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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,516 | OWR-15436-001 | Recombination, Selection, and Duality in Multilocus Ancestry Models | For the multilocus ancestry and diffusion models, can one incorporate recombination and selection, determine the function $m(\cdot)$ in closed form beyond the one-locus reversible case, and extend the strong-recombination diffusion-limit arguments from $L=2$ to $L>2$ with a posterior dual? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804](https://doi.org/10.4171/owr/2017/28)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15436-001",
"literature-status:open",
"owr-year:2017"
] | The report still identifies both the closed-form dual normalizer m and the extension to more than two loci with posterior dual strong recombination as unresolved; related multilocus inference work does not settle these specific questions. | [
{
"url": "https://doi.org/10.4171/owr/2017/28",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/28 | null | null | null | For the multilocus ancestry and diffusion models, can one incorporate recombination and selection, determine the function $m(\cdot)$ in closed form beyond the one-locus reversible case, and extend the strong-recombination diffusion-limit arguments from $L=2$ to $L>2$ with a posterior dual? | For the multilocus ancestry and diffusion models, can one incorporate recombination and selection, determine the function m(\cdot) in closed form beyond the one-locus reversible case, and extend the strong-recombination diffusion-limit arguments from L=2 to L>2 with a posterior dual? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804 |
30,003,517 | OWR-15436-003 | Persistence and Permanence of Weakly Reversible Reaction Networks | For mass-action dynamical systems arising from weakly reversible chemical reaction networks, do all solutions have persistent dynamics with a positive lower bound and permanent dynamics with uniform positive lower and finite upper bounds for all sufficiently large time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804](https://doi.org/10.4171/owr/2017/28)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,017 | 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-15436-003",
"literature-status:open",
"owr-year:2017"
] | The global-attractor result is proved for complex-balanced systems, but the broader persistence and permanence assertions for all weakly reversible networks in this record remain conjectural. | [
{
"url": "https://arxiv.org/abs/1501.02860",
"label": "Craciun, global attractor conjecture"
},
{
"url": "https://people.tamu.edu/~annejls/geometricGAC.pdf",
"label": "current geometric approach"
},
{
"url": "https://doi.org/10.4171/owr/2017/28",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/28 | null | null | null | For mass-action dynamical systems arising from weakly reversible chemical reaction networks, do all solutions have persistent dynamics with a positive lower bound and permanent dynamics with uniform positive lower and finite upper bounds for all sufficiently large time? | For mass-action dynamical systems arising from weakly reversible chemical reaction networks, do all solutions have persistent dynamics with a positive lower bound and permanent dynamics with uniform positive lower and finite upper bounds for all sufficiently large time? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804 |
30,003,518 | OWR-15436-004 | Multistationarity in Kinetic-Proofreading Networks | For the kinetic-proofreading module in the T-cell activation model, which has deficiency one under the strongest simplifying assumptions, does the dynamical system admit multiple positive steady states, and what are the asymptotics of its solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804](https://doi.org/10.4171/owr/2017/28)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,017 | 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 | {
"source_url": "https://zenodo.org/records/23049794",
"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, **Multistationarity of the Altan-Bonnet–Germain Kinetic-Proofreading Network: A Partial Answer to a Question of Rendall** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23049794) | [
"owr",
"oberwolfach-reports",
"OWR-15436-004",
"literature-status:open",
"owr-year:2017"
] | The report explicitly leaves multiplicity of steady states for the Altan--Bonnet--Germain proofreading module unknown; later results located concern simpler or modified proofreading networks and do not settle this exact model. | [
{
"url": "https://doi.org/10.4171/owr/2017/28",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/28 | null | null | null | For the kinetic-proofreading module in the T-cell activation model, which has deficiency one under the strongest simplifying assumptions, does the dynamical system admit multiple positive steady states, and what are the asymptotics of its solutions? | For the kinetic-proofreading module in the T-cell activation model, which has deficiency one under the strongest simplifying assumptions, does the dynamical system admit multiple positive steady states, and what are the asymptotics of its solutions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804 |
30,003,519 | OWR-15436-005 | Canonical Equations for Spatial Adaptive Dynamics | In the spatial adaptive-dynamics limit described by the jump process of monomorphic equilibria, can one derive a canonical equation governing evolution under asymptotically small mutation steps? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804](https://doi.org/10.4171/owr/2017/28)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,017 | 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-15436-005",
"literature-status:open",
"owr-year:2017"
] | Canonical equations have rigorous derivations for several well-mixed and specially structured models, but the general spatial adaptive-dynamics limit requested here is not settled; the cited work obtains a jump-process limit under restrictive assumptions rather than the desired spatial canonical equation. | [
{
"url": "https://doi.org/10.4171/owr/2017/28",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.matpur.2013.10.003",
"label": "Champagnat, Jabin, and Meleard, structured model"
},
{
"url": "https://arxiv.org/abs/2303.09936",
"label": "Champagnat and Hass, canoni... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/28 | null | null | null | In the spatial adaptive-dynamics limit described by the jump process of monomorphic equilibria, can one derive a canonical equation governing evolution under asymptotically small mutation steps? | In the spatial adaptive-dynamics limit described by the jump process of monomorphic equilibria, can one derive a canonical equation governing evolution under asymptotically small mutation steps? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reaction Networks and Population Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/28, pp. 1747--1804 |
30,003,520 | OWR-15437-002 | Spectra of Nonlinear Problems with Energy-Dependent Boundary Conditions | Are the observed spectral features—nontrivial discrete spectrum and, in irrational geometry, existence of a frequency limit point—general for nonlinear boundary-value problems with energy-dependent boundary conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Partial Differential Equations on Graphs (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/29, pp. 1805--1868](https://doi.org/10.4171/owr/2017/29)
## Literature review (checked ... | 3 | open | null | 2,017 | 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-15437-002",
"literature-status:open",
"owr-year:2017"
] | The 2019 follow-up classifies a substantial subfamily of double-bridge standing waves, but explicitly leaves the complete classification of the original energy-dependent boundary-value problem unresolved. | [
{
"url": "https://doi.org/10.1016/j.jde.2018.07.038",
"label": "Noja--Rolando--Secchi, Journal of Differential Equations"
},
{
"url": "https://doi.org/10.4171/owr/2017/29",
"label": "Oberwolfach Report 29/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/29 | null | null | null | Are the observed spectral features—nontrivial discrete spectrum and, in irrational geometry, existence of a frequency limit point—general for nonlinear boundary-value problems with energy-dependent boundary conditions? | Are the observed spectral features—nontrivial discrete spectrum and, in irrational geometry, existence of a frequency limit point—general for nonlinear boundary-value problems with energy-dependent boundary conditions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Nonlinear Partial Differential Equations on Graphs (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/29, pp. 1805--1868 |
30,003,521 | OWR-15437-003 | NLS Approximation on Periodic Nonlinear Wave Graphs | Can the nonlinear Schrödinger (NLS) approximation be justified for original nonlinear wave systems on periodic graphs with quadratic nonlinearities and Kirchhoff vertex conditions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Partial Differential Equations on Graphs (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/29, pp. 1805--1868](https://doi.org/10.4171/owr/2017/29)
## Literature review (checked ... | 3 | open | null | 2,017 | 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-15437-003",
"literature-status:open",
"owr-year:2017"
] | The cubic NLS approximation on periodic quantum graphs is justified, but the quadratic-nonlinearity case remains explicitly open because graph vertex regularity obstructs the required normal-form analysis. | [
{
"url": "https://doi.org/10.1007/s00030-016-0417-7",
"label": "Gilg--Pelinovsky--Schneider, NoDEA"
},
{
"url": "https://doi.org/10.1002/mana.202100009",
"label": "Gilg et al., Mathematische Nachrichten"
},
{
"url": "https://doi.org/10.4171/owr/2017/29",
"label": "Oberwolfach Report ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/29 | null | null | null | Can the nonlinear Schrödinger (NLS) approximation be justified for original nonlinear wave systems on periodic graphs with quadratic nonlinearities and Kirchhoff vertex conditions? | Can the nonlinear Schrödinger (NLS) approximation be justified for original nonlinear wave systems on periodic graphs with quadratic nonlinearities and Kirchhoff vertex conditions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Nonlinear Partial Differential Equations on Graphs (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/29, pp. 1805--1868 |
30,003,522 | OWR-15438-003 | The Dupont–Monod Comparison-Map Conjecture | For every connected semisimple Lie group $G$ with finite center, is the comparison map
$$H^n_{\mathrm{cb}}(G;\mathbb R)\longrightarrow H^n_{\mathrm c}(G;\mathbb R)$$
an isomorphism for every degree $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Structures in Group Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/30, pp. 1869--1915](https://doi.org/10.4171/owr/2017/30)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,017 | 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-15438-003",
"literature-status:partially-solved",
"owr-year:2017"
] | The relevant bounded-cohomology conjecture is established in low degrees and in important special cases, including degree three for complex classical groups, but no general all-degree theorem is known. | [
{
"url": "https://arxiv.org/1811.07558",
"label": "Ott, Transgression in bounded cohomology"
},
{
"url": "https://arxiv.org/abs/2304.00607",
"label": "De la Cruz Mengual, Degree-three bounded cohomology"
},
{
"url": "https://doi.org/10.4171/owr/2017/30",
"label": "Oberwolfach Report ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/30 | null | null | null | For every connected semisimple Lie group $G$ with finite center, is the comparison map
$$H^n_{\mathrm{cb}}(G;\mathbb R)\longrightarrow H^n_{\mathrm c}(G;\mathbb R)$$
an isomorphism for every degree $n$? | Dupont–Monod conjecture: for every connected semisimple Lie group G with finite center, the comparison map H^n_{\mathrm{cb}}(G;\mathbb R)\to H^n_{\mathrm{c}}(G;\mathbb R) is an isomorphism for every degree n. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Geometric Structures in Group Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/30, pp. 1869--1915 |
30,003,523 | OWR-15439-002 | Equivariant Minimal Surfaces for Semisimple Representations | Let $\Sigma$ be a closed surface of genus at least $2$, let $\rho:\pi_1(\Sigma)\to G$ be a representation into a semisimple Lie group, and let $X=G/K$. Does there exist a smooth $\rho$-equivariant map $\widetilde\Sigma\to X$ whose image is a minimal surface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/31, pp. 1917--1971](https://doi.org/10.4171/owr/2017/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,017 | 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-15439-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Existence and uniqueness of equivariant minimal immersions are proved for quasi-isometric, Hitchin, and maximal representations in several rank-two settings, but the question for arbitrary semisimple representations remains open. | [
{
"url": "https://arxiv.org/abs/1702.08799",
"label": "Collier--Tholozan--Toulisse, Maximal representations"
},
{
"url": "https://doi.org/10.4171/owr/2017/31",
"label": "Oberwolfach Report 31/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/31 | null | null | null | Let $\Sigma$ be a closed surface of genus at least $2$, let $\rho:\pi_1(\Sigma)\to G$ be a representation into a semisimple Lie group, and let $X=G/K$. Does there exist a smooth $\rho$-equivariant map $\widetilde\Sigma\to X$ whose image is a minimal surface? | Let \Sigma be a closed surface of genus at least 2, let \rho:\pi_1(\Sigma)\to G be a representation into a semisimple Lie group, and let X=G/K. Does there exist a smooth \rho-equivariant map \widetilde{\Sigma}\to X whose image is a minimal surface? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Großen (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/31, pp. 1917--1971 |
30,003,524 | OWR-15575-001 | Viterbo's Symplectic Capacity–Volume Conjecture | For every convex domain $X\subset\mathbb R^{2n}$, is
$$
c_{\mathrm{EHZ}}(X)^n\leq n!\operatorname{vol}(X)
$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.4007/annals.2026.203.2.5",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no, for every n ≥ 2)**. M. Hutchings (joint with J. Chaidez; OWR 32/2017, p. 1991) recalls that Viterbo's conjecture implies c_EHZ(X)^n ≤ n! vol(X) for convex X ⊂ R^{2n}. Haim-Kislev–Ostrover, [Ann. of Math. 203 (2026)](https://doi.org/10.4007/annals.2026.203.2.5)... | [
"owr",
"oberwolfach-reports",
"OWR-15575-001",
"literature-status:open",
"owr-year:2017"
] | Viterbo's capacity-volume conjecture remains open for normalized capacities such as the Ekeland--Hofer--Zehnder capacity; only perturbative and special-case results are known. | [
{
"url": "https://doi.org/10.1007/s00039-024-00689-4",
"label": "Abbondandolo et al., Disk-like surfaces and symplectic capacities"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Oberwolfach Report 32/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | For every convex domain $X\subset\mathbb R^{2n}$, is
$$
c_{\mathrm{EHZ}}(X)^n\leq n!\operatorname{vol}(X)
$$? | Viterbo conjecture: for every convex domain X\subset\mathbb R^{2n}, does c_{\mathrm{EHZ}}(X)^n\le n!\operatorname{vol}(X) hold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,525 | OWR-15575-002 | Periodic Orbits Bounding Global Surfaces of Section | Given a smooth flow $\varphi_t$ on a closed smooth $3$-manifold $M$ and periodic orbits $\gamma_1,\ldots,\gamma_N$, when does their union bound a global surface of section? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,017 | 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-15575-002",
"literature-status:partially-solved",
"owr-year:2017"
] | General global-surface-of-section questions have strong sufficient criteria, and Birkhoff's retrograde-orbit conjecture is proved in Hill's lunar problem, but the full problem and the general restricted three-body setting remain unresolved. | [
{
"url": "https://doi.org/10.4171/JEMS/1220",
"label": "Hryniewicz--Salomao--Wysocki, Global surfaces of section"
},
{
"url": "https://arxiv.org/abs/2606.12912",
"label": "Liu--Salomao, Birkhoff conjecture in Hill's problem"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | Given a smooth flow $\varphi_t$ on a closed smooth $3$-manifold $M$ and periodic orbits $\gamma_1,\ldots,\gamma_N$, when does their union bound a global surface of section? | Given a smooth flow \phi_t on a smooth closed 3-manifold M and periodic orbits \gamma_1,\ldots,\gamma_N, does their collection bound a global surface of section? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,526 | OWR-15575-003 | Optimal Systolic Ratio of the Two-Sphere | For the Riemannian systolic ratio $\rho(S^2,\cdot)$, is the supremum equal to $2\sqrt3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-003",
"literature-status:open",
"owr-year:2017"
] | The supremum of the systolic ratio for metrics or contact forms on the two-sphere is still unknown; Zoll forms are locally maximizing, but this does not determine the global supremum. | [
{
"url": "https://doi.org/10.1007/s00039-023-00624-z",
"label": "Abbondandolo--Benedetti, Local systolic optimality"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Oberwolfach Report 32/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | For the Riemannian systolic ratio $\rho(S^2,\cdot)$, is the supremum equal to $2\sqrt3$? | For the Riemannian systolic ratio \rho(S^2,\cdot), is the supremum equal to 2\sqrt{3} ? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,527 | OWR-15575-006 | Movable Invariant Neighborhoods of Compact Flow Sets | Let $\varphi$ be a flow on $\mathbb R^3$ with compact invariant set $A$. Does every neighborhood of $A$ contain a movable compact invariant set that contains $A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-006",
"literature-status:open",
"owr-year:2017"
