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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,916 | OWR-13852-008 | Kähler–Ricci Flow from Currents with Positive Lelong Numbers | What happens to the Kähler–Ricci flow when its initial positive current $T_0$ has positive Lelong numbers? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807](https://doi.org/10.4171/owr/2015/31)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 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-13852-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Weak Kähler Ricci flow from positive currents is understood in several regularity and uniqueness settings, including divisorial singularities, but the full positive-Lelong-number behavior remains unsettled. | [
{
"url": "https://doi.org/10.4171/owr/2015/31",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.10.011",
"label": "Di Nezza and Lu primary paper"
},
{
"url": "https://arxiv.org/abs/2606.15816",
"label": "Di Nezza Guedj and Lu primary paper"
}
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/31 | null | null | null | What happens to the Kähler–Ricci flow when its initial positive current $T_0$ has positive Lelong numbers? | What happens for the Kahler--Ricci flow when the initial positive current T0 has positive Lelong numbers? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Differentialgeometrie im Großen (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/31, pp. 1759--1807 |
30,002,917 | OWR-13853-004 | Unbounded Degrees of Full Belyi Maps | For a finite set of primes $P$, let $N(P)$ be the set of degrees $n\geq4$ for which a full Belyi map over $\mathbb{Q}$ has bad reduction only at primes in $P$. If $P$ contains all prime divisors of the order of some nonabelian finite simple group, is $N(P)$ infinite? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/32, pp. 1809--1866](https://doi.org/10.4171/owr/2015/32)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 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-13853-004",
"literature-status:open",
"owr-year:2015"
] | The unboundedness conjecture for Belyi maps with prescribed anabelian bad-reduction primes is still presented as a conjecture, with no proof located. | [
{
"url": "https://doi.org/10.4171/owr/2015/32",
"label": "original Oberwolfach report"
},
{
"url": "https://www.numdam.org/item/10.5802/pmb.21.pdf",
"label": "Roberts primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/32 | null | null | null | For a finite set of primes $P$, let $N(P)$ be the set of degrees $n\geq4$ for which a full Belyi map over $\mathbb{Q}$ has bad reduction only at primes in $P$. If $P$ contains all prime divisors of the order of some nonabelian finite simple group, is $N(P)$ infinite? | Conjecture: If P is an anabelian set of primes, then N(P) is infinite. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Explicit Methods in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/32, pp. 1809--1866 |
30,002,918 | OWR-13853-006 | Polynomial Time Zeta Functions for Hyperelliptic Curves | Can Zp(T), the zeta function of a genus-g hyperelliptic curve over a finite field of characteristic p, be computed in time polynomial in both g and log p? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/32, pp. 1809--1866](https://doi.org/10.4171/owr/2015/32)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,015 | 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-13853-006",
"literature-status:open",
"owr-year:2015"
] | Algorithms achieve important average-case polynomial bounds, but polynomial time simultaneously in genus and log p for the stated zeta-function computation remains a major open question. | [
{
"url": "https://doi.org/10.4171/owr/2015/32",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4007/annals.2014.179.2.7",
"label": "Harvey primary paper"
},
{
"url": "https://arxiv.org/abs/2004.10189",
"label": "Sutherland primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/32 | null | null | null | Can Zp(T), the zeta function of a genus-g hyperelliptic curve over a finite field of characteristic p, be computed in time polynomial in both g and log p? | Can Zp(T), the zeta function of a genus-g hyperelliptic curve over a finite field of characteristic p, be computed in time polynomial in both g and log p? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Explicit Methods in Number Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/32, pp. 1809--1866 |
30,002,919 | OWR-13854-002 | Strong Cosmic Censorship at Weak Regularity | For generic perturbations of Kerr initial data whose maximal globally hyperbolic developments have continuously extendible Cauchy horizons, are those developments nevertheless inextendible by Lorentzian metrics of regularity $C^0\cap W_{\mathrm{loc}}^{1,2}$? More generally, for generic asymptotically flat vacuum initia... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935](https://doi.org/10.4171/owr/2015/33)
## Literature review (checked 2026-08-... | 3 | open | null | 2,015 | 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-13854-002",
"literature-status:open",
"owr-year:2015"
] | The C0 extendibility and weak null singularity are proved, but generic inextendibility as a weak Einstein solution with locally square-integrable connection remains unresolved. | [
{
"url": "https://annals.math.princeton.edu/2025/202-2/p01",
"label": "Dafermos--Luk, Annals of Mathematics"
},
{
"url": "https://scholars.cityu.edu.hk/files/237941363/228746328.pdf",
"label": "Luk, Strong cosmic censorship with bounded curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/33 | null | null | null | For generic perturbations of Kerr initial data whose maximal globally hyperbolic developments have continuously extendible Cauchy horizons, are those developments nevertheless inextendible by Lorentzian metrics of regularity $C^0\cap W_{\mathrm{loc}}^{1,2}$? More generally, for generic asymptotically flat vacuum initia... | Conjecture 3: For a generic subclass of the perturbations in Theorem 1, the maximal globally hyperbolic development is inextendible with a Lorentzian metric in C0 intersected with locally W1,2. Conjecture 4: For generic asymptotically flat vacuum initial data, it is inextendible as a weak solution of the Einstein vacuu... | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935 |
30,002,920 | OWR-13854-004 | Transferring Resonant Blowup to the Full Einstein System | How can the finite-time blowup result for the resonant system be transferred to the full system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935](https://doi.org/10.4171/owr/2015/33)
## Literature review (checked 2026-08-... | 3 | open | null | 2,015 | 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-13854-004",
"literature-status:open",
"owr-year:2015"
] | The resonant system exhibits the relevant blowup mechanism, but a rigorous transfer of that result to the full Einstein--massless-scalar system is still not proved. | [
{
"url": "https://arxiv.org/abs/1506.03519",
"label": "Bizon--Maliborski--Rostworowski, Resonant dynamics and instability of AdS"
},
{
"url": "https://link.springer.com/article/10.1007/s00222-022-01152-7",
"label": "Moschidis, instability results for Einstein--Vlasov"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/33 | null | null | null | How can the finite-time blowup result for the resonant system be transferred to the full system? | How can the finite-time blowup result for the resonant system be transferred to the full system? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935 |
30,002,921 | OWR-13854-006 | Local Well-Posedness of Lovelock Equations | Can one establish local existence and uniqueness of solutions, together with continuous dependence on initial data, for the Lovelock-theory equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935](https://doi.org/10.4171/owr/2015/33)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,015 | 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-13854-006",
"literature-status:partially-solved",
"owr-year:2015"
] | Modified harmonic gauges yield strong hyperbolicity and local well-posedness in the weak-coupling Lovelock regime, while generic backgrounds and gauges can fail hyperbolicity, so the broad question remains unsettled. | [
{
"url": "https://arxiv.org/abs/1705.04370",
"label": "Papallo--Reall, local well-posedness of Lovelock theories"
},
{
"url": "https://arxiv.org/abs/2003.08398",
"label": "Kovacs--Reall, well-posed Lovelock formulation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/33 | null | null | null | Can one establish local existence and uniqueness of solutions, together with continuous dependence on initial data, for the Lovelock-theory equations? | Can one establish local existence and uniqueness of solutions, together with continuous dependence on initial data, for the Lovelock-theory equations? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mathematical Aspects of General Relativity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/33, pp. 1867--1935 |
30,002,922 | OWR-13855-002 | Full-Measure Families of Ergodic Irrational Polygons | Does there exist a set of full Lebesgue measure consisting of ergodic non-rational polygons with any prescribed number of edges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988](https://doi.org/10.4171/owr/2015/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | open | null | 2,015 | 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-13855-002",
"literature-status:open",
"owr-year:2015"
] | Residual and topological genericity results for weak mixing do not establish ergodicity for a full Lebesgue-measure set of non-rational polygons, so the stated measure-theoretic problem remains open. | [
{
"url": "https://arxiv.org/abs/2003.00890",
"label": "Chaika--Forni, Weakly mixing polygonal billiards"
},
{
"url": "https://doi.org/10.4171/owr/2015/34",
"label": "Oberwolfach Report on polygonal billiards"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/34 | null | null | null | Does there exist a set of full Lebesgue measure consisting of ergodic non-rational polygons with any prescribed number of edges? | Does there exist a set of full Lebesgue measure consisting of ergodic non-rational polygons with any prescribed number of edges? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988 |
30,002,923 | OWR-13855-004 | Three Closed Reeb Orbits Beyond Lens Spaces | Does every Reeb vector field on a three-manifold that is not a lens space have at least three closed Reeb orbits? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988](https://doi.org/10.4171/owr/2015/34)
## Literature review (checked 2026-08-21)
**Status:** open
*... | 3 | solved | null | 2,015 | 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 | {
"source_url": "https://doi.org/10.4310/jdg/1452002876",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. D. Cristofaro-Gardiner (joint with M. Hutchings and V. Ramos; OWR 34/2015, p. 1969) conjectures that a Reeb vector field on a closed 3-manifold that is not a lens space has at least three closed orbits. Every contact form on a closed 3-manifold has at leas... | [
"owr",
"oberwolfach-reports",
"OWR-13855-004",
"literature-status:open",
"owr-year:2015"
] | Examples with exactly two Reeb orbits are known, but the extracted record asks broadly what further configurations can occur and does not state a resolved classification theorem. | [
{
"url": "https://arxiv.org/abs/2102.04970",
"label": "Contact three-manifolds with exactly two simple Reeb orbits"
},
{
"url": "https://doi.org/10.4171/owr/2015/34",
"label": "Oberwolfach Report on Reeb dynamics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/34 | null | null | null | Does every Reeb vector field on a three-manifold that is not a lens space have at least three closed Reeb orbits? | Conjecture: A Reeb vector field on a manifold that is not a lens space has at least three closed Reeb orbits. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988 |
30,002,924 | OWR-13855-007 | Weak Limits of Discrete Wave-Turbulence Spectra | For the damped, randomly forced nonlinear Schrödinger equation on the torus $\mathbb T_L^d$, impose $\nu=\varepsilon^2$, $\rho=L^{1/2}\rho_0$, and $b_k=L^{-d/2}b_k^0$. Under the iterated limit $\lim_{L\to\infty}\lim_{\nu\to0}$, do the averaged actions
$$n_k^{\nu,L}(\tau)=\frac12\mathbb E\lvert v_k^{\nu,L}(\tau)\rvert^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988](https://doi.org/10.4171/owr/2015/34)
## Literature review (checked 2026-08-21)
**Status:** partial... | 3 | partially_solved | null | 2,015 | 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-13855-007",
"literature-status:partially-solved",
"owr-year:2015"
] | Rigorous limits are known for the first averaging step and for several truncated, finite-time, or alternative kinetic regimes, but the exact iterated double limit and full damped-driven wave-kinetic claim in the record is not completely established. | [
{
"url": "https://doi.org/10.1016/j.physd.2015.04.002",
"label": "Kuksin--Maiocchi, derivation of a wave kinetic equation"
},
{
"url": "https://doi.org/10.1007/s00205-026-02181-9",
"label": "Grande--Hani, rigorous damped-driven wave turbulence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/34 | null | null | null | For the damped, randomly forced nonlinear Schrödinger equation on the torus $\mathbb T_L^d$, impose $\nu=\varepsilon^2$, $\rho=L^{1/2}\rho_0$, and $b_k=L^{-d/2}b_k^0$. Under the iterated limit $\lim_{L\to\infty}\lim_{\nu\to0}$, do the averaged actions
$$n_k^{\nu,L}(\tau)=\frac12\mathbb E\lvert v_k^{\nu,L}(\tau)\rvert^... | Conjecture: Under the double limit nu tending to zero and L tending to infinity, the discrete spectrum function n superscript nu,L sub k of tau converges weakly to a function n superscript 0 sub k of tau that solves equation (8). | corrected_verified | The official report was checked. The reconstruction replaces the unusable reference to equation (8) with the source-defined stochastic NLS model, scaling, averaged actions, iterated limit, and named limiting equation. | null | null | null | null | null | Dynamische Systeme (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/34, pp. 1937--1988 |
30,002,925 | OWR-13856-001 | Limit Theorems in the Condensation Regime | In the stochastic house-of-cards model, let $\beta$ be the mutation probability and $\mu$ the mutant-fitness distribution. In the condensation regime
$$\beta\int_0^1\frac{\mu(dx)}{1-x}<1,$$
the population size $N(t)$ has exponential growth rate $\lambda^*=1-\beta$ but is not strictly exponential. Determine the correc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 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-13856-001",
"literature-status:open",
"owr-year:2015"
] | The reinforced-branching literature proves the exponential growth rate and non-extensive condensation, but the precise logarithmic correction and associated growth limit requested in the record remains conjectural. | [
{
"url": "https://arxiv.org/abs/1601.08128",
"label": "Dereich--Mailler--Morters, Non-extensive condensation in reinforced branching"
},
{
"url": "https://doi.org/10.4171/owr/2015/35",
"label": "Oberwolfach Report on condensation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | In the stochastic house-of-cards model, let $\beta$ be the mutation probability and $\mu$ the mutant-fitness distribution. In the condensation regime
$$\beta\int_0^1\frac{\mu(dx)}{1-x}<1,$$
the population size $N(t)$ has exponential growth rate $\lambda^*=1-\beta$ but is not strictly exponential. Determine the correc... | In the condensation regime, what corrections to the non-strictly exponential growth are needed to prove a limit theorem? | corrected_verified | The official report was checked. The reconstruction restores the stochastic growth model, condensation criterion, population variable, exponential rate, and the precise object requiring a limit-theorem correction. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,926 | OWR-13856-002 | Gamma Profiles of Waves Entering a Condensate | In the stochastic house-of-cards condensation model, suppose the mutant-fitness distribution satisfies $\mu(1-\varepsilon,1)=\varepsilon^\alpha\ell(\varepsilon)$, where $\alpha>0$ and $\ell$ is slowly varying at zero. If $\Xi_t$ is the empirical fitness distribution and $\gamma(\beta)$ is the condensate mass, is
$$\li... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 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-13856-002",
"literature-status:open",
"owr-year:2015"
] | The gamma profile is proved for a simpler Kingman model, but the gamma-shape conjecture for the condensation wave in the reinforced branching model of the record remains unproved. | [
{
"url": "https://arxiv.org/abs/1601.08128",
"label": "Dereich--Mailler--Morters, reinforced branching condensation"
},
{
"url": "https://doi.org/10.4171/owr/2015/35",
"label": "Oberwolfach Report on condensation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | In the stochastic house-of-cards condensation model, suppose the mutant-fitness distribution satisfies $\mu(1-\varepsilon,1)=\varepsilon^\alpha\ell(\varepsilon)$, where $\alpha>0$ and $\ell$ is slowly varying at zero. If $\Xi_t$ is the empirical fitness distribution and $\gamma(\beta)$ is the condensate mass, is
$$\li... | Conjecture: In the condensation model, the suitably rescaled wave entering the condensate has a gamma-distribution shape. | corrected_verified | The official report was checked. The reconstruction restores the regular-variation hypothesis and the explicit gamma-profile limit conjectured for the condensing wave. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,927 | OWR-13856-003 | Expository Metastability Heading for a Nonlocal Dirichlet Problem | Can metastable states be stable in the stationary nonlocal Dirichlet problem described in the report? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report uses this broad question as the title and motivation for an account that proves existence of stationary metastable profi) | [
"OWR-13856-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13856-003",
"literature-status:open",
"owr-year:2015"
] | Stationary metastable profiles have been constructed for a restricted Kac-Ising setting, but the broad question whether metastable states are dynamically stable has not been resolved. | [
{
"url": "https://arxiv.org/abs/1009.4652",
"label": "De Masi--Presutti--Tsgkarogiannis, Fourier law and stationary Stefan problem"
},
{
"url": "https://doi.org/10.4171/owr/2015/35",
"label": "Oberwolfach Report on metastable states"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | null | Can metastable states be stable in the stationary nonlocal Dirichlet problem described in the report? | unrecoverable | The official report uses this broad question as the title and motivation for an account that proves existence of stationary metastable profiles; the specific unresolved uniqueness conjecture is represented by OWR-13856-004. It is not a separate source-stated open problem. No separate clean statement is promoted; the or... | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,928 | OWR-13856-004 | Uniqueness of Condensation-Model Parameters | Fix $\beta>1$, let $m_\beta>0$ solve $m_\beta=\tanh(\beta m_\beta)$, and put $m^*=\sqrt{1-\beta^{-1}}$. For $u_+\in(m^*,m_\beta)$, consider a profile $q:\mathbb R_{\leq0}\to\mathbb R$ satisfying
