id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,916 | OWR-16411-009 | Reverse Burnett Problem for Einstein–Vlasov Limits | Given a solution $g_0$ of the Einstein equations coupled to a massless Vlasov field, can one construct vacuum Einstein metrics $g_\lambda$ converging to $g_0$ in a high-frequency weak limit with $g_\lambda\to g_0$ strongly in $L^2_{\mathrm{loc}}$ and $\partial g_\lambda$ bounded in $L^2_{\mathrm{loc}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,018 | 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-16411-009",
"literature-status:partially-solved",
"owr-year:2018"
] | The reverse Burnett problem has constructive results in restricted high-frequency regimes, but the 2024 review still identifies both Burnett directions as conjectural with open problems remaining. | [
{
"url": "https://arxiv.org/abs/2404.07659",
"label": "Huneau--Luk 2024"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Given a solution $g_0$ of the Einstein equations coupled to a massless Vlasov field, can one construct vacuum Einstein metrics $g_\lambda$ converging to $g_0$ in a high-frequency weak limit with $g_\lambda\to g_0$ strongly in $L^2_{\mathrm{loc}}$ and $\partial g_\lambda$ bounded in $L^2_{\mathrm{loc}}$? | Reverse Burnett problem: given a solution of the Einstein equations coupled to a massless Vlasov field, can one construct vacuum Einstein metrics g_{\lambda} converging to it in the prescribed weak high-frequency limit? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,917 | OWR-16411-010 | Mass–Angular-Momentum Inequalities with Trapped and Multiple Horizons | For axisymmetric initial data with ADM mass $m$ and total angular momentum $J_\infty$, prove $m\geq\sqrt{|J_\infty|}$ for manifolds with a trapped inner boundary. For multiple black holes satisfying $m\geq\mathcal M_{\mathrm{many}}$, determine the value and parameter dependence of $\mathcal M_{\mathrm{many}}$ and ident... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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-16411-010",
"literature-status:open",
"owr-year:2018"
] | The report explicitly lists extension to trapped inner boundaries and the multiple-black-hole extension as open problems; later inequalities cover special cases but not the stated general extensions. | [
{
"url": "https://doi.org/10.1007/s41114-018-0014-7",
"label": "Gabach Clement--Jaramillo review"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | For axisymmetric initial data with ADM mass $m$ and total angular momentum $J_\infty$, prove $m\geq\sqrt{|J_\infty|}$ for manifolds with a trapped inner boundary. For multiple black holes satisfying $m\geq\mathcal M_{\mathrm{many}}$, determine the value and parameter dependence of $\mathcal M_{\mathrm{many}}$ and ident... | Extend the inequality m\geq J_{\infty} to initial data with a trapped inner boundary, and understand its multiple-black-hole extension, including the value and dependence of the many-hole functional M_{\mathrm{many}} and the meaning of its minimizer. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,918 | OWR-16411-011 | Area–Angular-Momentum Inequalities with Nonpositive Cosmological Constant | Extend the area–angular-momentum inequality $A\geq8\pi|J_S|$ to cosmological constant $\Lambda\leq0$, determine the role of extremal anti–de Sitter geometries in the sharp estimate, and prove the equality rigidity statement for the area–charge inequality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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-16411-011",
"literature-status:open",
"owr-year:2018"
] | The negative-cosmological-constant extension and the equality rigidity statement are explicitly open in the report; known positive-cosmological-constant and special-symmetry results do not settle both claims. | [
{
"url": "https://doi.org/10.1007/s41114-018-0014-7",
"label": "Gabach Clement--Jaramillo review"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Extend the area–angular-momentum inequality $A\geq8\pi|J_S|$ to cosmological constant $\Lambda\leq0$, determine the role of extremal anti–de Sitter geometries in the sharp estimate, and prove the equality rigidity statement for the area–charge inequality. | Extend the area-angular-momentum inequality A\geq 8\pi J_S to cosmological constant \Lambda\leq 0, determine the role of extremal anti-de Sitter geometries, and establish the rigidity statement in the area-charge inequality. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,919 | OWR-16411-012 | Global Geometric Inequalities for Material Bodies | Establish purely global geometric inequalities for material bodies and determine whether their sharp forms require convexity, roundedness, or a related shape condition. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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-16411-012",
"literature-status:open",
"owr-year:2018"
] | Purely global inequalities and the role of convexity or roundedness are presented only as broad open directions, and no general theorem resolving the extracted claims was found. | [
{
"url": "https://doi.org/10.1007/s41114-018-0014-7",
"label": "Geometrical inequalities review"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Establish purely global geometric inequalities for material bodies and determine whether their sharp forms require convexity, roundedness, or a related shape condition. | Determine purely global inequalities for material bodies and clarify the relevance of convexity or roundedness of the body in such inequalities. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,920 | OWR-16411-013 | Hawking Energy Limits and the Null Penrose Inequality | For general null cones, characterize convergence of the Hawking energy, compare its limit with the Trautman–Bondi mass, and derive the corresponding null Penrose inequality. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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-16411-013",
"literature-status:open",
"owr-year:2018"
] | Hawking-energy limits and null Penrose inequalities are proved in important special foliations and geometries, but the general physical characterization described in the fragment remains unresolved. | [
{
"url": "https://arxiv.org/abs/1506.01545",
"label": "Mars--Soria 2015"
},
{
"url": "https://arxiv.org/abs/1511.06242",
"label": "Mars--Soria null Penrose inequality"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | For general null cones, characterize convergence of the Hawking energy, compare its limit with the Trautman–Bondi mass, and derive the corresponding null Penrose inequality. | For general null cones, characterize the convergence of Hawking energy and compare its limiting value with the Trautman--Bondi mass, thereby establishing the corresponding null Penrose inequality. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,921 | OWR-16411-014 | Global Attractors for Expanding Torus Symmetric Spacetimes | For expanding $T^2$-symmetric spacetimes, is the local attractor global for $B_0$ solutions? For non-$B_0$ solutions, does there exist a local attractor satisfying $V_\tau\to1/2$ and $Q_\tau=O(e^{-3\tau/2})$, and is it global within the $T^2$-symmetric class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,018 | 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-16411-014",
"literature-status:partially-solved",
"owr-year:2018"
] | The stated T superscript 2-symmetric attractor conjectures have partial stability and asymptotic results in polarized or otherwise restricted classes, but the asserted global attractor picture is not proved in full generality. | [
{
"url": "https://arxiv.org/abs/1408.02084",
"label": "Ringstrom T2 asymptotics"
},
{
"url": "https://arxiv.org/abs/2311.17180",
"label": "Bellati--Reiris 2026"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | For expanding $T^2$-symmetric spacetimes, is the local attractor global for $B_0$ solutions? For non-$B_0$ solutions, does there exist a local attractor satisfying $V_\tau\to1/2$ and $Q_\tau=O(e^{-3\tau/2})$, and is it global within the $T^2$-symmetric class? | For expanding T^2-symmetric spacetimes, conjecture that the local attractor is global for B_0 solutions; that a local attractor with V_\tau\to 1/2 and Q_\tau=O(e^{-3\tau/2}) exists for non-B_0 solutions; and that this non-B_0 attractor is global for T^2-symmetric solutions. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,922 | OWR-16412-002 | Connected Interiors of Conservative Hénon Filled Sets | For a volume-preserving Hénon map $f$ with $|\delta|=1$, can the interior of the forward filled set $K^+$ be connected and satisfy $\overline{\operatorname{int}K^+}=K^+$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-002",
"literature-status:open",
"owr-year:2018"
] | The Oberwolfach report formulates connected-interior and closure-equals-K for conservative H\acute{e}non maps as an unanswered question; no later primary result located settles it. | [
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | For a volume-preserving Hénon map $f$ with $|\delta|=1$, can the interior of the forward filled set $K^+$ be connected and satisfy $\overline{\operatorname{int}K^+}=K^+$? | For a volume-preserving (conservative) H\'enon map f with |\delta|=1, can the interior of the forward filled set K^+ be connected and have closure equal to the filled set K? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,923 | OWR-16412-003 | Global Linearization of Rank-One Rotation Domains | If $\Omega$ is a rank-one rotation domain, is $(f|_\Omega,\Omega)$ biholomorphically conjugate to $(L,D)$, where $D\subset\mathbb C^2$ and $$L=\operatorname{diag}(\alpha^p,\alpha^q),\qquad\gcd(p,q)=1,$$ with $|\alpha|=1$ and $\alpha$ not a root of unity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-003",
"literature-status:open",
"owr-year:2018"
] | For rank-one rotation domains the report asks whether a global (p,q)-linear model always exists; it proves linearization when a fixed point exists, but does not settle the fixed-point-free case. | [
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | If $\Omega$ is a rank-one rotation domain, is $(f|_\Omega,\Omega)$ biholomorphically conjugate to $(L,D)$, where $D\subset\mathbb C^2$ and $$L=\operatorname{diag}(\alpha^p,\alpha^q),\qquad\gcd(p,q)=1,$$ with $|\alpha|=1$ and $\alpha$ not a root of unity? | If \Omega is a rank-one rotation domain, is (f|_{\Omega},\Omega) biholomorphically conjugate to (L,D), where D\subset\mathbb{C}^2 and L=\operatorname{diag}(\alpha^p,\alpha^q) with (p,q)=1, |\alpha|=1, and \alpha not a root of unity? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,924 | OWR-16412-004 | Reinhardt Models of Rank-Two Rotation Domains | Which Reinhardt domains occur as linear models of rank-two rotation domains? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-004",
"literature-status:open",
"owr-year:2018"
] | The report leaves open which Reinhardt domains occur as rank-two rotation-domain models, explicitly including the bidisk and ball cases; no definitive classification was found. | [
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Which Reinhardt domains occur as linear models of rank-two rotation domains? | What kinds of Reinhardt domains can occur as linear models of rank-two rotation domains? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,925 | OWR-16412-005 | Smooth Stein Neighborhood Domains Beyond One H Convexity | Does there exist a bounded pseudoconvex domain $\Omega\subset\mathbb C^2$ with $C^2$ or $C^\infty$ boundary and a Stein neighborhood basis that is not $1$-$H$-convex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16412-005",
"literature-status:open",
"owr-year:2018"
] | The cited work constructs a C^{1,1} counterexample, but the smooth C^2 or C^\infty existence question for a Stein-neighborhood-basis domain that is not 1-H-convex remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
},
{
"url": "https://arxiv.org/abs/0705.0507",