] | The movable-invariant-set question remains an open problem for arbitrary compact invariant sets; positive results are restricted to special solenoids and constructed examples. | [
{
"url": "https://topology.nipissingu.ca/tp/reprints/v31/tp31132.pdf",
"label": "Kuperberg, Open problems in dynamics"
},
{
"url": "https://auetd.auburn.edu/bitstream/handle/10415/1316/SINDELAROVA_PETRA_14.pdf",
"label": "Sindelarova, Movable approximations"
},
{
"url": "https://doi.org/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | Let $\varphi$ be a flow on $\mathbb R^3$ with compact invariant set $A$. Does every neighborhood of $A$ contain a movable compact invariant set that contains $A$? | Let \phi be a flow on \mathbb{R}^3 with compact invariant set A. Does every neighborhood of A contain a movable compact invariant set containing A? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,528 | OWR-15575-007 | Number of Simple Reeb Orbits on Three-Manifolds | What can one say about the number of simple Reeb orbits of a contact form on a closed three-manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,017 | 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-15575-007",
"literature-status:partially-solved",
"owr-year:2017"
] | The two-or-infinity alternative is proved for nondegenerate contact forms on closed three-manifolds and for all forms with torsion first Chern class, but the unrestricted degenerate case is not covered by these theorems. | [
{
"url": "https://arxiv.org/abs/2001.01448",
"label": "Colin--Dehornoy--Rechtman, Supporting broken books"
},
{
"url": "https://arxiv.org/abs/2310.07636",
"label": "Cristofaro-Gardiner et al., Two-or-infinity conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Ob... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | What can one say about the number of simple Reeb orbits of a contact form on a closed three-manifold? | What can one say about the number of simple Reeb orbits of a contact form on a closed three-manifold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,529 | OWR-15575-008 | Contact Entropy and Fundamental-Group Growth | If a contact $3$-manifold $(Y,\xi)$ has positive entropy, meaning that every Reeb flow has positive topological entropy, must $\pi_1(Y)$ have exponential growth? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-008",
"literature-status:open",
"owr-year:2017"
] | Known positive-entropy contact three-manifolds have exponentially growing fundamental group, but the proposed implication for every contact three-manifold remains a conjecture with no general proof or counterexample. | [
{
"url": "https://arxiv.org/abs/1410.3380",
"label": "Alves, Cylindrical contact homology and entropy"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Oberwolfach Report 32/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | If a contact $3$-manifold $(Y,\xi)$ has positive entropy, meaning that every Reeb flow has positive topological entropy, must $\pi_1(Y)$ have exponential growth? | If a contact 3-manifold (Y,\xi) has positive entropy, meaning every Reeb flow has positive topological entropy, must \pi_1(Y) grow exponentially? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,530 | OWR-15575-009 | Measure of Rational-Direction Geodesics on Finsler Tori | For a zero-topological-entropy Finsler metric on $T^2$, is
$$
\mu_L\left(\bigcup_{\substack{\xi\in S^1\\ \xi\text{ rational}}}E_\xi\right)<\mu_L(ST^2),
$$
where $\mu_L$ is Liouville measure and $E_\xi$ is the set of geodesics with rational asymptotic direction $\xi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-009",
"literature-status:open",
"owr-year:2017"
] | The zero-entropy torus theory gives strong structure and many examples, but the listed measure and rational-direction questions, especially the classification of integrable Riemannian metrics, remain unresolved in general. | [
{
"url": "https://arxiv.org/abs/0707.0666",
"label": "Glasmachers--Knieper, Geodesic flows on the two-torus"
},
{
"url": "https://arxiv.org/abs/1101.1660",
"label": "Glasmachers--Knieper, Minimal geodesic foliations"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Oberwo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | For a zero-topological-entropy Finsler metric on $T^2$, is
$$
\mu_L\left(\bigcup_{\substack{\xi\in S^1\\ \xi\text{ rational}}}E_\xi\right)<\mu_L(ST^2),
$$
where $\mu_L$ is Liouville measure and $E_\xi$ is the set of geodesics with rational asymptotic direction $\xi$? | For a zero-topological-entropy Finsler metric on T^2, is \mu_L(\bigcup_{\xi\in S^1 \mathrm{rational}}E_\xi)<\mu_L(ST^2), where \mu_L is Liouville measure? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,531 | OWR-15575-010 | Exceptional Rational Directions of Zero-Entropy Finsler Tori | For a zero-topological-entropy Finsler metric on $T^2$, let $E_\xi$ be the set of nonminimal geodesics having rational asymptotic direction $\xi$. Does some rational $\xi$ satisfy $E_\xi=\varnothing$? Is $\{\xi\in S^1:\xi\text{ is rational and }E_\xi\neq\varnothing\}$ finite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-010",
"literature-status:open",
"owr-year:2017"
] | Classification of Riemannian metrics on the two-torus with integrable geodesic flow is still incomplete; known Liouville and finite-cover classifications do not settle the general problem. | [
{
"url": "https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/deformational-rigidity-of-integrable-metrics-on-the-torus/4F3C0B4C21F97A4E359EEB841FDBF9BD",
"label": "Deformational rigidity of integrable torus metrics"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | For a zero-topological-entropy Finsler metric on $T^2$, let $E_\xi$ be the set of nonminimal geodesics having rational asymptotic direction $\xi$. Does some rational $\xi$ satisfy $E_\xi=\varnothing$? Is $\{\xi\in S^1:\xi\text{ is rational and }E_\xi\neq\varnothing\}$ finite? | For a zero-topological-entropy Finsler metric on T^2, with E_\xi the non-minimal geodesics of rational asymptotic direction \xi, does some rational \xi satisfy E_\xi=\varnothing, and is \{\xi\in S^1:\xi is rational and E_\xi\ne\varnothing\} finite? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,532 | OWR-15575-011 | Hamiltonian Pseudo-Rotations of the Complex Projective Plane | Can the Anosov–Katok conjugation method be used to construct genuine Hamiltonian pseudo-rotations of $\mathbb{CP}^2$ with exactly three periodic points that are not true rotations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046](https://doi.org/10.4171/owr/2017/32)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,017 | 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-15575-011",
"literature-status:open",
"owr-year:2017"
] | Floer-theoretic results establish invariant sets and recurrence properties for Hamiltonian pseudo-rotations of complex projective spaces, but the requested general construction and the existence of ghost pseudo-rotations remain open. | [
{
"url": "https://arxiv.org/abs/1712.09766",
"label": "Ginzburg--Gurel, Hamiltonian pseudo-rotations"
},
{
"url": "https://arxiv.org/abs/1812.05782",
"label": "Ginzburg--Gurel, Pseudo-rotations versus rotations"
},
{
"url": "https://doi.org/10.4171/owr/2017/32",
"label": "Oberwolfach... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/32 | null | null | null | Can the Anosov–Katok conjugation method be used to construct genuine Hamiltonian pseudo-rotations of $\mathbb{CP}^2$ with exactly three periodic points that are not true rotations? | Can the Anosov--Katok conjugation method be carried out to construct genuine Hamiltonian pseudo-rotations of \mathbb{CP}^2, with exactly three periodic points, beyond true rotations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Dynamische Systeme (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/32, pp. 1987--2046 |
30,003,533 | OWR-15576-002 | High-Frequency Coercivity on Nonconvex Nontrapping Domains | For high-frequency scattering, does coercivity of the combined boundary-integral operator $A_k$ persist for strongly nontrapping, nonconvex domains such as smooth star-shaped domains, possibly with a coercivity constant $\gamma(k)$ that degenerates mildly as $k\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Material Theories (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/33, pp. 2047--2099](https://doi.org/10.4171/owr/2017/33)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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-15576-002",
"literature-status:open",
"owr-year:2017"
] | Uniform coercivity is known for convex and star-shaped formulations, but the stated high-frequency coercivity question for general strongly non-trapping non-convex domains remains open. | [
{
"url": "https://doi.org/10.1002/cpa.21543",
"label": "Spence--Kamotski--Smyshlyaev, Combined boundary integral equations"
},
{
"url": "https://doi.org/10.4171/owr/2017/33",
"label": "Oberwolfach Report 33/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/33 | null | null | null | For high-frequency scattering, does coercivity of the combined boundary-integral operator $A_k$ persist for strongly nontrapping, nonconvex domains such as smooth star-shaped domains, possibly with a coercivity constant $\gamma(k)$ that degenerates mildly as $k\to\infty$? | For high-frequency scattering, does coercivity of the combined boundary integral operator A_k continue to hold, perhaps with a mildly degenerating coercivity constant \gamma(k) as k\to\infty, for strongly non-trapping non-convex domains such as smooth star-shaped domains? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Material Theories (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/33, pp. 2047--2099 |
30,003,534 | OWR-15577-002 | $L^p$ Bounds for the Triangular Hilbert Transform | Determine the range of exponents for which the triangular Hilbert transform, the trilinear singular integral with kernel $(x+y+z)^{-1}$, is bounded on the corresponding $L^p$ spaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | open | null | 2,017 | 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-15577-002",
"literature-status:open",
"owr-year:2017"
] | No general Lp boundedness theorem is known for the triangular Hilbert transform; current work still identifies it as a major unresolved singular-integral problem. | [
{
"url": "https://arxiv.org/abs/2410.15791",
"label": "Hsu--Lin, Triangular Hilbert transform along curves"
},
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "Oberwolfach Report 34/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | Determine the range of exponents for which the triangular Hilbert transform, the trilinear singular integral with kernel $(x+y+z)^{-1}$, is bounded on the corresponding $L^p$ spaces. | Determine the L^p-boundedness of the triangular Hilbert transform, the trilinear singular integral with kernel 1/(x+y+z). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,535 | OWR-15577-003 | Bounds for Multilinear and Simplex Hilbert Transforms | Establish bounds in the appropriate $L^p$ ranges for multilinear and simplex Hilbert transforms, including the higher-dimensional singular forms arising from the corners problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | open | null | 2,017 | 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-15577-003",
"literature-status:open",
"owr-year:2017"
] | Bounds for the multilinear and simplex Hilbert transforms remain beyond current methods; recent work continues to state these estimates as open problems. | [
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "Oberwolfach Report 34/2017"
},
{
"url": "https://arxiv.org/abs/2410.15791",
"label": "Hsu--Lin, Related triangular bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | Establish bounds in the appropriate $L^p$ ranges for multilinear and simplex Hilbert transforms, including the higher-dimensional singular forms arising from the corners problem. | Establish bounds in appropriate L^p ranges for the multilinear and simplex Hilbert transforms, including the higher-dimensional singular forms arising from the corners problem. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,536 | OWR-15577-004 | Maximum Principle for Intermediate Riesz Kernels | For $s\in(1,d-1)$ and $K(x)=x/|x|^{s+1}$, does there exist $C>0$ such that every nonnegative smooth compactly supported function $f$ satisfies
$$
\sup_{x\in\mathbb R^d}|K*f(x)|\leq C\sup_{x\in\operatorname{supp}f}|K*f(x)|
$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | partially_solved | null | 2,017 | 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-15577-004",
"literature-status:partially-solved",
"owr-year:2017"
] | The Riesz-transform maximum principle is proved for positive data when the exponent is below one and when it is at least dimension minus one, while the intermediate range remains open; it is false for signed data. | [
{
"url": "https://arxiv.org/abs/1701.04500",
"label": "Eiderman--Nazarov, Maximum principle for the Riesz transform"
},
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "Oberwolfach Report 34/2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | For $s\in(1,d-1)$ and $K(x)=x/|x|^{s+1}$, does there exist $C>0$ such that every nonnegative smooth compactly supported function $f$ satisfies
$$
\sup_{x\in\mathbb R^d}|K*f(x)|\leq C\sup_{x\in\operatorname{supp}f}|K*f(x)|
$$? | For s\in(1,d-1) and K(x)=x/|x|^{s+1}, does there exist C>0 such that every non-negative smooth compactly supported f satisfies \sup_{\mathbb{R}^d}|K*f|\le C\sup_{\operatorname{supp}f}|K*f|? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,537 | OWR-15577-006 | Sharp Weighted Bounds for Rough Singular Integrals | For a rough homogeneous singular integral $T_\Omega$ with $\Omega\in L^\infty(S^{n-1})$ and mean zero, can the weighted estimate $\lVert T_\Omega\rVert_{L^2(w)\to L^2(w)}\lesssim[w]_{A_2}^2$ be improved to linear dependence on $[w]_{A_2}$? Is the maximal singular integral $T_\Omega^\star$ of weak type $(1,1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | partially_solved | null | 2,017 | 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-15577-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The maximal rough singular integral weak-type (1,1) question was resolved by Lai, but the conjectured linear dependence on the A_2 characteristic for T_\Omega remains open; quadratic bounds are still the general benchmark. | [
{
"url": "https://arxiv.org/abs/1510.05789",
"label": "Hytönen--Roncal--Tapiola, quantitative rough bounds"
},
{
"url": "https://arxiv.org/abs/2508.17737",
"label": "Lai, maximal rough singular integral endpoint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | For a rough homogeneous singular integral $T_\Omega$ with $\Omega\in L^\infty(S^{n-1})$ and mean zero, can the weighted estimate $\lVert T_\Omega\rVert_{L^2(w)\to L^2(w)}\lesssim[w]_{A_2}^2$ be improved to linear dependence on $[w]_{A_2}$? Is the maximal singular integral $T_\Omega^\star$ of weak type $(1,1)$? | For rough homogeneous singular integrals T_\Omega with \Omega\in L^\infty(S^{n-1}) and mean zero, can the weighted estimate \|T_\Omega\|_{L^2(w)\to L^2(w)}\lesssim [w]_{A_2}^2 be improved to linear dependence on [w]_{A_2}; and is the maximal singular integral T_\Omega^\star of weak type (1,1)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,538 | OWR-15577-010 | Equivalence of Hardy Spaces on Noncompact Manifolds | For a complete connected noncompact Riemannian manifold $M$, do the Hardy spaces $H_R^1(M)$, $H_H^1(M)$, and $H_P^1(M)$, defined through the Riesz transform, heat maximal operator, and Poisson maximal operator, respectively, coincide and admit atomic decompositions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | partially_solved | null | 2,017 | 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-15577-010",
"literature-status:partially-solved",
"owr-year:2017"
] | Heat and Poisson maximal Hardy spaces have atomic characterizations under standard doubling and bounded-geometry hypotheses, and special symmetric spaces are understood, but the general equality with the Riesz-transform Hardy space and atomic decomposition remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "Meda, Martini, Vallarino, Hardy spaces report"
},
{
"url": "https://arxiv.org/abs/1908.10057",
"label": "Martini--Meda--Vallarino, nondoubling Hardy spaces"
},
{
"url": "https://link.springer.com/article/10.1007/s00209-021-02856-x... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | For a complete connected noncompact Riemannian manifold $M$, do the Hardy spaces $H_R^1(M)$, $H_H^1(M)$, and $H_P^1(M)$, defined through the Riesz transform, heat maximal operator, and Poisson maximal operator, respectively, coincide and admit atomic decompositions? | For a complete connected noncompact Riemannian manifold M, do the Hardy spaces H_R^1(M), H_H^1(M), and H_P^1(M), defined through the Riesz transform, heat maximal operator, and Poisson maximal operator, respectively, agree and admit atomic decompositions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,539 | OWR-15577-011 | Sharp Exponents in the Fourier Restriction Conjecture | Determine the sharp exponent range in the Fourier restriction inequality
$$
\lVert\widehat f\rVert_{L^q(S^{d-1})}\leq C\lVert f\rVert_{L^p(\mathbb R^d)},
$$
especially when $q<2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | open | null | 2,017 | 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-15577-011",
"literature-status:open",
"owr-year:2017"
] | The question is the general Fourier restriction conjecture below the Tomas--Stein exponent q=2; substantial partial ranges are known, but no all-dimensional resolution of the q<2 problem exists. | [
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00041-025-10201-7",
"label": "recent spherical restriction results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | Determine the sharp exponent range in the Fourier restriction inequality
$$
\lVert\widehat f\rVert_{L^q(S^{d-1})}\leq C\lVert f\rVert_{L^p(\mathbb R^d)},
$$