$$q(x)=\tanh\!\left(\beta(J*q)(x)+\beta h_*\right),\qquad \lim_{x\to-\infty}q(x)=m_-,\qquad q(0)=u_+.$$
Are the parameters ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 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... | [
"OWR-13856-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13856-004",
"literature-status:open",
"owr-year:2015"
] | Existence is proved for some parameter values, but the source states the all-parameter existence and uniqueness assertion as a conjecture and no authoritative proof of that full statement was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/35",
"label": "Oberwolfach Report on the stationary problem"
},
{
"url": "https://doi.org/10.1007/s00205-011-0423-1",
"label": "De Masi--Presutti--Tsgkarogiannis, stationary Stefan problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | Fix $\beta>1$, let $m_\beta>0$ solve $m_\beta=\tanh(\beta m_\beta)$, and put $m^*=\sqrt{1-\beta^{-1}}$. For $u_+\in(m^*,m_\beta)$, consider a profile $q:\mathbb R_{\leq0}\to\mathbb R$ satisfying
$$q(x)=\tanh\!\left(\beta(J*q)(x)+\beta h_*\right),\qquad \lim_{x\to-\infty}q(x)=m_-,\qquad q(0)=u_+.$$
Are the parameters ... | Conjecture: For every u plus in the interval from m star to m beta, the parameters h star and m minus are uniquely determined. | corrected_verified | The official report was checked. The reconstruction restores the half-line profile equation, boundary conditions, parameter range, and definitions needed by the source conjecture. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,929 | OWR-13856-005 | Positive Probability of Zero Total Superfluid Momentum | For superfluids, is the total momentum zero with positive asymptotic probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 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-13856-005",
"literature-status:open",
"owr-year:2015"
] | Suto presents the zero-total-momentum assertion for superfluids as a conjecture; subsequent literature located through the cutoff does not prove the stated positive-probability claim. | [
{
"url": "https://arxiv.org/abs/1504.06528",
"label": "Suto, The total momentum of quantum fluids"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | For superfluids, is the total momentum zero with positive asymptotic probability? | Conjecture: For superfluids, the total momentum is zero with positive asymptotic probability. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,930 | OWR-13856-006 | Uniform Corrector Moments and Quantitative Stochastic Homogenization | Can one prove bounds on moments of the stochastic corrector that are uniform in space or have a precise divergence rate, and can one prove a corresponding quantitative two-scale expansion for stochastic homogenization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | partially_solved | null | 2,015 | 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-13856-006",
"literature-status:partially-solved",
"owr-year:2015"
] | Under spectral-gap, finite-range, or related quantitative assumptions, optimal corrector moment and growth estimates and quantitative two-scale expansions are available, but the general ergodic statement in the record is not fully resolved. | [
{
"url": "https://arxiv.org/abs/1409.0801",
"label": "Gloria--Otto, quantitative corrector estimates"
},
{
"url": "https://arxiv.org/abs/1510.08290",
"label": "Gloria--Otto, corrector rates and two-scale expansion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | Can one prove bounds on moments of the stochastic corrector that are uniform in space or have a precise divergence rate, and can one prove a corresponding quantitative two-scale expansion for stochastic homogenization? | Can one prove bounds on moments of the stochastic corrector that are uniform in space or have a precise divergence rate, and can one prove a corresponding quantitative two-scale expansion for stochastic homogenization? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,931 | OWR-13856-007 | Persistence Exponents of Multiply Integrated Brownian Motion | Let $B$ be standard Brownian motion, set $A_t^{(1)}=\int_0^t B_s\,ds$, and recursively define $A_t^{(d)}=\int_0^t A_s^{(d-1)}\,ds$. If $\theta_d$ is the persistence exponent governing the long-time probability that $A^{(d)}$ stays positive, determine $\theta_d$ for every $d\geq2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | open | null | 2,015 | 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-13856-007",
"literature-status:open",
"owr-year:2015"
] | For the persistence problem in the record, only the one-dimensional exponent is known exactly; higher-dimensional exponents remain an open problem despite numerical and scaling results. | [
{
"url": "https://doi.org/10.4171/owr/2015/35",
"label": "Oberwolfach Report on persistence probabilities"
},
{
"url": "https://arxiv.org/abs/cond-mat/9904208",
"label": "Newman--Stein, blocking and persistence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | Let $B$ be standard Brownian motion, set $A_t^{(1)}=\int_0^t B_s\,ds$, and recursively define $A_t^{(d)}=\int_0^t A_s^{(d-1)}\,ds$. If $\theta_d$ is the persistence exponent governing the long-time probability that $A^{(d)}$ stays positive, determine $\theta_d$ for every $d\geq2$. | For the persistence exponent theta sub d of multiply integrated Brownian motion, can one compute theta sub d for every dimension d at least 2? | corrected_verified | The official report was checked. The reconstruction restores the recursive definition of multiply integrated Brownian motion and identifies the persistence exponent whose computation is asked for. | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,932 | OWR-13856-008 | Motivating Fixed-Point Question for Chinese Restaurant Permutations | For the Chinese Restaurant Process growth of permutations, what are the pathwise properties of A1(n), the number of fixed points; for example, how often does A1(n) equal zero occur as n varies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064](https://doi.org/10.4171/owr/2015/35)
## Literature review... | 3 | partially_solved | null | 2,015 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report introduces this pathwise question as motivation and then gives the relevant time-change limit results rather than presen) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13856-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Gnedin and Stark resolve the principal time-average questions for fixed points in the discrete Chinese restaurant process and its continuous-time embedding, but the broad request for all pathwise properties of A1 remains open. | [
{
"url": "https://arxiv.org/abs/2209.12781",
"label": "Gnedin--Stark, Random permutations and queues"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/35 | null | null | null | null | For the Chinese Restaurant Process growth of permutations, what are the pathwise properties of A1(n), the number of fixed points; for example, how often does A1(n) equal zero occur as n varies? | unrecoverable | The official report introduces this pathwise question as motivation and then gives the relevant time-change limit results rather than presenting it as a separate unresolved problem. The extraction does not isolate a source-stated open claim. No separate clean statement is promoted; the original record remains publicly ... | null | null | null | null | null | Interplay of Analysis and Probability in Applied Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/35, pp. 1989--2064 |
30,002,933 | OWR-13857-001 | Isoperimetric Regions of Fixed Volume in General Spaces | For a space X and fixed volume v, what is the minimum area needed to enclose v, does an optimal shape exist, and if so can it be described? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | partially_solved | null | 2,015 | 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-13857-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Sharp isoperimetric inequalities, rigidity, and classification of optimizers are proved for important essentially non-branching spaces with synthetic lower Ricci bounds, but the three questions are not solved for an arbitrary metric-measure space X. | [
{
"url": "https://arxiv.org/abs/1502.06465",
"label": "Cavalletti--Mondino, sharp and rigid isoperimetry"
},
{
"url": "https://arxiv.org/abs/1610.05044",
"label": "Cavalletti--Mondino, finite-perimeter isoperimetry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | For a space X and fixed volume v, what is the minimum area needed to enclose v, does an optimal shape exist, and if so can it be described? | For a space X and fixed volume v, what is the minimum area needed to enclose v, does an optimal shape exist, and if so can it be described? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,934 | OWR-13857-002 | Index Bounds for Minimal-Hypersurface Volume | Let $M^n$ be a closed minimal hypersurface in a Riemannian manifold $N$ with strictly positive sectional curvature. If $\operatorname{index}(M)=I$, is $\mathcal H^n(M)\leq C(N,I)$? Consequently, must bounded-index sequences have uniformly bounded volume and volume-divergent sequences have index tending to infinity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,015 | 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-13857-002",
"literature-status:open",
"owr-year:2015"
] | Bounded-index compactness and curvature quantization are known with an area bound, and the surface case has stronger positive-curvature results, but the stated uniform area bound from index and positive sectional curvature remains conjectural in the general dimensions. | [
{
"url": "https://arxiv.org/abs/1512.01047",
"label": "Buzano--Sharp, bounded index and area estimates"
},
{
"url": "https://doi.org/10.4171/owr/2015/36",
"label": "Oberwolfach Report on minimal hypersurfaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | Let $M^n$ be a closed minimal hypersurface in a Riemannian manifold $N$ with strictly positive sectional curvature. If $\operatorname{index}(M)=I$, is $\mathcal H^n(M)\leq C(N,I)$? Consequently, must bounded-index sequences have uniformly bounded volume and volume-divergent sequences have index tending to infinity? | Conjecture: If a minimal hypersurface M in a positively curved ambient manifold N has index I, then its n-dimensional volume is bounded by a constant C(N,I); consequently, bounded-index sequences have bounded volume and volume-divergent sequences have index tending to infinity. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,935 | OWR-13857-003 | Conformal Positivity of Weighted $\sigma_2$-Curvature | Let $(M^n,g)$ be compact. If $\sup_{\Gamma_2^\infty}W_2<\infty$, does the conformal class $[g]$ contain a metric with positive weighted $\sigma_2$-curvature? In particular, does every compact four-dimensional gradient Ricci soliton satisfy $\chi(M^4)>\tfrac32|\tau(M^4)|$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,015 | 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-13857-003",
"literature-status:open",
"owr-year:2015"
] | The weighted sigma-two framework gives variational and soliton results, but the extracted conformal existence conjecture and its unconditional topological consequence remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2015/36",
"label": "Oberwolfach Report on weighted sigma-two curvature"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.03.010",
"label": "Case--Khaitan, weighted sigma-k curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | Let $(M^n,g)$ be compact. If $\sup_{\Gamma_2^\infty}W_2<\infty$, does the conformal class $[g]$ contain a metric with positive weighted $\sigma_2$-curvature? In particular, does every compact four-dimensional gradient Ricci soliton satisfy $\chi(M^4)>\tfrac32|\tau(M^4)|$? | Conjecture 1: If a compact Riemannian manifold satisfies finite supremum of W2 over Gamma infinity squared, then some metric in its conformal class has positive weighted sigma2-curvature; in particular, a compact four-dimensional gradient Ricci soliton satisfies 3 chi(M4) greater than 2 tau(M4). | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,936 | OWR-13857-004 | Duplicate Weighted-Curvature Extraction | Conjecture 2: For a compact Riemannian manifold, either the supremum of W2 over Gamma infinity squared is monotone along the Ricci flow, or the negative gradient flow of W2 is well-posed within Gamma infinity squared. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,015 | 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 passage duplicates the weighted-curvature flow alternatives recorded in OWR-13857-005 and does not state an independent problem. No sepa) | [
"OWR-13857-005"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13857-004",
"literature-status:open",
"owr-year:2015"
] | No proof was found that the weighted sigma-two supremum is Ricci-flow monotone or that its negative gradient flow is well-posed throughout the indicated cone; the source records this as a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2015/36",
"label": "Oberwolfach Report on weighted sigma-two flows"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.03.010",
"label": "Case--Khaitan, weighted sigma-k curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | null | Conjecture 2: For a compact Riemannian manifold, either the supremum of W2 over Gamma infinity squared is monotone along the Ricci flow, or the negative gradient flow of W2 is well-posed within Gamma infinity squared. | unrecoverable | The passage duplicates the weighted-curvature flow alternatives recorded in OWR-13857-005 and does not state an independent problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,937 | OWR-13857-005 | Flows for Weighted $\sigma_2$-Entropy | For a compact Riemannian manifold $(M^n,g)$, is at least one of the following true: $\sup_{\Gamma_2^\infty}W_2$ is monotone along Ricci flow, or the negative gradient flow of $W_2$ is well posed within $\Gamma_2^\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,015 | 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-13857-004"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13857-005",
"literature-status:open",
"owr-year:2015"
] | The extracted Ricci flow alternative still depends on an Obata type extension. Later work on sigma curvature gives related results, but no resolution of this conjecture was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2309.12431",
"label": "Case 2023"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | For a compact Riemannian manifold $(M^n,g)$, is at least one of the following true: $\sup_{\Gamma_2^\infty}W_2$ is monotone along Ricci flow, or the negative gradient flow of $W_2$ is well posed within $\Gamma_2^\infty$? | For a compact Riemannian manifold (M^n,g), is at least one of the following true: (a) \sup_{\Gamma_2^\infty}W_2 is monotone along the Ricci flow; or (b) the negative gradient flow of W_2 is well-posed within \Gamma_2^\infty? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,938 | OWR-13857-006 | Extensions of CMC Gluing Constructions | For constant-mean-curvature hypersurfaces built by gluing spheres and Delaunay pieces along a balanced graph, can this gluing scheme be extended to more general ambient manifolds or to hypersurfaces of infinite topology? Are the resulting hypersurfaces nondegenerate, so that nearby graph deformations produce curves in ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124](https://doi.org/10.4171/owr/2015/36)
## Literature review (checked 2026-08-21)
**Statu... | 3 | open | null | 2,015 | 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-13857-006",
"literature-status:open",
"owr-year:2015"
] | The extracted questions concern generalizing a hypersurface gluing construction to broader ambient manifolds and infinite topology. They remain forward looking, with no definitive general theorem located. | [
{
"url": "https://doi.org/10.4171/owr/2015/36",
"label": "original OWR report"
},
{
"url": "https://ems.press/content/serial-article-files/46583?nt=1",
"label": "full report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/36 | null | null | null | For constant-mean-curvature hypersurfaces built by gluing spheres and Delaunay pieces along a balanced graph, can this gluing scheme be extended to more general ambient manifolds or to hypersurfaces of infinite topology? Are the resulting hypersurfaces nondegenerate, so that nearby graph deformations produce curves in ... | For the constructed constant-mean-curvature hypersurfaces, what requirements are needed on \Gamma and what restrictions on the ambient manifold; can the construction include hypersurfaces of infinite topology; and are the resulting hypersurfaces non-degenerate? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Partial Differential Equations (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/36, pp. 2065--2124 |
30,002,939 | OWR-13858-001 | Global Regularity of Three-Dimensional Euler and Navier–Stokes Flows | Are smooth solutions of the three-dimensional incompressible Euler equations or the three-dimensional Navier–Stokes equations globally regular, or can they develop singularities in finite time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187](https://doi.org/10.4171/owr/2015/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,015 | 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-13858-001",
"literature-status:open",
"owr-year:2015"
] | Global regularity and finite time singularity for three dimensional Euler or Navier Stokes remain unresolved as of the checked date. | [
{
"url": "https://www.claymath.org/wp-content/uploads/2022/06/navierstokes.pdf",
"label": "Clay problem statement"
},
{
"url": "https://link.springer.com/article/10.1007/s40818-025-00214-2",
"label": "2025 Euler paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/37 | null | null | null | Are smooth solutions of the three-dimensional incompressible Euler equations or the three-dimensional Navier–Stokes equations globally regular, or can they develop singularities in finite time? | Are smooth solutions of the three-dimensional incompressible Euler equations or three-dimensional Navier--Stokes equations globally regular, or can they develop singularities in finite time? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187 |
30,002,940 | OWR-13858-002 | Optimal Mixing Rates Under Palinstrophy Constraints | For passive-scalar transport with a velocity field constrained by a uniform palinstrophy, or $H^2$, budget, what is the optimal long-time decay rate of the mix-norm, and is it polynomial or exponential? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187](https://doi.org/10.4171/owr/2015/37)