"label": "Strong Stein neighborhood bases"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Does there exist a bounded pseudoconvex domain $\Omega\subset\mathbb C^2$ with $C^2$ or $C^\infty$ boundary and a Stein neighborhood basis that is not $1$-$H$-convex? | Does there exist a bounded pseudoconvex domain \Omega\subset\mathbb{C}^2 with C^2 (or C^\infty) boundary and a Stein neighborhood basis that is not 1-H-convex? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,926 | OWR-16412-006 | Holomorphic Homogeneous Regularity of Infinite-Dimensional Convex Domains | Is every bounded convex domain in an infinite-dimensional Hilbert space holomorphic homogeneous regular? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-006",
"literature-status:open",
"owr-year:2018"
] | The convex infinite-dimensional Hilbert-space HHR question remains open; later work proves HHR only for uniformly elliptic domains, while the bounded-symmetric-domain part is addressed separately. | [
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
},
{
"url": "https://arxiv.org/abs/1808.03416",
"label": "Infinite dimensional holomorphic homogeneous regular domains"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Is every bounded convex domain in an infinite-dimensional Hilbert space holomorphic homogeneous regular? | Is every convex bounded domain in an infinite-dimensional Hilbert space holomorphic homogeneous regular (HHR), and can one compute the constant value of the squeezing function for bounded homogeneous domains? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,927 | OWR-16412-007 | Squeezing Constants of Bounded Homogeneous Domains | Can the constant value of the squeezing function be computed for every bounded homogeneous domain? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,018 | 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-16412-007",
"literature-status:partially-solved",
"owr-year:2018"
] | Chu, Kim, and Kim compute the squeezing constants for all bounded symmetric domains, including infinite-dimensional finite-rank factors, but the broader question for arbitrary bounded homogeneous domains is not settled by that result. | [
{
"url": "https://arxiv.org/abs/1808.03416",
"label": "Infinite dimensional holomorphic homogeneous regular domains"
},
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Can the constant value of the squeezing function be computed for every bounded homogeneous domain? | Can one compute the constant value of the squeezing function for bounded homogeneous domains? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,928 | OWR-16412-008 | Bounded Plurisubharmonic Functions and Manifold Cores | For a complex manifold $M$ and $w_0\in M$, is $A_{cb}(w_0)=A_{cb}^e(w_0)$, is $A_{cb}(w_0)\subseteq c(M)$, and does there exist a nonnegative function $u\in\operatorname{PSH}_{cb}(M)$ with zero set $\{u=0\}=c(M)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-008",
"literature-status:open",
"owr-year:2018"
] | The Poletsky--Shcherbina paper proves structural results for A_{cb}^{e} and the core, but the three displayed equalities and inclusions are retained as open problems and no later resolution was located. | [
{
"url": "https://doi.org/10.1090/proc/14222",
"label": "Plurisubharmonically separable complex manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2018/37",
"label": "Oberwolfach Report 37/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | For a complex manifold $M$ and $w_0\in M$, is $A_{cb}(w_0)=A_{cb}^e(w_0)$, is $A_{cb}(w_0)\subseteq c(M)$, and does there exist a nonnegative function $u\in\operatorname{PSH}_{cb}(M)$ with zero set $\{u=0\}=c(M)$? | For a complex manifold M, is A_{cb}(w_0)=A^e_{cb}(w_0); does A_{cb}(w_0)\subset c(M); and does there exist a nonnegative u\in PSH_{cb}(M) with \{u=0\}=c(M)? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,929 | OWR-16412-009 | Optimal Dimensions for Polynomially Convex Embeddings | Determine the least integer $n=n(m)$ such that every compact smooth real $m$-manifold admits a polynomially convex smooth embedding into $\mathbb C^n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-009",
"literature-status:open",
"owr-year:2018"
] | Recent work lowers universal upper bounds, including n\geq\lfloor 5m/4\rfloor for smooth manifolds, but does not identify the least possible n for every m; the optimal-dimension problem remains open. | [
{
"url": "https://arxiv.org/abs/2504.01895",
"label": "Polynomially convex embeddings and CR singularities of real manifolds"
},
{
"url": "https://doi.org/10.2422/2036-2145.201811_008",
"label": "Polynomially convex embeddings of even-dimensional compact manifolds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Determine the least integer $n=n(m)$ such that every compact smooth real $m$-manifold admits a polynomially convex smooth embedding into $\mathbb C^n$. | What is the least n such that every m-dimensional compact real manifold admits a polynomially convex embedding into \mathbb{C}^n, in the smooth-embedding setting? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,930 | OWR-16412-011 | Smooth Levi-Flat Hypersurfaces in Complex Projective Planes | Does $\mathbb{CP}^2$ contain a smooth Levi-flat real hypersurface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302](https://doi.org/10.4171/owr/2018/37)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,018 | 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-16412-011",
"literature-status:open",
"owr-year:2018"
] | Nonexistence is proved in complex projective dimension at least three and for real-analytic hypersurfaces in CP^2, but existence or nonexistence of a smooth Levi-flat hypersurface in CP^2 remains a longstanding open problem. | [
{
"url": "https://academic.oup.com/imrn/article/2024/3/1801/7046029",
"label": "Oka Domains in Euclidean Spaces"
},
{
"url": "https://math.sci.uwo.ca/~shafikov/papers/levi-flats2025.pdf",
"label": "Levi-flats in CP^n: a survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/37 | null | null | null | Does $\mathbb{CP}^2$ contain a smooth Levi-flat real hypersurface? | Does complex projective space \mathbb{CP}^2 contain a smooth Levi-flat real hypersurface? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric Methods of Complex Analysis (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/37, pp. 2253--2302 |
30,003,931 | OWR-16413-002 | Statistical Optimality and Validation in Learning-and-Optimization Models | For learning-and-optimization models, should statistical optimality be defined through the probability that a solution is $\varepsilon$-optimal rather than through deterministic optimality? How should generalizability be defined, and can hypothesis tests validate such models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,018 | 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-16413-002",
"literature-status:partially-solved",
"owr-year:2018"
] | The LEO literature proposes statistical optimality, generalization error, model-fidelity tests, and model-selection procedures, but a complete theory of generalization and validation for arbitrary LEO models remains open. | [
{
"url": "https://optimization-online.org/2017/03/5904/",
"label": "Learning Enabled Optimization: Towards a Fusion of Statistical Learning and Stochastic Optimization"
},
{
"url": "https://optimization-online.org/2020/03/7661/",
"label": "Distribution-free Algorithms for Learning Enabled Optimi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | For learning-and-optimization models, should statistical optimality be defined through the probability that a solution is $\varepsilon$-optimal rather than through deterministic optimality? How should generalizability be defined, and can hypothesis tests validate such models? | For learning-and-optimization (LEO) models, is deterministic optimality the appropriate goal, or is there a notion of statistical optimality that quantifies the probability that a solution is \epsilon-optimal; how should generalizability be defined; and are hypothesis tests for model validation possible? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,932 | OWR-16413-003 | Basis Selection for Lagrangian Decision-Rule Approximations | For LDR restrictions in Lagrangian duals of the multistage stochastic mixed-integer program (MSMIP), which basis functions should be used in the LDR approximations, and how can the resulting restricted Lagrangian-dual problems be optimized efficiently? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,018 | 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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"id": 3,
"level": 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-16413-003",
"literature-status:partially-solved",
"owr-year:2018"
] | Later Lagrangian dual decision-rule work supplies computable stagewise and nonanticipative bounds and primal policies, but general basis selection with convergence guarantees and uniformly efficient optimization is not resolved. | [
{
"url": "https://doi.org/10.1287/opre.2022.2366",
"label": "Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer Programming"
},
{
"url": "https://doi.org/10.4171/owr/2018/38",
"label": "Oberwolfach Report 38/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | For LDR restrictions in Lagrangian duals of the multistage stochastic mixed-integer program (MSMIP), which basis functions should be used in the LDR approximations, and how can the resulting restricted Lagrangian-dual problems be optimized efficiently? | For LDR restrictions in Lagrangian duals of the multistage stochastic mixed-integer program (MSMIP), which basis functions should be used in the LDR approximations, and how can the resulting restricted Lagrangian-dual problems be optimized efficiently? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,933 | OWR-16413-004 | Bit Complexity of Graver-Basis Augmentation | Given an integer program with equality constraints and a Graver basis $\mathcal G(E)$, is Graver-basis augmentation efficient in bit complexity, even with oracle access to $\mathcal G(E)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,018 | 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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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16413-004",
"literature-status:partially-solved",
"owr-year:2018"
] | The basic single-Graver-step algorithm can require exponentially many iterations, while Graver-best and structured-block algorithms give polynomial or fixed-parameter results in important classes; no general efficient implementation follows. | [
{
"url": "https://doi.org/10.1007/s10107-009-0276-7",
"label": "A polynomial oracle-time algorithm for convex integer minimization"
},
{
"url": "https://arxiv.org/abs/1904.01361",
"label": "An Algorithmic Theory of Integer Programming"
},
{
"url": "https://doi.org/10.4171/owr/2018/38",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | Given an integer program with equality constraints and a Graver basis $\mathcal G(E)$, is Graver-basis augmentation efficient in bit complexity, even with oracle access to $\mathcal G(E)$? | Given an integer program with equality constraints and a Graver basis G(E), is the Graver-basis augmentation algorithm efficient in bit complexity, even with oracle access to G(E)? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,934 | OWR-16413-005 | Uniqueness of Equilibria in Rank-One Bimatrix Games | Is deciding whether a rank-one bimatrix game has a unique equilibrium co-NP-hard? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,018 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
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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",
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"OWR-16413-005",
"literature-status:open",
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] | Rank-one games have polynomial-time algorithms for finding one equilibrium and can have exponentially many equilibria, but the conjectured co-NP-hardness of deciding uniqueness remains unproved. | [
{
"url": "https://doi.org/10.1287/opre.2020.1981",
"label": "Fast Algorithms for Rank-1 Bimatrix Games"
},
{
"url": "https://doi.org/10.4171/owr/2018/38",