especially when $q<2$. | For the Fourier restriction inequality \|\widehat f\|_{L^q(S^{d-1})}\le C\|f\|_{L^p(\mathbb{R}^d)}, determine the sharp range of exponents, especially for q<2, as asked by the Fourier restriction conjecture. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,540 | OWR-15577-012 | Gaussian Extremizers for Strichartz Inequalities | Do Gaussian functions extremize the Strichartz inequality
$$
\lVert u\rVert_{L^{2+4/d}(\mathbb R^{d+1})}\leq C\lVert f\rVert_{L^2(\mathbb R^d)}
$$
for solutions $u$ of the free Schrödinger equation in every dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | partially_solved | null | 2,017 | 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-15577-012",
"literature-status:partially-solved",
"owr-year:2017"
] | The hyperboloid endpoint constants and extremizers are known in several low-dimensional cases, including all non-endpoints in dimensions one and two, but the all-dimensional Gaussian-extremizer question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1708.03826",
"label": "Carneiro--Oliveira e Silva--Sousa, hyperboloid extremizers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | Do Gaussian functions extremize the Strichartz inequality
$$
\lVert u\rVert_{L^{2+4/d}(\mathbb R^{d+1})}\leq C\lVert f\rVert_{L^2(\mathbb R^d)}
$$
for solutions $u$ of the free Schrödinger equation in every dimension? | Do Gaussians extremize the Strichartz inequality \|u\|_{L^{2+4/d}(\mathbb{R}^{d+1})}\le C\|f\|_{L^2(\mathbb{R}^d)} for solutions of the free Schr\ddot{o}dinger equation in all dimensions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,541 | OWR-15577-013 | Riesz Transform Boundedness and $\beta$-Number Carleson Conditions | Let $\mu$ be a Borel measure on $\mathbb R^{n+1}$ satisfying $\mu(B(x,r))\leq c_0r^n$. Is the codimension-one Riesz transform bounded on $L^2(\mu)$ if and only if every ball $B$ satisfies
$$
\int_B\int_0^{r(B)}\beta_{\mu,2}(x,r)^2\Theta_\mu(x,r)\,\frac{dr}{r}\,d\mu(x)\leq C\mu(B),
$$
where $\Theta_\mu(x,r)=\mu(B(x,r))/... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164](https://doi.org/10.4171/owr/2017/34)
## Literature review (checked ... | 3 | partially_solved | null | 2,017 | 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-15577-013",
"literature-status:partially-solved",
"owr-year:2017"
] | The codimension-one Riesz-transform characterization is proved for n=1 and for AD-regular measures, while the stated polynomial-growth characterization for general measures remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/34",
"label": "Tolsa, Riesz transforms and rectifiability"
},
{
"url": "https://arxiv.org/abs/1501.01572",
"label": "Azzam--Tolsa, Jones square function"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/34 | null | null | null | Let $\mu$ be a Borel measure on $\mathbb R^{n+1}$ satisfying $\mu(B(x,r))\leq c_0r^n$. Is the codimension-one Riesz transform bounded on $L^2(\mu)$ if and only if every ball $B$ satisfies
$$
\int_B\int_0^{r(B)}\beta_{\mu,2}(x,r)^2\Theta_\mu(x,r)\,\frac{dr}{r}\,d\mu(x)\leq C\mu(B),
$$
where $\Theta_\mu(x,r)=\mu(B(x,r))/... | Let \mu be a Borel measure on \mathbb{R}^{n+1} with \mu(B(x,r))\le c_0r^n. Is the codimension-one Riesz transform bounded on L^2(\mu) if and only if \int_B\int_0^{r(B)}\beta_{\mu,2}(x,r)^2\Theta_\mu(x,r) \frac{dr}{r} d\mu(x)\le C\mu(B) for every ball B, where \Theta_\mu(x,r)=\mu(B(x,r))/r^n and \beta_{\mu,2} is the Jon... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/34, pp. 2101--2164 |
30,003,542 | OWR-15578-006 | Closed Magnetic Geodesics and Multiplicity-One Minimal Hypersurfaces | Does every topological two-sphere in a magnetic field admit a closed embedded curve of each prescribed constant geodesic curvature? Separately, does the min–max construction of minimal hypersurfaces always produce a hypersurface with multiplicity one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/35, pp. 2165--2222](https://doi.org/10.4171/owr/2017/35)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,017 | 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-15578-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Zhou and Zhu proved existence of a nontrivial closed CMC hypersurface for every prescribed constant in a closed ambient manifold, and nonzero min-max solutions have multiplicity one; the minimal multiplicity-one problem is known only under additional generic hypotheses. | [
{
"url": "https://arxiv.org/abs/1707.08012",
"label": "Zhou--Zhu, CMC min--max theory"
},
{
"url": "https://annals.math.princeton.edu/2020/192-3/p03",
"label": "Zhou, multiplicity one for bumpy metrics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/35 | null | null | null | Does every topological two-sphere in a magnetic field admit a closed embedded curve of each prescribed constant geodesic curvature? Separately, does the min–max construction of minimal hypersurfaces always produce a hypersurface with multiplicity one? | Does every topological two-sphere in a magnetic field admit a closed embedded curve of each prescribed constant geodesic curvature, and does the min--max construction of minimal hypersurfaces always have multiplicity one? | 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 | Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/35, pp. 2165--2222 |
30,003,543 | OWR-15578-008 | Cartan–Hadamard Isoperimetric Conjecture | Does every Cartan–Hadamard manifold $(M^{n+1},g)$ satisfy
$$
|\Omega|\leq n^{-(n+1)/n}\omega_{n+1}^{-1/n}|\partial\Omega|^{(n+1)/n}
$$
for every bounded sufficiently regular open set $\Omega\subset M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/35, pp. 2165--2222](https://doi.org/10.4171/owr/2017/35)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,017 | 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-15578-008",
"literature-status:partially-solved",
"owr-year:2017"
] | The Cartan--Hadamard isoperimetric conjecture is proved in the low-dimensional cases stated and in several special higher-dimensional geometries, but remains open in general dimensions at least five. | [
{
"url": "https://arxiv.org/abs/2605.24638",
"label": "Ghomi, Cartan--Hadamard spaces with nullity"
},
{
"url": "https://arxiv.org/abs/2608.12020",
"label": "Ghomi, pinched Cartan--Hadamard manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2017/35",
"label": "original OWR report"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/35 | null | null | null | Does every Cartan–Hadamard manifold $(M^{n+1},g)$ satisfy
$$
|\Omega|\leq n^{-(n+1)/n}\omega_{n+1}^{-1/n}|\partial\Omega|^{(n+1)/n}
$$
for every bounded sufficiently regular open set $\Omega\subset M$? | Does every Cartan--Hadamard manifold (M^{n+1},g) satisfy the isoperimetric inequality |\Omega|\le n^{-n}\omega_{n+1}|\partial\Omega|^{(n+1)/n} for bounded sufficiently regular open sets \Omega? | 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 | Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/35, pp. 2165--2222 |
30,003,544 | OWR-15579-001 | Goldberg Conjecture in Four Dimensions | If a closed almost Kähler four-manifold $(M,g,J,\omega)$ is Einstein, must its almost complex structure $J$ be integrable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | open | null | 2,017 | 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-15579-001",
"literature-status:open",
"owr-year:2017"
] | Sekigawa\textquotesingle s nonnegative-scalar-curvature theorem and several extra-curvature results are known, but the compact Einstein almost-Kähler Goldberg conjecture in full generality, including the negative-scalar-curvature case, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1409.4437",
"label": "Conti--Fernandez, almost-cokähler analogue"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | If a closed almost Kähler four-manifold $(M,g,J,\omega)$ is Einstein, must its almost complex structure $J$ be integrable? | If a closed almost K\ddot{a}hler four-manifold (M,g,J,\omega) is Einstein, must its almost complex structure J be integrable? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,545 | OWR-15579-002 | Nonexistence of Edge-Cone Yamabe Metrics at Small Cone Angles | For $1<\beta<2$, does the conformal class $[h_\beta]$ of the standard edge-cone metric of cone angle $2\pi\beta$ on $(S^n,S^{n-2})$ admit no edge-cone Yamabe metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | partially_solved | null | 2,017 | 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... | [
"OWR-15579-006"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15579-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Nonexistence of an edge-cone Yamabe minimizer is proved for cone angle at least 4\pi, while the conjectured nonexistence for angles between 2\pi and 4\pi remains unresolved. | [
{
"url": "https://arxiv.org/abs/1909.09367",
"label": "Akutagawa--Mondello, singular Yamabe minimizers"
},
{
"url": "https://doi.org/10.4171/owr/2017/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | For $1<\beta<2$, does the conformal class $[h_\beta]$ of the standard edge-cone metric of cone angle $2\pi\beta$ on $(S^n,S^{n-2})$ admit no edge-cone Yamabe metric? | For every 1<\beta<2, is there no edge-cone Yamabe metric in the conformal class [h_\beta] on S^n, as asserted by the known theorem for \beta\ge2? | corrected_verified | The official report was checked. It proves nonexistence for beta at least two and states precisely this remaining range as a conjecture. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,546 | OWR-15579-003 | Removal of Conical Singularities in Higher-Dimensional Vacuum Metrics | For a prescribed rod structure in the higher-dimensional stationary vacuum construction, can the conical singularities along the bounded axis rods be removed by adjusting the parameters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | partially_solved | null | 2,017 | 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-15579-003",
"literature-status:partially-solved",
"owr-year:2017"
] | Integrability and rod-structure methods produce regular higher-dimensional stationary vacuum black holes in many cases, while other rod structures are provably obstructed by conical singularities; a general parameter-removal criterion is not known. | [
{
"url": "https://arxiv.org/abs/2008.12761",
"label": "Lucietti--Tomlinson, stationary vacuum black-hole moduli"
},
{
"url": "https://doi.org/10.1007/JHEP02(2021)005",
"label": "Lucietti--Tomlinson, vacuum black lens obstruction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | For a prescribed rod structure in the higher-dimensional stationary vacuum construction, can the conical singularities along the bounded axis rods be removed by adjusting the parameters? | For a prescribed rod structure in the higher-dimensional stationary vacuum construction, can the conical singularities along the bounded axis rods be removed by adjusting the parameters? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,547 | OWR-15579-004 | Composition of Positive-Scalar-Curvature Concordance Classes | In the category of Lie manifolds, can one define an appropriate composition law on concordance classes of metrics relative to a fixed compatible positive-scalar-curvature metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | open | null | 2,017 | 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-15579-004",
"literature-status:open",
"owr-year:2017"
] | Group structures on concordance classes are available for important closed-manifold settings after fixing a PSC metric, but the requested composition in the category of Lie manifolds remains an open structural problem. | [
{
"url": "https://doi.org/10.4171/owr/2017/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1712.03722",
"label": "relative higher index and PSC concordance"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | In the category of Lie manifolds, can one define an appropriate composition law on concordance classes of metrics relative to a fixed compatible positive-scalar-curvature metric? | In the category of Lie manifolds, can one define an appropriate composition law on concordance classes of metrics relative to a fixed compatible positive-scalar-curvature metric? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,548 | OWR-15579-005 | Sphere Rigidity from Scalar Curvature and Injectivity Radius | Does there exist $\varepsilon=\varepsilon(n)>0$ such that every closed $n$-dimensional Riemannian manifold $M$ with $\operatorname{scal}_M\geq n(n-1)$ and injectivity radius at least $\pi-\varepsilon(n)$ is diffeomorphic to the standard $n$-sphere? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | partially_solved | null | 2,017 | 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-15579-005",
"literature-status:partially-solved",
"owr-year:2017"
] | Differentiable sphere stability is proved under additional curvature, volume, or derivative bounds, and strengthened injectivity estimates are known in selected topologies; the bare scalar-curvature and near-\pi injectivity-radius statement remains unresolved. | [
{
"url": "https://arxiv.org/abs/1408.3006",
"label": "Tuschmann--Wiemeler, differentiable stability"
},
{
"url": "https://arxiv.org/abs/2404.09573",
"label": "Richard, strengthened injectivity bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | Does there exist $\varepsilon=\varepsilon(n)>0$ such that every closed $n$-dimensional Riemannian manifold $M$ with $\operatorname{scal}_M\geq n(n-1)$ and injectivity radius at least $\pi-\varepsilon(n)$ is diffeomorphic to the standard $n$-sphere? | Does there exist \varepsilon=\varepsilon(n)>0 such that every closed n-dimensional Riemannian manifold M with \operatorname{scal}_M\ge n(n-1) and injectivity radius at least \pi-\varepsilon(n) is diffeomorphic to the standard n-sphere? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,549 | OWR-15579-006 | Duplicate Edge-Cone Yamabe Nonexistence Conjecture | For a sphere with a codimension-2 singularity of cone angle \alpha>2\pi, no Yamabe metric exists; this is known for \alpha>4\pi and conjectured for every \alpha>2\pi. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298](https://doi.org/10.4171/owr/2017/36)
## Literatur... | 3 | partially_solved | null | 2,017 | 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 | Duplicate/merged OWR extraction (The official report restates the same edge-cone Yamabe nonexistence conjecture represented canonically and with its standard metric notation) | [
"OWR-15579-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15579-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The Yamabe-minimizer nonexistence conjecture is proved for cone angles at least 4\pi, and the sub-2\pi regime is characterized, but the intermediate angle range corresponding to 1<\beta<2 remains open. | [
{
"url": "https://arxiv.org/abs/1909.09367",
"label": "Akutagawa--Mondello, singular Yamabe minimizers"
},
{
"url": "https://doi.org/10.4171/owr/2017/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/36 | null | null | null | null | For a sphere with a codimension-2 singularity of cone angle \alpha>2\pi, no Yamabe metric exists; this is known for \alpha>4\pi and conjectured for every \alpha>2\pi. | unrecoverable | The official report restates the same edge-cone Yamabe nonexistence conjecture represented canonically and with its standard metric notation by OWR-15579-002. The substitution $\alpha=2\pi\beta$ makes the two parameter ranges identical. No separate clean statement is promoted; the original record remains publicly visib... | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/36, pp. 2223--2298 |
30,003,550 | OWR-15580-001 | Cutting Planes Lower Bounds for Random CNF Formulas | Can one prove superpolynomial lower bounds on the size of Cutting Planes refutations of random $k$-CNF formulas? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,017 | 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-15580-001",
"literature-status:partially-solved",
"owr-year:2017"
] | Fleming, Pankratov, Pitassi, and Robere proved exponential Cutting Planes lower bounds for random k-CNF formulas when k=\Theta(\log n), but lower bounds across the broader random-CNF regimes motivating the problem remain open. | [
{
"url": "https://arxiv.org/abs/1703.02469",
"label": "Fleming--Pankratov--Pitassi--Robere, random CNFs"
},
{
"url": "https://ieee-focs.org/FOCS-2017-Papers/3464a121.pdf",
"label": "Fleming et al., FOCS result"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Can one prove superpolynomial lower bounds on the size of Cutting Planes refutations of random $k$-CNF formulas? | Prove lower bounds on the size of Cutting Planes refutations for random k-CNF formulas; this is a long-standing open problem with recent progress. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,551 | OWR-15580-003 | Bit-Width-Independent Verification of Integer Multipliers | Find a general-purpose method for verifying bounded-bit-width integer multiplier properties, including ring identities, without exponential scaling in the bit-width. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,017 | 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-15580-003",
"literature-status:partially-solved",
"owr-year:2017"
] | Polynomial or quasipolynomial resolution verification is known for several structured integer multipliers, but the general purpose bit width independent verification problem in the record remains unresolved. | [
{
"url": "https://doi.org/10.1145/3319396",
"label": "Beame and Liew on nonlinear integer arithmetic"
},
{
"url": "https://doi.org/10.4171/owr/2017/37",
"label": "Proof Complexity and Beyond"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Find a general-purpose method for verifying bounded-bit-width integer multiplier properties, including ring identities, without exponential scaling in the bit-width. | Find a general-purpose method for verifying bounded-bit-width integer multiplier properties, including ring identities, without exponential scaling in the bit-width. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,552 | OWR-15580-004 | Resolution Lower Bounds for Clique Certification | Can one prove an unconditional lower bound of the form $n^{\Omega(k)}$ for resolution, or for another restricted proof system, when certifying that an $n$-vertex graph has no $k$-clique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,017 | 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-15580-004",