## Literature review (checked 2026-08-21)
... | 3 | solved | null | 2,015 | 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 | {
"source_url": "https://doi.org/10.1088/0951-7715/27/5/973",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (exponential)**. A. L. Mazzucato (OWR 37/2015, p. 2157) asks whether the optimal decay of the mix-norm under a uniform-in-time H² (palinstrophy) bound on the velocity is polynomial or exponential. It cannot be faster than exponential, since an H² bound implies the ... | [
"owr",
"oberwolfach-reports",
"OWR-13858-002",
"literature-status:open",
"owr-year:2015"
] | Rigorous lower bounds and polynomial mixing constructions are known for important classes, but no proof of the exact optimal decay rate for all palinstrophy constrained flows was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/37",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1707.01352",
"label": "Crippa and Schulze 2017"
},
{
"url": "https://doi.org/10.3934/mine.2023006",
"label": "Crippa and Schulze 2023"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/37 | null | null | null | For passive-scalar transport with a velocity field constrained by a uniform palinstrophy, or $H^2$, budget, what is the optimal long-time decay rate of the mix-norm, and is it polynomial or exponential? | For passive-scalar transport with a velocity field constrained by a uniform palinstrophy (Sobolev H^2) budget, what is the optimal long-time decay rate of the mix-norm, and is it polynomial or exponential? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187 |
30,002,941 | OWR-13858-003 | Determining Wavenumbers Near Three-Dimensional Turbulence | For three-dimensional Navier–Stokes dynamics with intermittency dimension $d$ near $3$, is the time-averaged determining wavenumber $\langle\Lambda\rangle$ bounded by a constant multiple of the Kolmogorov dissipation wavenumber $\kappa_d$, as predicted by Kolmogorov turbulence theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187](https://doi.org/10.4171/owr/2015/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,015 | 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-13858-003",
"literature-status:open",
"owr-year:2015"
] | The report explicitly identifies extending the anomalous diffusion bound to dimensions near three as an open problem, and no later definitive resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/37",
"label": "original OWR report"
},
{
"url": "https://ems.press/content/serial-article-files/46590",
"label": "full report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/37 | null | null | null | For three-dimensional Navier–Stokes dynamics with intermittency dimension $d$ near $3$, is the time-averaged determining wavenumber $\langle\Lambda\rangle$ bounded by a constant multiple of the Kolmogorov dissipation wavenumber $\kappa_d$, as predicted by Kolmogorov turbulence theory? | For three-dimensional Navier--Stokes dynamics with intermittency dimension d near 3, is the time-averaged determining wavenumber \langle\Lambda\rangle bounded by a constant multiple of the Kolmogorov dissipation wavenumber \kappa_d, as predicted by Kolmogorov turbulence theory? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187 |
30,002,942 | OWR-13858-004 | BMO Blowup Criteria for Incompressible Flow Potentials | For incompressible Navier–Stokes flow, does blowup at a finite time $t_*$ imply $\lVert A\rVert_{\mathrm{BMO}}\to\infty$ in three dimensions and $\lVert\psi\rVert_{\mathrm{BMO}}\to\infty$ in two dimensions, where $A$ is the three-dimensional vector potential and $\psi$ is the two-dimensional stream function? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187](https://doi.org/10.4171/owr/2015/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,015 | 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-13858-004",
"literature-status:open",
"owr-year:2015"
] | The general BMO blow up criterion for the vector potential in three dimensions or stream function in two dimensions remains unproved. | [
{
"url": "https://eprints.whiterose.ac.uk/id/eprint/111101/",
"label": "Ohkitani 2017"
},
{
"url": "https://doi.org/10.4171/owr/2015/37",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/37 | null | null | null | For incompressible Navier–Stokes flow, does blowup at a finite time $t_*$ imply $\lVert A\rVert_{\mathrm{BMO}}\to\infty$ in three dimensions and $\lVert\psi\rVert_{\mathrm{BMO}}\to\infty$ in two dimensions, where $A$ is the three-dimensional vector potential and $\psi$ is the two-dimensional stream function? | For incompressible Navier--Stokes flow, does blowup at a finite time t_* imply \|A\|_{BMO}\to\infty in three dimensions, and \|\psi\|_{BMO}\to\infty in two dimensions, where A is the 3D vector potential and \psi the 2D stream function? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/37, pp. 2125--2187 |
30,002,943 | OWR-13859-001 | Pointwise Subsequence Convergence of Approximation Operators | Given Banach spaces $B_1,B_2$, a sequence of bounded linear approximation operators $T_N:B_1\to B_2$ that converges on a dense subset but may diverge elsewhere, does every $f\in B_1$ admit a subsequence $N_k(f)$ such that $\|T_{N_k(f)}f-Tf\|_{B_2}\to0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263](https://doi.org/10.4171/owr/2015/38)
## Literature review (checked ... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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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 | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-29] **solved (no; answered in the source)**. H. Boche (joint with V. Pohl; OWR 38/2015, p. 2200) asks whether every f admits its own subsequence N_k(f) with T_{N_k(f)}f → Tf. The same abstract answers it: strong divergence (lim_N ‖T_N f\*‖ = ∞ for some f\*) rules out every conv... | [
"owr",
"oberwolfach-reports",
"OWR-13859-001",
"literature-status:open",
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] | Strong divergence and finite search horizon obstructions are proved for important approximation schemes, but the universal function dependent subsequence question remains unresolved. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021904516000034",
"label": "Boche and Pohl 2016"
},
{
"url": "https://doi.org/10.4171/owr/2015/38",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/38 | null | null | null | Given Banach spaces $B_1,B_2$, a sequence of bounded linear approximation operators $T_N:B_1\to B_2$ that converges on a dense subset but may diverge elsewhere, does every $f\in B_1$ admit a subsequence $N_k(f)$ such that $\|T_{N_k(f)}f-Tf\|_{B_2}\to0$? | Given Banach spaces B_1,B_2, a sequence of bounded linear approximation operators T_N:B_1\to B_2 that converges on a dense subset but may diverge elsewhere, does every f\in B_1 admit a subsequence N_k(f) such that \|T_{N_k(f)}f-Tf\|_{B_2}\to0? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263 |
30,002,944 | OWR-13859-004 | Variable Bandwidth for Locally Oscillatory Signals | What is a rigorous notion of variable bandwidth for signals $f\in L^2(\mathbb R)$ that captures local frequency variation while retaining appropriate sampling, density, and analyticity properties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263](https://doi.org/10.4171/owr/2015/38)
## Literature review (checked ... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-13859-004",
"literature-status:partially-solved",
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] | Rigorous spectral and time frequency definitions of variable bandwidth now have sampling theories, but the literature contains multiple frameworks rather than one canonical notion. | [
{
"url": "https://arxiv.org/abs/1512.06663",
"label": "Groechenig and Klotz"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0022247X11003763",
"label": "Aceska and Feichtinger 2011"
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{
"url": "https://arxiv.org/abs/2305.17290",
"label": "Andreolli and Groechenig 20... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/38 | null | null | null | What is a rigorous notion of variable bandwidth for signals $f\in L^2(\mathbb R)$ that captures local frequency variation while retaining appropriate sampling, density, and analyticity properties? | What is a rigorous notion of variable bandwidth for signals f\in L^2(\mathbb R) that captures local frequency variation while retaining appropriate sampling, density, and analyticity properties? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263 |
30,002,945 | OWR-13859-006 | Global Optimality and Initialization in Sparse Dictionary Learning | In sparse dictionary learning, is the generating dictionary a global optimum of the K-SVD/ITKsM criteria; are there efficient initialization strategies when sparsity $S=O(\mu^{-2})$; and can the convergence radii of ITKsM and ITKrM be extended to $O(1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263](https://doi.org/10.4171/owr/2015/38)
## Literature review (checked ... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"slug": "analysis",
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"created_at": "2026-07-31T15:26:25.671Z"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13859-006",
"literature-status:open",
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] | Local convergence and improved empirical global recovery are known, but general global optimality, efficient inverse square coherence initialization, and broad convergence radius extensions remain unresolved. | [
{
"url": "https://jmlr.org/papers/volume16/schnass15a/schnass15a.pdf",
"label": "Schnass 2015"
},
{
"url": "https://arxiv.org/abs/1804.07101",
"label": "Pali and Schnass 2018"
},
{
"url": "https://doi.org/10.4171/owr/2015/38",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/38 | null | null | null | In sparse dictionary learning, is the generating dictionary a global optimum of the K-SVD/ITKsM criteria; are there efficient initialization strategies when sparsity $S=O(\mu^{-2})$; and can the convergence radii of ITKsM and ITKrM be extended to $O(1)$? | In sparse dictionary learning, is the generating dictionary a global optimum of the K-SVD/ITKsM criteria; are there efficient initialization strategies when sparsity S=O(\mu^{-2}); and can the convergence radii of ITKsM and ITKrM be extended to O(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 | Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263 |
30,002,946 | OWR-13859-007 | Constructive Algorithms for Nonlinear Sparse Approximation | How can one devise effective constructive algorithms for nonlinear sparse approximation, including m-term approximation with respect to bases and redundant dictionaries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263](https://doi.org/10.4171/owr/2015/38)
## Literature review (checked ... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-13859-007",
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] | This is a broad foundational question about constructive nonlinear approximation methods, not a single theorem with a definitive resolution. | [
{
"url": "https://doi.org/10.4171/owr/2015/38",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/38 | null | null | null | How can one devise effective constructive algorithms for nonlinear sparse approximation, including m-term approximation with respect to bases and redundant dictionaries? | How can one devise effective constructive algorithms for nonlinear sparse approximation, including m-term approximation with respect to bases and redundant dictionaries? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Applied Harmonic Analysis and Sparse Approximation (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/38, pp. 2189--2263 |
30,002,947 | OWR-13860-003 | Smoothness of Ekedahl–Kottwitz–Oort–Rapoport Strata | For a parahoric-level Shimura variety, is the finite morphism from every Kottwitz–Rapoport stratum at Iwahori level to its corresponding EKOR stratum finite étale, and consequently are all EKOR strata smooth? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328](https://doi.org/10.4171/owr/2015/39)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1215/00127094-2021-0047",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (proved for Kisin–Pappas models of abelian type). M. Rapoport (joint with X. He; OWR 39/2015, p. 2278, Remark 3.9) conjectures that the finite morphism from a Kottwitz–Rapoport stratum at Iwahori level onto the corresponding EKOR stratum is finite étale... | [
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{
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"url": "https://ems.press/content/serial-article-files/46591",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/39 | null | null | null | For a parahoric-level Shimura variety, is the finite morphism from every Kottwitz–Rapoport stratum at Iwahori level to its corresponding EKOR stratum finite étale, and consequently are all EKOR strata smooth? | For a parahoric-level Shimura variety, is the finite morphism from each Kottwitz--Rapoport stratum at Iwahori level to the corresponding EKOR stratum finite etale, and consequently are all EKOR strata smooth? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328 |
30,002,948 | OWR-13860-005 | Local Determination of Serre Weights for Unitary Groups | In the weight part of Serre's conjecture for unitary groups of semisimple rank greater than one, is the set of modular Serre weights W(r) determined by the local restrictions $r|_{G_{F_w}}$ through the predicted local sets $W^?(r|_{G_{F_w}})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328](https://doi.org/10.4171/owr/2015/39)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
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"created_at": "2026-07-31T15:26:25.670Z"
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
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{
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{
"url": "https://arxiv.org/abs/2007.05398",
"label": "later local model results"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/39 | null | null | null | In the weight part of Serre's conjecture for unitary groups of semisimple rank greater than one, is the set of modular Serre weights W(r) determined by the local restrictions $r|_{G_{F_w}}$ through the predicted local sets $W^?(r|_{G_{F_w}})$? | In the weight part of Serre's conjecture for unitary groups of semisimple rank greater than one, is the set of modular Serre weights W(r) determined by the local restrictions r|_{G_{F_w}} through the predicted local sets W^?(r|_{G_{F_w}})? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328 |
30,002,949 | OWR-13860-006 | Agreement of Affine Deligne–Lusztig Stratifications | For affine Deligne–Lusztig varieties, does the new invariant $f_g$ induce the same stratification as the generalized Ekedahl–Oort invariant in every case studied by Görtz and He? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328](https://doi.org/10.4171/owr/2015/39)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
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"label": "full report text"
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"url": "https://doi.org/10.4153/S0008414X22000608",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/39 | null | null | null | For affine Deligne–Lusztig varieties, does the new invariant $f_g$ induce the same stratification as the generalized Ekedahl–Oort invariant in every case studied by Görtz and He? | For affine Deligne--Lusztig varieties, does the new invariant f_g induce the same stratification as the generalized Ekedahl--Oort invariant in all cases studied by Gortz and He? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328 |
30,002,950 | OWR-13860-007 | Orbit Structure of Generic A-Number-One Loci | For the affine Deligne–Lusztig invariant $f_g$, does the locus of $p$-divisible groups with generic $a$-number $1$ form a single $J_b(F)$-orbit of strata even when $b$ is not basic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328](https://doi.org/10.4171/owr/2015/39)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,015 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13860-007",
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{
"url": "https://ems.press/content/serial-article-files/46591",
"label": "full report text"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/39 | null | null | null | For the affine Deligne–Lusztig invariant $f_g$, does the locus of $p$-divisible groups with generic $a$-number $1$ form a single $J_b(F)$-orbit of strata even when $b$ is not basic? | For the affine Deligne--Lusztig invariant associated with f_g, does the locus of p-divisible groups with generic a-number 1 coincide with one J_b(F)-orbit of strata even when b is not basic? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Reductions of Shimura Varieties (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/39, pp. 2265--2328 |
30,002,951 | OWR-13861-005 | Joint Boltzmann–Grad and Long-Time Limits for Lorentz Gases | For the periodic Lorentz gas with scatterer radius $r$ and time $t$, can one establish a joint limit as $r\to0$ and $t\to\infty$, rather than taking the limits successively? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/40, pp. 2329--2398](https://doi.org/10.4171/owr/2015/40)
## Literature review (checked 2... | 3 | open | null | 2,015 | 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-13861-005",
"literature-status:open",
"owr-year:2015"
] | The report asks for a joint long-time and Boltzmann--Grad limit in the periodic Lorentz gas. The established results take the limits successively, and later work still identifies the joint limit as open. | [
{
"url": "https://doi.org/10.1007/s00220-016-2578-y",
"label": "Marklof--Toth, Superdiffusion in the Periodic Lorentz Gas"
},
{
"url": "https://doi.org/10.1007/s00440-023-01197-6",
"label": "Boca--Zaharescu, Periodic Lorentz Gas with Small Scatterers"
},
{
"url": "https://doi.org/10.4171... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/40 | null | null | null | For the periodic Lorentz gas with scatterer radius $r$ and time $t$, can one establish a joint limit as $r\to0$ and $t\to\infty$, rather than taking the limits successively? | For the periodic Lorentz gas with scatterer radius r and time t, can one establish a joint limit as r\to0 and t\to\infty, rather than taking the limits successively? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/40, pp. 2329--2398 |
30,002,952 | OWR-13861-007 | Resistance Exponents of Critical Branching Random-Walk Traces | For the trace of critical branching random walk in dimension $d<6$, what polynomial exponent governs the growth of its effective resistance $R(n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/40, pp. 2329--2398](https://doi.org/10.4171/owr/2015/40)