"label": "Oberwolfach Report 38/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | Is deciding whether a rank-one bimatrix game has a unique equilibrium co-NP-hard? | Conjecture: deciding whether a rank-1 bimatrix game has a unique equilibrium is co-NP-hard. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,935 | OWR-16413-006 | Strong Convergence of Ensemble Kalman Inversion | Does the discrete ensemble Kalman inversion iteration converge strongly to continuous paths of its limiting stochastic system in the general nonlinear setting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,018 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16413-006",
"literature-status:partially-solved",
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] | The discrete stochastic EKI is proved to converge to the continuous-time paths in probability for nonlinear forward maps and in moments for linear maps; strong convergence in the general nonlinear setting asked in the record remains unresolved. | [
{
"url": "https://doi.org/10.1137/21M1437561",
"label": "Continuous time limit of the stochastic ensemble Kalman inversion"
},
{
"url": "https://doi.org/10.1137/17M1132367",
"label": "A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | Does the discrete ensemble Kalman inversion iteration converge strongly to continuous paths of its limiting stochastic system in the general nonlinear setting? | Does the discrete ensemble Kalman inversion iteration converge strongly to continuous paths of its limiting stochastic system in the general nonlinear setting? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,936 | OWR-16413-007 | Source-Resolved Random-Domain Modeling Agenda | For a free-boundary problem on a random domain D(\omega) with random diffusion, what is a suitable model ensuring that D(\omega) is almost surely well-defined, how should the expectation of a random domain be defined, and how can the solution and the domain's expectation and deviation be computed numerically? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384](https://doi.org/10.4171/owr/2018/38)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,018 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report poses these questions as the agenda of a contribution and then supplies its well-posedness framework, expectation and de) | null | null | null | [
"owr",
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"OWR-16413-007",
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] | For the Dynamic Monge--Kantorovich flow, existence beyond local time, global well-posedness, and convergence to the OT density and potential remain open; numerical evidence and Lyapunov candidates do not constitute a proof. | [
{
"url": "https://doi.org/10.1137/16M1098383",
"label": "Towards a stationary Monge--Kantorovich dynamics"
},
{
"url": "https://doi.org/10.4171/owr/2018/39",
"label": "Oberwolfach Report 39/2018"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/38 | null | null | null | null | For a free-boundary problem on a random domain D(\omega) with random diffusion, what is a suitable model ensuring that D(\omega) is almost surely well-defined, how should the expectation of a random domain be defined, and how can the solution and the domain's expectation and deviation be computed numerically? | unrecoverable | The official report poses these questions as the agenda of a contribution and then supplies its well-posedness framework, expectation and deviation concepts, and numerical method. The extraction is not an unresolved standalone problem. No separate clean statement is promoted; the original record remains publicly visibl... | null | null | null | null | null | New Directions in Stochastic Optimisation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/38, pp. 2303--2384 |
30,003,937 | OWR-16414-001 | Convergence of Dynamic Monge–Kantorovich Systems | For the dynamic Monge–Kantorovich system, does the solution pair $(\mu(t),u(t))$ converge as $t\to\infty$ to the optimal-transport density and potential $(\mu^*,u^*)$ solving the Monge–Kantorovich equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473](https://doi.org/10.4171/owr/2018/39)
## Literature review (checked 2026-08... | 3 | open | null | 2,018 | 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.",
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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-16414-001",
"literature-status:open",
"owr-year:2018"
] | The proposed Lyapunov functional has the OT density as its unique minimizer and numerical experiments support convergence, but global convergence of the continuous dynamics is still stated as a conjecture. | [
{
"url": "https://doi.org/10.1137/16M1098383",
"label": "Towards a stationary Monge--Kantorovich dynamics"
},
{
"url": "https://doi.org/10.4171/owr/2018/39",
"label": "Oberwolfach Report 39/2018"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/39 | null | null | null | For the dynamic Monge–Kantorovich system, does the solution pair $(\mu(t),u(t))$ converge as $t\to\infty$ to the optimal-transport density and potential $(\mu^*,u^*)$ solving the Monge–Kantorovich equations? | Conjecture: as t tends to infinity, the solution pair (\mu(t),u(t)) converges to the optimal-transport density and potential (\mu^*,u^*) solving the Monge-Kantorovich equations. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473 |
30,003,938 | OWR-16414-002 | Dynamic Limits for Congested and Branched Transport | For the dynamic optimal-transport system with exponent $\beta>0$, does $(\mu(t),u(t))$ converge as $t\to\infty$ to an equilibrium associated with congested transport when $0<\beta<1$ and with branched transport when $\beta>1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473](https://doi.org/10.4171/owr/2018/39)
## Literature review (checked 2026-08... | 3 | open | null | 2,018 | 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": "Open and partially solved problems 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-16414-002",
"literature-status:open",
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] | For the extended dynamics, the congested and branched transport interpretations and long-time convergence are presented as conjectures; later work remains primarily variational or numerical rather than a general convergence theorem. | [
{
"url": "https://doi.org/10.48550/arXiv.1811.12691",
"label": "Extended Dynamic-Monge-Kantorovich equations"
},
{
"url": "https://doi.org/10.1016/j.jcp.2021.110700",
"label": "Branching structures emerging from a continuous optimal transport model"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/39 | null | null | null | For the dynamic optimal-transport system with exponent $\beta>0$, does $(\mu(t),u(t))$ converge as $t\to\infty$ to an equilibrium associated with congested transport when $0<\beta<1$ and with branched transport when $\beta>1$? | Conjecture: for the dynamic optimal-transport system with exponent \beta>0, the solution pair (\mu(t),u(t)) converges as t tends to infinity to an equilibrium related to congested transport when 0<\beta<1 and to branched transport when \beta>1. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473 |
30,003,939 | OWR-16414-003 | Singular Branched-Transport Structures as Lyapunov Minima | For $\beta>1$, determine whether the singular structures observed in long-time numerical solutions are related to local minima of the candidate Lyapunov functional $L_{\beta}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473](https://doi.org/10.4171/owr/2018/39)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,018 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
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"description": "PDEs and their applications in physics and geometry.",
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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-16414-003",
"literature-status:partially-solved",
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] | The 2021 primary study derives a Lyapunov functional and numerically finds singular and fractal-like equilibria associated with its minima, but a general theorem identifying all such structures with local minima is not established. | [
{
"url": "https://doi.org/10.1016/j.jcp.2021.110700",
"label": "Branching structures emerging from a continuous optimal transport model"
},
{
"url": "https://doi.org/10.4171/owr/2018/39",
"label": "Oberwolfach Report 39/2018"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/39 | null | null | null | For $\beta>1$, determine whether the singular structures observed in long-time numerical solutions are related to local minima of the candidate Lyapunov functional $L_{\beta}$. | For \beta>1, determine whether the singular structures observed in long-time numerical solutions are related to local minima of the candidate Lyapunov functional L_{\beta}. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473 |
30,003,940 | OWR-16414-004 | Chemotactic Cell Sorting in Keller–Segel Models | In the two-dimensional Keller–Segel chemotaxis model, can chemotaxis be the principal mechanism of cell sorting, and what occurs in the regime $\chi_2\ll1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473](https://doi.org/10.4171/owr/2018/39)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,018 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16414-004",
"literature-status:partially-solved",
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] | For the two-species Keller--Segel model, radial estimates give regimes of global existence and blow-up, and show that blow-up of one species forces the other in the stated theorem; the small-\chi_{2} sorting question is not fully resolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/39",
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{
"url": "https://doi.org/10.48550/arXiv.1704.04179",
"label": "Sorting Phenomena in a Mathematical Model for Two Species"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/39 | null | null | null | In the two-dimensional Keller–Segel chemotaxis model, can chemotaxis be the principal mechanism of cell sorting, and what occurs in the regime $\chi_2\ll1$? | In the two-dimensional Keller-Segel chemotaxis model, can chemotaxis serve as the main mechanism for cell sorting, and what happens in the regime \chi_2\ll1? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473 |
30,003,941 | OWR-16414-005 | Cell Segregation by Differential Attraction and Repulsion | For a two-species model with differential attraction, repulsion, and diffusion, can these mechanisms lead to cell sorting and segregation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473](https://doi.org/10.4171/owr/2018/39)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,018 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16414-005",
"literature-status:partially-solved",
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] | Rigorous one-dimensional results prove fully segregated stationary states for broad attractive-repulsive kernels, while later work studies additional steady states and dynamics; the general sorting question remains model-dependent and open. | [
{
"url": "https://doi.org/10.48550/arXiv.1704.04179",
"label": "Sorting Phenomena in a Mathematical Model for Two Species"
},
{
"url": "https://doi.org/10.1137/17M1128782",
"label": "Zoology of a Nonlocal Cross-Diffusion Model for Two Species"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/39 | null | null | null | For a two-species model with differential attraction, repulsion, and diffusion, can these mechanisms lead to cell sorting and segregation? | For a two-species model with differential attraction, repulsion, and diffusion, can these mechanisms lead to cell sorting and segregation? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/39, pp. 2385--2473 |
30,003,942 | OWR-16415-001 | Good Curve Graphs with Unbounded Mapping-Class Orbits | Given a surface $S$, does there exist a connected graph whose vertices are essential simple closed curves, on which the mapping class group acts with unbounded orbits? In terms of the source complexity $f(S)$, is the answer negative when $f(S)=1$, while both positive and negative examples occur when $f(S)\in\{2,3\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | partially_solved | null | 2,018 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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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... | [