"literature-status:partially-solved",
"owr-year:2017"
] | Strong average case lower bounds are proved for k Clique in regular resolution, including n to an order k size bounds, but the broader restricted algorithm lower bound question in the record is not settled. | [
{
"url": "https://doi.org/10.1145/3449352",
"label": "Clique Is Hard on Average for Regular Resolution"
},
{
"url": "https://doi.org/10.4171/owr/2017/37",
"label": "Proof Complexity and Beyond"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Can one prove an unconditional lower bound of the form $n^{\Omega(k)}$ for resolution, or for another restricted proof system, when certifying that an $n$-vertex graph has no $k$-clique? | Prove unconditional lower bounds such as n^{\Omega(k)} for resolution or another restricted proof class certifying that an n-vertex graph has no k-clique. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,553 | OWR-15580-005 | Random CNF Lower Bounds beyond Cutting Planes | Can one establish lower bounds in proof systems other than Cutting Planes that are analogous to the exponential Cutting Planes lower bound for random $O(\log n)$-CNF formulas? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,017 | 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-15580-005",
"literature-status:open",
"owr-year:2017"
] | Exponential lower bounds are now known for random logarithmic width CNFs in Cutting Planes, but comparable results across the other proof systems contemplated by the record remain an open problem. | [
{
"url": "https://doi.org/10.1145/3486680",
"label": "Random CNFs are Hard for Cutting Planes"
},
{
"url": "https://doi.org/10.4171/owr/2017/37",
"label": "Proof Complexity and Beyond"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Can one establish lower bounds in proof systems other than Cutting Planes that are analogous to the exponential Cutting Planes lower bound for random $O(\log n)$-CNF formulas? | Establish lower bounds analogous to the exponential Cutting Planes lower bound for random O(\log n)-CNF formulas in other proof systems. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,554 | OWR-15580-006 | PSD Rank Bounds for Polynomial-Size Selector Matrices | Does the positive-semidefinite-rank lower bound for the selector matrix $M_f^{\operatorname{SEL}_m}$ remain valid when $m\leq n^{O(1)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,017 | 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-15580-006",
"literature-status:open",
"owr-year:2017"
] | Known semidefinite extension complexity lower bounds use exponentially many constraints, while the requested polynomial constraint regime and its MAX 3 SAT consequence remain unresolved. | [
{
"url": "https://doi.org/10.1145/2746539.2746599",
"label": "Lower bounds on semidefinite programming relaxations"
},
{
"url": "https://doi.org/10.4171/owr/2017/37",
"label": "Proof Complexity and Beyond"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Does the positive-semidefinite-rank lower bound for the selector matrix $M_f^{\operatorname{SEL}_m}$ remain valid when $m\leq n^{O(1)}$? | Does the positive-semidefinite-rank lower bound for the selector matrix M_f^{\mathrm{SEL}_m} remain valid when m\leq n^{O(1)}, rather than only under the currently known larger-range hypothesis? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,555 | OWR-15580-008 | Practical Sum-of-Squares Tensor Completion | Generalize exact sum-of-squares tensor-completion results beyond orthogonal components, and determine whether the sum-of-squares tensor-completion algorithm can be made faster and practically usable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361](https://doi.org/10.4171/owr/2017/37)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,017 | 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-15580-008",
"literature-status:open",
"owr-year:2017"
] | The report explicitly lists both extension beyond the non orthogonal tensor case and a faster practical sum of squares tensor completion method as open questions; no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2017/37",
"label": "Proof Complexity and Beyond"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/37 | null | null | null | Generalize exact sum-of-squares tensor-completion results beyond orthogonal components, and determine whether the sum-of-squares tensor-completion algorithm can be made faster and practically usable. | Generalize exact sum-of-squares tensor-completion results beyond orthogonal components, and determine whether the sum-of-squares tensor-completion algorithm can be made faster and practically usable. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Proof Complexity and Beyond (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/37, pp. 2299--2361 |
30,003,556 | OWR-15581-002 | Lehmer’s Mahler Measure Problem | Given $\varepsilon>0$, does there exist an integral polynomial $f(x)$ with $1<M(f)<1+\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 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-15581-002",
"literature-status:open",
"owr-year:2017"
] | Lehmer question remains open in general despite substantial bounds and partial results for restricted polynomial families. | [
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
},
{
"url": "https://www.ams.org/journals/mcom/1998-67-224/S0025-5718-98-01006-0/",
"label": "Mossinghoff on small Mahler measure"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Given $\varepsilon>0$, does there exist an integral polynomial $f(x)$ with $1<M(f)<1+\varepsilon$? | Given \varepsilon>0, does there exist an integral polynomial f(x) with 1<M(f)<1+\varepsilon? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,557 | OWR-15581-003 | Spanning-Tree Growth Rates Near One | In the graph-complexity reformulation of Lehmer's Mahler-measure problem (Hironaka), for a planar graph $G$ embedded in the punctured plane $\mathbb{R}^2 \setminus \{0\}$, let $G_r$ be its $r$-fold cyclic covering graph and let $\tau(G_r)$ be the number of spanning trees of $G_r$. Given $\varepsilon > 0$, does there ex... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15581-003",
"literature-status:open",
"owr-year:2017"
] | The graph reformulation is equivalent to Lehmer question, so it remains open in general; known special cases do not establish the asserted arbitrarily small gap above one. | [
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
},
{
"url": "https://arxiv.org/abs/1106.1304",
"label": "Lehmer question and graph complexity"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | In the graph-complexity reformulation of Lehmer's Mahler-measure problem (Hironaka), for a planar graph $G$ embedded in the punctured plane $\mathbb{R}^2 \setminus \{0\}$, let $G_r$ be its $r$-fold cyclic covering graph and let $\tau(G_r)$ be the number of spanning trees of $G_r$. Given $\varepsilon > 0$, does there ex... | Equivalently, given \varepsilon>0, does there exist a graph G in the punctured plane such that 1<\lim_{r\to\infty}\tau(G_r)^{1/r}<1+\varepsilon? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,558 | OWR-15581-004 | The Strong Slope Conjecture for Colored Jones Polynomials | Does the asymptotic degree growth of the colored Jones polynomial of every knot determine the boundary slopes, Euler characteristics, and numbers of sheets of essential Jones surfaces, as predicted by the Strong Slope Conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,017 | 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-15581-004",
"literature-status:partially-solved",
"owr-year:2017"
] | The Strong Slope Conjecture is proved for important classes including broad families of Montesinos knots, but the record asks for the conjecture beyond those verified classes and no general proof is known. | [
{
"url": "https://nyjm.albany.edu/j/2019/25-2.html",
"label": "Slope conjectures for 3 string Montesinos knots"
},
{
"url": "https://arxiv.org/abs/1807.00957",
"label": "The Slope Conjecture for Montesinos knots"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimens... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Does the asymptotic degree growth of the colored Jones polynomial of every knot determine the boundary slopes, Euler characteristics, and numbers of sheets of essential Jones surfaces, as predicted by the Strong Slope Conjecture? | The Strong Slope Conjecture asserts that the asymptotic degree growth of the colored Jones polynomial of a knot determines boundary slopes and further data, including the Euler characteristic and number of sheets, of essential Jones surfaces. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,559 | OWR-15581-005 | Verlinde Formulas and Lusztig Characters for New Weight Families | Can one find Verlinde-like dimension formulas for other families of dominant weights, and do the resulting character formulas coincide with those predicted by Lusztig’s conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15581-005",
"literature-status:partially-solved",
"owr-year:2017"
] | The dimension formula question is answered for the p minus 1 fundamental weights, while the broader family question remains open; the related general Lusztig conjecture is known false but that does not settle this specific character comparison. | [
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
},
{
"url": "https://doi.org/10.1016/j.aim.2015.04.022",
"label": "Light leaves and Lusztig conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Can one find Verlinde-like dimension formulas for other families of dominant weights, and do the resulting character formulas coincide with those predicted by Lusztig’s conjecture? | Can one find Verlinde-like dimension formulas for other families of dominant weights, and do the resulting character formulas coincide with those predicted by Lusztig’s conjecture? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,560 | OWR-15581-006 | Rational Formula for the Knot Invariant $\rho_1$ | For a knot $K \subset S^3$, let $P^{(1)}(t)$ be the $1$-loop polynomial (perturbed Alexander invariant) arising in the asymptotic expansion of the colored Jones polynomial, and let $\rho_1(t)$ be Rozansky's rational $1$-loop knot invariant. Does the conjectured identity
$$
\rho_1(t^2) = \frac{t^2}{(1 - t^2)^2} P^{(1)}(... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 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-15581-006",
"literature-status:open",
"owr-year:2017"
] | The extracted rho one identity is presented as a conjectural formula for the perturbed Alexander invariant; current primary work still describes the invariant as lacking a topological explanation and does not establish this identity. | [
{
"url": "https://doi.org/10.4171/QT/206",
"label": "A perturbed Alexander invariant"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | For a knot $K \subset S^3$, let $P^{(1)}(t)$ be the $1$-loop polynomial (perturbed Alexander invariant) arising in the asymptotic expansion of the colored Jones polynomial, and let $\rho_1(t)$ be Rozansky's rational $1$-loop knot invariant. Does the conjectured identity
$$
\rho_1(t^2) = \frac{t^2}{(1 - t^2)^2} P^{(1)}(... | For the knot invariant \rho_1, conjecturally \rho_1(t^2)=\frac{t^2}{(1-t^2)^2}P^{(1)}(t). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,561 | OWR-15581-008 | Relations Between Arithmetic Milnor Invariants | For $\ell=2,3$, is there a relation between the mod-$\ell$ Milnor invariants $\mu_\ell(I)$ of primes and the $\ell$-adic Milnor invariants $\mu^{(\ell)}(g;I)$ of Galois elements? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,017 | 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-15581-008",
"literature-status:partially-solved",
"owr-year:2017"
] | The relation between the two invariants is proved for quadratic and cubic cases with index length three, but the record asks for l equal to two or three without restricting the index and the general relation remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.jnt.2018.10.010",
"label": "Arithmetic topology in Ihara theory II"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | For $\ell=2,3$, is there a relation between the mod-$\ell$ Milnor invariants $\mu_\ell(I)$ of primes and the $\ell$-adic Milnor invariants $\mu^{(\ell)}(g;I)$ of Galois elements? | For l=2,3, is there a relation between the mod-l Milnor invariants \mu_l(I) of primes and the l-adic Milnor invariants \mu^{(l)}(g;I) of Galois elements? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,562 | OWR-15581-009 | Volume Bounds from Mahler Measures of Biperiodic Links | Let $L$ be a semi-regular biperiodic alternating link, let $\Lambda$ be its toroidally alternating quotient, and let $p(z,w)$ be the characteristic polynomial of the associated toroidal dimer model. Is
$$\operatorname{vol}\!\left(T^2\times(-1,1)\setminus L\right)\leq2\pi m(p(z,w))$$
hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 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-15581-009",
"literature-status:open",
"owr-year:2017"
] | The Mahler measure versus volume inequality is proved for several toroidal link examples, but the conjecture for general semi regular biperiodic alternating links remains open. | [
{
"url": "https://doi.org/10.1112/jlms.12200",
"label": "Mahler measure and the Vol Det conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Let $L$ be a semi-regular biperiodic alternating link, let $\Lambda$ be its toroidally alternating quotient, and let $p(z,w)$ be the characteristic polynomial of the associated toroidal dimer model. Is
$$\operatorname{vol}\!\left(T^2\times(-1,1)\setminus L\right)\leq2\pi m(p(z,w))$$
hold? | For a semi-regular biperiodic alternating link L with toroidally alternating quotient \Lambda and characteristic polynomial p(z,w), conjecturally \operatorname{vol}(T^2\times(-1,1)-L)\leq 2\pi m(p(z,w)). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,563 | OWR-15581-010 | Betti Sequences of Closed Smooth Manifolds | Which sequences $b_0=1,b_1,\ldots,b_{4k}=1$ with $b_{2k}$ odd can occur as the Betti numbers of a closed smooth $4k$-manifold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,017 | 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-15581-010",
"literature-status:partially-solved",
"owr-year:2017"
] | Many Betti number patterns are realized and the odd middle Betti case is reduced to rational projective plane existence, but rational projective planes and hence the full realization classification remain unknown in some dimensions. | [
{
"url": "https://msp.org/agt/2026/26-2/agt-v26-n2-p10-p.pdf",
"label": "Betti numbers of closed manifolds"
},
{
"url": "https://www.math.princeton.edu/events/what-are-betti-numbers-closed-manifolds-2023-10-26t170000",
"label": "What are the Betti numbers of closed manifolds"
},
{
"url":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Which sequences $b_0=1,b_1,\ldots,b_{4k}=1$ with $b_{2k}$ odd can occur as the Betti numbers of a closed smooth $4k$-manifold? | Which sequences b_0=1,b_1,\ldots,b_{4k}=1 with b_{2k} odd can occur as the Betti numbers of a closed smooth 4k-manifold? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,564 | OWR-15581-011 | Volume Envelopes of Cusped Hyperbolic Three-Manifolds | Can one prove an explicit upper bound for the asymptotic envelope function $\Omega_{\mathrm{cm}}(t)$ of normalized volumes of cusped hyperbolic $3$-manifolds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 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-15581-011",
"literature-status:open",
"owr-year:2017"
] | The report gives the Adams lower bound for the cusped volume envelope but asks for an explicit upper bound; no general explicit upper bound resolving that question was located. | [
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | Can one prove an explicit upper bound for the asymptotic envelope function $\Omega_{\mathrm{cm}}(t)$ of normalized volumes of cusped hyperbolic $3$-manifolds? | Can one prove an explicit upper bound for the asymptotic envelope function \Omega_{\mathrm{cm}}(t) of normalized volumes of cusped hyperbolic 3-manifolds? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,565 | OWR-15581-013 | Complexified Volume Conjecture for Hyperbolic Knots | For every hyperbolic knot $K\subset S^3$, is
$$\lim_{N\to\infty}\frac{2\pi\log J_N\!\left(K;e^{2\pi i/N}\right)}{N}=\operatorname{Vol}(S^3\setminus K)+i\operatorname{CS}(S^3\setminus K),$$
where $J_N$ is the $N$-colored Jones invariant with the indicated root-of-unity specialization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15581-014"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15581-013",
"literature-status:open",
"owr-year:2017"
] | The truncated record identifies the general quantum knot invariant volume relation, whose general hyperbolic knot case remains an unresolved volume conjecture. | [
{
"url": "https://doi.org/10.1007/BF02392716",
"label": "The colored Jones polynomial and the simplicial volume"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | For every hyperbolic knot $K\subset S^3$, is
$$\lim_{N\to\infty}\frac{2\pi\log J_N\!\left(K;e^{2\pi i/N}\right)}{N}=\operatorname{Vol}(S^3\setminus K)+i\operatorname{CS}(S^3\setminus K),$$
where $J_N$ is the $N$-colored Jones invariant with the indicated root-of-unity specialization? | For every hyperbolic knot K\subset S^3, the Volume Conjecture predicts \lim_{N\to\infty}\frac{2\pi\log J_N(K)}{N}=\operatorname{Vol}(K)+\sqrt{-1} \operatorname{CS}(K). | corrected_verified | The official report was checked. The reconstruction restores the root-of-unity evaluation and identifies the volume and Chern–Simons terms as invariants of the knot complement. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,566 | OWR-15581-014 | Duplicate Complexified Volume Conjecture | For every hyperbolic knot K\subset S^3, the colored-Jones Volume Conjecture predicts \lim_{N\to\infty}\frac{2\pi\log J_N(K)}{N}=\operatorname{Vol}(K)+\sqrt{-1} \operatorname{CS}(K). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report contains one complexified Volume Conjecture for the colored Jones invariant, represented canonically by OWR-15581-013. T) | [