## Literature review (checked 2... | 3 | open | null | 2,015 | 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-13861-007",
"literature-status:open",
"owr-year:2015"
] | For the effective resistance of the low-dimensional critical branching random-walk trace, the literature proves sublinear upper bounds and studies critical corrections, but no precise polynomial growth exponent for d<6 has been established. | [
{
"url": "https://arxiv.org/abs/1305.1092",
"label": "Nachmias--Járai, Electrical Resistance of the Low Dimensional Critical Branching Random Walk"
},
{
"url": "https://arxiv.org/abs/2006.09005",
"label": "Járai--Nachmias, Logarithmic Correction to Resistance"
},
{
"url": "https://doi.or... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/40 | null | null | null | For the trace of critical branching random walk in dimension $d<6$, what polynomial exponent governs the growth of its effective resistance $R(n)$? | For the critical branching random walk trace in dimension d<6, what precise polynomial exponent governs the growth of its effective resistance R(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 | Scaling Limits in Models of Statistical Mechanics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/40, pp. 2329--2398 |
30,002,953 | OWR-13863-002 | Attainable Sum Distributions and Joint Mixability | For given marginal distributions $F_1,\ldots,F_n$, characterize $D_n(F_1,\ldots,F_n)=\{\operatorname{cdf}(X_1+\cdots+X_n):X_i\sim F_i\}$ under arbitrary dependence, and find an analytical method to decide when $D_n$ contains a point mass (joint mixability). | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Mathematics and Statistics of Quantitative Risk Management (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/42, pp. 2481--2532](https://doi.org/10.4171/owr/2015/42)
## Literature revi... | 3 | open | null | 2,015 | 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-13863-002",
"literature-status:open",
"owr-year:2015"
] | The report explicitly states that a direct characterization and a general analytic verification method for the attainable-sums set D_n are unavailable; no complete general characterization was identified. | [
{
"url": "https://doi.org/10.4171/owr/2015/42",
"label": "Oberwolfach Report 42, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/42 | null | null | null | For given marginal distributions $F_1,\ldots,F_n$, characterize $D_n(F_1,\ldots,F_n)=\{\operatorname{cdf}(X_1+\cdots+X_n):X_i\sim F_i\}$ under arbitrary dependence, and find an analytical method to decide when $D_n$ contains a point mass (joint mixability). | For given marginal distributions F_1,\ldots,F_n, characterize D_n(F_1,\ldots,F_n)=\{\operatorname{cdf}(X_1+\cdots+X_n):X_i\sim F_i\} for arbitrary dependence, and find an analytical method to decide when D_n contains a point mass (joint mixability). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Mathematics and Statistics of Quantitative Risk Management (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/42, pp. 2481--2532 |
30,002,954 | OWR-13863-003 | Elicitability and Backtesting of Expected Shortfall | How is elicitability relevant to backtesting risk measures, especially Expected Shortfall, given that Expected Shortfall is not singly elicitable but is jointly elicitable with Value at Risk? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Mathematics and Statistics of Quantitative Risk Management (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/42, pp. 2481--2532](https://doi.org/10.4171/owr/2015/42)
## Literature revi... | 3 | open | null | 2,015 | 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-13863-003",
"literature-status:open",
"owr-year:2015"
] | The extracted question concerns the role of elicitability in backtesting. The primary risk-measure literature settles non-elicitability of Expected Shortfall and joint elicitability with Value at Risk, but does not yield a single definitive answer to the broad relevance question. | [
{
"url": "https://doi.org/10.1111/j.1467-9965.2011.00486.x",
"label": "Gneiting, Making and Evaluating Point Forecasts"
},
{
"url": "https://doi.org/10.1214/15-AOS1339",
"label": "Fissler--Ziegel, Higher-order Elicitability"
},
{
"url": "https://doi.org/10.4171/owr/2015/42",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/42 | null | null | null | How is elicitability relevant to backtesting risk measures, especially Expected Shortfall, given that Expected Shortfall is not singly elicitable but is jointly elicitable with Value at Risk? | How is elicitability relevant to backtesting risk measures, especially Expected Shortfall, given that Expected Shortfall is not singly elicitable but is jointly elicitable with Value at Risk? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | The Mathematics and Statistics of Quantitative Risk Management (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/42, pp. 2481--2532 |
30,002,955 | OWR-13940-002 | Computational Topological Similarity of Curves | How can topological similarity measures for curves, such as homology area and homotopy area, be applied, computed, and used efficiently in higher-dimensional settings? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | open | null | 2,015 | 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-13940-002",
"literature-status:open",
"owr-year:2015"
] | The record asks for efficient higher-dimensional applications of topological curve-similarity measures without specifying a single theorem or algorithmic target; the question remains unresolved at that level of generality. | [
{
"url": "https://doi.org/10.4171/owr/2015/45",
"label": "Oberwolfach Report 45, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | How can topological similarity measures for curves, such as homology area and homotopy area, be applied, computed, and used efficiently in higher-dimensional settings? | How can topological similarity measures for curves, such as homology area and homotopy area, be applied, computed, and used efficiently in higher-dimensional settings? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,956 | OWR-13940-003 | Complexity of Embedding Two-Complexes in Three-Manifolds | Determine the decidability and computational complexity of deciding whether a given 2-complex embeds in a 3-manifold, including the case of non-orientable surfaces of even Euler genus and the related thickenability problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | partially_solved | null | 2,015 | 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"
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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-13940-003",
"literature-status:partially-solved",
"owr-year:2015"
] | The report combines an NP-hardness claim with an NP-completeness result only for the odd-Euler-genus case, while explicitly leaving even Euler genus unresolved; thus the broad embeddability problem is only partially settled. | [
{
"url": "https://doi.org/10.1007/s00454-017-9900-0",
"label": "Burton--de Mesmay--Wagner, Finding Non-orientable Surfaces"
},
{
"url": "https://arxiv.org/abs/1402.0815",
"label": "Matoušek--Sedgwick--Tancer--Wagner, Embeddability in the 3-sphere"
},
{
"url": "https://doi.org/10.4171/owr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | Determine the decidability and computational complexity of deciding whether a given 2-complex embeds in a 3-manifold, including the case of non-orientable surfaces of even Euler genus and the related thickenability problem. | Determine the decidability and computational complexity of deciding whether a given 2-complex embeds in a 3-manifold, including the case of non-orientable surfaces of even Euler genus and the related thickenability problem. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,957 | OWR-13940-005 | Delaunay Simplices in Flag Complexes of Random Triangulations | For a Poisson point process in $\mathbb R^d$ with Delaunay triangulation $T$, form the flag complex of the $1$-skeleton of $T$. How many $d$-simplices, and more generally how many $k$-simplices for $k\leq d$, of this flag complex are Delaunay? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | partially_solved | null | 2,015 | 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"
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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-13940-005",
"literature-status:partially-solved",
"owr-year:2015"
] | For Poisson--Delaunay mosaics, primary stochastic-geometry work gives explicit expected simplex intensities and exact low-dimensional values, but it does not provide a general closed answer to the flag-complex fraction question in arbitrary dimension. | [
{
"url": "https://doi.org/10.1017/apr.2017.4",
"label": "Edelsbrunner--Nikitenko--Reitzner, Expected Sizes of Poisson--Delaunay Mosaics"
},
{
"url": "https://doi.org/10.4171/owr/2015/45",
"label": "Oberwolfach Report 45, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | For a Poisson point process in $\mathbb R^d$ with Delaunay triangulation $T$, form the flag complex of the $1$-skeleton of $T$. How many $d$-simplices, and more generally how many $k$-simplices for $k\leq d$, of this flag complex are Delaunay? | For a Poisson point process in R^{d} with Delaunay triangulation T, form the flag complex of the 1-skeleton of T. How many d-simplices, and more generally how many k-simplices for k\le d, of this flag complex are Delaunay? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,958 | OWR-13940-006 | Universal Sequences of Plane Curves for Knot Diagrams | For a sequence of generic plane immersions of the circle that eventually carries every knot after resolving double points, what characterizes such a universal sequence of plane curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | open | null | 2,015 | 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-13940-006",
"literature-status:open",
"owr-year:2015"
] | The characterization of sequences of plane immersions that eventually carry every knot is posed without a known necessary-and-sufficient criterion; the report records only examples and necessary conditions. | [
{
"url": "https://doi.org/10.4171/owr/2015/45",
"label": "Oberwolfach Report 45, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | For a sequence of generic plane immersions of the circle that eventually carries every knot after resolving double points, what characterizes such a universal sequence of plane curves? | For a sequence of generic plane immersions of the circle that eventually carries every knot after resolving double points, what characterizes such a universal sequence of plane curves? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,959 | OWR-13940-007 | Minimal Triangulated Sphere Eversions | For simplicial immersions of triangulated $2$-spheres, which spheres can be turned inside out; what is the smallest sphere that can be everted; and what is the smallest triangulated sphere with $2^{2g}$ discrete regular homotopy classes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | open | null | 2,015 | 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-13940-007",
"literature-status:open",
"owr-year:2015"
] | Discrete sphere eversion and the smallest triangulated sphere realizing specified discrete regular-homotopy classes remain unresolved; smooth sphere eversion results do not settle the discrete simplicial problem. | [
{
"url": "https://doi.org/10.1016/j.topol.2017.08.005",
"label": "Kamada, Sphere Eversion from the Viewpoint of Generic Homotopy"
},
{
"url": "https://doi.org/10.4171/owr/2015/45",
"label": "Oberwolfach Report 45, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | For simplicial immersions of triangulated $2$-spheres, which spheres can be turned inside out; what is the smallest sphere that can be everted; and what is the smallest triangulated sphere with $2^{2g}$ discrete regular homotopy classes? | For simplicial immersions of triangulated 2-spheres, which spheres can be turned inside out; what is the smallest sphere that can be everted; and what is the smallest triangulated sphere with 2^{2g} discrete regular homotopy classes? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,960 | OWR-13940-008 | Three-Dimensional Coloring Number of the Sphere | What is the $3$-dimensional coloring number $\chi_3(S^3)$ for triangulations of the $3$-sphere, where monochromatic triangles are allowed but monochromatic tetrahedra are forbidden; in particular, is it finite or is there an upper bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699](https://doi.org/10.4171/owr/2015/45)
## Literature review (checked 2026... | 3 | solved | null | 2,015 | 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 | {
"source_url": "https://doi.org/10.1007/s00454-026-00856-4",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (χ₃(S³) = ∞)**. F. H. Lutz (OWR 45/2015, pp. 2693–2694, Problem SEVEN) asks for χ₃(S³), the least m such that every triangulated 3-sphere has a vertex m-colouring with no monochromatic tetrahedron, and whether it is finite; the report knows only χ₃ ≥ 2. It is infin... | [
"owr",
"oberwolfach-reports",
"OWR-13940-008",
"literature-status:open",
"owr-year:2015"
] | The proposed relation between knot complexity and the treewidth of minimal triangulations of knot complements is posed as a necessary condition for an algorithmic strategy, and no general diverging function f is established. | [
{
"url": "https://doi.org/10.4171/owr/2015/45",
"label": "Oberwolfach Report 45, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/45 | null | null | null | What is the $3$-dimensional coloring number $\chi_3(S^3)$ for triangulations of the $3$-sphere, where monochromatic triangles are allowed but monochromatic tetrahedra are forbidden; in particular, is it finite or is there an upper bound? | What is the 3-dimensional coloring number \chi_{3}(S^{3}) for triangulations of the 3-sphere, where monochromatic triangles are allowed but monochromatic tetrahedra are forbidden; in particular, is it finite or is there an upper bound? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Computational Geometric and Algebraic Topology (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/45, pp. 2637--2699 |
30,002,961 | OWR-13941-001 | Open Problems in Mixed-Integer Nonlinear Optimization | Why is semidefinite programming computationally slow? For
$$X(\alpha,\beta,\gamma)=\{(x_1,x_2,t_1,t_2,z_1,z_2)\in\mathbb R^4\times\{0,1\}^2:t_i\geq x_i^2,\ 0\leq\alpha x_1+\beta x_2\leq z_1,\ 0\leq\gamma x_2\leq z_2\},$$
find a scalable compact description of $\operatorname{conv}X(\alpha,\beta,\gamma)$. What is the min... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 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-13941-001",
"literature-status:open",
"owr-year:2015"
] | The record is a bundle of broad open questions on SDP, semialgebraic convexification, copositivity, structure recognition, and global optimization rather than one resolved proposition; the combined extracted claim remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/46",
"label": "Oberwolfach Report 46, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | Why is semidefinite programming computationally slow? For
$$X(\alpha,\beta,\gamma)=\{(x_1,x_2,t_1,t_2,z_1,z_2)\in\mathbb R^4\times\{0,1\}^2:t_i\geq x_i^2,\ 0\leq\alpha x_1+\beta x_2\leq z_1,\ 0\leq\gamma x_2\leq z_2\},$$
find a scalable compact description of $\operatorname{conv}X(\alpha,\beta,\gamma)$. What is the min... | For the mixed-integer optimization questions in the report: explain why semidefinite programming can be slow; find scalable compact convex-hull descriptions for X(\alpha,\beta,\gamma); determine the minimum auxiliary dimension for semialgebraic representations of non-semialgebraic convex hulls; develop randomized copos... | 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 | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,962 | OWR-13941-002 | Convexification and Complexity in Mixed-Integer Optimization | Are the intermediate SOS sets $\Sigma^k_{n,d}=\{p:\exists q\in\mathbb{R}[x]^k,\ q\text{ is SOS and }pq\text{ is SOS}\}$ convex? What is the complexity of selecting $s_i\in S_i$ such that $0\in\operatorname{conv}\{s_0,\ldots,s_d\}$? What are the complexities of finding a separating Chvátal–Gomory inequality and of integ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 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-13941-002",
"literature-status:open",
"owr-year:2015"
] | The record bundles several unresolved questions, including convexity of intermediate SOS sets, complexity of a selection problem, practical SDP--RLT rules, and convexification of mixed-integer nonlinear sets; no complete resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/46",
"label": "Oberwolfach Report 46, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | Are the intermediate SOS sets $\Sigma^k_{n,d}=\{p:\exists q\in\mathbb{R}[x]^k,\ q\text{ is SOS and }pq\text{ is SOS}\}$ convex? What is the complexity of selecting $s_i\in S_i$ such that $0\in\operatorname{conv}\{s_0,\ldots,s_d\}$? What are the complexities of finding a separating Chvátal–Gomory inequality and of integ... | Are the intermediate SOS sets \Sigma^{k}_{n,d}=\{p\mid\exists q\in R[x]^{k}:q is SOS and pq is SOS\} convex; what is the complexity of selecting s_i\in S_i with 0\in\operatorname{conv}\{s_0,\ldots,s_d\}; what are the complexities of finding a separating Chvatal--Gomory inequality and of integer quadratic optimization i... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,963 | OWR-13941-003 | Unspecified Convex-Hull Conjecture for a Pooling Relaxation | For the remaining considered cases of the structured nonconvex subset of the pooling problem, is the conjectured full description of its convex hull correct? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report only says that a structured nonconvex pooling relaxation has a conjectured full convex-hull description in the remaining) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13941-003",
"literature-status:open",
"owr-year:2015"
] | The extracted statement is an explicit conjecture about the remaining cases of a nonconvex pooling-problem convex hull description; the source identifies proving it as future work, and no complete proof was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/46",
"label": "Oberwolfach Report 46, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | null | For the remaining considered cases of the structured nonconvex subset of the pooling problem, is the conjectured full description of its convex hull correct? | unrecoverable | The official report only says that a structured nonconvex pooling relaxation has a conjectured full convex-hull description in the remaining cases; it does not state the subset, cases, or conjectured inequalities. No separate clean statement is promoted, and the original record remains visible for provenance. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,964 | OWR-13941-004 | Complexity and Rank of Completely Positive Matrices | Let $CP_n=\{BB^T:B\in\mathbb R_{\geq0}^{n\times k}\text{ for some }k\}$ be the cone of completely positive matrices. Is membership in $CP_n$ in NP? How can the cp-rank $\operatorname{cp}(A)=\min\{k:A=BB^T,\ B\in\mathbb R_{\geq0}^{n\times k}\}$ of an arbitrary $A\in CP_n$ be determined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 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-13941-004",