"OWR-16415-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-001",
"literature-status:partially-solved",
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] | The finite-invariance index classifies many cases: good curve graphs exist for index at least four and not for index zero, while the index-one, two, and three cases are not completely classified. | [
{
"url": "https://doi.org/10.5802/aif.3217",
"label": "Graphs of curves on infinite-type surfaces with mapping class group actions"
},
{
"url": "https://arxiv.org/abs/2106.14916",
"label": "Curve graphs of surfaces with finite-invariance index 1"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Given a surface $S$, does there exist a connected graph whose vertices are essential simple closed curves, on which the mapping class group acts with unbounded orbits? In terms of the source complexity $f(S)$, is the answer negative when $f(S)=1$, while both positive and negative examples occur when $f(S)\in\{2,3\}$? | Given a surface S, does there exist a good graph made of curves, meaning a connected graph whose vertices are essential simple closed curves and on which the mapping class group acts with unbounded orbits? The conjecture is that the answer is negative for f(S)=1, while for f(S)=2 or 3 both positive and negative example... | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,943 | OWR-16415-002 | Duplicate Good-Curve-Graph Conjecture | Conjecture: for surfaces S with f(S)=1 the motivating good-graph question has a negative answer, whereas for f(S)=2 or 3 there are surfaces with both positive and negative answers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | partially_solved | null | 2,018 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 (This record is the conjectural answer to the same good-curve-graph question represented canonically and completely by OWR-16415-001. No sepa) | [
"OWR-16415-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-002",
"literature-status:partially-solved",
"owr-year:2018"
] | The f(S)=1 conjecture is proved for surfaces without nondisplaceable compact subsurfaces, but that hypothesis is itself unresolved; examples settle some positive and negative cases for f(S)=2 or 3 without a full classification. | [
{
"url": "https://arxiv.org/abs/2106.14916",
"label": "Curve graphs of surfaces with finite-invariance index 1"
},
{
"url": "https://doi.org/10.5802/aif.3217",
"label": "Graphs of curves on infinite-type surfaces with mapping class group actions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | null | Conjecture: for surfaces S with f(S)=1 the motivating good-graph question has a negative answer, whereas for f(S)=2 or 3 there are surfaces with both positive and negative answers. | unrecoverable | This record is the conjectural answer to the same good-curve-graph question represented canonically and completely by OWR-16415-001. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,944 | OWR-16415-006 | Stable-Range Comparison of Torelli Lie Algebras | In the stable genus range, is $\mathfrak t_g(k)\cong\mathfrak m_g(k)$ for every degree $k\neq2$, where $\mathfrak t_g$ and $\mathfrak m_g$ denote the Torelli and symplectic-derivation graded Lie algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-006",
"literature-status:open",
"owr-year:2018"
] | The map is known to be an isomorphism in low degrees, including k=3,4,5,6, while the report conjectures it for every k not equal to 2; later Johnson-cokernel work does not prove the full conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Torelli problem"
},
{
"url": "https://arxiv.org/abs/2608.17673",
"label": "Morita--Sakasai--Suzuki, first Galois obstruction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | In the stable genus range, is $\mathfrak t_g(k)\cong\mathfrak m_g(k)$ for every degree $k\neq2$, where $\mathfrak t_g$ and $\mathfrak m_g$ denote the Torelli and symplectic-derivation graded Lie algebras? | Conjecture: in the stable genus range, t_g(k) is isomorphic to m_g(k) for every k not equal to 2. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,945 | OWR-16415-007 | Cubulation of Hyperbolic Surface-by-Free Groups | If $1\to\pi_1(S)\to G\to Q\to1$ is exact, $S$ is a closed surface of genus greater than one, $G$ is hyperbolic, and $Q$ is finitely generated free, is $G$ cubulable, meaning that it acts freely, properly, and cocompactly on a $\operatorname{CAT}(0)$ cube complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-007",
"literature-status:open",
"owr-year:2018"
] | Cubulating surface-by-free groups proves sufficient conditions and examples, but explicitly leaves the general hyperbolic surface-by-free cubulability question open. | [
{
"url": "https://arxiv.org/abs/1908.03545",
"label": "Mj--Manning--Sageev, Cubulating Surface-by-free Groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | If $1\to\pi_1(S)\to G\to Q\to1$ is exact, $S$ is a closed surface of genus greater than one, $G$ is hyperbolic, and $Q$ is finitely generated free, is $G$ cubulable, meaning that it acts freely, properly, and cocompactly on a $\operatorname{CAT}(0)$ cube complex? | If 1 \to \pi_1(S) \to G \to Q \to 1 is exact, S is a closed surface of genus greater than one, G is hyperbolic, and Q is finitely generated free, is G cubulable, meaning that it acts freely, properly, and cocompactly on a CAT(0) cube complex? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,946 | OWR-16415-008 | Equality of Variationally Minimizing Maps | Let $X$ be a finite ideal hyperbolic simplicial complex with vertex set $S$, and let $\sigma,\tau\in\mathcal T(X)$. Let $\mathcal Y$ be the facewise $W^{1,2}$ maps $(X\setminus S,\sigma)\to(X\setminus S,\tau)$ that preserve every edge and face, and let $\mathcal D\subset\mathcal Y$ consist of maps restricting to a diff... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-008",
"literature-status:open",
"owr-year:2018"
] | The source explicitly labels the equality of the two minimizing maps as Conjecture 2 and notes unresolved singular-edge and noncompactness difficulties; no later proof was found. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Conjecture 2"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Let $X$ be a finite ideal hyperbolic simplicial complex with vertex set $S$, and let $\sigma,\tau\in\mathcal T(X)$. Let $\mathcal Y$ be the facewise $W^{1,2}$ maps $(X\setminus S,\sigma)\to(X\setminus S,\tau)$ that preserve every edge and face, and let $\mathcal D\subset\mathcal Y$ consist of maps restricting to a diff... | Conjecture: the minimizing maps in Y and in D are identical; equivalently, the minimizing map u in Y restricts to a diffeomorphism on each face of X. | corrected_verified | The official report was checked. The reconstruction restores the simplicial complex, punctures, two metrics, admissible map classes, and equivalent facewise-diffeomorphism formulation. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,947 | OWR-16415-009 | Finite-Sided Weil–Petersson Dirichlet Domains | Does the mapping class group action on the Weil–Petersson completion of Teichmüller space admit a finite-sided Dirichlet fundamental domain? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-009",
"literature-status:open",
"owr-year:2018"
] | The finite-sided Dirichlet-domain question remains unresolved; later work on WP completion and CAT(0) geometry does not establish the required finite-sided fundamental domain. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Wolpert problem"
},
{
"url": "https://arxiv.org/abs/math/0502528",
"label": "Wolpert, WP completion geometry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Does the mapping class group action on the Weil–Petersson completion of Teichmüller space admit a finite-sided Dirichlet fundamental domain? | For the Weil-Petersson completion of the Teichmuller space of a surface, show that some Dirichlet fundamental domain for the mapping class group action is finite-sided. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,948 | OWR-16415-010 | Eigenfunction Averages Along Simple Closed Geodesics | Let $S$ be a compact hyperbolic surface with Laplace eigenfunctions $\phi_n$ and eigenvalues $\lambda_n$. Do constants $\alpha,\beta>0$ exist such that
$$\frac{\sum_{\ell(C)\leq T}\int_C\phi_n\,ds}{\#\{C:\ell(C)\leq T\}}=O(\lambda_n^{-\alpha}T^{-\beta})$$
when the sum ranges over simple closed geodesics $C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-010",
"literature-status:open",
"owr-year:2018"
] | Known restriction estimates for eigenfunctions on individual geodesics do not prove the requested averaged estimate over simple closed geodesics with simultaneous eigenvalue and length decay. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Burger problem"
},
{
"url": "https://arxiv.org/abs/math/0403437",
"label": "Reznikov, geodesic restrictions of eigenfunctions"
},
{
"url": "https://arxiv.org/abs/1604.03189",
"label": "Sogge--Xi--Zhang, ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Let $S$ be a compact hyperbolic surface with Laplace eigenfunctions $\phi_n$ and eigenvalues $\lambda_n$. Do constants $\alpha,\beta>0$ exist such that
$$\frac{\sum_{\ell(C)\leq T}\int_C\phi_n\,ds}{\#\{C:\ell(C)\leq T\}}=O(\lambda_n^{-\alpha}T^{-\beta})$$
when the sum ranges over simple closed geodesics $C$? | For a compact hyperbolic surface S with Laplace eigenfunctions \phi_n and eigenvalues \lambda_n, prove that the average over simple closed geodesics of length at most T satisfies \frac{\sum_{\ell(C)\le T}\int_C\phi_n ds}{\#\{C:\ell(C)\le T\}}=O(\lambda_n^{-\alpha}T^{-\beta}) for some \alpha,\beta. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,949 | OWR-16415-011 | McShane Identities for Laplace Spectra | Construct a McShane-type identity involving the eigenvalues of the Laplacian of a compact hyperbolic surface. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-011",
"literature-status:open",
"owr-year:2018"
] | McShane-type identities for geodesic lengths and higher-rank representations are known, but no identity in terms of Laplacian eigenvalues answering this problem was found. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, A'Campo problem"
},
{
"url": "https://arxiv.org/abs/1203.3860",
"label": "McShane-type identity for closed surfaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Construct a McShane-type identity involving the eigenvalues of the Laplacian of a compact hyperbolic surface. | Construct a McShane-type identity involving the eigenvalues of the Laplacian of a compact hyperbolic surface. | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,950 | OWR-16415-012 | Boundary Maps for Distorted Hyperbolic Subgroups | Let $H$ be a Gromov-hyperbolic subgroup of a Lie group $G$, without assuming that $H$ is undistorted. Is there an asymptotically continuous map from the Gromov boundary of $H$ to $G/P$? In rank one, is $H$ asymptotically embedded even when it is not convex cocompact? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-012",
"literature-status:open",
"owr-year:2018"
] | The report gives a positive answer only for the special rank-one case G=PO(3,1); the proposed relaxation for general Lie groups and hyperbolic subgroups remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Mj problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Let $H$ be a Gromov-hyperbolic subgroup of a Lie group $G$, without assuming that $H$ is undistorted. Is there an asymptotically continuous map from the Gromov boundary of $H$ to $G/P$? In rank one, is $H$ asymptotically embedded even when it is not convex cocompact? | If an Anosov subgroup H of a Lie group G is replaced by a merely Gromov-hyperbolic subgroup without the undistortedness assumption, is there asymptotically a continuous map from the Gromov boundary of H to G/P? In rank one, this asks for asymptotic embeddedness of non-convex-cocompact subgroups. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,951 | OWR-16415-013 | Collected Problems in Higher Teichmüller and Representation Theory | Resolve the following problems in higher Teichmüller and representation theory.
