, connected Riemannian manifold of dimension n \geq 2, with boundary \partialΩ. The Steklov eigenvalues of (Ω, g) form an unbounded sequence 0 = \sigma0 < \sigma1 \leq \sigma2 \leq \cdot \cdot \cdot ր +\infty, where each e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report gives a counterexample and explicitly explains why the genus dependence cannot be removed; the extracted question is res) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-019",
"literature-status:open",
"owr-year:2023"
] | Known upper bounds for normalized Steklov eigenvalues retain genus dependence, and the report's question of removing genus from the relevant bound has not been resolved in the checked literature. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "Oberwolfach Report 36"
},
{
"url": "https://arxiv.org/abs/1202.5108",
"label": "Girouard and Polterovich primary bounds"
},
{
"url": "https://dms.umontreal.ca/~iossif/steklov_surfaces.pdf",
"label": "Current Steklov survey"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | null | What about the genus \gamma of the surface Ω? Could we remove it from (3)? Let (Ω, g) be a compact, connected Riemannian manifold of dimension n \geq 2, with boundary \partialΩ. The Steklov eigenvalues of (Ω, g) form an unbounded sequence 0 = \sigma0 < \sigma1 \leq \sigma2 \leq \cdot \cdot \cdot ր +\infty, where each e... | unrecoverable | The official report gives a counterexample and explicitly explains why the genus dependence cannot be removed; the extracted question is resolved negatively. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,612 | OWR-14297736-020 | Universal Steklov Isoperimetric Questions | In other words, given a closed submanifold Σ \subset Rn of dimension n − 2, the question is to determine if the following quantity is finite or not: sup\{\sigma1 (Ω) : Ω \subset Rn is a submanifold with \partialΩ = Σ\}. Could a similar inquality hold without involving Volg (Ω)? The report passage is retained verbatim a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report answers both extracted questions negatively by giving unbounded constructions, so they are not open problems.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-020",
"literature-status:open",
"owr-year:2023"
] | The prescribed-boundary Steklov literature proves bounds proportional to the interior volume, but the volume-free finiteness question for fixed boundary remains explicitly open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1711.06458",
"label": "Colbois--Girouard--Gittins, prescribed-boundary Steklov spectrum"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | null | In other words, given a closed submanifold Σ \subset Rn of dimension n − 2, the question is to determine if the following quantity is finite or not: sup\{\sigma1 (Ω) : Ω \subset Rn is a submanifold with \partialΩ = Σ\}. Could a similar inquality hold without involving Volg (Ω)? The report passage is retained verbatim a... | unrecoverable | The official report answers both extracted questions negatively by giving unbounded constructions, so they are not open problems. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,613 | OWR-14297736-021 | Dense Pure Point Spectrum on Quasi-Conical Domains | Choose the hole sizes in a connected quasi-conical domain so that its Dirichlet Laplacian has neither absolutely continuous nor singular continuous spectrum, and hence has dense pure point spectrum. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-021",
"literature-status:open",
"owr-year:2023"
] | The 2024 construction achieves empty absolutely continuous spectrum and embedded eigenvalues, while the authors still leave emptiness of the singular continuous spectrum open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/blms.13113",
"label": "Krejcirik--Lotoreichik, quasi-conical domains"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Choose the hole sizes in a connected quasi-conical domain so that its Dirichlet Laplacian has neither absolutely continuous nor singular continuous spectrum, and hence has dense pure point spectrum. | It remains an open problem whether the sizes of the holes can be chosen so that both the absolutely continuous and the singular continuous spectra of the Dirichlet Laplacian on such a domain are empty. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,614 | OWR-14297736-025 | Landau-Level Multiplicities and Sign-Changing Spherical Interfaces | Determine the multiplicities of Landau levels under delta-interactions supported on general finite $C^{1,1}$ curves. Separately, characterize interfaces on $S^2$ for which a sign-changing elliptic problem has no eigenvalues $-1/2+i\eta$ with nonzero real $\eta$ when the material contrast is below $-1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-025",
"literature-status:open",
"owr-year:2023"
] | Existing results reduce multiplicity at perturbed Landau levels to Berezin--Toeplitz kernels and treat circles and generic cases, but the general finite C^{1,1} interface problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4171/JST/422",
"label": "Behrndt--Holzmann--Lotoreichik--Raikov, Landau delta interactions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Determine the multiplicities of Landau levels under delta-interactions supported on general finite $C^{1,1}$ curves. Separately, characterize interfaces on $S^2$ for which a sign-changing elliptic problem has no eigenvalues $-1/2+i\eta$ with nonzero real $\eta$ when the material contrast is below $-1$. | A more detailed investigation on the multiplicity of the perturbed Landau levels for general finite C 1,1 -smooth curves Σ remains open. The open question is the following: under which condition on the interface \partial̟+ = \partial̟− does this result remain true? leading term in the corresponding Weyl asymptotics. Th... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
30,005,615 | OWR-14297736-026 | Pólya-Type Spectral Inequalities for Manifold Families | Develop Pólya-type lower eigenvalue inequalities, with appropriate correction terms, that hold uniformly over natural families of Riemannian manifolds. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106](https://doi.org/10.4171/owr/2023/36)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,023 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14297736-026",
"literature-status:open",
"owr-year:2023"
] | The stated lower bounds for the spectral quantity rho_k over convex and general domains are presented as conjectures, and no general proof or counterexample was found. | [
{
"url": "https://doi.org/10.4171/owr/2023/36",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2023/36 | null | null | null | Develop Pólya-type lower eigenvalue inequalities, with appropriate correction terms, that hold uniformly over natural families of Riemannian manifolds. | Open problem: Are there similar inequalities valid for families of manifolds? Based on the results obtained in [5] for rectangles and unions of rectangles, we conjecture that similar results will hold for convex and general domains in Rn : Conjecture: Given positive numbers \alpha and M , there exist positive constants... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Geometric Spectral Theory (2024), Oberwolfach Reports, DOI 10.4171/owr/2023/36, pp. 2017--2106 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.