"literature-status:open",
"owr-year:2015"
] | Completely-positive membership is known to be NP-hard, while membership in NP remains unresolved, and computing cp-rank is still explicitly open in current primary literature. | [
{
"url": "https://doi.org/10.1007/s10589-022-00417-4",
"label": "Badenbroek--de Klerk, Completely Positive Factorization"
},
{
"url": "https://doi.org/10.1007/s10589-013-9564-0",
"label": "Dickinson--Gijben, Complexity of CP-Cone Membership"
},
{
"url": "https://doi.org/10.4171/owr/2015/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | Let $CP_n=\{BB^T:B\in\mathbb R_{\geq0}^{n\times k}\text{ for some }k\}$ be the cone of completely positive matrices. Is membership in $CP_n$ in NP? How can the cp-rank $\operatorname{cp}(A)=\min\{k:A=BB^T,\ B\in\mathbb R_{\geq0}^{n\times k}\}$ of an arbitrary $A\in CP_n$ be determined? | Is membership A\in CP_n, the cone of completely positive matrices, in the complexity class NP, and how can the cp-rank of an arbitrary completely positive matrix be determined? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,965 | OWR-13941-005 | Volume of the Boolean Quadric Polytope | For $n\geq2$, let $P_n$ be the Boolean quadric polytope, the convex hull in dimension $d=n(n+1)/2$ of the $0/1$ points satisfying $y_{ij}=x_ix_j$ for $i<j$. Find a formula or nontrivial upper and lower bounds for the $d$-dimensional volume of $P_n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 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 | {
"source_url": "https://ems.press/journals/owr/articles/13941",
"checked_at": "2026-10-16",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 update, 2026-10-16] The record asks for a formula **or nontrivial volume bounds** for the Boolean quadric polytope. The [original Jon Lee contribution](https://ems.press/journals/owr/articles/13941), printed pp. 2737–2738, explicitly allows a substantial upper-bound improvement and/or a nontrivial lower ... | [
"owr",
"oberwolfach-reports",
"OWR-13941-005",
"literature-status:open",
"owr-year:2015"
] | The exact or useful asymptotic volume of the Boolean Quadric Polytope remains open in the complete-graph case; later work gives volumes for relaxations and structured sparse graphs, not the requested general formula or bounds. | [
{
"url": "https://arxiv.org/abs/1703.02444",
"label": "Lee--Morris--Speakman, Volume Computation for Sparse Boolean Quadric Relaxations"
},
{
"url": "https://doi.org/10.1016/0012-365X(95)00343-U",
"label": "Ko--Lee--Steingrímsson, Volume of Relaxed Boolean-quadric Polytopes"
},
{
"url": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | For $n\geq2$, let $P_n$ be the Boolean quadric polytope, the convex hull in dimension $d=n(n+1)/2$ of the $0/1$ points satisfying $y_{ij}=x_ix_j$ for $i<j$. Find a formula or nontrivial upper and lower bounds for the $d$-dimensional volume of $P_n$. | For n\ge2, let P_n be the Boolean quadric polytope, the convex hull in dimension d=n(n+1)/2 of the 0/1 points satisfying y_{ij}=x_i x_j for i<j. Find a formula or nontrivial upper and lower bounds for the d-dimensional volume of P_n. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,966 | OWR-13941-006 | Core Points of Transitive Permutation Groups | For every transitive permutation group that is not $2$-homogeneous, are there infinitely many core points up to integral translations of the fixed space? Equivalently, does the conjecture hold in the remaining case of primitive permutation groups with rational invariant subspaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766](https://doi.org/10.4171/owr/2015/46)
## Litera... | 3 | open | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13941-006",
"literature-status:open",
"owr-year:2015"
] | The core-point conjecture for primitive transitive permutation groups with rational invariant subspaces is explicitly left open; later formulations with normalizer equivalence generalize rather than settle the original conjecture. | [
{
"url": "https://doi.org/10.1007/s10107-017-1173-0",
"label": "Herr--Rehn--Schürmann, Core Points and Normalizer Equivalence"
},
{
"url": "https://doi.org/10.4171/owr/2015/46",
"label": "Oberwolfach Report 46, 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/46 | null | null | null | For every transitive permutation group that is not $2$-homogeneous, are there infinitely many core points up to integral translations of the fixed space? Equivalently, does the conjecture hold in the remaining case of primitive permutation groups with rational invariant subspaces? | For every transitive permutation group not covered by the finite-core-point cases, do infinitely many core points exist up to integral translations of the fixed space, especially for primitive groups with only rational invariant subspaces? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/46, pp. 2701--2766 |
30,002,967 | OWR-13943-001 | Connections Among Weyl Groupoids, Nichols Algebras, and Cluster Algebras | Is there a deeper connection between Weyl groupoids or Nichols algebras and cluster algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894](https://doi.org/10.4171/owr/2015/48)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,015 | 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-13943-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Rank-two reflection groupoids have a precise connection with type-A cluster algebras, but no general equivalence or deeper connection for Weyl groupoids or Nichols algebras has been established. | [
{
"url": "https://doi.org/10.1016/j.jcta.2010.12.003",
"label": "Cuntz--Heckenberger, Reflection Groupoids of Rank Two"
},
{
"url": "https://arxiv.org/abs/0911.3051",
"label": "Cuntz--Heckenberger, arXiv version"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3318/OWR_2012... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/48 | null | null | null | Is there a deeper connection between Weyl groupoids or Nichols algebras and cluster algebras? | Is there a deeper connection between Weyl groupoids or Nichols algebras and cluster algebras? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894 |
30,002,968 | OWR-13943-002 | Snake-Graph Models for Generalized Cluster Variables | For a generalized cluster algebra of type $C_n$ with generalized exchange polynomials, does every cluster variable correspond to a connected subgraph of its generalized snake graph? Do analogous snake-graph descriptions hold for the affine types covered by the same construction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894](https://doi.org/10.4171/owr/2015/48)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,015 | 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-13943-002",
"literature-status:open",
"owr-year:2015"
] | The 2015 perfect-matching conjecture for the stated generalized type-C exchange polynomials remains unresolved; later work proves perfect-matching formulas for ordinary type B and C cluster algebras, not this generalized conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/46598",
"label": "Gleitz, Generalised Cluster Algebras and Perfect Matchings"
},
{
"url": "https://arxiv.org/abs/2405.14915",
"label": "Ciliberti, Cluster Expansion Formulas for Type B and C"
},
{
"url": "https://doi.org/10.46298/d... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/48 | null | null | null | For a generalized cluster algebra of type $C_n$ with generalized exchange polynomials, does every cluster variable correspond to a connected subgraph of its generalized snake graph? Do analogous snake-graph descriptions hold for the affine types covered by the same construction? | For the stated generalized cluster algebra of type C_n with its generalized exchange polynomials, does every cluster variable correspond to a connected subgraph of the associated generalized snake graph, with analogous descriptions for the indicated affine types? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894 |
30,002,969 | OWR-13943-004 | Lamination Realization of Higher Tropical Friezes | Can every higher tropical frieze pattern be realized by an A-lamination? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894](https://doi.org/10.4171/owr/2015/48)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,015 | 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-13943-004",
"literature-status:open",
"owr-year:2015"
] | Higher-dimensional A-laminations are known to produce higher tropical frieze patterns, but a converse realization theorem for all such patterns has not been proved. | [
{
"url": "https://ems.press/content/serial-article-files/46598",
"label": "Oppermann--Thomas, Higher-Dimensional Cluster Combinatorics"
},
{
"url": "https://arxiv.org/abs/1209.0812",
"label": "Le, Higher Laminations and Affine Buildings"
},
{
"url": "https://ems.press/content/serial-arti... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/48 | null | null | null | Can every higher tropical frieze pattern be realized by an A-lamination? | Can every higher tropical frieze pattern be realized by an A-lamination? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894 |
30,002,970 | OWR-13943-005 | Classification of Laminations and Higher Tropical Frieze Patterns | Is there a useful description of all A-laminations, and an explicit description of all higher tropical frieze patterns? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894](https://doi.org/10.4171/owr/2015/48)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,015 | 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-13943-005",
"literature-status:open",
"owr-year:2015"
] | Classical tropical friezes admit an A-lamination description, and higher tropical friezes have categorical constructions, but a complete description of all higher A-laminations or all higher tropical patterns is still unavailable. | [
{
"url": "https://ems.press/content/serial-article-files/46598",
"label": "Friezes Workshop Open Questions"
},
{
"url": "https://arxiv.org/abs/1806.02108",
"label": "Jorgensen, Tropical Friezes and the Index"
},
{
"url": "https://arxiv.org/abs/1209.0812",
"label": "Le, Higher Laminat... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/48 | null | null | null | Is there a useful description of all A-laminations, and an explicit description of all higher tropical frieze patterns? | Is there a useful description of all A-laminations, and an explicit description of all higher tropical frieze patterns? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Friezes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/48, pp. 2859--2894 |
30,002,971 | OWR-13944-001 | Long-Range Mechanical Signaling in Tissue Morphogenesis | In morphogenesis, how can global tissue-size information be transmitted when cell regulation is local; in particular, can active mechanical stress or its derivative provide a scale-dependent signal beyond the fixed characteristic length of reaction–diffusion mechanisms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Differential Growth, Morphogenesis, and Pattern Selection (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/49, pp. 2895--2910](https://doi.org/10.4171/owr/201... | 3 | open | null | 2,015 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13944-001",
"literature-status:open",
"owr-year:2015"
] | Mechanochemical stress, morphogen gradients, and biochemical feedback provide plausible transmission mechanisms, but the general question of how local cells acquire global size information remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.ijnonlinmec.2014.11.027",
"label": "Ambrosi--Pettinati--Ciarletta, Active Stress"
},
{
"url": "https://doi.org/10.1038/nrm.2017.139",
"label": "Collinet--Lecuit, Programmed and Self-Organized Information Flow"
},
{
"url": "https://doi.org/10.1016/j.gde... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/49 | null | null | null | In morphogenesis, how can global tissue-size information be transmitted when cell regulation is local; in particular, can active mechanical stress or its derivative provide a scale-dependent signal beyond the fixed characteristic length of reaction–diffusion mechanisms? | In morphogenesis, how can global tissue-size information be transmitted when cell regulation is local; in particular, can active mechanical stress or its derivative provide a scale-dependent signal beyond the fixed characteristic length of reaction--diffusion mechanisms? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Mathematics of Differential Growth, Morphogenesis, and Pattern Selection (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/49, pp. 2895--2910 |
30,002,972 | OWR-13946-003 | Geometric Description of Involutions on K3 Hilbert Squares | Let $S$ be a generic projective K3 surface with $\operatorname{Pic}(S)=\mathbb ZH$ and $H^2=20$. Find a geometric description of the nontrivial nonsymplectic involution on the Hilbert square $S^{[2]}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-003",
"literature-status:partially-solved",
"owr-year:2015"
] | The involution is arithmetically characterized and several geometric constructions now exist, including EPW and related realizations, but no uniform geometric description covers all cases posed in the 2015 question. | [
{
"url": "https://doi.org/10.1002/mana.201800557",
"label": "Cattaneo, Automorphisms of Hilbert Schemes"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2023.01.013",
"label": "Geometric Description of Polarized Hilbert Squares"
},
{
"url": "https://doi.org/10.1007/s12215-025-01342-1",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Let $S$ be a generic projective K3 surface with $\operatorname{Pic}(S)=\mathbb ZH$ and $H^2=20$. Find a geometric description of the nontrivial nonsymplectic involution on the Hilbert square $S^{[2]}$. | How can one find a geometric description of the non-symplectic involution on S^{[2]} associated with the genus-11 K3-surface case? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,973 | OWR-13946-004 | Birational Geometry of Ball-Quotient Moduli Spaces | For the complex ball quotient moduli spaces of $K3^{[2]}$-type fourfolds with a nonsymplectic automorphism of prime order, determine their Kodaira dimensions and identify the rational cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-004",
"literature-status:partially-solved",
"owr-year:2015"
] | The period-map construction of the relevant ball quotients is established and many order-three K3 cases are rational, but the Kodaira dimensions and rationality of the full higher-dimensional family remain unsettled. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2018.03.012",
"label": "Boissiere--Camere--Sarti, Complex Ball Quotients"
},
{
"url": "https://arxiv.org/abs/1208.5826",
"label": "Ma--Ohashi--Taki, Rationality of Eisenstein K3 Moduli"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/205e22d5... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For the complex ball quotient moduli spaces of $K3^{[2]}$-type fourfolds with a nonsymplectic automorphism of prime order, determine their Kodaira dimensions and identify the rational cases. | What is the Kodaira dimension of the relevant complex ball quotient moduli space arising from K3^{[2]}-type fourfolds with a non-symplectic automorphism, and in which cases is it rational? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,974 | OWR-13946-005 | Dual Graphs of Negative Curves on Enriques Surfaces | Can the abstract good dual graphs in the Enriques lattice be classified, and can Enriques surfaces realizing the corresponding $(-2)$-configurations be found? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-005",
"literature-status:partially-solved",
"owr-year:2015"
] | Many realizable (-2)-curve configurations and complete classifications in important finite-automorphism cases are known, but the classification of all abstract good dual graphs in the Enriques lattice is not complete. | [
{
"url": "https://doi.org/10.1093/imrn/rnx074",
"label": "Katsura--Kondo--Martin, Enriques Surfaces in Characteristic Two"
},
{
"url": "https://doi.org/10.46298/ag.2020.7.390",
"label": "Martin, Classification of Enriques Surfaces"
},
{
"url": "https://doi.org/10.1007/s00208-022-02459-9"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Can the abstract good dual graphs in the Enriques lattice be classified, and can Enriques surfaces realizing the corresponding $(-2)$-configurations be found? | Can the abstract good dual graphs in the Enriques lattice be classified, and can Enriques surfaces realizing the corresponding (\!-2)-configurations be found? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,975 | OWR-13946-006 | Irreducibility of Severi Varieties on Polarized K3 Surfaces | Let $\mathcal V_{p,n,\delta}$ be the universal Severi variety of triples $((X,L),C)$, where $(X,L)$ is a primitively polarized K3 surface of genus $p$ and $C\in|nL|$ is irreducible with exactly $\delta$ nodes. Is $\mathcal V_{p,n,\delta}$ irreducible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-006",
"literature-status:partially-solved",
"owr-year:2015"
] | Irreducibility of Severi varieties is proved in broad ranges, including p\geq4\delta-3 for primitive classes and small-node ranges for general K3 surfaces, but the full V_{p,n,\delta} question remains open. | [
{
"url": "https://arxiv.org/abs/1809.03914",
"label": "Ciliberto--Dedieu, Irreducibility of Severi Varieties"
},
{
"url": "https://arxiv.org/abs/2112.09398",
"label": "Bruno--Lelli-Chiesa, Irreducibility of Severi Varieties"
},
{
"url": "https://arxiv.org/abs/1502.07378",
"label": "C... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Let $\mathcal V_{p,n,\delta}$ be the universal Severi variety of triples $((X,L),C)$, where $(X,L)$ is a primitively polarized K3 surface of genus $p$ and $C\in|nL|$ is irreducible with exactly $\delta$ nodes. Is $\mathcal V_{p,n,\delta}$ irreducible? | For a general polarized K3 surface and the corresponding Severi variety V_{p,n,\delta} of nodal curves, is V_{p,n,\delta} irreducible? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,976 | OWR-13946-007 | Irreducibility of Nodal-Curve Spaces on K3 Surfaces | Let $(X,L)$ be a general primitively polarized K3 surface of genus $p$, and let $0<\delta<n^2(p-1)+1$. Is the Severi variety $V_{n,\delta}(X)$ of irreducible $\delta$-nodal curves in $|nL|$ irreducible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-007",
"literature-status:partially-solved",
"owr-year:2015"