1. Define a cluster superalgebra incorporating spin structures and a Laurent phenomenon, and determine whether spectral networks have a super analogue in higher super-Teichmüller theory.
2. Is the direct sum of a quasi-Fuchsian representa... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-013",
"literature-status:open",
"owr-year:2018"
] | Recent spectral-network work develops related non-super constructions, but the super analogue, stability beyond Anosov representations, and the minimal-dimensional RAAG embedding questions remain open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3662/OWR_2018_40.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 40, Problem 6"
},
{
"url": "https://arxiv.org/abs/2412.03588",
"label": "Kineider et al., Spectral Networks"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Resolve the following problems in higher Teichmüller and representation theory.
1. Define a cluster superalgebra incorporating spin structures and a Laurent phenomenon, and determine whether spectral networks have a super analogue in higher super-Teichmüller theory.
2. Is the direct sum of a quasi-Fuchsian representa... | Open questions include: what is the correct notion of cluster superalgebra incorporating spin structure and the Laurent phenomenon; what role do spectral networks play in higher super Teichmuller theory and is there a super analogue; whether the direct sum of a quasi-Fuchsian representation and a geometrically infinite... | corrected_verified | The official problem-session report was checked. The three source problems were retained and the ambient Lie groups and representation-theoretic objects were made explicit. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,952 | OWR-16415-015 | Smooth Lifts of the Dehn-Twist Braid Relation | Let $a$ and $b$ be right Dehn twists about essential simple closed curves meeting once, so that $aba=bab$ in the mapping class group. Can they be lifted to homeomorphisms $A$ and $B$ satisfying $ABA=BAB$? Can such lifts be chosen of class $C^1$, or more generally $C^r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-015",
"literature-status:open",
"owr-year:2018"
] | Non-realization results for full braid or mapping class groups do not settle the two-generator lift of the Dehn-twist braid relation; the specific homeomorphism-lift question remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Problem 9"
},
{
"url": "https://arxiv.org/abs/1808.08248",
"label": "Chen, non-realizability of braid groups"
},
{
"url": "https://doi.org/10.1112/blms/bdw016",
"label": "Salter--Tshishiku, braid groups ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Let $a$ and $b$ be right Dehn twists about essential simple closed curves meeting once, so that $aba=bab$ in the mapping class group. Can they be lifted to homeomorphisms $A$ and $B$ satisfying $ABA=BAB$? Can such lifts be chosen of class $C^1$, or more generally $C^r$? | If two essential simple closed curves meet once and their right Dehn twists a and b satisfy aba=bab in the mapping class group, can they be lifted to homeomorphisms A and B satisfying ABA=BAB, including lifts that are once continuously differentiable or r-times continuously differentiable? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,953 | OWR-16415-016 | Rectifiable Nonsmooth Limit Curves of Anosov Representations | For the fundamental group $\Gamma$ of a closed orientable surface of genus $g\geq2$, does there exist a $1$-Anosov representation $\Gamma\to\operatorname{PGL}(d,\mathbb R)$ whose circular limit set in $\mathbb P(\mathbb R^d)$ is rectifiable but not $C^{1,\alpha}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-016",
"literature-status:open",
"owr-year:2018"
] | Zhang--Zimmer give necessary and sufficient regularity criteria for irreducible surface-group representations, but the requested existence of a rectifiable non-C1alpha limit circle is not settled by that work. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Zhang problem"
},
{
"url": "https://arxiv.org/abs/1903.11021",
"label": "Zhang--Zimmer, regularity of Anosov limit sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | For the fundamental group $\Gamma$ of a closed orientable surface of genus $g\geq2$, does there exist a $1$-Anosov representation $\Gamma\to\operatorname{PGL}(d,\mathbb R)$ whose circular limit set in $\mathbb P(\mathbb R^d)$ is rectifiable but not $C^{1,\alpha}$? | For the fundamental group \Gamma of a closed orientable surface of genus g\ge2, does there exist a 1-Anosov representation of \Gamma in PGL(d,\mathbb{R}) whose circular limit set in P(\mathbb{R}^d) is rectifiable but not C^{1,\alpha}? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,954 | OWR-16415-017 | Noncongruence Normal Subgroups of Mapping Class Groups | What are the proper normal subgroups of a mapping class group that are not contained in any congruence subgroup, or alternatively in the union of the congruence subgroups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | partially_solved | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16415-017",
"literature-status:partially-solved",
"owr-year:2018"
] | Clay--Mangahas--Margalit construct explicit proper normal subgroups outside every level congruence subgroup, settling existence, but the requested classification remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Lanier problem"
},
{
"url": "https://arxiv.org/abs/2001.10587",
"label": "Clay--Mangahas--Margalit, RAAG normal subgroups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | What are the proper normal subgroups of a mapping class group that are not contained in any congruence subgroup, or alternatively in the union of the congruence subgroups? | What are the proper normal subgroups of a mapping class group that are not contained in any congruence subgroup, or alternatively in the union of the congruence subgroups? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,955 | OWR-16415-018 | Disconnected Preimages of Subsurfaces Under Finite Covers | Given a finite cover $f:S_h\to S_g$ with $h>g\geq2$, is there always a four-holed sphere $H$ with essential boundary components in $S_g$ such that the interior of $f^{-1}(H)$ is disconnected, and what is the answer for a three-holed sphere? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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://zenodo.org/records/23272252",
"checked_at": "2026-10-10",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-10] I have released an unrefereed preprint, **A Finite Cover of the Genus-Two Surface in Which Every Four-Holed Sphere Has Connected Preimage: A Partial Answer to a Question of D. Gekhtman** (Alper Ferudun, Mercury Software GmbH). It gives a partial answer: for the four-holed qu... | [
"owr",
"oberwolfach-reports",
"OWR-16415-018",
"literature-status:open",
"owr-year:2018"
] | The finite-cover preimage-disconnection question is posed as an unresolved problem, and no general theorem answering the four-holed or three-holed sphere versions was found. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3662/OWR_2018_40.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 40, Gekhtman problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Given a finite cover $f:S_h\to S_g$ with $h>g\geq2$, is there always a four-holed sphere $H$ with essential boundary components in $S_g$ such that the interior of $f^{-1}(H)$ is disconnected, and what is the answer for a three-holed sphere? | Given a finite cover f:S_h\to S_g with h>g\ge2, is there always a four-holed sphere H with essential boundary components in S_g such that the interior of f^{-1}(H) is disconnected, and what is the answer for a three-holed sphere? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,956 | OWR-16415-019 | Mapping-Class Orbit Counting in the Thurston Metric | For $x,y$ in Teichmüller space, determine as $R\to\infty$ the number of points in the mapping-class-group orbit of $y$ lying in the Thurston-metric ball of radius $R$ about $x$. How is this asymptotic related to orbit counting by extremal length rather than hyperbolic length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | partially_solved | null | 2,018 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s00039-019-00502-7",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (the count is known). W. Su (problem session, OWR 40/2018, p. 2528, Problem 13) asks for the asymptotic number of mapping-class orbit points of y in the Thurston-metric ball of radius R about x, and how this relates to, or can be unified with, counting ... | [
"owr",
"oberwolfach-reports",
"OWR-16415-019",
"literature-status:open",
"owr-year:2018"
] | Orbit counting is known for the Teichmuller metric and there are partial Thurston-metric and extremal-length results, but the requested extremal-length asymptotics and unification remain unproved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3662/OWR_2018_40.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 40, Su problem"
},
{
"url": "https://arxiv.org/abs/1210.0743",
"label": "Su, variation of extremal length"
},
{
"url": "https://link.springer.com/article/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | For $x,y$ in Teichmüller space, determine as $R\to\infty$ the number of points in the mapping-class-group orbit of $y$ lying in the Thurston-metric ball of radius $R$ about $x$. How is this asymptotic related to orbit counting by extremal length rather than hyperbolic length? | For points x,y in Teichmuller space, determine the asymptotics as R tends to infinity of the number of points in the mapping class orbit of y lying in the Thurston-metric ball of radius R about x, and relate or unify this counting problem with counting by extremal length rather than hyperbolic length. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,957 | OWR-16415-020 | Local Branching of Holonomy Maps for Geometric Structures | For a closed manifold $M$, is the holonomy map from the deformation space of $(G,X)$-structures on $M$ to the representation variety $\operatorname{Rep}(\pi_1(M),G)$, which is an open map with discrete fibers, always a branched local homeomorphism? Find conditions under which it is a local homeomorphism. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-020",
"literature-status:open",
"owr-year:2018"
] | The Ehresmann--Thurston principle gives local homeomorphism in standard compact settings and special loci are understood, but the universal branched-local-homeomorphism claim and general criteria remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Alessandrini problem"
},
{
"url": "https://math.umd.edu/~wmg/gstom.pdf",
"label": "Goldman, geometric structures on manifolds"
},
{
"url": "https://doi.org/10.48550/arXiv.2110.15407",
"label": "Projectiv... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | For a closed manifold $M$, is the holonomy map from the deformation space of $(G,X)$-structures on $M$ to the representation variety $\operatorname{Rep}(\pi_1(M),G)$, which is an open map with discrete fibers, always a branched local homeomorphism? Find conditions under which it is a local homeomorphism. | For a closed manifold M, is the holonomy map from the deformation space of (G,X)-structures on M to the representation variety Rep(\pi_1(M),G), which is an open map with discrete fibers, always a branched local homeomorphism? Find conditions under which it is a local homeomorphism. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,958 | OWR-16415-021 | Hitchin Curves and Weil–Petersson Boundary Dynamics | Find an ordinary differential equation describing at least some finite-dimensional families of $C^1$ curves arising from Hitchin representations. For universal Weil–Petersson Teichmüller space, determine the limit points in the Thurston boundary of Weil–Petersson geodesics, or construct analogues of earthquake paths. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534](https://doi.org/10.4171/owr/2018/40)