"OWR-15581-013"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15581-014",
"literature-status:open",
"owr-year:2017"
] | The stated complex volume limit is proved for selected knots such as the figure eight and Borromean examples, but it is not proved for arbitrary hyperbolic knots. | [
{
"url": "https://doi.org/10.1007/BF02392716",
"label": "The colored Jones polynomial and the simplicial volume"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensional Topology and Number Theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | null | For every hyperbolic knot K\subset S^3, the colored-Jones Volume Conjecture predicts \lim_{N\to\infty}\frac{2\pi\log J_N(K)}{N}=\operatorname{Vol}(K)+\sqrt{-1} \operatorname{CS}(K). | unrecoverable | The official report contains one complexified Volume Conjecture for the colored Jones invariant, represented canonically by OWR-15581-013. This record repeats that same conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,567 | OWR-15581-015 | Positivity and Evenness in HOMFLY-PT Knot Homology | For which knots does the HOMFLY-PT polynomial have positive coefficients when expressed in $q$ and $-a$, and for which knots is triply graded Khovanov–Rozansky homology concentrated in even homological degrees? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426](https://doi.org/10.4171/owr/2017/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,017 | 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-15581-015",
"literature-status:partially-solved",
"owr-year:2017"
] | Triply graded homology and even degree concentration are established for broad positive torus knot and link families, but positivity and the requested evenness classification for general knots remain open. | [
{
"url": "https://doi.org/10.2140/gt.2022.26.47",
"label": "Homology of torus knots"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/blms.12761",
"label": "Triply graded link homology"
},
{
"url": "https://doi.org/10.4171/owr/2017/38",
"label": "Low dimensio... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/38 | null | null | null | For which knots does the HOMFLY-PT polynomial have positive coefficients when expressed in $q$ and $-a$, and for which knots is triply graded Khovanov–Rozansky homology concentrated in even homological degrees? | For which knots does the HOMFLY-PT polynomial have positive coefficients in q and -a, and for which knots is triply graded Khovanov--Rozansky homology concentrated in even degrees? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/38, pp. 2363--2426 |
30,003,568 | OWR-15582-002 | Classification of Codimension-One Projective Foliations | Is every codimension-one holomorphic foliation $\mathcal F$ on a projective manifold $X$ either transversely projective or the pullback $\mathcal F=\pi^*\mathcal G$ of a one-dimensional foliation $\mathcal G$ on a projective surface under a rational map $\pi:X\dashrightarrow Y$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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... | [
"OWR-15582-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15582-002",
"literature-status:open",
"owr-year:2017"
] | The Cerveau Lins Neto conjecture is explicitly still a conjecture; several special cases and structural results are known, but the stated dichotomy for all projective manifolds is unresolved. | [
{
"url": "https://www.ams.org/notices/202408/rnoti-p1025.pdf",
"label": "Foliations and the Cerveau Lins Neto conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "Komplexe Analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | Is every codimension-one holomorphic foliation $\mathcal F$ on a projective manifold $X$ either transversely projective or the pullback $\mathcal F=\pi^*\mathcal G$ of a one-dimensional foliation $\mathcal G$ on a projective surface under a rational map $\pi:X\dashrightarrow Y$? | Every codimension-one holomorphic foliation \mathcal F on a projective manifold X is either transversely projective or is the pullback of a foliation on a projective surface by a rational map X\dashrightarrow Y. | corrected_verified | The official report was checked. The statement is the Cerveau–Lins Neto conjecture, with the two alternatives and pullback data restored. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,569 | OWR-15582-003 | Theorem on Orbicurve Factorization of Holonomy Representations | If X is quasi-projective and \rho:\pi_1(X)\to\operatorname{Diff}(\mathbb C,0) has non-virtually-abelian image \Gamma, then \rho factors through an orbicurve representation \pi_1^{\mathrm{orb}}(C)\to\Gamma/\operatorname{Center}(\Gamma) induced by a morphism X\to C. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report labels this factorization assertion as Theorem 2 and explains that it supplies evidence for the distinct foliation conje) | [
"OWR-15582-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15582-003",
"literature-status:open",
"owr-year:2017"
] | The extracted text is a theorem fragment followed by the Cerveau Lins Neto conjecture and does not isolate a resolved standalone problem; the associated general conjectural classification remains open. | [
{
"url": "https://www.ams.org/notices/202408/rnoti-p1025.pdf",
"label": "Foliations and the Cerveau Lins Neto conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "Komplexe Analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | null | If X is quasi-projective and \rho:\pi_1(X)\to\operatorname{Diff}(\mathbb C,0) has non-virtually-abelian image \Gamma, then \rho factors through an orbicurve representation \pi_1^{\mathrm{orb}}(C)\to\Gamma/\operatorname{Center}(\Gamma) induced by a morphism X\to C. | unrecoverable | The official report labels this factorization assertion as Theorem 2 and explains that it supplies evidence for the distinct foliation conjecture represented by OWR-15582-002. It is not a source-stated open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for p... | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,570 | OWR-15582-004 | Heegner Divisors and the Pseudo-Effective Cone | Is the cone generated by primitive Heegner divisors on $\mathcal F_{2d}$ a strict subcone of the pseudo-effective cone $\operatorname{Eff}(\mathcal F_{2d})$, or do the two cones coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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-15582-004",
"literature-status:open",
"owr-year:2017"
] | The equality of the cone generated by effective Heegner divisors with the full pseudo-effective cone remains open; finite generation and substantial arithmetic cases are known, but not the asserted equality. | [
{
"url": "https://doi.org/10.1090/jag/734",
"label": "Bruinier--Moller"
},
{
"url": "https://arxiv.org/abs/2504.16730",
"label": "Extremal divisors on K3 moduli"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | Is the cone generated by primitive Heegner divisors on $\mathcal F_{2d}$ a strict subcone of the pseudo-effective cone $\operatorname{Eff}(\mathcal F_{2d})$, or do the two cones coincide? | Is the cone generated by primitive Heegner divisors on \mathcal F_{2d} a strict subcone of the pseudo-effective cone \operatorname{Eff}(\mathcal F_{2d}), or do the two cones coincide? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,571 | OWR-15582-005 | Relative Kähler–Ricci Flow on Projective-Space Fibrations | For a projective-space fibration $f:X\to S$ arising from a rank-$r$ bundle $E$, can the relative Kähler–Ricci flow be developed directly on $\mathcal O_E(r)$, using
$$K_{X/S}^{-1}\cong\mathcal O_E(r)\otimes f^*(\det E)^{-1},$$
rather than on $K_{X/S}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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-15582-005",
"literature-status:open",
"owr-year:2017"
] | The extracted entry is a proposed relative Kahler--Ricci-flow research direction rather than a settled theorem; special relative flows are understood, but the proposed general program remains unresolved. | [
{
"url": "https://arxiv.org/abs/1002.3717",
"label": "Berman"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | For a projective-space fibration $f:X\to S$ arising from a rank-$r$ bundle $E$, can the relative Kähler–Ricci flow be developed directly on $\mathcal O_E(r)$, using
$$K_{X/S}^{-1}\cong\mathcal O_E(r)\otimes f^*(\det E)^{-1},$$
rather than on $K_{X/S}$? | Study the relative Kähler--Ricci flow on the bundle O_E(r) instead of on K_{X/S}, for a projective-space fibration, under the canonical relation K_{X/S}^{-1} \cong O_E(r)\otimes f^*(\det E)^{-1}. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,572 | OWR-15582-006 | Universal-Cover Decomposition for Nef Anticanonical Manifolds | If $X$ is a compact Kähler manifold with nef anticanonical class, does its universal cover decompose as
$$\widetilde X\simeq\mathbb C^q\times\prod_jY_j\times\prod_kS_k\times Z,$$
where each $Y_j$ is an irreducible Calabi–Yau manifold, each $S_k$ is an irreducible hyperkähler manifold, and $Z$ is rationally connected? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 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-15582-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The conjectural universal-cover decomposition is proved for projective manifolds and under additional hypotheses, while the full compact Kahler statement remains unresolved. | [
{
"url": "https://arxiv.org/abs/1706.08814",
"label": "Cao--Horing"
},
{
"url": "https://arxiv.org/abs/2506.23218",
"label": "Nef anticanonical compact Kahler manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | If $X$ is a compact Kähler manifold with nef anticanonical class, does its universal cover decompose as
$$\widetilde X\simeq\mathbb C^q\times\prod_jY_j\times\prod_kS_k\times Z,$$
where each $Y_j$ is an irreducible Calabi–Yau manifold, each $S_k$ is an irreducible hyperkähler manifold, and $Z$ is rationally connected? | Conjecture: If X is a compact Kähler manifold with nef anticanonical class, then its universal cover decomposes as \widetilde X \simeq \mathbb C^q\times\prod_j Y_j\times\prod_k S_k\times Z, where the Y_j are irreducible Calabi--Yau manifolds, the S_k are irreducible hyperkähler manifolds, and Z is rationally connected. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,573 | OWR-15582-007 | Kobayashi Pseudometric Vanishing on Calabi–Yau Manifolds | Does the Kobayashi pseudometric vanish identically on every compact Calabi–Yau manifold? In particular, must every such manifold be Kobayashi non-hyperbolic and contain an entire curve? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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-15582-007",
"literature-status:open",
"owr-year:2017"
] | Vanishing of the Kobayashi pseudometric is established for K3 and many hyperkahler examples, but no general proof for all compact Calabi--Yau manifolds is known. | [
{
"url": "https://doi.org/10.1112/jlms/jdu038",
"label": "Kamenova--Lu--Verbitsky"
},
{
"url": "https://arxiv.org/abs/2212.11411",
"label": "Non-hyperbolicity of holomorphic symplectic varieties"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | Does the Kobayashi pseudometric vanish identically on every compact Calabi–Yau manifold? In particular, must every such manifold be Kobayashi non-hyperbolic and contain an entire curve? | Kobayashi conjecture: The Kobayashi pseudometric vanishes on every compact Calabi--Yau manifold; in particular, every compact Calabi--Yau manifold is Kobayashi non-hyperbolic and contains an entire curve. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,574 | OWR-15582-009 | Intrinsic $L^2$ Extension Beyond Nilpotent Sections | Let $0=m_0<m_1<\cdots$ be the jumping numbers of a multiplier-ideal filtration $\mathcal I(m\psi)$, let $J=\mathcal I(m_p\psi):\mathcal I(m_{p-1}\psi)$, and let $Y=V(J)$. Without requiring a section $f$ on $Y$ to be nilpotent and associated with $\mathcal I(m_{p-1}\psi)/\mathcal I(m_p\psi)$, is there an intrinsic $L^2$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473](https://doi.org/10.4171/owr/2017/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 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-15582-009",
"literature-status:open",
"owr-year:2017"
] | The intrinsic L2 estimate without the nilpotent-section hypothesis is explicitly identified as open; available extension results cover important special cases but not the general formulation. | [
{
"url": "https://www-fourier.ujf-grenoble.fr/~demailly/source_files/holom_extension/holom_extension_ltx1.pdf",
"label": "Demailly"
},
{
"url": "https://doi.org/10.4171/owr/2017/39",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/39 | null | null | null | Let $0=m_0<m_1<\cdots$ be the jumping numbers of a multiplier-ideal filtration $\mathcal I(m\psi)$, let $J=\mathcal I(m_p\psi):\mathcal I(m_{p-1}\psi)$, and let $Y=V(J)$. Without requiring a section $f$ on $Y$ to be nilpotent and associated with $\mathcal I(m_{p-1}\psi)/\mathcal I(m_p\psi)$, is there an intrinsic $L^2$... | Without assuming that the section f is nilpotent and associated with the ideal sheaf of the previous jumping number, does there exist a reasonably intrinsic L2 estimate for the corresponding extension problem? | corrected_verified | The official report was checked. The reconstruction restores the multiplier-ideal jumping-number setup, conductor ideal, subvariety, and the two linked unresolved objects. | null | null | null | null | null | Komplexe Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/39, pp. 2427--2473 |
30,003,575 | OWR-15583-003 | Generalized Riemann Hypothesis for Automorphic L-Functions | For every automorphic $L$-function having an Euler product, the Ramanujan bounds, analytic continuation, and a functional equation, do all nontrivial zeros lie on the critical line $\operatorname{Re}(s)=1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,017 | 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-15583-003",
"literature-status:open",
"owr-year:2017"
] | The generalized Riemann hypothesis for the automorphic L-functions described in the entry remains unproved; subconvexity and zero-density results do not establish it. | [
{
"url": "https://doi.org/10.4171/owr/2017/40",
"label": "OWR report"
},
{
"url": "https://doi.org/10.4007/annals.2010.172.1469",
"label": "Soundararajan"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | For every automorphic $L$-function having an Euler product, the Ramanujan bounds, analytic continuation, and a functional equation, do all nontrivial zeros lie on the critical line $\operatorname{Re}(s)=1/2$? | Generalized Riemann Hypothesis: For an L-function satisfying the stated Euler-product, Ramanujan, continuation, and functional-equation axioms, every zero in the critical strip 0\leq\Re(s)\leq1 lies on the critical line \Re(s)=1/2. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,576 | OWR-15583-004 | Simplicity of Nonreal Zeros of Cusp-Form L-Functions | For a primitive holomorphic cusp form $f$, are all nonreal zeros of $L(s,f)$ simple? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,017 | 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-15583-004",
"literature-status:open",
"owr-year:2017"
] | Infinitely many simple zeros and quantitative lower bounds are known, but the conjecture that all nonreal zeros are simple remains unresolved, including at arbitrary level. | [
{
"url": "https://doi.org/10.4171/JEMS/603",
"label": "Booker"
},
{
"url": "https://doi.org/10.1112/S0025579318000530",
"label": "Booker--Milinovich--Ng"
},
{
"url": "https://doi.org/10.4171/JEMS/1559",
"label": "de Faveri"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | For a primitive holomorphic cusp form $f$, are all nonreal zeros of $L(s,f)$ simple? | Conjecture: For a primitive holomorphic cusp form f, all nonreal zeros of its L-function L(s,f) are simple. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,577 | OWR-15583-005 | Power-Rate Arithmetic Quantum Unique Ergodicity | For Hecke–Maass cusp forms $\phi$ on the modular surface with Laplace eigenvalue $\lambda\to\infty$, prove quantitative equidistribution of the probability measures $\mu_\phi$ toward hyperbolic area measure $\mu$ at a power rate $O(\lambda^{-\delta})$ for some $\delta>0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,017 | 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-15583-005",
"literature-status:open",
"owr-year:2017"
] | Arithmetic quantum unique ergodicity is known, including level-aspect results, but the power-saving rate asserted by strong AQUE remains open. | [
{
"url": "https://arxiv.org/abs/1702.02908",
"label": "Nelson"
},
{
"url": "https://doi.org/10.4171/owr/2017/40",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | For Hecke–Maass cusp forms $\phi$ on the modular surface with Laplace eigenvalue $\lambda\to\infty$, prove quantitative equidistribution of the probability measures $\mu_\phi$ toward hyperbolic area measure $\mu$ at a power rate $O(\lambda^{-\delta})$ for some $\delta>0$. | Strong AQUE problem: For Hecke--Maass cusp forms on the modular surface with eigenvalue \lambda\to\infty, prove quantitative equidistribution \mu_\phi\to\mu at a power rate \lambda^{-\delta} for some \delta>0. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,578 | OWR-15583-006 | Variance of Gaussian Prime Angles in Short Arcs | Let $N$ be the number of Gaussian-prime angles with norm at most $X$, and let $N_{K,X}(\theta)$ count those in an arc of angular scale $1/K$. Is $$\frac{\operatorname{Var}(N_{K,X})}{N/K}\sim\min\!\left\{1,\frac{2\log K}{\log N}\right\}$$ as $X\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,017 | 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-15583-006",
"literature-status:open",
"owr-year:2017"
] | The stated variance law for angles of Gaussian primes remains a conjecture; unconditional work proves only partial almost-all-sector results and related function-field analogues. | [
{
"url": "https://doi.org/10.1007/s11856-019-1867-5",
"label": "Rudnick--Waxman"
},
{
"url": "https://doi.org/10.4064/aa190331-23-7",
"label": "Huang--Liu--Rudnick"
},
{