] | For general K3 surfaces, fixed-surface Severi varieties are irreducible in substantial primitive and low-node ranges, but irreducibility for arbitrary n and \delta is not known. | [
{
"url": "https://arxiv.org/abs/1809.03914",
"label": "Ciliberto--Dedieu, Primitive Irreducibility"
},
{
"url": "https://arxiv.org/abs/2112.09398",
"label": "Bruno--Lelli-Chiesa, General K3 Surfaces"
},
{
"url": "https://www.math.univ-toulouse.fr/~tdedieu/severi.pdf",
"label": "Sever... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Let $(X,L)$ be a general primitively polarized K3 surface of genus $p$, and let $0<\delta<n^2(p-1)+1$. Is the Severi variety $V_{n,\delta}(X)$ of irreducible $\delta$-nodal curves in $|nL|$ irreducible? | For a general primitively polarized K3 surface (X,L) and admissible n,\delta, is the Severi variety V_{n,\delta}(X) of irreducible \delta-nodal curves in |nL| irreducible? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,977 | OWR-13946-008 | Generic Finiteness of K3 Severi Moduli Maps | For a general polarized K3 surface $(X,L)$ and an irreducible component $V\subset V_{n,\delta}(X)$, is the moduli map $\psi_{X,n,\delta}|_V$ generically finite, or birational when $g>1$, onto its image in $M_g$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-008",
"literature-status:partially-solved",
"owr-year:2015"
] | Generically finite and birational moduli maps are proved in many ranges, but the question for all components and all p,n,\delta remains open. | [
{
"url": "https://doi.org/10.1016/j.aim.2017.01.021",
"label": "Ciliberto--Flamini--Galati--Knutsen, Moduli of Nodal Curves"
},
{
"url": "https://arxiv.org/abs/1401.1047",
"label": "The Moduli of Singular Curves on K3 Surfaces"
},
{
"url": "https://doi.org/10.1016/j.jms.2021.104832",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For a general polarized K3 surface $(X,L)$ and an irreducible component $V\subset V_{n,\delta}(X)$, is the moduli map $\psi_{X,n,\delta}|_V$ generically finite, or birational when $g>1$, onto its image in $M_g$? | For a general polarized K3 surface (X,L) and an irreducible component V\subset V_{n,\delta}(X), is the moduli map \psi_{X,n,\delta}|_V generically finite, or birational when g>1, onto its image in M_g? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,978 | OWR-13946-009 | Divisorial Images of Universal K3 Moduli Maps | Can the image of the universal K3 moduli map $\psi_{p,n,\delta}$ be a divisor when $g\leq11$? Can some images $\operatorname{Im}(\psi_{p,n,\delta})$ be described by higher-rank Brill–Noether theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-009",
"literature-status:partially-solved",
"owr-year:2015"
] | The genus-ten K3 image has a higher-rank Brill--Noether realization, and related loci have been studied, but a general divisorial-image criterion for g\le11 and systematic descriptions of all images are open. | [
{
"url": "https://arxiv.org/1102.0276",
"label": "Farkas--Ortega, Higher-Rank Brill--Noether Theory"
},
{
"url": "https://arxiv.org/1502.07378",
"label": "Moduli of Nodal Curves on K3 Surfaces"
},
{
"url": "https://arxiv.org/2411.14562",
"label": "Knutsen--Torelli, Brill--Noether Loc... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Can the image of the universal K3 moduli map $\psi_{p,n,\delta}$ be a divisor when $g\leq11$? Can some images $\operatorname{Im}(\psi_{p,n,\delta})$ be described by higher-rank Brill–Noether theory? | Can the image of the universal K3 moduli map \psi_{p,n,\delta} be a divisor for g\le 11, and can some such images be described using higher-rank Brill--Noether theory? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,979 | OWR-13946-010 | Kodaira Dimension of K3 Severi Images | For a maximal-rank component of a K3 Severi moduli map, what is the Kodaira dimension of its image in $M_g$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | open | null | 2,015 | 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-13946-010",
"literature-status:open",
"owr-year:2015"
] | Known results determine dimensions and birational behavior of some K3 images, but no general computation of the Kodaira dimension of the images in the question has been established. | [
{
"url": "https://doi.org/10.1016/j.aim.2017.01.021",
"label": "Moduli of Nodal Curves on K3 Surfaces"
},
{
"url": "https://arxiv.org/1701.07224",
"label": "Degeneration of Differentials and Moduli"
},
{
"url": "https://ems.press/content/serial-article-files/46597",
"label": "Origina... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For a maximal-rank component of a K3 Severi moduli map, what is the Kodaira dimension of its image in $M_g$? | For a maximal-rank component of a K3 Severi moduli map, what is the Kodaira dimension of its image in M_g? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,980 | OWR-13946-011 | Brill–Noether Intersections of K3 Moduli Images | What can be said about $\operatorname{Im}(\psi_{X,n,\delta})\cap M^r_{g,d}$ and $\operatorname{Im}(\psi_{p,n,\delta})\cap M^r_{g,d}$, and what consequences does the first intersection have for the Mori theory of $X^{[d]}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-011",
"literature-status:partially-solved",
"owr-year:2015"
] | Brill--Noether loci in Severi varieties and their relation to rational curves in Hilbert schemes are substantially developed, but the requested intersections and resulting Mori-theoretic consequences are not classified in general. | [
{
"url": "https://doi.org/10.1016/j.jsc.2013.11.007",
"label": "Ciliberto--Knutsen, k-Gonal Loci on K3 Surfaces"
},
{
"url": "https://arxiv.org/2411.14562",
"label": "Knutsen--Torelli, Prescribed-Ramification Brill--Noether Loci"
},
{
"url": "https://citeseerx.ist.psu.edu/document?doi=20... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | What can be said about $\operatorname{Im}(\psi_{X,n,\delta})\cap M^r_{g,d}$ and $\operatorname{Im}(\psi_{p,n,\delta})\cap M^r_{g,d}$, and what consequences does the first intersection have for the Mori theory of $X^{[d]}$? | What can be said about \operatorname{Im}(\psi_{X,n,\delta})\cap M^r_{g,d} and \operatorname{Im}(\psi_{p,n,\delta})\cap M^r_{g,d}, and what consequences does the first intersection have for the Mori theory of X^{[d]}? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,981 | OWR-13946-012 | Coranks of Modified Wahl Maps for Nodal Curves | For a general nodal curve $C$ in a component of $\mathcal V_{p,n,\delta}$, what are the coranks of the Kemeny–Wahl map $kw_C$ and the Halic–Wahl map $hw_C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-012",
"literature-status:partially-solved",
"owr-year:2015"
] | Modified Wahl maps are known to be non-surjective in important nodal K3 cases and one-nodal surjectivity is known in high genus, but the coranks for a general component of V_{p,n,\delta} are not determined generally. | [
{
"url": "https://doi.org/10.1007/s00209-010-0830-2",
"label": "Halic, Modular Properties of Nodal Curves"
},
{
"url": "https://arxiv.org/abs/1701.04801",
"label": "Sernesi, Wahl Map of One-Nodal Curves"
},
{
"url": "https://doi.org/10.1016/j.jsc.2015.05.001",
"label": "The Moduli of... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For a general nodal curve $C$ in a component of $\mathcal V_{p,n,\delta}$, what are the coranks of the Kemeny–Wahl map $kw_C$ and the Halic–Wahl map $hw_C$? | For a general nodal curve C in a component of V_{p,n,\delta}, what are the coranks of the Kemeny--Wahl map kw_C and Halic--Wahl map hw_C, and can Wahl's conjecture be extended to nodal curves using these maps? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,982 | OWR-13946-013 | Wahl's Conjecture for Nodal Curves | Can Wahl's conjecture for smooth curves and the Arbarello–Bruno–Sernesi theorem be extended to nodal curves using the Kemeny–Wahl map $kw_C$, the Halic–Wahl map $hw_C$, or both? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-013",
"literature-status:partially-solved",
"owr-year:2015"
] | The nodal setting admits natural modified Wahl maps and several non-surjectivity and obstruction results, but a full Wahl-conjecture analogue and its Arbarello--Bruno--Sernesi theorem remain open. | [
{
"url": "https://doi.org/10.1007/s00209-010-0830-2",
"label": "Halic, Modular Properties of Nodal Curves"
},
{
"url": "https://arxiv.org/abs/1312.3492",
"label": "Halic, Surjectivity of the Wahl Map"
},
{
"url": "https://doi.org/10.1016/j.jsc.2015.05.001",
"label": "The Moduli of Si... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Can Wahl's conjecture for smooth curves and the Arbarello–Bruno–Sernesi theorem be extended to nodal curves using the Kemeny–Wahl map $kw_C$, the Halic–Wahl map $hw_C$, or both? | Can Wahl's conjecture and the Arbarello--Bruno--Sernesi theorem be extended to nodal curves using the Kemeny--Wahl map kw_C or Halic--Wahl map hw_C? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,983 | OWR-13946-014 | Density of Nodal Curves in Equigeneric Families | Let $V_g^\xi$ parametrize reduced curves of genus $g$ in class $\xi$ on a smooth projective surface. Is the locus of curves having only ordinary nodes dense in $V_g^\xi$? Can this be proved using the criterion that the equisingular ideal $I$ is properly contained in $A$ exactly for singularities worse than nodes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-014",
"literature-status:partially-solved",
"owr-year:2015"
] | Equigeneric deformations to nodal curves are proved in broad classes and some K3 cases, while counterexamples and remaining K3 cases show that density is not settled in general. | [
{
"url": "https://doi.org/10.5565/PUBLMAT_61117_07",
"label": "Dedieu--Sernesi, Equigeneric and Equisingular Families"
},
{
"url": "https://ems.press/content/serial-article-files/46597",
"label": "Dedieu--Sernesi, Density Problem"
},
{
"url": "https://doi.org/10.1090/S0002-9947-1974-0419... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Let $V_g^\xi$ parametrize reduced curves of genus $g$ in class $\xi$ on a smooth projective surface. Is the locus of curves having only ordinary nodes dense in $V_g^\xi$? Can this be proved using the criterion that the equisingular ideal $I$ is properly contained in $A$ exactly for singularities worse than nodes? | Let V^\xi_g parametrize reduced curves of genus g in class \xi on a smooth projective surface. Is the locus of curves having only ordinary nodes dense in V^\xi_g, using that the equisingular ideal I\subset A exactly when singularities are worse than nodes? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,984 | OWR-13946-015 | Degenerations and Compactifications of Hyperkähler Manifolds | For hyperkähler manifolds of dimension greater than two, how can their degenerations be classified, what examples are known, what is known about their versal deformation spaces, and when do their moduli spaces admit partial compactifications? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | partially_solved | null | 2,015 | 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-13946-015",
"literature-status:partially-solved",
"owr-year:2015"
] | Kulikov-type models, monodromy constraints, and smoothing results give substantial control over hyperkähler degenerations, but classification of higher-dimensional degenerations, all examples, and versal spaces is far from complete. | [
{
"url": "https://doi.org/10.5802/aif.3228",
"label": "Kollar--Laza--Sacca--Voisin, Degenerations of Hyper-Kahler Manifolds"
},
{
"url": "https://arxiv.org/abs/2108.01587",
"label": "Huybrechts--Mauri, Type II Degenerations"
},
{
"url": "https://arxiv.org/abs/2604.14890",
"label": "D... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For hyperkähler manifolds of dimension greater than two, how can their degenerations be classified, what examples are known, what is known about their versal deformation spaces, and when do their moduli spaces admit partial compactifications? | For hyperkähler manifolds of dimension greater than two, how can their degenerations be classified, what examples are known, what is known about their versal deformation spaces, and when do their moduli spaces admit partial compactifications? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,985 | OWR-13946-016 | Closedness of the K3 Locus and Fake K3 Surfaces | For $g\geq12$, is the locus $(K3)_g\subset M_g$ of curves lying on K3 surfaces closed? Can Lazarsfeld's proof of the Gieseker–Petri theorem be generalized to curves on fake K3 surfaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | open | null | 2,015 | 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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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13946-016",
"literature-status:open",
"owr-year:2015"
] | The K3 locus has been studied through period maps, Wahl maps, and Brill--Noether theory, and Lazarsfeld's theorem has broad extensions, but closedness of the smooth K3 locus and the proposed fake-K3 generalization are not settled in the stated generality. | [
{
"url": "https://doi.org/10.4310/JDG/1214440116",
"label": "Lazarsfeld, Brill--Noether--Petri Without Degenerations"
},
{
"url": "https://arxiv.org/1507.05002",
"label": "On Hyperplane Sections of K3 Surfaces"
},
{
"url": "https://arxiv.org/2306.11664",
"label": "Haburcak, Curves on... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | For $g\geq12$, is the locus $(K3)_g\subset M_g$ of curves lying on K3 surfaces closed? Can Lazarsfeld's proof of the Gieseker–Petri theorem be generalized to curves on fake K3 surfaces? | For g\ge 12, is the locus (K3)_g\subset M_g of curves lying on a K3 surface closed, and can Lazarsfeld's proof of the Gieseker--Petri theorem be generalized to curves on a fake K3 surface? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,986 | OWR-13946-018 | Compactifiable Lagrangian Fibrations from Abelian Fibrations | Given an abelian fibration, when does its total space admit a symplectic structure making it a Lagrangian fibration compactifiable to a possibly singular irreducible symplectic variety? Separately, let a family of curves over a polydisk in $\mathbb C^k$ be a multiversal unfolding of the singularities of its central fib... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967](https://doi.org/10.4171/owr/2015/51)
## Li... | 3 | open | null | 2,015 | 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-13946-018",
"literature-status:open",
"owr-year:2015"
] | The exact toroidality question in the stated simple-singularity range remains unresolved; the literature gives important special cases and related compactifications but no general proof for the extracted hypotheses. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/205e22d5-f548-4915-b721-7e608401c35b/content",
"label": "Oberwolfach report question"
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{
"url": "https://doi.org/10.1070/IM1995v059n01ABEH000007",
"label": "Markushevich on Lagrangian fibrations"
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{
"url": "https://arxiv.o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/51 | null | null | null | Given an abelian fibration, when does its total space admit a symplectic structure making it a Lagrangian fibration compactifiable to a possibly singular irreducible symplectic variety? Separately, let a family of curves over a polydisk in $\mathbb C^k$ be a multiversal unfolding of the singularities of its central fib... | Given an abelian fibration, when can its total space be endowed with a symplectic structure making it a Lagrangian fibration compactifiable to a possibly singular irreducible symplectic variety, and is the specified relative compactified Jacobian toroidal for a multiversal family with only the stated A_\mu and D_\mu si... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mini-Workshop: Singular Curves on \$K3\$ Surfaces and Hyperkähler Manifolds (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/51, pp. 2939--2967 |
30,002,987 | OWR-13947-001 | Faithful Simulation of Rare Genetic Variants | How should rare-variant data be generated or simulated so that small-sample allele-frequency data faithfully represent rare variants, singletons, and doubletons for association-method comparisons? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Recent Developments in Statistical Methods with Applications to Genetics and Genomics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/52, pp. 2969--3005](https://doi.org/10... | 3 | open | null | 2,015 | 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"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13947-001",
"literature-status:open",
"owr-year:2015"
] | The extracted text is a methodological note rather than a standalone theorem; newer demographic models exist, but no definitive resolution of the underlying problem is identified. | [
{
"url": "https://doi.org/10.4171/owr/2015/52",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1309.6551",
"label": "Gazave et al. demographic model"
},
{
"url": "https://pubmed.ncbi.nlm.nih.gov/37974506/",
"label": "Recent rare-variant review"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/52 | null | null | null | How should rare-variant data be generated or simulated so that small-sample allele-frequency data faithfully represent rare variants, singletons, and doubletons for association-method comparisons? | How should rare-variant data be generated or simulated so that small-sample allele-frequency data faithfully represent rare variants, singletons, and doubletons for association-method comparisons? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Recent Developments in Statistical Methods with Applications to Genetics and Genomics (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/52, pp. 2969--3005 |
30,002,988 | OWR-13948-001 | Intermediate Regularity Regime for Monge–Ampère Solutions | What is the qualitative behavior of weak and very weak solutions of the Monge–Ampère equation $\operatorname{Det}\nabla^2v=-\tfrac12\operatorname{curl}\operatorname{curl}(\nabla v\otimes\nabla v)=f$ in the regularity regime $1/3<\alpha<2/3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 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"
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"level": 3,
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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-13948-001",
"literature-status:partially-solved",
"owr-year:2015"
] | Rigidity and convexity are understood above the two-thirds threshold and flexible constructions occur below the one-third threshold, while the qualitative behavior in the intermediate range one-third less than alpha less than two-thirds remains unresolved. | [
{
"url": "https://link.springer.com/article/10.1007/s00526-025-03019-0",
"label": "Recent very weak Monge--Ampere results"
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{
"url": "https://arxiv.org/abs/2310.06693",
"label": "Intermediate-regularity analysis"
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{