## Literature review (c... | 3 | open | null | 2,018 | 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-16415-021",
"literature-status:open",
"owr-year:2018"
] | Hitchin and related higher Teichmuller literature describes the representation families, but no ordinary differential equation answering the posed problem was found. | [
{
"url": "https://doi.org/10.4171/owr/2018/40",
"label": "Oberwolfach Report 40, Burger problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/40 | null | null | null | Find an ordinary differential equation describing at least some finite-dimensional families of $C^1$ curves arising from Hitchin representations. For universal Weil–Petersson Teichmüller space, determine the limit points in the Thurston boundary of Weil–Petersson geodesics, or construct analogues of earthquake paths. | Find an ordinary differential equation describing at least some finite-dimensional families of C^1 curves arising from Hitchin representations; and, for universal Weil--Petersson Teichmuller space, determine limit points in the Thurston boundary of Weil--Petersson geodesics or give examples analogous to earthquake path... | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | New Trends in Teichmüller Theory and Mapping Class Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/40, pp. 2475--2534 |
30,003,959 | OWR-16416-001 | Diffusive Limits for the Random Lorentz Gas | For the random Lorentz-gas trajectory $X^{r,\rho}(t)$, conditioned on the particle not being trapped, does
$$t\longmapsto\frac{X^{r,\rho}(Tt)}{\sqrt T},\qquad 0\leq t\leq1,$$
converge weakly as $T\to\infty$ to a Wiener process with nondegenerate variance, in either the quenched or averaged-quenched setting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581](https://doi.org/10.4171/owr/2018/41)
## Literature review (checked 2... | 3 | open | null | 2,018 | 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... | [
"OWR-16772-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16416-001",
"literature-status:open",
"owr-year:2018"
] | The invariance principle for the conditioned nontrapped Lorentz particle is still identified as a major open problem; later Lorentz-gas work records the corresponding periodic higher-dimensional invariance problem as open. | [
{
"url": "https://doi.org/10.4171/owr/2018/41",
"label": "Oberwolfach Report 41, Lorentz particle"
},
{
"url": "https://doi.org/10.1007/s00220-020-03852-8",
"label": "Lutsko--Toth, Lorentz gas invariance principle"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/41 | null | null | null | For the random Lorentz-gas trajectory $X^{r,\rho}(t)$, conditioned on the particle not being trapped, does
$$t\longmapsto\frac{X^{r,\rho}(Tt)}{\sqrt T},\qquad 0\leq t\leq1,$$
converge weakly as $T\to\infty$ to a Wiener process with nondegenerate variance, in either the quenched or averaged-quenched setting? | For the random Lorentz gas trajectory X^{r,\rho}(t), conditioned on the particle not being trapped, prove the diffusive scaling limit t\mapsto X^{r,\rho}(Tt)/\sqrt{T} as T\to\infty on [0,1], namely weak convergence to a Wiener process with nondegenerate variance, in the quenched or averaged-quenched setting. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581 |
30,003,960 | OWR-16416-002 | Extensive Amenability of Wobbling-Group Actions | Is the action of the wobbling group $W(\mathbb Z^d)$ on $\mathbb Z^d$ extensively amenable? Equivalently, for every symmetric finitely supported probability measure $\mu$ on $W(\mathbb Z^d)$, every $\varepsilon>0$, and all sufficiently large $n$, do the inverted orbits $O_n$ satisfy
$$\mathbb P(\lvert O_n\rvert<\varep... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581](https://doi.org/10.4171/owr/2018/41)
## Literature review (checked 2... | 3 | open | null | 2,018 | 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... | [
"OWR-16416-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16416-002",
"literature-status:open",
"owr-year:2018"
] | Extensive amenability is settled for the wobbling actions in dimensions 1 and 2, while the d at least 3 case and the all-measures formulation remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/41",
"label": "Oberwolfach Report 41, extensive amenability"
},
{
"url": "https://arxiv.org/abs/1804.01981",
"label": "Garban, inverted orbits and extensive amenability"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/41 | null | null | null | Is the action of the wobbling group $W(\mathbb Z^d)$ on $\mathbb Z^d$ extensively amenable? Equivalently, for every symmetric finitely supported probability measure $\mu$ on $W(\mathbb Z^d)$, every $\varepsilon>0$, and all sufficiently large $n$, do the inverted orbits $O_n$ satisfy
$$\mathbb P(\lvert O_n\rvert<\varep... | Is the action of the wobbling group W(\mathbb{Z}^d) on \mathbb{Z}^d extensively amenable? Equivalently, for every symmetric finitely supported probability measure \mu on W(\mathbb{Z}^d), do the inverted orbits O_n of the induced random walk satisfy, for every \varepsilon>0 and all sufficiently large n, P(|O_n|<\varepsi... | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581 |
30,003,961 | OWR-16416-003 | Duplicate Wobbling-Group Nonamenability Conjecture | Conjecture: the action of W(\mathbb{Z}^d) on \mathbb{Z}^d is not extensively amenable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581](https://doi.org/10.4171/owr/2018/41)
## Literature review (checked 2... | 3 | open | null | 2,018 | 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 | Duplicate/merged OWR extraction (The official report presents this as the conjectured negative answer to the extensive-amenability question represented canonically by OWR-16) | [
"OWR-16416-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16416-003",
"literature-status:open",
"owr-year:2018"
] | The cited random-walk construction yields only partial evidence and explicitly conjectures non-extensive amenability for d at least 3; this conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/41",
"label": "Oberwolfach Report 41, non-extensive amenability"
},
{
"url": "https://arxiv.org/abs/1804.01981",
"label": "Garban, inverted orbits and extensive amenability"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/41 | null | null | null | null | Conjecture: the action of W(\mathbb{Z}^d) on \mathbb{Z}^d is not extensively amenable. | unrecoverable | The official report presents this as the conjectured negative answer to the extensive-amenability question represented canonically by OWR-16416-002, not as a distinct problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Scaling Limits in Models of Statistical Mechanics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/41, pp. 2535--2581 |
30,003,962 | OWR-16417-002 | Complete Curves and Positivity in Differential Strata | For strata of holomorphic differentials, can a stratum contain a complete curve; which powers of the tautological class $\eta$ vanish on the stratum; and how can positivity of other divisor classes on compactified strata be determined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | partially_solved | null | 2,018 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.5802/crmath.34",
"checked_at": "2026-10-02",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-02] **partially_solved**. D. Chen (OWR 42/2018, p. 2600) asks whether strata of holomorphic differentials can contain a complete curve, which powers of the tautological class η vanish on the strata, and how to decide positivity of other divisor classes on the compactified strat... | [
"owr",
"oberwolfach-reports",
"OWR-16417-002",
"literature-status:open",
"owr-year:2018"
] | Complete curves are ruled out in the unprojectivized holomorphic strata, but complete curves in the projectivized strata and the requested vanishing and positivity questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "Oberwolfach Report 42, strata problems"
},
{
"url": "https://doi.org/10.5802/crmath.416",
"label": "Chen, complete curves in strata of differentials"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | For strata of holomorphic differentials, can a stratum contain a complete curve; which powers of the tautological class $\eta$ vanish on the stratum; and how can positivity of other divisor classes on compactified strata be determined? | For strata of holomorphic differentials, can a stratum contain a complete curve; which powers of the tautological class \eta vanish on the stratum; and how can positivity of other divisor classes on compactified strata be determined? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,963 | OWR-16417-003 | Compactified Universal Jacobians over Stable Curves | How can a degree-$d$ universal Jacobian over the moduli space of smooth marked curves be extended over the moduli space of stable marked curves by adding well-behaved compactified Jacobian fibers, and which degenerate line bundles or multidegrees should be included? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | partially_solved | null | 2,018 | 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-16417-003",
"literature-status:partially-solved",
"owr-year:2018"
] | Compactified Jacobians and proper moduli of stable torsion-free sheaves have been constructed for broad stability data, with wall-crossing described, but there is no single complete degeneration theory covering all curves and choices. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "Oberwolfach Report 42, compactified Jacobians"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | How can a degree-$d$ universal Jacobian over the moduli space of smooth marked curves be extended over the moduli space of stable marked curves by adding well-behaved compactified Jacobian fibers, and which degenerate line bundles or multidegrees should be included? | How can a degree-d universal Jacobian over the moduli space of smooth marked curves be extended over the moduli space of stable marked curves by adding well-behaved compactified Jacobian fibers, and which degenerate line bundles or multidegrees should be included? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,964 | OWR-16417-004 | Thin Kontsevich–Zorich Monodromy Groups | How frequently are Kontsevich–Zorich monodromy groups thin, especially for square-tiled surfaces of genus 3; in particular, can one find thin monodromy groups among genus-3 square-tiled surfaces without one-cylinder decompositions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,018 | 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-16417-004",
"literature-status:open",
"owr-year:2018"
] | Genus-three arithmetic examples and families are known, but the frequency and existence of thin Kontsevich--Zorich monodromies in the general genus-three problem remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "Oberwolfach Report 42, thin monodromy"
},
{
"url": "https://arxiv.org/abs/1806.09855",
"label": "Hubert--Matheus, genus-three arithmetic monodromy"
},
{