"url": "https://doi.org/10.4171/owr/2017/40",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | Let $N$ be the number of Gaussian-prime angles with norm at most $X$, and let $N_{K,X}(\theta)$ count those in an arc of angular scale $1/K$. Is $$\frac{\operatorname{Var}(N_{K,X})}{N/K}\sim\min\!\left\{1,\frac{2\log K}{\log N}\right\}$$ as $X\to\infty$? | Gaussian-prime variance conjecture: If N is the number of Gaussian-prime angles with p\leq X and N_{K,X}(\theta) counts those in an arc of scale 1/K, then Var(N_{K,X})/(N/K)\sim\min\{1,2\log K/\log N\} as X\to\infty. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,579 | OWR-15583-007 | Equidistribution of Automorphic L Functions over Function Fields | Establish equidistribution of local factors, or of complete $L$-functions, in families of automorphic representations over function fields with specified local conditions, preferably by a method that also proves the Ramanujan conjecture for those families. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | open | null | 2,017 | 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-15583-007",
"literature-status:open",
"owr-year:2017"
] | The Ramanujan conjecture is known in several cases and strong bounds are available, but the general automorphic statement over number fields remains open. | [
{
"url": "https://doi.org/10.4007/annals.2011.174.1.18",
"label": "Blomer--Brumley"
},
{
"url": "https://doi.org/10.4171/owr/2017/40",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | Establish equidistribution of local factors, or of complete $L$-functions, in families of automorphic representations over function fields with specified local conditions, preferably by a method that also proves the Ramanujan conjecture for those families. | Establish equidistribution of local factors, or of full L-functions, in families of automorphic representations over function fields with specified local conditions, ideally by a method that also proves the Ramanujan conjecture. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,580 | OWR-15583-008 | Keating–Snaith Distribution of Central L-Values | In each standard family of central $L$-values, is the logarithm of the central value asymptotically Gaussian with the Keating–Snaith mean and variance? More precisely, for primitive characters modulo $q$, are the mean and variance asymptotic to $0$ and $\tfrac12\log\log q$; for quadratic characters $\chi_d$, to $\tfrac... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537](https://doi.org/10.4171/owr/2017/40)
## Literature review (checked 2026-08-21)
**Sta... | 3 | partially_solved | null | 2,017 | 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-15583-008",
"literature-status:partially-solved",
"owr-year:2017"
] | For quadratic twists, sharp upper bounds and a one-sided central limit theorem are proved, with conditional lower bounds later obtained, but the full conjectural value distribution is not established. | [
{
"url": "https://arxiv.org/abs/1403.7067",
"label": "Radziwill--Soundararajan"
},
{
"url": "https://doi.org/10.4064/aa230805-3-1",
"label": "Conditional lower bounds"
},
{
"url": "https://doi.org/10.4171/owr/2017/40",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/40 | null | null | null | In each standard family of central $L$-values, is the logarithm of the central value asymptotically Gaussian with the Keating–Snaith mean and variance? More precisely, for primitive characters modulo $q$, are the mean and variance asymptotic to $0$ and $\tfrac12\log\log q$; for quadratic characters $\chi_d$, to $\tfrac... | Keating--Snaith value-distribution conjecture: In the standard families of central L-values, the logarithm of the central value is asymptotically Gaussian; for primitive characters modulo q its mean and variance are approximately 0 and one-half\log\log q, for quadratic characters \chi_d its mean and variance are approx... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Automorphic Forms and Arithmetic (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/40, pp. 2475--2537 |
30,003,581 | OWR-15584-001 | Lower-Bounded Hamiltonians for Many-Body Point Interactions | Construct a self-adjoint Hamiltonian, bounded from below, that models pairwise point interactions in a many-body quantum system. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/41, pp. 2539--2599](https://doi.org/10.4171/owr/2017/... | 3 | open | null | 2,017 | 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-15584-001",
"literature-status:open",
"owr-year:2017"
] | Constructing a self-adjoint, lower-bounded Hamiltonian for the stated many-body point-interaction model remains a difficult unresolved problem; regularized or modified models do not settle the original one. | [
{
"url": "https://arxiv.org/abs/2107.07188",
"label": "Three-body zero-range interactions"
},
{
"url": "https://arxiv.org/abs/2403.12594",
"label": "Contact-interaction Hamiltonians"
},
{
"url": "https://doi.org/10.4171/owr/2017/41",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/41 | null | null | null | Construct a self-adjoint Hamiltonian, bounded from below, that models pairwise point interactions in a many-body quantum system. | Construct a self-adjoint Hamiltonian bounded from below that models pairwise point interactions for a many-body quantum system. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/41, pp. 2539--2599 |
30,003,582 | OWR-15584-003 | Quantum Backflow Bounds with External Potentials | For a quantum particle scattering from an external potential, is the smeared probability-flux operator on positive incoming states bounded below, analogously to the free-particle quantum-backflow inequality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/41, pp. 2539--2599](https://doi.org/10.4171/owr/2017/... | 3 | partially_solved | null | 2,017 | 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-15584-003",
"literature-status:partially-solved",
"owr-year:2017"
] | Lower bounds for backflow-type flux are proved for important short-range potential classes, but a general theorem for arbitrary potentials remains unresolved. | [
{
"url": "https://doi.org/10.1103/PhysRevA.96.012112",
"label": "Bostelmann--Cadamuro--Lechner"
},
{
"url": "https://arxiv.org/abs/1710.04322",
"label": "Cadamuro"
},
{
"url": "https://doi.org/10.4171/owr/2017/41",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/41 | null | null | null | For a quantum particle scattering from an external potential, is the smeared probability-flux operator on positive incoming states bounded below, analogously to the free-particle quantum-backflow inequality? | For a quantum particle scattering from an external potential, can the smeared probability-flux operator for positive incoming states still be bounded below, as in the free-particle quantum-backflow inequality? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/41, pp. 2539--2599 |
30,003,583 | OWR-15585-001 | Single-Prime Characterizations of the UCT Problem | Does the characterization of the UCT problem remain valid if the quantifier over primes is restricted exclusively to $p=2$, or to another single prime? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-001",
"literature-status:open",
"owr-year:2017"
] | The UCT/model-action argument still leaves open whether one may restrict the construction to a single prime, such as p equals 2; no general resolution of that question was found. | [
{
"url": "https://doi.org/10.1016/j.aim.2017.06.024",
"label": "Barlak--Li"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | Does the characterization of the UCT problem remain valid if the quantifier over primes is restricted exclusively to $p=2$, or to another single prime? | Does the characterization of the UCT problem remain valid if the quantifier over primes is restricted exclusively to p=2, or to another single prime? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,584 | OWR-15585-002 | Nuclear Dimension of Transformation-Group Crossed Products | For a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$, when does the crossed product $C_0(X)\rtimes G$ have finite nuclear dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Finite nuclear dimension is established for broad classes of crossed products under dynamical regularity assumptions, but there is no complete characterization for all continuous actions in the extracted question. | [
{
"url": "https://doi.org/10.1007/s00222-020-01013-1",
"label": "Castillejos--Evington--Tikuisis--White--Winter"
},
{
"url": "https://doi.org/10.4171/JEMS/995",
"label": "Kerr"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | For a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$, when does the crossed product $C_0(X)\rtimes G$ have finite nuclear dimension? | For a continuous action of a locally compact group G on a locally compact Hausdorff space X, when does the crossed product C_0(X)\rtimes G have finite nuclear dimension? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,585 | OWR-15585-003 | Toms–Winter Regularity Conjecture | For every nonelementary simple separable unital nuclear $C^*$-algebra $A$, are finite nuclear dimension, tensorial absorption of the Jiang–Su algebra $\mathcal Z$, and strict comparison of positive elements equivalent? When $A$ is stably finite, is finite decomposition rank equivalent to these conditions as well? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-003",
"literature-status:partially-solved",
"owr-year:2017"
] | For simple separable unital nuclear C-star algebras, finite nuclear dimension and Z-stability are equivalent, while the remaining strict-comparison implication in the full Toms--Winter equivalence is not known in general. | [
{
"url": "https://doi.org/10.1007/s00222-020-01013-1",
"label": "Castillejos--Evington--Tikuisis--White--Winter"
},
{
"url": "https://doi.org/10.1093/imrn/rnaa282",
"label": "Uniform property Gamma"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | For every nonelementary simple separable unital nuclear $C^*$-algebra $A$, are finite nuclear dimension, tensorial absorption of the Jiang–Su algebra $\mathcal Z$, and strict comparison of positive elements equivalent? When $A$ is stably finite, is finite decomposition rank equivalent to these conditions as well? | Toms--Winter conjecture: For every non-elementary simple separable unital nuclear C*-algebra A, finite nuclear dimension, tensorial absorption of the Jiang--Su algebra Z, and strict comparison of positive elements are equivalent; when A is stably finite, finite decomposition rank is conjecturally equivalent as well. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,586 | OWR-15585-004 | Uniform Property Gamma for Nuclear $C^*$-Algebras | Does every simple separable unital nuclear $C^*$-algebra have uniform property $\Gamma$; that is, for every $k\geq2$, does its central sequence algebra contain $k$ pairwise orthogonal positive contractions whose trace is $1/k$ for every limit trace? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-004",
"literature-status:open",
"owr-year:2017"
] | Uniform property Gamma is proved for important classes, but it remains open whether every simple separable unital infinite-dimensional nuclear C-star algebra has the property. | [
{
"url": "https://doi.org/10.1093/imrn/rnaa282",
"label": "Uniform property Gamma"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | Does every simple separable unital nuclear $C^*$-algebra have uniform property $\Gamma$; that is, for every $k\geq2$, does its central sequence algebra contain $k$ pairwise orthogonal positive contractions whose trace is $1/k$ for every limit trace? | Does every simple, separable, unital, nuclear C*-algebra have property \Gamma, namely, for each k\geq2, does its central sequence algebra contain k pairwise orthogonal positive contractions with equal trace 1/k against every limit trace? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,587 | OWR-15585-006 | Strong Approximate Innerness of Quasi-Free Actions | Is every finite abelian group action on a simple purely infinite Cuntz–Krieger algebra by diagonal quasi-free automorphisms strongly approximately inner in Izumi's sense? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Strong approximate innerness is proved for outer finite abelian diagonal quasi-free actions on simple Cuntz--Krieger algebras with aperiodic matrices, but the broader extracted formulation is not fully settled. | [
{
"url": "https://doi.org/10.7146/math.scand.a-114823",
"label": "Barlak--Szabo"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | Is every finite abelian group action on a simple purely infinite Cuntz–Krieger algebra by diagonal quasi-free automorphisms strongly approximately inner in Izumi's sense? | Is every finite abelian group action on a simple purely infinite Cuntz--Krieger algebra by diagonal quasi-free automorphisms strongly approximately inner in Izumi's sense? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,588 | OWR-15585-008 | Cartan Subalgebras in Classifiable $C^*$-Algebras | Does the Razak–Jacelon algebra $\mathcal W$ have a Cartan subalgebra? Does the Jiang–Su algebra $\mathcal Z$ have a distinguished one-dimensional Cartan subalgebra? Do strongly self-absorbing Cartan pairs admit useful existence and uniqueness theorems? What $K$-theory map is induced by the inclusion of a Cartan subalge... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-008",
"literature-status:partially-solved",
"owr-year:2017"
] | The compound list is mixed: Li constructs Cartan subalgebras for the Razak--Jacelon and Jiang--Su algebras in the classifiable simple setting, and Blackadar constructs CAR diagonals with non-totally-disconnected spectrum; the remaining classification, equivariant, and automorphism questions are not settled in general. | [
{
"url": "https://arxiv.org/abs/1802.01190",
"label": "Li, Cartan subalgebras in classifiable simple C*-algebras"
},
{
"url": "https://doi.org/10.2307/1971472",
"label": "Blackadar, Symmetries of the CAR algebra"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"label": "original O... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | Does the Razak–Jacelon algebra $\mathcal W$ have a Cartan subalgebra? Does the Jiang–Su algebra $\mathcal Z$ have a distinguished one-dimensional Cartan subalgebra? Do strongly self-absorbing Cartan pairs admit useful existence and uniqueness theorems? What $K$-theory map is induced by the inclusion of a Cartan subalge... | Open Cartan-subalgebra questions include whether W has a Cartan subalgebra, whether Z has distinguished one-dimensional Cartan subalgebras, whether strongly self-absorbing Cartan pairs admit a useful existence and uniqueness theory, what K-theory map is induced by inclusion, what equivalence relation models Popa intert... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,589 | OWR-15585-009 | Composite of Unrelated Operator-Algebra Questions | Let A be an AF algebra and let \alpha be an action of a finite cyclic group on A. Does the crossed product A\rtimes_\alpha\mathbb Z_n always satisfy the UCT, can the UCT problem be reduced to such crossed products, and does the answer change when A is UHF? Is the hyperfinite II_1 factor R quasidiagonal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629](https://doi.org/10.4171/owr/2017/42)
## Literature review (check... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 problem-session list shows that this extraction combines the UCT question for finite cyclic crossed products of AF algebras wit) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15585-009",
"literature-status:open",
"owr-year:2017"
] | The UCT inheritance question for the stated crossed products remains tied to the unresolved UCT problem; Barlak--Szabo reduce the general UCT problem to special crossed products of the Razak--Jacelon algebra, while Barlak--Li obtain permanence only under additional Cartan hypotheses. | [
{
"url": "https://arxiv.org/abs/1712.00823",
"label": "Barlak--Szabo, crossed products of the Razak--Jacelon algebra"
},
{
"url": "https://arxiv.org/abs/1511.02697",
"label": "Barlak--Li, Cartan subalgebras and the UCT problem"
},
{
"url": "https://doi.org/10.4171/owr/2017/42",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/42 | null | null | null | null | Let A be an AF algebra and let \alpha be an action of a finite cyclic group on A. Does the crossed product A\rtimes_\alpha\mathbb Z_n always satisfy the UCT, can the UCT problem be reduced to such crossed products, and does the answer change when A is UHF? Is the hyperfinite II_1 factor R quasidiagonal? | unrecoverable | The official problem-session list shows that this extraction combines the UCT question for finite cyclic crossed products of AF algebras with a separate quasidiagonality question for the hyperfinite factor. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: MASAs and Automorphisms of C*-Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/42, pp. 2601--2629 |
30,003,590 | OWR-15586-001 | Openness of Cones Generated by Ample Subvarieties | Let $X$ be a projective variety. Is the convex cone in $N_d(X)$ generated by numerical classes of ample $d$-dimensional subvarieties open? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-001",
"literature-status:open",
"owr-year:2017"
] | Higher-codimension positivity results show that ample-subvariety classes generate meaningful full-dimensional positive cones, but no general theorem identifies the cone generated by those classes with an open cone in the numerical cycle space. | [
{
"url": "https://content.algebraicgeometry.nl/2017-1/2017-1-001.pdf",
"label": "Fulger--Lehmann, positive cones of dual cycle classes"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "Fulger--Kuronya--Lehmann, OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Let $X$ be a projective variety. Is the convex cone in $N_d(X)$ generated by numerical classes of ample $d$-dimensional subvarieties open? | For a projective variety X, is the convex cone in N_d(X) generated by classes of ample d-dimensional subvarieties open? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,591 | OWR-15586-002 | Convex Geometry and Limits of Asymptotic Higher Cohomology | Is there a convex-geometric analogue of the Newton–Okounkov interpretation of volume for the asymptotic higher-cohomology functions $$\widehat h^i(D)=(\dim X)!\limsup_{m\to\infty}\frac{\dim H^i(X,\mathcal O_X(mD))}{m^{\dim X}}?$$ In particular, can $\widehat h^i(D)$ be realized as a Euclidean volume, and can the limsup... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-002",