"url": "https://sites.pitt.edu/~lewicka/preprints/Flexible-Monge9.pd... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | What is the qualitative behavior of weak and very weak solutions of the Monge–Ampère equation $\operatorname{Det}\nabla^2v=-\tfrac12\operatorname{curl}\operatorname{curl}(\nabla v\otimes\nabla v)=f$ in the regularity regime $1/3<\alpha<2/3$? | What is the qualitative behavior of weak and very weak solutions of the Monge--Ampere equation \operatorname{Det}\nabla^2v=-\tfrac12\operatorname{curl}\operatorname{curl}(\nabla v\otimes\nabla v)=f in the regularity regime 1/3<\alpha<2/3? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,989 | OWR-13948-002 | Numerical Simulation of Dislocation Polygonization | Can numerical methods correctly simulate polygonization in bent single-crystal beams, where dislocations align into polygonization patterns? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 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-13948-002",
"literature-status:partially-solved",
"owr-year:2015"
] | Polygonization has established continuum energetics and discrete-dislocation numerical models for bent single crystals, but a general predictive simulation of the aligned-dislocation dynamics and kinetics is not complete. | [
{
"url": "https://doi.org/10.1016/j.ijplas.2013.02.010",
"label": "Polygonization in bent crystals"
},
{
"url": "https://doi.org/10.1016/j.ijengsci.2012.03.005",
"label": "Polygonization theory"
},
{
"url": "https://doi.org/10.1080/01418619708205157",
"label": "Numerical polygonizati... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | Can numerical methods correctly simulate polygonization in bent single-crystal beams, where dislocations align into polygonization patterns? | Can numerical methods correctly simulate polygonization in bent single-crystal beams, where dislocations align into polygonization patterns? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,990 | OWR-13948-003 | Duplicate Quasiconvexity Extraction | If f:B\times\operatorname{Hom}(\mathbb R^m,TM)\to[0,+\infty) is quasiconvex, is the associated Q-integrand e_M(x,\nu_i,N_i)=\sum_{i=1}^Q f(x,\nu_i,N_i) quasiconvex on multiple-valued functions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The passage duplicates the multiple-valued quasiconvexity question recorded in OWR-13948-004. No separate clean statement is promoted; the o) | [
"OWR-13948-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13948-003",
"literature-status:partially-solved",
"owr-year:2015"
] | Positive results are known for polyconvex integrands and for some low-dimensional quadratic cases, but general quasiconvexity for multiple-valued functions remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46600",
"label": "Oberwolfach Q-valued report"
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{
"url": "https://arxiv.org/abs/2603.20788",
"label": "Uniform polyconvexity and Q-graphs"
},
{
"url": "https://arxiv.org/abs/0803.0060",
"label": "Q-valued variational regulari... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | null | If f:B\times\operatorname{Hom}(\mathbb R^m,TM)\to[0,+\infty) is quasiconvex, is the associated Q-integrand e_M(x,\nu_i,N_i)=\sum_{i=1}^Q f(x,\nu_i,N_i) quasiconvex on multiple-valued functions? | unrecoverable | The passage duplicates the multiple-valued quasiconvexity question recorded in OWR-13948-004. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,991 | OWR-13948-004 | Quasiconvexity of Multiple-Valued Integrands | Let $f:B\times\operatorname{Hom}(\mathbb{R}^m,TM)\to\mathbb{R}_{\geq0}$ be quasiconvex and define $e_M(x,\nu_1,\ldots,\nu_Q,N_1,\ldots,N_Q)=\sum_{i=1}^Qf(x,\nu_i,N_i)$. Is $e_M$ quasiconvex on the space of $Q$-valued maps into $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 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... | [
"OWR-13948-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13948-004",
"literature-status:open",
"owr-year:2015"
] | The extracted sentence is a fragment of the general Q-valued quasiconvexity question; special structured cases are known, but no general resolution or counterexample for the stated problem was found. | [
{
"url": "https://ems.press/content/serial-article-files/46600",
"label": "Oberwolfach Q-valued report"
},
{
"url": "https://arxiv.org/abs/2603.20788",
"label": "Uniform polyconvexity and Q-graphs"
},
{
"url": "https://arxiv.org/abs/0803.0060",
"label": "Q-valued variational regulari... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | Let $f:B\times\operatorname{Hom}(\mathbb{R}^m,TM)\to\mathbb{R}_{\geq0}$ be quasiconvex and define $e_M(x,\nu_1,\ldots,\nu_Q,N_1,\ldots,N_Q)=\sum_{i=1}^Qf(x,\nu_i,N_i)$. Is $e_M$ quasiconvex on the space of $Q$-valued maps into $M$? | If f:B\times\operatorname{Hom}(\mathbb R^m,TM)\to[0,+\infty) is quasiconvex, is e_M(x,\nu_1,\ldots,\nu_Q,N_1,\ldots,N_Q)=\sum_{i=1}^Q f(x,\nu_i,N_i) quasiconvex in the space of multiple-valued functions? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,992 | OWR-13948-005 | Partial Regularity of Multivalued Quasiconvex Minimizers | Do minimizers of quasiconvex functionals on Q-valued functions have partial regularity, and for which subclasses of functionals do regularity results hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | partially_solved | null | 2,015 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13948-005",
"literature-status:partially-solved",
"owr-year:2015"
] | The general partial-regularity problem for minimizers of Q-valued quasiconvex functionals remains open, while Dirichlet minimizers and several structured elliptic or polyconvex subclasses have substantial regularity theory. | [
{
"url": "https://ems.press/content/serial-article-files/46600",
"label": "Oberwolfach Q-valued report"
},
{
"url": "https://arxiv.org/abs/0803.0060",
"label": "Dirichlet Q-valued regularity"
},
{
"url": "https://arxiv.org/abs/2603.20788",
"label": "Q-graph ellipticity framework"
}... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | Do minimizers of quasiconvex functionals on Q-valued functions have partial regularity, and for which subclasses of functionals do regularity results hold? | Do minimizers of quasiconvex functionals on Q-valued functions have partial regularity, and for which subclasses of functionals do regularity results hold? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,993 | OWR-13948-006 | Collapse of Multivalued Minimizers with Single-Valued Boundary Data | If u minimizes a quasiconvex functional and $u|_{\partial B}=Q\llbracket\phi\rrbracket$, must $u=Q\llbracket\Phi\rrbracket$ for some single-valued minimizer $\Phi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048](https://doi.org/10.4171/owr/2015/53)
## Literature review (checked 2026-08-21)
**... | 3 | open | null | 2,015 | 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",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13948-006",
"literature-status:open",
"owr-year:2015"
] | The general branching implication for minimizers with collapsed multiple-of-one-valued boundary data remains unresolved; existing Dirichlet theory does not establish the claimed conclusion for the full variational setting. | [
{
"url": "https://ems.press/content/serial-article-files/46600",
"label": "Oberwolfach Q-valued report"
},
{
"url": "https://arxiv.org/abs/0803.0060",
"label": "Q-valued Dirichlet theory"
},
{
"url": "https://arxiv.org/abs/2603.20788",
"label": "Current Q-graph framework"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/53 | null | null | null | If u minimizes a quasiconvex functional and $u|_{\partial B}=Q\llbracket\phi\rrbracket$, must $u=Q\llbracket\Phi\rrbracket$ for some single-valued minimizer $\Phi$? | If u minimizes a quasiconvex functional and u|_{\partial B}=Q\llbracket\phi\rrbracket, must u=Q\llbracket\Phi\rrbracket for some single-valued minimizer \Phi? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Mini-Workshop: Scales in Plasticity (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/53, pp. 3007--3048 |
30,002,994 | OWR-13949-001 | Consequences of Indistinguishability Obfuscation | The indistinguishability obfuscation conjecture asserts the feasibility of obfuscating functionally equivalent programs so their obfuscations cannot be distinguished; what are its precise consequences and relations to one-way functions and $P\neq NP$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13949-001",
"literature-status:open",
"owr-year:2015"
] | The extracted text is a contextual fragment about the relationship between the IO and OWF conjectures, not a complete standalone claim; its resolution cannot be established from the fragment and no definitive resolution was identified. | [
{
"url": "https://www.wisdom.weizmann.ac.il/~oded/PDF/owr-cc15.pdf",
"label": "Oberwolfach complexity report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | The indistinguishability obfuscation conjecture asserts the feasibility of obfuscating functionally equivalent programs so their obfuscations cannot be distinguished; what are its precise consequences and relations to one-way functions and $P\neq NP$? | The indistinguishability obfuscation conjecture asserts the feasibility of obfuscating functionally equivalent programs so their obfuscations cannot be distinguished; what are its precise consequences and relations to one-way functions and P\ne NP? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,002,995 | OWR-13949-002 | Karchmer–Raz–Wigderson Formula Lower-Bound Conjecture | Can the Karchmer–Raz–Wigderson conjecture be proved in full generality, thereby implying superpolynomial formula-size lower bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,015 | 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-13949-002",
"literature-status:partially-solved",
"owr-year:2015"
] | The specific open question attributed to Håstad was answered by the average-case depth-hierarchy result, but the broader Karchmer--Raz--Wigderson conjecture and the associated general formula lower bounds remain open. | [
{
"url": "https://www.cs.columbia.edu/~rocco/papers/focs15.html",
"label": "Rossman--Servedio--Tan"
},
{
"url": "https://doi.org/10.1137/15M1018319",
"label": "Subsequent KRW analysis"
},
{
"url": "https://doi.org/10.1007/BF01206317",
"label": "Karchmer--Raz--Wigderson"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | Can the Karchmer–Raz–Wigderson conjecture be proved in full generality, thereby implying superpolynomial formula-size lower bounds? | Can the Karchmer--Raz--Wigderson conjecture be proved in full generality, thereby implying super-polynomial formula lower bounds? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,002,996 | OWR-13949-003 | Accurate Answers to Adaptively Chosen Statistical Queries | Given a population distribution P on X and an i.i.d. sample S of size n, can a possibly randomized procedure M(S) answer every adaptively chosen sequence of statistical queries accurately with high probability over S and M's randomness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13949-003",
"literature-status:partially-solved",
"owr-year:2015"
] | Differential privacy, reusable holdouts, and stability provide accurate answers for broad but bounded adaptive query families, while the unrestricted interactive statistical-query problem remains subject to tradeoffs and lower bounds. | [
{
"url": "https://doi.org/10.1126/science.aaa9375",
"label": "Reusable holdout"
},
{
"url": "https://arxiv.org/abs/1506.02629",
"label": "Adaptive data analysis"
},
{
"url": "https://arxiv.org/abs/1408.1655",
"label": "Computational lower bound"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | Given a population distribution P on X and an i.i.d. sample S of size n, can a possibly randomized procedure M(S) answer every adaptively chosen sequence of statistical queries accurately with high probability over S and M's randomness? | Given a population distribution P on X and an i.i.d. sample S of size n, can a possibly randomized procedure M(S) answer every adaptively chosen sequence of statistical queries accurately with high probability over S and M's randomness? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,002,997 | OWR-13949-004 | Limits of False Discovery Control in Interactive Analysis | Can the computational and query-complexity limitations on procedures that prevent false discovery in interactive data analysis be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,015 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13949-004",
"literature-status:partially-solved",
"owr-year:2015"
] | Several limitations in interactive data analysis can be mitigated by privacy and holdout mechanisms, but the full set of accuracy, adaptivity, sample, and computational limitations cannot be removed simultaneously. | [
{
"url": "https://doi.org/10.1126/science.aaa9375",
"label": "Reusable holdout"
},
{
"url": "https://arxiv.org/abs/1506.02629",
"label": "Adaptive data analysis"
},
{
"url": "https://arxiv.org/abs/1408.1655",
"label": "Computational lower bound"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | Can the computational and query-complexity limitations on procedures that prevent false discovery in interactive data analysis be removed? | Can the computational and query-complexity limitations on procedures that prevent false discovery in interactive data analysis be removed? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,002,998 | OWR-13949-005 | Refutation Lower Bounds for Random k-SAT Instances | Does a random $k$-SAT instance with, for example, $m=n^{0.4k}$ clauses lack a polynomial-size refutation with high probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,015 | 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-13949-005",
"literature-status:open",
"owr-year:2015"
] | The stated random kSAT refutation lower bound remains a conjectural barrier: known sum-of-squares and related lower bounds do not establish the full polynomial-size refutation claim in the extracted regime. | [
{
"url": "https://ems.press/content/serial-article-files/46601",
"label": "Oberwolfach complexity report"
},
{
"url": "https://arxiv.org/abs/1701.04521",
"label": "Sum-of-squares lower bounds"
},
{
"url": "https://www.cs.cmu.edu/~srallen/papers/csp-refutation.pdf",
"label": "Random C... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | Does a random $k$-SAT instance with, for example, $m=n^{0.4k}$ clauses lack a polynomial-size refutation with high probability? | Does a random kSAT instance with m=n^{0.4k} clauses, say, lack a polynomial-size refutation with high probability? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,002,999 | OWR-13949-006 | Randomized Communication Complexity of Distributed Triangle Detection | What is the randomized communication complexity of detecting a triangle when each graph vertex is assigned to a player who receives all incident edges, so each edge is known to its two endpoint players? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,015 | 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-13949-006",
"literature-status:partially-solved",
"owr-year:2015"
] | Recent work proves nontrivial randomized and deterministic lower bounds for distributed triangle detection, but the exact randomized communication complexity in the stated edge-partition model is not fully characterized. | [
{
"url": "https://arxiv.org/abs/2504.01802",
"label": "Distributed triangle detection lower bounds"
},
{
"url": "https://doi.org/10.1109/FOCS63196.2025.00040",
"label": "FOCS 2025 version"
},
{
"url": "https://arxiv.org/abs/1807.06624",
"label": "Distributed triangle detection algori... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | What is the randomized communication complexity of detecting a triangle when each graph vertex is assigned to a player who receives all incident edges, so each edge is known to its two endpoint players? | What is the randomized communication complexity of detecting a triangle when each graph vertex is assigned to a player who receives all incident edges, so each edge is known to its two endpoint players? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,003,000 | OWR-13949-007 | Depth-Three Lower Bounds for an Explicit Trilinear Function | Can one prove a lower bound larger than $\exp(\sqrt n)$ on the size of standard depth-three circuits computing the explicit trilinear function $F_{\mathrm{tet}}(x,y,z)=\sum_{i_1,i_2,i_3:\sum_{j=1}^3|i_j-n/2|\leq n/2}x_{i_1}y_{i_2}z_{i_3}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099](https://doi.org/10.4171/owr/2015/54)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,015 | 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-13949-007",
"literature-status:partially-solved",
"owr-year:2015"
] | The random Toeplitz rigidity problem has been resolved in a substantial parameter range and explicit depth-three lower bounds are known, but the extracted natural problem of obtaining better than exponential lower bounds for the standard depth-three target remains open. | [
{
"url": "https://www.wisdom.weizmann.ac.il/~oded/p_rigid.html",
"label": "Goldreich--Tal rigidity results"
},
{
"url": "https://www.wisdom.weizmann.ac.il/~oded/R2/rigid.pdf",
"label": "Rigidity paper"
},
{
"url": "https://ems.press/content/serial-article-files/46601",
"label": "Ober... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/54 | null | null | null | Can one prove a lower bound larger than $\exp(\sqrt n)$ on the size of standard depth-three circuits computing the explicit trilinear function $F_{\mathrm{tet}}(x,y,z)=\sum_{i_1,i_2,i_3:\sum_{j=1}^3|i_j-n/2|\leq n/2}x_{i_1}y_{i_2}z_{i_3}$? | Can one prove a lower bound larger than \exp(\sqrt n) on the size of standard depth-three circuits computing the explicit trilinear function F_{tet}(x,y,z)=\sum_{i_1,i_2,i_3:\sum_{j=1}^3|i_j-n/2|\le n/2}x_{i_1}y_{i_2}z_{i_3}? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Complexity Theory (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/54, pp. 3049--3099 |
30,003,001 | OWR-13950-001 | Formation of Singular Cytoskeleton Profiles from Smooth Data | For the spatially one-dimensional hyperbolic-parabolic cytoskeleton model, can the explicitly constructed Dirac peaks, moving profiles, and shocks arise dynamically from a suitable class of smooth initial data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Partial Differential Equations: Surface and Bulk Processes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/55, pp. 3101--3178](https://doi.org/10.4171/owr/2015/55)
## Literatur... | 3 | open | null | 2,015 | 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"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13950-001",
"literature-status:open",
"owr-year:2015"
] | The report explicitly poses whether the displayed shocks, peaks, or profiles can arise dynamically from suitable smooth initial data; no definitive general answer was identified in the current literature. | [
{
"url": "https://doi.org/10.4171/owr/2015/55",