"url": "https://arxiv.org/abs/2206.06595",
"label": "Bonnafoux et al., ar... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | How frequently are Kontsevich–Zorich monodromy groups thin, especially for square-tiled surfaces of genus 3; in particular, can one find thin monodromy groups among genus-3 square-tiled surfaces without one-cylinder decompositions? | How frequently are Kontsevich--Zorich monodromy groups thin, especially for square-tiled surfaces of genus 3; in particular, can one find thin monodromy groups among genus-3 square-tiled surfaces without one-cylinder decompositions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,965 | OWR-16417-006 | Lifting Tropical Divisors with Prescribed Rank | Given a tropical curve $\Gamma$ and a divisor $D=\sum_{i=1}^n a_i p_i$ of degree $d$ and rank $r$ on $\Gamma$, does there exist a smooth projective curve $X$ over a non-Archimedean field $K$ with dual tropical curve $\Gamma$ and a divisor $\widetilde D$ on $X$ of multiplicity profile $(a_1,\ldots,a_n)$ and rank $r$ who... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,018 | 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-16417-006",
"literature-status:open",
"owr-year:2018"
] | The general realizability problem is explicitly left difficult by Murphy law; canonical and pluri-canonical cases have criteria, but no general solution is known. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1710.06401",
"label": "Tropical canonical divisors"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.70027",
"label": "Tropical pluri-canonical divis... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | Given a tropical curve $\Gamma$ and a divisor $D=\sum_{i=1}^n a_i p_i$ of degree $d$ and rank $r$ on $\Gamma$, does there exist a smooth projective curve $X$ over a non-Archimedean field $K$ with dual tropical curve $\Gamma$ and a divisor $\widetilde D$ on $X$ of multiplicity profile $(a_1,\ldots,a_n)$ and rank $r$ who... | Given a tropical curve \Gamma and a divisor D=\sum_{i=1}^n a_i p_i of degree d and rank r on \Gamma, does there exist a smooth projective curve X over a non-Archimedean field K with dual tropical curve \Gamma and a divisor \widetilde D on X of multiplicity profile (a_1,\ldots,a_n) and rank r whose specialization is D? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,966 | OWR-16417-007 | Teichmüller Projections of Hitchin Components | Does there exist a mapping-class-group-equivariant projection from the Hitchin component for $\operatorname{PSL}(n,\mathbb{R})$ to Teichmüller space $T(\Sigma_g)$ whose fiber over a Riemann surface $X$ is $\bigoplus_{i=3}^n H^0(X,K_X^i)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,018 | 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-16417-007",
"literature-status:open",
"owr-year:2018"
] | Rank two cases are proved, while later work disproves a related minimal map uniqueness conjecture in higher rank; the exact equivariant fibration and fiber statement remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "OWR report"
},
{
"url": "https://annals.math.princeton.edu/articles/22504",
"label": "Unstable minimal surfaces"
},
{
"url": "https://arxiv.org/abs/2208.04885",
"label": "Hitchin component fibration"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | Does there exist a mapping-class-group-equivariant projection from the Hitchin component for $\operatorname{PSL}(n,\mathbb{R})$ to Teichmüller space $T(\Sigma_g)$ whose fiber over a Riemann surface $X$ is $\bigoplus_{i=3}^n H^0(X,K_X^i)$? | Does there exist a mapping-class-group-equivariant projection from the Hitchin component for PSL(n,\mathbb{R}) to Teichmuller space T(\Sigma_g) whose fiber over a Riemann surface X is \bigoplus_{i=3}^n H^0(X,K_X^i)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,967 | OWR-16417-008 | Finite-Volume Symplectic Quotients of Hitchin Components | Is there a group of symplectomorphisms acting properly discontinuously on the Hitchin component with a finite-volume quotient? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650](https://doi.org/10.4171/owr/2018/42)
## Literature review (checked 2026-08-21)
**S... | 3 | open | null | 2,018 | 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-16417-008",
"literature-status:open",
"owr-year:2018"
] | The report poses this as an open question; later symplectic and Hamiltonian results do not provide a properly discontinuous finite volume action on the Hitchin component. | [
{
"url": "https://doi.org/10.4171/owr/2018/42",
"label": "OWR report"
},
{
"url": "https://ul.qucosa.de/api/qucosa%3A97838/attachment/ATT-0/",
"label": "Hamiltonian flows on character varieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/42 | null | null | null | Is there a group of symplectomorphisms acting properly discontinuously on the Hitchin component with a finite-volume quotient? | Is there a group of symplectomorphisms acting properly discontinuously on the Hitchin component with a finite-volume quotient? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Flat Surfaces and Algebraic Curves (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/42, pp. 2583--2650 |
30,003,968 | OWR-16418-001 | Weak Tumor-Invasion Solutions Without Growth Compatibility | Let $n_1,n_2$ satisfy
$$\partial_tn_1-\operatorname{div}(n_1\nabla p)=n_1F_1(p)+n_2G_1(p),$$
$$\partial_tn_2-\operatorname{div}(n_2\nabla p)=n_1F_2(p)+n_2G_2(p)$$
on $\mathbb R^d$ for $t\geq0$, where $n=n_1+n_2$, $p=n^\gamma$, $\gamma>1$, $F=F_1+F_2$, $G=G_1+G_2$, and $F(p),G(p)\leq0$ for $p\geq P_H$. Can weak soluti... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differential Equations arising from Organising Principles in Biology (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/43, pp. 2651--2701](https://doi.org/10.4171/owr/2018/43)
## Literatur... | 3 | open | null | 2,018 | 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-16418-001",
"literature-status:open",
"owr-year:2018"
] | The record is an incomplete fragment of a tissue growth model; the source calls removal of the homeostatic pressure assumption open, and later work proves existence only under assumptions. | [
{
"url": "https://doi.org/10.4171/owr/2018/43",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1809.01867",
"label": "Two species tissue growth"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/43 | null | null | null | Let $n_1,n_2$ satisfy
$$\partial_tn_1-\operatorname{div}(n_1\nabla p)=n_1F_1(p)+n_2G_1(p),$$
$$\partial_tn_2-\operatorname{div}(n_2\nabla p)=n_1F_2(p)+n_2G_2(p)$$
on $\mathbb R^d$ for $t\geq0$, where $n=n_1+n_2$, $p=n^\gamma$, $\gamma>1$, $F=F_1+F_2$, $G=G_1+G_2$, and $F(p),G(p)\leq0$ for $p\geq P_H$. Can weak soluti... | For the two-population tumor-invasion pressure model with p=n^\gamma and combined growth terms F and G, can the existence theory for weak solutions be proved without the condition sup_{0\le p\le P_H}|F(p)-G(p)|^2/p^{1/\gamma}\le C_H? | corrected_verified | The official report was checked. The reconstruction restores the two population equations, pressure law, growth terms, homeostatic assumption, and the compatibility condition whose removal is open. | null | null | null | null | null | Differential Equations arising from Organising Principles in Biology (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/43, pp. 2651--2701 |
30,003,969 | OWR-16627-001 | Bounded-Length Strong Ramsey Games | For every integer $t$, is there a constant $c_t$ such that the length $L(K_t,n)$ of the strong Ramsey game on $K_n$ is at most $c_t$ for every $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738](https://doi.org/10.4171/owr/2018/44)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16627-001",
"literature-status:open",
"owr-year:2018"
] | The Beck conjecture is proved for t at most 4, but the bounded length assertion remains open from t equal to 5 onward. | [
{
"url": "https://doi.org/10.4171/owr/2018/44",
"label": "OWR report"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0195669820300172",
"label": "Strong Ramsey games"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/44 | null | null | null | For every integer $t$, is there a constant $c_t$ such that the length $L(K_t,n)$ of the strong Ramsey game on $K_n$ is at most $c_t$ for every $n$? | Beck\textquotesingle s conjecture: for every integer t, there is a constant c_t such that the length L(K_t,n) of the strong Ramsey game on K_n is at most c_t for all n. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738 |
30,003,970 | OWR-16627-002 | Uniform Winning Times in Strong Ramsey Games | For fixed $k$, does the first player have a winning strategy in the strong Ramsey game $R(K_n,K_k)$ using a number of moves bounded independently of $n$ as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738](https://doi.org/10.4171/owr/2018/44)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16627-002",
"literature-status:open",
"owr-year:2018"
] | The cited primary literature still describes Becks bounded time complete graph question as open. | [
{
"url": "https://doi.org/10.4171/owr/2018/44",
"label": "OWR report"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0195669820300172",
"label": "Strong Ramsey games"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/44 | null | null | null | For fixed $k$, does the first player have a winning strategy in the strong Ramsey game $R(K_n,K_k)$ using a number of moves bounded independently of $n$ as $n\to\infty$? | For fixed k, does the first player have a winning strategy in the strong Ramsey game R(K_n,K_k) in a number of moves bounded independently of n as n\to\infty? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738 |
30,003,971 | OWR-16627-003 | Threshold Bias in the Odd-Cycle Game | In the Maker–Breaker odd-cycle game on $K_n$, is the threshold bias $b_{\mathrm{MB}}(OC_n)=(1/2+o(1))n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738](https://doi.org/10.4171/owr/2018/44)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16627-003",
"literature-status:open",
"owr-year:2018"
] | The odd cycle threshold has improved lower bounds, but the claimed asymptotic value one half has not been established. | [
{
"url": "https://doi.org/10.4171/owr/2018/44",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.ejc.2020.103140",
"label": "Odd cycle game"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/44 | null | null | null | In the Maker–Breaker odd-cycle game on $K_n$, is the threshold bias $b_{\mathrm{MB}}(OC_n)=(1/2+o(1))n$? | In the Maker--Breaker odd-cycle game on K_n, is the threshold bias b_{MB}(OC_n)=(1/2+o(1))n? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738 |
30,003,972 | OWR-16627-004 | Equivalence of Graphs in Strong Ramsey Games | Determine the largest $t=t(k)$ such that $K_k$ is 2-equivalent to $K_k+K_{1,t}$, and the largest $t=t(k)$ for which some tree $T$ on $t$ vertices satisfies $K_k\sim_2 K_k+T$; moreover, for each $q\ge 2$, do there exist two non-isomorphic connected $q$-equivalent graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738](https://doi.org/10.4171/owr/2018/44)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16627-004",
"literature-status:open",
"owr-year:2018"
] | Known Ramsey equivalence results give partial restrictions and examples, but the requested connected graph classification and largest t values remain open. | [
{
"url": "https://doi.org/10.4171/owr/2018/44",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1809.09232",