"literature-status:open",
"owr-year:2017"
] | Kuronya proved continuity and numerical invariance of the asymptotic cohomological functions, but the normalized higher-cohomology limsup is still not known to be a limit in general. The 2026 progress on limits concerns the volume function, not this higher-cohomology question. | [
{
"url": "https://arxiv.org/abs/math/0501491",
"label": "Kuronya, asymptotic cohomological functions"
},
{
"url": "https://arxiv.org/abs/2607.09021",
"label": "Li, asymptotic cohomological functions and volumes"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "original OW... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Is there a convex-geometric analogue of the Newton–Okounkov interpretation of volume for the asymptotic higher-cohomology functions $$\widehat h^i(D)=(\dim X)!\limsup_{m\to\infty}\frac{\dim H^i(X,\mathcal O_X(mD))}{m^{\dim X}}?$$ In particular, can $\widehat h^i(D)$ be realized as a Euclidean volume, and can the limsup... | Is there a convex-geometric analogue of the Newton--Okounkov interpretation of volume for the higher cohomology functions h^i(D), with Euclidean volume naturally equal to h^i(D)=(\dim X)!\limsup_{m\to\infty}\dim H^i(X,O_X(mD))/m^{\dim X}, and can the limsup be replaced by a limit? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,592 | OWR-15586-003 | Polyhedrality of Movable Cycle Cones on Toric Varieties | If $X$ is a smooth toric variety and $\operatorname{Mov}_d(X)$ is the closed cone generated by numerical classes of movable $d$-dimensional subvarieties, is $\operatorname{Mov}_d(X)$ rational polyhedral? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-003",
"literature-status:open",
"owr-year:2017"
] | The toric divisor and curve cases are polyhedral, and later work proves rational polyhedrality for related ample-in-codimension cones on Mori dream spaces, including toric varieties. This does not establish the stated rational polyhedrality of movable higher-dimensional subvariety classes in every codimension. | [
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "original OWR report"
},
{
"url": "https://pure.mpg.de/pubman/item/item_3592150_4/component/file_3644841/Brambilla-Dumitrescu-Postinghel-Sanchez_Duality%20and%20polyhedrality%20of%20cones%20for%20Mori%20dream%20spaces_2025.pdf",
"label": "... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | If $X$ is a smooth toric variety and $\operatorname{Mov}_d(X)$ is the closed cone generated by numerical classes of movable $d$-dimensional subvarieties, is $\operatorname{Mov}_d(X)$ rational polyhedral? | If X is a smooth toric variety and Mov_d(X) is the closed cone generated by numerical classes of movable d-dimensional subvarieties, is Mov_d(X) rational polyhedral? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,593 | OWR-15586-004 | Newton–Okounkov Geometry for Positive Curve Classes | Can the positivity theory for curve classes in $N_1(X)$ be expressed through Newton–Okounkov-type convex bodies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-004",
"literature-status:open",
"owr-year:2017"
] | Newton--Okounkov bodies give a convex interpretation for volume and several restricted invariants, while higher asymptotic cohomology has only special-case formulas such as toric and surface results. No general Newton--Okounkov-type convex-body model for the higher cohomology functions is known. | [
{
"url": "https://arxiv.org/abs/math/0501491",
"label": "Kuronya, asymptotic cohomological functions"
},
{
"url": "https://arxiv.org/abs/math/0501104",
"label": "Hering--Kuronya--Payne, toric asymptotic cohomology"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "original... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Can the positivity theory for curve classes in $N_1(X)$ be expressed through Newton–Okounkov-type convex bodies? | Can the positivity theory for curve classes in N_1(X) be extended to a Newton--Okounkov-type convex-body picture? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,594 | OWR-15586-005 | Big Divisor Geometry Relative to Subvarieties | Let $X$ be a smooth complex projective variety, let $V\subset X$ be a subvariety, and let $D$ be a big $\mathbb Q$- or $\mathbb R$-divisor. Determine the positivity and birational geometry of the numerical class of $D$ relative to $V$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-005",
"literature-status:open",
"owr-year:2017"
] | Intersection numbers, restricted volumes, and positivity notions give partial information about a big divisor relative to a subvariety, but the requested general geometric determination is not a theorem with a settled answer. | [
{
"url": "https://ems.press/content/serial-article-files/46714",
"label": "Lozovanu--Kuronya, continuity and convexity"
},
{
"url": "https://arxiv.org/abs/math/0308116",
"label": "Kuronya, asymptotic invariants of base loci"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Let $X$ be a smooth complex projective variety, let $V\subset X$ be a subvariety, and let $D$ be a big $\mathbb Q$- or $\mathbb R$-divisor. Determine the positivity and birational geometry of the numerical class of $D$ relative to $V$. | Let X be a smooth complex projective variety, V\subset X a subvariety, and D a big \mathbb{Q}- or \mathbb{R}-divisor. How can one determine the geometry of the numerical class of D relative to V? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,595 | OWR-15586-006 | Non-Bigness of Diagonals in Projective Varieties | Let $X$ be a smooth projective variety. Develop criteria proving that the diagonal $\Delta_X\subset X\times X$ is not big. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-006",
"literature-status:open",
"owr-year:2017"
] | Lehmann--Ottem prove strong necessary conditions and classify the nef-and-big diagonal in dimensions two and three, but explicitly describe the general classification of varieties with big diagonal as subtle. The methodological question is therefore unresolved in general. | [
{
"url": "https://sites.bc.edu/lehmann/wp-content/uploads/sites/36/2019/12/posdiag.pdf",
"label": "Lehmann--Ottem, positivity of the diagonal"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Let $X$ be a smooth projective variety. Develop criteria proving that the diagonal $\Delta_X\subset X\times X$ is not big. | Given a smooth projective variety X, how can one prove that its diagonal \Delta_X\subset X\times X is not big? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,596 | OWR-15586-007 | Polyhedral Global Newton–Okounkov Bodies for Mori Dream Spaces | Does every smooth Mori dream space $X$ admit an admissible flag for which its global Newton–Okounkov body is rational polyhedral? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657](https:... | 3 | open | null | 2,017 | 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-15586-007",
"literature-status:open",
"owr-year:2017"
] | Rational polyhedral global Newton--Okounkov bodies are known for toric varieties, Mori dream spaces with suitable flags, and several homogeneous families, but no theorem gives such a flag for every smooth projective variety. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2017.07.018",
"label": "Schmitz--Seppanen, global Okounkov bodies"
},
{
"url": "https://arxiv.org/abs/1306.2028",
"label": "Postinghel--Urbinati, Newton--Okounkov bodies"
},
{
"url": "https://doi.org/10.4171/OWR/2017/43",
"label": "origina... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/43 | null | null | null | Does every smooth Mori dream space $X$ admit an admissible flag for which its global Newton–Okounkov body is rational polyhedral? | Let X be a smooth Mori dream space. Does there exist an admissible flag with respect to which the global Newton--Okounkov body of X is rational polyhedral? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton–Okounkov Bodies (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/43, pp. 2631--2657 |
30,003,597 | OWR-15587-001 | Maximum Volume of Canonical Fano Polytopes | For $d\geq4$, let $P$ be a $d$-dimensional canonical Fano lattice polytope, and define the Sylvester sequence by $s_1=2$ and $s_{i+1}=s_1\cdots s_i+1$. Is
$$
\operatorname{vol}(P)\leq\frac{2(s_d-1)^2}{d!},
$$
with equality only for the canonical Fano simplex $R_{(d)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 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-15587-001",
"literature-status:open",
"owr-year:2017"
] | The canonical Fano volume bound is proved for canonical Fano simplices and the dual-volume analogue is proved in general, but the stated sharp primal-volume bound and equality characterization remain open for general canonical Fano polytopes. | [
{
"url": "https://doi.org/10.1017/fms.2022.93",
"label": "Balletti--Kasprzyk--Nill, maximum dual volume"
},
{
"url": "https://arxiv.org/abs/1309.7967",
"label": "Averkov--Krumpelmann--Nill, largest integral simplices"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "origi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | For $d\geq4$, let $P$ be a $d$-dimensional canonical Fano lattice polytope, and define the Sylvester sequence by $s_1=2$ and $s_{i+1}=s_1\cdots s_i+1$. Is
$$
\operatorname{vol}(P)\leq\frac{2(s_d-1)^2}{d!},
$$
with equality only for the canonical Fano simplex $R_{(d)}$? | For d\geq4, let P be a d-dimensional canonical Fano lattice polytope and let s_1=2, s_{i+1}=s_1\cdots s_i+1 be the Sylvester sequence. Is \operatorname{vol}(P)\leq 2(s_d-1)^2/d!, with equality only for the canonical Fano simplex R(d)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,598 | OWR-15587-002 | Non-Unimodal Ehrhart Polynomials of Reflexive Simplices | Among the reflexive simplices $\Delta_{(1,q)}=\operatorname{conv}(e_1,\ldots,e_n,-q)$ having the integer-decomposition property, which have a nonunimodal Ehrhart $h^*$-polynomial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (none; preprint)**; the dataset currently labels it partially solved. L. Solus, OWR 44/2017, p. 2677: which reflexive simplices conv(e₁,…,eₙ,−q) with the integer decomposition property have a non-unimodal h∗-polynomial? K. A. Adiprasito, S. A. Papadakis, V. Petroto... | [
"owr",
"oberwolfach-reports",
"OWR-15587-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Explicit formulas and broad families of the simplices Delta(1,q) have proved h-star-unimodality, while reflexive stabilizations supply non-unimodal examples outside the IDP regime. No theorem determines the frequency or general avoidance question for the full family. | [
{
"url": "https://doi.org/10.1016/j.aam.2018.06.003",
"label": "Braun--Davis--Solus, reflexive simplices"
},
{
"url": "https://arxiv.org/abs/2103.17156",
"label": "Braun et al., weighted projective space simplices"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | Among the reflexive simplices $\Delta_{(1,q)}=\operatorname{conv}(e_1,\ldots,e_n,-q)$ having the integer-decomposition property, which have a nonunimodal Ehrhart $h^*$-polynomial? | Among the simplices \Delta(1,q)=\operatorname{conv}(e_1,\ldots,e_n,-q) satisfying the reflexivity and IDP conditions, how likely is it that the Ehrhart h^*-polynomial is non-unimodal?} | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,599 | OWR-15587-003 | Geometric Criteria for Ehrhart Positivity | Which families of integral polytopes are Ehrhart positive, and what geometric methods can prove Ehrhart positivity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 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-15587-003",
"literature-status:open",
"owr-year:2017"
] | Ehrhart positivity is established for several families and disproved for others, but there is no general classification of the families of integral polytopes having positive Ehrhart coefficients. | [
{
"url": "https://arxiv.org/abs/1711.09962",
"label": "Liu, positivity of Ehrhart polynomials"
},
{
"url": "https://arxiv.org/abs/1909.08448",
"label": "Jochemko--Ravichandran, generalized permutohedra"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original OWR report"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | Which families of integral polytopes are Ehrhart positive, and what geometric methods can prove Ehrhart positivity? | Which families of integral polytopes are Ehrhart positive, and what geometric methods can prove Ehrhart positivity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,600 | OWR-15587-006 | Normality and Very Ampleness of Lattice Polytopes | If $B\subset\mathbb R^n$ is a ball, is $\operatorname{conv}(B\cap\mathbb Z^n)$ normal? Does there exist a very ample nonnormal simple lattice polytope, or even a very ample nonnormal lattice simplex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23371741",
"checked_at": "2026-10-14",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-14] I have released an unrefereed preprint, **Lattice Hulls of Euclidean Balls Need Not Be Normal: Counterexamples in Every Dimension at Least Six** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23371741) | [
"owr",
"oberwolfach-reports",
"OWR-15587-006",
"literature-status:open",
"owr-year:2017"
] | Lattice points in a Euclidean ball are conjectured to form a normal polytope, and very ample nonnormal polytopes are known, but the requested simple-polytope and simplex versions remain unresolved. | [
{
"url": "https://www.home.uni-osnabrueck.de/wbruns/brunsw/pdf-article/2-quest-WB.pdf",
"label": "Bruns, questions on normal polytopes"
},
{
"url": "https://arxiv.org/abs/1406.4070",
"label": "Lason--Michalek, nonnormal very ample polytopes"
},
{
"url": "https://doi.org/10.4171/OWR/2017/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | If $B\subset\mathbb R^n$ is a ball, is $\operatorname{conv}(B\cap\mathbb Z^n)$ normal? Does there exist a very ample nonnormal simple lattice polytope, or even a very ample nonnormal lattice simplex? | Let B be a ball in \mathbb{R}^n. Is \operatorname{conv}(B\cap\mathbb{Z}^n) a normal polytope? Does there exist a very ample, nonnormal simple polytope, or even a very ample, nonnormal simplex? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,601 | OWR-15587-007 | Log-Concavity of Cohen–Macaulay H-Vectors | If $R$ is a standard graded Cohen–Macaulay domain with normal $\operatorname{Proj}(R)$, must its $h$-vector be log-concave? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (no; preprint)**; the dataset currently labels it open. M. Michałek, OWR 44/2017, p. 2685, Conjecture 6: do normal standard graded Cohen–Macaulay domains, or those with normal Proj, have log-concave h-vectors? J. Hofscheier, V. Kurylenko, B. Nill, preprint arXiv:25... | [
"owr",
"oberwolfach-reports",
"OWR-15587-007",
"literature-status:open",
"owr-year:2017"
] | The existence of a very ample nonnormal simple polytope would give a counterexample to Oda's conjecture, but no such example is known; the general smooth-polytope normality conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2512.20680",
"label": "Hofscheier--Kasprzyk, smooth polytopes and IDP"
},
{
"url": "https://www.home.uni-osnabrueck.de/wbruns/brunsw/pdf-article/2-quest-WB.pdf",
"label": "Bruns, questions on normal polytopes"
},
{
"url": "https://doi.org/10.4171/OWR/2017/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | If $R$ is a standard graded Cohen–Macaulay domain with normal $\operatorname{Proj}(R)$, must its $h$-vector be log-concave? | If R is a standard graded Cohen--}Macaulay domain with normal \operatorname{Proj}(R), must its h-vector be log-}concave?} | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,602 | OWR-15587-008 | Normality of Smooth Lattice Polytopes | Is every smooth lattice polytope normal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 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-15587-008",
"literature-status:open",
"owr-year:2017"
] | Oda's conjecture that every smooth lattice polytope is normal remains unanswered in general as of the cutoff date. There is substantial progress for special classes, including centrally symmetric three-dimensional polytopes, but neither a general proof nor a counterexample is known. | [
{
"url": "https://arxiv.org/abs/2512.20680",
"label": "Hofscheier--Kasprzyk, smooth polytopes and IDP"
},
{
"url": "https://arxiv.org/abs/2603.14227",
"label": "Oda's conjecture and smooth Fano polytopes"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original OWR repor... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | Is every smooth lattice polytope normal? | Is every smooth lattice polytope normal? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,603 | OWR-15587-012 | Real-Rootedness and Log-Concavity of Ehrhart Vectors | Can the implication diagram for Ehrhart $h^*-vectors$ and properties such as smoothness, very ampleness, and spanning be extended to include real-rootedness or log-concavity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15587-012",
"literature-status:open",
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] | There are isolated real-rooted and log-concave families and many counterexamples to naive implications, but no general structural extension of the unimodality diagram to real-rooted or log-concave h-star vectors is known. | [
{
"url": "https://arxiv.org/2307.10852",
"label": "Ferroni--Higashitani, examples and counterexamples"
},
{
"url": "https://arxiv.org/1505.07377",
"label": "Braun, unimodality problems"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | Can the implication diagram for Ehrhart $h^*-vectors$ and properties such as smoothness, very ampleness, and spanning be extended to include real-rootedness or log-concavity? | Can the implication diagram for Ehrhart h^*-vectors and properties such as smoothness, very ampleness, and spanning be extended to include real-}rootedness or log-}concavity?} | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,604 | OWR-15587-013 | Volume Bounds for Clean Lattice Tetrahedra | For a clean tetrahedron in $\mathbb{R}^3$ with $k>0$ interior lattice points, is Duong's volume conjecture true when the interior points are collinear? If they are not collinear, is the volume then strictly below the maximum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "geometry",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15587-013",