"label": "Geometric PDE Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/55 | null | null | null | For the spatially one-dimensional hyperbolic-parabolic cytoskeleton model, can the explicitly constructed Dirac peaks, moving profiles, and shocks arise dynamically from a suitable class of smooth initial data? | For the spatially one-dimensional hyperbolic-parabolic cytoskeleton model, can the explicitly constructed Dirac peaks, moving profiles, and shocks arise dynamically from a suitable class of smooth initial data? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Geometric Partial Differential Equations: Surface and Bulk Processes (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/55, pp. 3101--3178 |
30,003,002 | OWR-13951-003 | Strong Reverse Minkowski Conjecture | For a symmetric convex body $K$ and an $n$-dimensional lattice $L$ in $\mathbb{R}^n$, is $|K\cap L|\leq M(O(\log n)K,L)$? For the Euclidean unit ball $B_2^n$, is $|B_2^n\cap L|\leq M(O(\sqrt{\log n})B_2^n,L)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,015 | 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-13951-003",
"literature-status:partially-solved",
"owr-year:2015"
] | The strong reverse Minkowski conjecture remains open in its full form, but reverse Minkowski theorems and lattice substructure results establish substantial weaker and special-case bounds. | [
{
"url": "https://arxiv.org/abs/1606.06913",
"label": "Strong reverse Minkowski program"
},
{
"url": "https://annals.math.princeton.edu/2024/199-1/p01",
"label": "Recent reverse Minkowski theorem"
},
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Original Oberwolfach conje... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | For a symmetric convex body $K$ and an $n$-dimensional lattice $L$ in $\mathbb{R}^n$, is $|K\cap L|\leq M(O(\log n)K,L)$? For the Euclidean unit ball $B_2^n$, is $|B_2^n\cap L|\leq M(O(\sqrt{\log n})B_2^n,L)$? | Conjecture Strong Reverse Minkowski: for every symmetric convex body K and n-dimensional lattice L in R^n, |K\cap L|\leq M(O(\log n)K,L) and |B_2^n\cap L|\leq M(O(\sqrt{\log n})B_2^n,L). | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,003 | OWR-13951-005 | Invariant Valuations for Noncompact Groups | For a noncompact transformation group $G$, such as $O(p,q)$, acting on convex bodies, what generalized valuation framework and kinematic formulas replace the compact-group theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,015 | 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-13951-005",
"literature-status:partially-solved",
"owr-year:2015"
] | The broad non-compact-group question has a substantial answer for indefinite orthogonal groups: continuous and generalized invariant valuations have been classified, but the extracted question is broader than that completed class. | [
{
"url": "https://arxiv.org/abs/1602.08760",
"label": "Valuations for indefinite orthogonal groups"
},
{
"url": "https://arxiv.org/abs/1612.01625",
"label": "Invariant Crofton formulas"
},
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | For a noncompact transformation group $G$, such as $O(p,q)$, acting on convex bodies, what generalized valuation framework and kinematic formulas replace the compact-group theory? | For invariant valuation theory and kinematic formulas associated with a non-compact group G such as O(p,q), what generalized valuation framework and kinematic formulas replace the compact-group theory? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,004 | OWR-13951-006 | Associativity in Operations on Convex Bodies | What is the role of associativity in classifying operations between arbitrary compact convex sets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-006",
"literature-status:open",
"owr-year:2015"
] | The literature gives partial classifications of operations between compact convex sets, but the role of associativity in the full arbitrary-operation classification is still explicitly unresolved. | [
{
"url": "https://doi.org/10.4171/JEMS/422",
"label": "Operations between convex sets"
},
{
"url": "https://arxiv.org/abs/1205.4327",
"label": "Classification of convex-set operations"
},
{
"url": "https://intlpress.com/site/pub/files/_fulltext/journals/cag/2018/0026/0004/CAG-2018-0026-0... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | What is the role of associativity in classifying operations between arbitrary compact convex sets? | What is the role of associativity in classifying operations between arbitrary compact convex sets? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,005 | OWR-13951-007 | Nonpointwise, Nonassociative Operations on Convex Objects | Find classification results for operations on convex functions or convex sets that are neither necessarily pointwise nor associative. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-007",
"literature-status:open",
"owr-year:2015"
] | No general classification is known for operations that are neither pointwise nor associative; existing theorems impose one or both structural hypotheses, so the extracted problem remains open. | [
{
"url": "https://doi.org/10.4171/JEMS/422",
"label": "Operations between convex sets"
},
{
"url": "https://arxiv.org/abs/1205.4327",
"label": "Classification of convex-set operations"
},
{
"url": "https://intlpress.com/site/pub/files/_fulltext/journals/cag/2018/0026/0004/CAG-2018-0026-0... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | Find classification results for operations on convex functions or convex sets that are neither necessarily pointwise nor associative. | Find classification results for operations on convex functions or convex sets that are neither necessarily pointwise nor associative. | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,006 | OWR-13951-009 | Structural Properties of Geometric Means of Convex Bodies | Let A and B be convex bodies containing the origin, let $A^\circ$ be the polar body, D the Euclidean unit ball, and G and $G_p$ their geometric means. Determine whether $G(A,B)=D$ implies $B=A^\circ$; whether $A+B=A^\circ+B^\circ$ implies $B=A^\circ$; whether a convex body P representable as $G(A,B)$ for every A must b... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-009",
"literature-status:open",
"owr-year:2015"
] | The report lists several general questions about polar characterization, geometric means, elliptic envelopes, and p-means; later work gives special-case results, but no general theorem resolves all of the extracted clauses. | [
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | Let A and B be convex bodies containing the origin, let $A^\circ$ be the polar body, D the Euclidean unit ball, and G and $G_p$ their geometric means. Determine whether $G(A,B)=D$ implies $B=A^\circ$; whether $A+B=A^\circ+B^\circ$ implies $B=A^\circ$; whether a convex body P representable as $G(A,B)$ for every A must b... | Let A and B be convex bodies containing the origin, let A^\circ be the polar body, D the Euclidean unit ball, and G and G_p their geometric means. Determine whether G(A,B)=D implies B=A^\circ; whether A+B=A^\circ+B^\circ implies B=A^\circ; whether a convex body P representable as G(A,B) for every A must be an ellipsoid... | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,007 | OWR-13951-010 | Exponential Maps for Convex Body Geometric Means | Does there exist an exponential map $E:K_0^n\to K_0^n$ with $E(\{0\})=D$ and $E((A+B)/2)=G(E(A),E(B))$ for all convex bodies A and B? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-010",
"literature-status:open",
"owr-year:2015"
] | The proposed exponential map for the convex-body geometric mean remains an open structural question; no general construction satisfying the stated arithmetic-geometric identity was found. | [
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | Does there exist an exponential map $E:K_0^n\to K_0^n$ with $E(\{0\})=D$ and $E((A+B)/2)=G(E(A),E(B))$ for all convex bodies A and B? | Does there exist an exponential map E:K_0^n\to K_0^n with E(\{0\})=D and E((A+B)/2)=G(E(A),E(B)) for all convex bodies A and B? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,008 | OWR-13951-011 | Logarithmic Linearization of Convex-Body Means | Does there exist a logarithmic map $L$ on a natural class of convex bodies satisfying $L(G(A,B))=(L(A)+L(B))/2$ for the geometric mean $G$? Is $G(M_{\mathrm{ag}}(A,B),M_{\mathrm{gh}}(A,B))=G(A,B)$, where $M_{\mathrm{ag}}$ and $M_{\mathrm{gh}}$ are the arithmetic–geometric and geometric–harmonic iterations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-011",
"literature-status:open",
"owr-year:2015"
] | The logarithmic linearization and the arithmetic-geometric versus geometric-harmonic mean identity are posed as open problems, and no general proof or counterexample was located. | [
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | Does there exist a logarithmic map $L$ on a natural class of convex bodies satisfying $L(G(A,B))=(L(A)+L(B))/2$ for the geometric mean $G$? Is $G(M_{\mathrm{ag}}(A,B),M_{\mathrm{gh}}(A,B))=G(A,B)$, where $M_{\mathrm{ag}}$ and $M_{\mathrm{gh}}$ are the arithmetic–geometric and geometric–harmonic iterations? | Does there exist a logarithmic map L on a natural domain such that L(G(A,B))=(L(A)+L(B))/2, and is G(M_{ag}(A,B),M_{gh}(A,B))=G(A,B)? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,009 | OWR-13951-012 | Reconstruction of Convex Bodies from Congruent Projections | For $2\leq k\leq n-1$, if convex bodies $K,L\subseteq\mathbb{R}^n$ have congruent projections onto every $H\in G(n,k)$, with the congruences induced by elements of $O(k,H)$, must K be a translate of $\pm L$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,015 | 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-13951-012",
"literature-status:partially-solved",
"owr-year:2015"
] | The general congruent-projection reconstruction question remains unresolved, while affirmative results are known for symmetric bodies, polytopes, and several additional non-symmetric cases. | [
{
"url": "https://arxiv.org/abs/1412.2727",
"label": "Alfonseca, Cordier, and Ryabogin on directly congruent projections"
},
{
"url": "https://doi.org/10.1007/s11856-016-1394-6",
"label": "published reconstruction results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | For $2\leq k\leq n-1$, if convex bodies $K,L\subseteq\mathbb{R}^n$ have congruent projections onto every $H\in G(n,k)$, with the congruences induced by elements of $O(k,H)$, must K be a translate of $\pm L$? | For 2\leq k\leq n-1, if convex bodies K,L\subseteq R^n have congruent projections onto every H\in G(n,k), with the congruences induced by elements of O(k,H), must K be a translate of \pm L? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,010 | OWR-13951-013 | Reconstruction from Directly Congruent Convex Projections | For $2\leq k\leq n-1$, if convex bodies $K,L\subseteq\mathbb{R}^n$ have directly congruent projections onto every $H\in G(n,k)$, with the congruences induced by elements of $SO(k,H)$, must K be a translate of $\pm L$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,015 | 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-13951-013",
"literature-status:partially-solved",
"owr-year:2015"
] | The special-orthogonal version has affirmative results under restrictions such as two-dimensional projections without rotational symmetries, but the full direct-rigid-motion problem remains open. | [
{
"url": "https://arxiv.org/abs/1412.2727",
"label": "Alfonseca, Cordier, and Ryabogin"
},
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | For $2\leq k\leq n-1$, if convex bodies $K,L\subseteq\mathbb{R}^n$ have directly congruent projections onto every $H\in G(n,k)$, with the congruences induced by elements of $SO(k,H)$, must K be a translate of $\pm L$? | For 2\leq k\leq n-1, if convex bodies K,L\subseteq R^n have directly congruent projections onto every H\in G(n,k), with the congruences induced by elements of SO(k,H), must K be a translate of \pm L? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,011 | OWR-13951-014 | Duplicate Petty-Conjecture Extraction | Conjecture: for d\geq3, the affine invariant P(K)=|\Pi K|/|K|^{d-1} is minimal if and only if K is an ellipsoid. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,015 | 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 passage duplicates Petty’s projection-body conjecture recorded in OWR-13951-015. No separate clean statement is promoted; the original r) | [
"OWR-13951-015"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13951-014",
"literature-status:partially-solved",
"owr-year:2015"
] | The ellipsoid extremal characterization for the affine projection invariant is proved in restricted settings, including three-dimensional or specially structured bodies, but the stated all-dimensional equivalence remains conjectural. | [
{
"url": "https://arxiv.org/abs/1409.4347",
"label": "Saroglou and Zvavitch on projection-body invariants"
},
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | null | Conjecture: for d\geq3, the affine invariant P(K)=|\Pi K|/|K|^{d-1} is minimal if and only if K is an ellipsoid. | unrecoverable | The passage duplicates Petty’s projection-body conjecture recorded in OWR-13951-015. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,012 | OWR-13951-015 | Petty’s Projection-Body Conjecture | For every convex body $K\subset\mathbb{R}^d$ with $d\geq3$, is the affine invariant $P(K)=|\Pi K|/|K|^{d-1}$ minimized exactly by ellipsoids? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269](https://doi.org/10.4171/owr/2015/56)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,015 | 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-13951-014"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13951-015",
"literature-status:open",
"owr-year:2015"
] | Petty's conjecture remains unresolved in its general form; related projection-body inequalities and special cases do not settle the conjecture described in the record. | [
{
"url": "https://arxiv.org/abs/1409.4347",
"label": "related projection-body extremal results"
},
{
"url": "https://doi.org/10.4171/owr/2015/56",
"label": "Convex Geometry and its Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/56 | null | null | null | For every convex body $K\subset\mathbb{R}^d$ with $d\geq3$, is the affine invariant $P(K)=|\Pi K|/|K|^{d-1}$ minimized exactly by ellipsoids? | Petty's conjecture: for every convex body K\subseteq R^d with d\geq3, the affine invariant P(K)=|\Pi K|/|K|^{d-1} is minimized exactly by ellipsoids. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Convex Geometry and its Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/56, pp. 3179--3269 |
30,003,013 | OWR-13952-002 | Comparison of Algebraic and Analytic Modular Forms | For a holomorphic modular form viewed both as an algebraic global section of $\omega^{\otimes k}$ on a modular curve and as an analytic function on the upper half-plane, how can these two points of view be identified or related? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,015 | 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-13952-002",
"literature-status:open",
"owr-year:2015"
] | The extracted text is only a broad transition question about passing between two viewpoints and does not specify a mathematical assertion whose truth can be checked; under the triage rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2015/57",
"label": "Non-Archimedean Geometry and Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | For a holomorphic modular form viewed both as an algebraic global section of $\omega^{\otimes k}$ on a modular curve and as an analytic function on the upper half-plane, how can these two points of view be identified or related? | For a holomorphic modular form viewed both as an algebraic global section of \omega^{\otimes k} on a modular curve and as an analytic function on the upper half-plane, how can these two points of view be identified or related? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,014 | OWR-13952-005 | Grothendieck–Katz p-Curvature Conjecture | If $X$ is a smooth variety over $\mathbb C$ and an integrable connection $(E,\nabla)$ has trivial $p$-curvature at every closed point of a nonempty open of definition, must $(E,\nabla)$ have finite monodromy, equivalently be trivialized by a finite étale cover? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,015 | 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-13952-005",
"literature-status:open",
"owr-year:2015"
] | The extracted statement is only a conditional consequence of the Grothendieck-Katz p-curvature conjecture; the general conjecture remains unproved, although semistability and special geometric cases are known. | [
{
"url": "https://doi.org/10.4171/owr/2015/57",
"label": "Non-Archimedean Geometry and Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | If $X$ is a smooth variety over $\mathbb C$ and an integrable connection $(E,\nabla)$ has trivial $p$-curvature at every closed point of a nonempty open of definition, must $(E,\nabla)$ have finite monodromy, equivalently be trivialized by a finite étale cover? | If X is a smooth variety over C and an integrable connection (E,\nabla) has trivial p-curvature at every closed point of a nonempty open of definition, must (E,\nabla) have finite monodromy, equivalently be trivialized by a finite etale cover? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
30,003,015 | OWR-13952-006 | Harmonic Metrizations of Line Bundles | For any line bundle $M$ on $X$, does there exist a metrization $\overline{M}$, unique up to scale, whose curvature $c_1(\overline{M})$ is $\omega$-harmonic, meaning it is $\omega$-bounded and satisfies $c_1(\overline{M})\omega^{n-1}=\lambda(M)\omega^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331](https://doi.org/10.4171/owr/2015/57)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,015 | 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-13952-006",
"literature-status:partially-solved",
"owr-year:2015"
] | The canonical harmonic metrization conjecture is proved for curves, model metrics, certain residue-characteristic-zero dual-complex cases, and polarized dynamical systems, but not in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2015/57",
"label": "Non-Archimedean Geometry and Applications report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2015/57 | null | null | null | For any line bundle $M$ on $X$, does there exist a metrization $\overline{M}$, unique up to scale, whose curvature $c_1(\overline{M})$ is $\omega$-harmonic, meaning it is $\omega$-bounded and satisfies $c_1(\overline{M})\omega^{n-1}=\lambda(M)\omega^n$? | For any line bundle M on X, does there exist a metrization \overline{M}, unique up to scale, whose curvature c_1(\overline{M}) is \omega-harmonic, meaning it is \omega-bounded and satisfies c_1(\overline{M}) \omega^{n-1}=\lambda(M) \omega^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 | Non-Archimedean Geometry and Applications (2016), Oberwolfach Reports, DOI 10.4171/owr/2015/57, pp. 3271--3331 |
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