"literature-status:partially-solved",
"owr-year:2017"
] | The workshop reports a proof of Duong's volume conjecture for the aligned or collinear-interior-point case, while the non-collinear case and the full uniqueness question remain unresolved. | [
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original OWR report"
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{
"url": "https://arxiv.org/1612.08918",
"label": "Balletti--Kasprzyk, three-dimensional polytopes with interior points"
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{
"url": "https://arxiv.org/1309.7967",
"label": "Averkov--Krumpelmann--Nill, ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | For a clean tetrahedron in $\mathbb{R}^3$ with $k>0$ interior lattice points, is Duong's volume conjecture true when the interior points are collinear? If they are not collinear, is the volume then strictly below the maximum? | For a clean tetrahedron in \mathbb{R}^3 with k>0 interior lattice points, is Duong's volume conjecture true when the interior points are collinear? If they are not collinear, is the volume then strictly below the maximum? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,605 | OWR-15587-014 | Centrally Symmetric Two-Level Reflexive Polytopes | What are the centrally symmetric 2-level reflexive polytopes? Can the characterization of the exhibited examples be generalized to larger classes of 2-level polytopes, or to all 2-level polytopes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-15587-014",
"literature-status:open",
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] | The classification question for centrally symmetric 2-level reflexive polytopes, and its proposed extensions to broader 2-level classes, remain open; known examples and narrower simplicial classifications do not give a general classification. | [
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "original OWR report"
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"url": "https://arxiv.org/abs/math/0511294",
"label": "Nill, pseudo-symmetric simplicial reflexive polytopes"
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{
"url": "https://arxiv.org/abs/1509.07884",
"label": "Castillo--Liu, generalized permu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | What are the centrally symmetric 2-level reflexive polytopes? Can the characterization of the exhibited examples be generalized to larger classes of 2-level polytopes, or to all 2-level polytopes? | What are the centrally symmetric 2-level reflexive polytopes? Can the characterization of the exhibited examples be generalized to larger classes of 2-level polytopes, or to all 2-level polytopes? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,606 | OWR-15587-015 | Unimodality of Gorenstein Hilbert Series | If $R$ is a standard graded Gorenstein domain, is the $h$-polynomial of its Hilbert series unimodal? Does the same conclusion hold for every standard graded Cohen–Macaulay domain, or with log-concavity replacing unimodality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15587-015",
"literature-status:partially-solved",
"owr-year:2017"
] | The full Cohen--Macaulay log-concavity conjecture is disproved by the Niesi--Robbiano example, while the standard graded Gorenstein-domain unimodality conjecture remains open in general. The compound record therefore contains both a settled counterexample and an unresolved weaker conjecture. | [
{
"url": "https://arxiv.org/abs/alg-geom/9202020",
"label": "Niesi--Robbiano, disproof of Hibi's conjecture"
},
{
"url": "https://par.nsf.gov/servlets/purl/10580612",
"label": "Conca--Singh--Varbaro, Gorenstein h-vectors"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"label": "o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | If $R$ is a standard graded Gorenstein domain, is the $h$-polynomial of its Hilbert series unimodal? Does the same conclusion hold for every standard graded Cohen–Macaulay domain, or with log-concavity replacing unimodality? | If R is a standard graded Gorenstein domain, is the h-polynomial of its Hilbert series unimodal? Does the same hold for standard graded Cohen--}Macaulay domains, or with log-}concavity in place of unimodality?} | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,607 | OWR-15587-016 | Unimodality and Log-Concavity under Integer Decomposition | For a lattice polytope $P$, does the integer-decomposition property imply that $h^*(P;z)$ is unimodal or log-concave? Do either of these conclusions follow if $P$ is both Gorenstein and has the integer-decomposition property? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15587-016",
"literature-status:partially-solved",
"owr-year:2017"
] | The Gorenstein IDP h-star-unimodality conjecture is proved by Adiprasito--Papadakis--Petrotou--Steinmeyer, while general IDP unimodality remains open and IDP log-concavity has explicit counterexamples. The four-part compound record is therefore only partially resolved. | [
{
"url": "https://arxiv.org/abs/2210.10734",
"label": "Adiprasito et al., beyond positivity in Ehrhart theory"
},
{
"url": "https://arxiv.org/abs/2505.18896",
"label": "Hofscheier--Kurylenko--Nill, non-log-concave IDP examples"
},
{
"url": "https://doi.org/10.4171/OWR/2017/44",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | For a lattice polytope $P$, does the integer-decomposition property imply that $h^*(P;z)$ is unimodal or log-concave? Do either of these conclusions follow if $P$ is both Gorenstein and has the integer-decomposition property? | For a lattice polytope P, are the following true: (1) IDP implies h^*(P;z) is unimodal; (2) IDP implies h^*(P;z) is log-concave; (3) Gorenstein and IDP imply h^*(P;z) is unimodal; and (4) Gorenstein and IDP imply h^*(P;z) is log-concave? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,608 | OWR-15587-017 | Volume of Minkowski Sums with Fixed Mixed Volume | For $d$-dimensional lattice polytopes $P_1,\ldots,P_d\subset\mathbb R^d$ with normalized mixed volume $V(P_1,\ldots,P_d)=m$, is the sharp upper bound for the normalized volume of $P_1+\cdots+P_d$ equal to $(m+d-1)^d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701](https://doi.org/10.4171/owr/2017/44)
## Literature r... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15587-017",
"literature-status:partially-solved",
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] | The conjectured sharp upper bound is proved in dimensions two and three and general bounds of the correct order are known, but the all-dimensional sharp equality remains unresolved. | [
{
"url": "https://doi.org/10.1112/mtk.12055",
"label": "Averkov Borger Soprunov 2020"
},
{
"url": "https://doi.org/10.1007/s00454-020-00246-4",
"label": "Averkov Borger Soprunov 2021"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/44 | null | null | null | For $d$-dimensional lattice polytopes $P_1,\ldots,P_d\subset\mathbb R^d$ with normalized mixed volume $V(P_1,\ldots,P_d)=m$, is the sharp upper bound for the normalized volume of $P_1+\cdots+P_d$ equal to $(m+d-1)^d$? | For d-dimensional lattice polytopes P_1,\ldots,P_d\subset\mathbb{R}^d with normalized mixed volume V(P_1,\ldots,P_d)=m, is the sharp upper bound for the normalized volume of P_1+\cdots+P_d equal to (m+d-1)^d? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/44, pp. 2659--2701 |
30,003,609 | OWR-15588-002 | L-Equivalence of Derived-Equivalent Simply Connected Varieties | If $X$ and $Y$ are smooth projective simply connected D-equivalent varieties over a field of characteristic zero, must they be L-equivalent, i.e. must $([X]-[Y])\mathbb L^r=0$ in $K_0(\operatorname{Var}/k)$ for some $r\geq0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | solved | null | 2,017 | 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"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2503.21511",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; accepted, not yet published)**. A. Kuznetsov (OWR 45/2017, p. 2726, Conjecture 5, from joint work with E. Shinder) conjectures that D-equivalent smooth projective simply connected varieties over a field of characteristic 0 are L-equivalent. R. Meinsma, [arXiv:... | [
"owr",
"oberwolfach-reports",
"OWR-15588-002",
"literature-status:open",
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{
"url": "https://doi.org/10.4171/owr/2017/45",
"label": "Oberwolfach Report 45 2017"
},
{
"url": "https://arxiv.org/abs/1612.07193",
"label": "Kuznetsov Shinder"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | If $X$ and $Y$ are smooth projective simply connected D-equivalent varieties over a field of characteristic zero, must they be L-equivalent, i.e. must $([X]-[Y])\mathbb L^r=0$ in $K_0(\operatorname{Var}/k)$ for some $r\geq0$? | If X and Y are smooth projective simply connected D-equivalent varieties over a field of characteristic zero, must they be L-equivalent, i.e. must ([X]-[Y])\mathbb{L}^r=0 in K_0(\operatorname{Var}/k) for some r\geq0? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,610 | OWR-15588-005 | Components of Rational-Curve Mapping Spaces | For a smooth projective variety $X$, how many irreducible components does $\operatorname{Mor}(\mathbb P^1,X)$ have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"description": "Geometric objects defined by polynomial equations.",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15588-005",
"literature-status:open",
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] | There is no general formula for the number of components of the rational-curve moduli space for arbitrary Fano varieties; known results cover important families and bounds. | [
{
"url": "https://doi.org/10.4171/owr/2017/45",
"label": "Oberwolfach Report 45 2017"
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{
"url": "https://doi.org/10.1112/S0010437X19007103",
"label": "Lehmann Tanimoto 2019"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | For a smooth projective variety $X$, how many irreducible components does $\operatorname{Mor}(\mathbb P^1,X)$ have? | For a smooth projective variety X, how many irreducible components does \operatorname{Mor}(\mathbb{P}^1,X) have? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,611 | OWR-15588-006 | Polynomial Bounds for Dominant Rational-Curve Components | Fix an ample divisor $L$ on a smooth projective Fano variety $X$. Is the number of dominant components of $\operatorname{Mor}(\mathbb P^1,X)$ of $L$-degree at most $d$ bounded above by a polynomial in $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | partially_solved | null | 2,017 | 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-15588-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Polynomial component bounds and related uniform estimates are established in broad settings, while the stated conjectural bound is not proved for all Fano varieties. | [
{
"url": "https://doi.org/10.1112/S0010437X19007103",
"label": "Lehmann Tanimoto 2019"
},
{
"url": "https://doi.org/10.1016/j.aim.2022.108557",
"label": "Beheshti Lehmann Riedl Tanimoto 2022"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | Fix an ample divisor $L$ on a smooth projective Fano variety $X$. Is the number of dominant components of $\operatorname{Mor}(\mathbb P^1,X)$ of $L$-degree at most $d$ bounded above by a polynomial in $d$? | Fix an ample divisor L on a smooth projective Fano variety X. Is the number of dominant components of \operatorname{Mor}(\mathbb{P}^1,X) of L-degree at most d bounded above by a polynomial in d? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,612 | OWR-15588-008 | Finite Factorization Bases for Breaking Maps | Let $X$ be a smooth uniruled projective variety. Is there a finite set of breaking maps $f_i:Y_i\to X$ such that every breaking map to $X$ factors rationally through one of the $f_i$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | open | null | 2,017 | 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-15588-008",
"literature-status:open",
"owr-year:2017"
] | The proposed finiteness of breaking maps is a central conjectural ingredient in the geometric Manin program and has no general proof. | [
{
"url": "https://doi.org/10.4171/owr/2017/45",
"label": "Oberwolfach Report 45 2017"
},
{
"url": "https://doi.org/10.1112/S0010437X19007103",
"label": "Lehmann Tanimoto 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | Let $X$ be a smooth uniruled projective variety. Is there a finite set of breaking maps $f_i:Y_i\to X$ such that every breaking map to $X$ factors rationally through one of the $f_i$? | Let X be a smooth uniruled projective variety. Is there a finite set of breaking maps f_i:Y_i\to X such that every breaking map to X factors rationally through one of the f_i? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,613 | OWR-15588-009 | Manin-Type Asymptotics for Rational-Curve Components | Let $X$ be a smooth projective Fano variety and let $N^\circ(X,q,d)$ sum $q^{\dim W}$ over dominant components $W$ of $\operatorname{Mor}(\mathbb P^1,X)$ of anticanonical degree $d$ whose family maps do not rationally factor through breaking maps. Must $N^\circ(X,q,d)\sim Cq^d d^{\rho(X)-1}$ as $d\to\infty$ for some $C... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | partially_solved | null | 2,017 | 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-15588-009",
"literature-status:partially-solved",
"owr-year:2017"
] | The conjectural Manin asymptotic after removing breaking maps has substantial upper-bound and special-family results, but is not established in general. | [
{
"url": "https://doi.org/10.4171/owr/2017/45",
"label": "Oberwolfach Report 45 2017"
},
{
"url": "https://doi.org/10.1112/S0010437X19007103",
"label": "Lehmann Tanimoto 2019"
},
{
"url": "https://doi.org/10.1016/j.aim.2022.108557",
"label": "Beheshti Lehmann Riedl Tanimoto 2022"
}... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | Let $X$ be a smooth projective Fano variety and let $N^\circ(X,q,d)$ sum $q^{\dim W}$ over dominant components $W$ of $\operatorname{Mor}(\mathbb P^1,X)$ of anticanonical degree $d$ whose family maps do not rationally factor through breaking maps. Must $N^\circ(X,q,d)\sim Cq^d d^{\rho(X)-1}$ as $d\to\infty$ for some $C... | Let X be a smooth projective Fano variety and let N^\circ(X,q,d) sum q^{\dim W} over dominant components W of \operatorname{Mor}(\mathbb{P}^1,X) of anticanonical degree d whose family maps do not rationally factor through breaking maps. Must N^\circ(X,q,d)\sim Cq^d d^{\rho(X)-1} as d\to\infty for some C>0? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,614 | OWR-15588-010 | Galois Semisimplicity of Cohomology over Finitely Generated Fields | For every smooth projective $X$ over a finitely generated field $K$ of characteristic zero, every $i,n$, and every prime $\ell$, is $H^i(X)(n)$ semisimple as a representation of the absolute Galois group $\Gamma_K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767](https://doi.org/10.4171/owr/2017/4... | 3 | partially_solved | null | 2,017 | 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-15588-010",
"literature-status:partially-solved",
"owr-year:2017"
] | Moonen proved in characteristic zero that the Tate cycle-class conjecture implies semisimplicity, but the general semisimplicity assertion in the record remains unresolved. | [
{
"url": "https://arxiv.org/abs/1709.04489",
"label": "Moonen A remark on the Tate conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2017/45",
"label": "Oberwolfach Report 45 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/45 | null | null | null | For every smooth projective $X$ over a finitely generated field $K$ of characteristic zero, every $i,n$, and every prime $\ell$, is $H^i(X)(n)$ semisimple as a representation of the absolute Galois group $\Gamma_K$? | For every smooth projective X over a finitely generated field K of characteristic zero, every i,n, and every prime \ell, is H^i(X)(n) semisimple as a representation of the absolute Galois group \Gamma_K? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Birational Classification, Derived Categories, and Moduli Spaces (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/45, pp. 2703--2767 |
30,003,615 | OWR-15951-001 | Topology and Symmetries of Aperiodic Tiling Spaces | How can aperiodic tilings be reconstructed as limits of growing coronae? Which homeomorphisms can occur between tiling spaces, how many such homeomorphisms can there be, and which extended symmetries can subshifts possess? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845](https://doi.org/10.4171/owr/2017/46)
## Lite... | 3 | open | null | 2,017 | 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-15951-001",
"literature-status:open",
"owr-year:2017"
] | The extracted record lists broad open questions about tiling-space limits, homeomorphisms, and extended symmetries; no general resolution is known. | [
{
"url": "https://doi.org/10.4171/owr/2017/46",
"label": "Oberwolfach Report 46 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/46 | null | null | null | How can aperiodic tilings be reconstructed as limits of growing coronae? Which homeomorphisms can occur between tiling spaces, how many such homeomorphisms can there be, and which extended symmetries can subshifts possess? | Open questions for aperiodic tiling and subshift systems include: how can tilings be understood as limits of growing coronae; what homeomorphisms can occur between tiling spaces, and how many are there; and what extended symmetries can subshifts have? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Spectral Structures and Topological Methods in Mathematical Quasicrystals (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/46, pp. 2781--2845 |
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