"label": "Ramsey equivalence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/44 | null | null | null | Determine the largest $t=t(k)$ such that $K_k$ is 2-equivalent to $K_k+K_{1,t}$, and the largest $t=t(k)$ for which some tree $T$ on $t$ vertices satisfies $K_k\sim_2 K_k+T$; moreover, for each $q\ge 2$, do there exist two non-isomorphic connected $q$-equivalent graphs? | Determine the largest t=t(k) such that K_k is 2-equivalent to K_k+K_{1,t}, and the largest t=t(k) for which some tree T on t vertices satisfies K_k\sim_2 K_k+T; moreover, for each q\ge2, do there exist two non-isomorphic connected q-equivalent graphs? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738 |
30,003,973 | OWR-16627-005 | Higher-Color Equivalence of Two-Equivalent Graphs | Is every pair of 2-equivalent graphs also 3-equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738](https://doi.org/10.4171/owr/2018/44)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16627-005",
"literature-status:open",
"owr-year:2018"
] | The implication from two equivalence to three equivalence is still stated as an open problem in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2018/44",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1809.09232",
"label": "Ramsey equivalence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/44 | null | null | null | Is every pair of 2-equivalent graphs also 3-equivalent? | Is every pair of 2-equivalent graphs also 3-equivalent? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Positional Games (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/44, pp. 2715--2738 |
30,003,974 | OWR-16628-001 | Irrationality of Seshadri Constants | Can a Seshadri constant be irrational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 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-16628-001",
"literature-status:open",
"owr-year:2018"
] | The irrationality question remains open; later work computes broad classes, including abelian surfaces, without producing an unconditional irrational example. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0007449722001130",
"label": "Seshadri constants in characteristic zero"
},
{
"url": "https://doi.org/10.1016/j.aim.2022.108827",
"label": "Seshadr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | Can a Seshadri constant be irrational? | Can Seshadri constants be irrational? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,975 | OWR-16628-004 | Stable Symbolic-Power Containments from a Single Containment | Let $R$ be a regular ring and let $I$ be a radical ideal of big height $h$. If $I^{(hk-C)}\subseteq I^k$ for some $k$, must $I^{(hn-C)}\subseteq I^n$ for all sufficiently large $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 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-16628-004",
"literature-status:open",
"owr-year:2018"
] | Later papers prove the stable containment for important classes and give sufficient criteria, but the general implication for arbitrary radical ideals remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1809.06955",
"label": "Stable Harbourne conjecture"
},
{
"url": "https://arxiv.org/abs/1903.12122",
"label": "Expected resurgences"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | Let $R$ be a regular ring and let $I$ be a radical ideal of big height $h$. If $I^{(hk-C)}\subseteq I^k$ for some $k$, must $I^{(hn-C)}\subseteq I^n$ for all sufficiently large $n$? | Let R be a regular ring and I a radical ideal of big height h. Does I^{(hk-C)}\subseteq I^k for some k imply I^{(hn-C)}\subseteq I^n for all sufficiently large n? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,976 | OWR-16628-005 | Symbolic-Power Noncontainments for Reflection Arrangements | For which irreducible complex reflection groups does the triple-point ideal $I_X$ of the reflection arrangement satisfy $I_X^{(3)}\not\subseteq I_X^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 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-16628-005",
"literature-status:open",
"owr-year:2018"
] | Several reflection group families are proved to give noncontainments, but the requested classification of all irreducible complex reflection groups remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2002.05353",
"label": "Reflection arrangements"
},
{
"url": "https://ems.press/content/serial-article-files/46948",
"label": "OWR 2022 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | For which irreducible complex reflection groups does the triple-point ideal $I_X$ of the reflection arrangement satisfy $I_X^{(3)}\not\subseteq I_X^2$? | Which irreducible complex reflection groups have reflection arrangements whose triple-point ideal I_X satisfies the noncontainment I_X^{(3)}\not\subseteq I_X^2? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,977 | OWR-16628-008 | (−1)-Curve Conjecture for Plane Blowups | Let $X_r$ be the blowup of $\mathbb P^2$ at $r\geq0$ general points. If $C\subset X_r$ is an irreducible reduced curve with $C^2<0$, must $C$ be a smooth rational curve with $C^2=-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 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-16628-008",
"literature-status:open",
"owr-year:2018"
] | The negative curve statement for blowups at very general points remains an open conjecture, especially beyond the del Pezzo range. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://mathdb.com/p/366322/the-1-curves-conjecture-for-blowups-of-the-projective-plane",
"label": "Current conjecture status"
},
{
"url": "https://doi.org/10.1016/j.jalgebra.2017.11.040",
"label": "Si... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | Let $X_r$ be the blowup of $\mathbb P^2$ at $r\geq0$ general points. If $C\subset X_r$ is an irreducible reduced curve with $C^2<0$, must $C$ be a smooth rational curve with $C^2=-1$? | (-1)-curves conjecture: if X_r is the blow-up of \mathbb{P}^2 at r\ge0 general points and C is an irreducible reduced curve on X_r with C^2<0, then C is a smooth rational (-1)-curve, so C^2=-1. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,978 | OWR-16628-010 | Irrational Seshadri Constants from the Nagata Conjecture | For $r\geq9$, does the Nagata conjecture for the blowup $X_r$ of $\mathbb P^2$ at $r$ general points imply the existence of an ample line bundle on $X_r$ whose Seshadri constant at a very general point is irrational? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 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-16628-010",
"literature-status:open",
"owr-year:2018"
] | The source restates the Nagata only question as open, and later work supplies conditional results rather than a proof from Nagata alone. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.jpaa.2020.106345",
"label": "Rationality of Seshadri constants"
},
{
"url": "https://www.cmi.ac.in/~krishna/irrational-seshadri-constants.pdf",
"label": "Irrational Seshadri c... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | For $r\geq9$, does the Nagata conjecture for the blowup $X_r$ of $\mathbb P^2$ at $r$ general points imply the existence of an ample line bundle on $X_r$ whose Seshadri constant at a very general point is irrational? | For r\ge9, does the existence of an ample line bundle L on the blow-up X_r of \mathbb{P}^2 with irrational Seshadri constant at a very general point follow assuming only the Nagata conjecture for X_r? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,979 | OWR-16628-011 | Origins of Unexpected Projective Varieties | What general geometric or algebraic mechanism produces unexpected varieties and unexpected hypersurfaces in projective space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767](https://doi.org/10.4171/owr/2018/45)
## Literature review (... | 3 | open | null | 2,018 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"description": "Geometric objects defined by polynomial equations.",
"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"
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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-16628-011",
"literature-status:open",
"owr-year:2018"
] | Later work gives classifications and infinite families of unexpected hypersurfaces, but the general origin and classification question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/45",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1805.10626",
"label": "Unexpected hypersurfaces"
},
{
"url": "https://arxiv.org/abs/1602.02300",
"label": "Line arrangements"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/45 | null | null | null | What general geometric or algebraic mechanism produces unexpected varieties and unexpected hypersurfaces in projective space? | What is the source or general mechanism behind examples of unexpected varieties (or unexpected hypersurfaces) in projective space? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/45, pp. 2739--2767 |
30,003,980 | OWR-16629-002 | Decomposition of Equiangular Tight Frames | Determine when an equiangular tight frame can be nontrivially decomposed as a disjoint union of equiangular tight frames for their respective spans. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803](https://doi.org/10.4171/owr/2018/46)
##... | 3 | open | null | 2,018 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
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"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
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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 | Duplicate/merged OWR extraction (The official report shows that this overview extraction duplicates the precise equiangular-tight-frame decomposition question retained as OW) | [
"OWR-16629-009"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16629-002",
"literature-status:open",
"owr-year:2018"
] | The workshop proves structural restrictions for decompositions, but no general characterization of nontrivial decompositions is established. | [
{
"url": "https://doi.org/10.4171/owr/2018/46",
"label": "OWR report"
},
{
"url": "https://www.math.colostate.edu/~king/publications/OWR_2018_46.pdf",
"label": "Tight frame decompositions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/46 | null | null | null | null | Determine when an equiangular tight frame can be nontrivially decomposed as a disjoint union of equiangular tight frames for their respective spans. | unrecoverable | The official report shows that this overview extraction duplicates the precise equiangular-tight-frame decomposition question retained as OWR-16629-009. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803 |
30,003,981 | OWR-16629-003 | Generic Recovery from Group Orbits on Subspaces | Given a representation $\rho:G\to\operatorname{GL}(\mathbb F^d)$, characterize the subspaces $S\subseteq\mathbb F^d$ for which the orbit $\{\rho(g)z:g\in G\}$ determines almost every $z\in S$ up to the unavoidable scalar ambiguities. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803](https://doi.org/10.4171/owr/2018/46)
##... | 3 | open | null | 2,018 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16629-003",
"literature-status:open",
"owr-year:2018"
] | The real case is settled, while complex generic sufficiency is known; counterexamples to the four d minus four lower bound and unresolved dimensions show that the general minimum remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/46",
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},
{
"url": "https://www.research.ed.ac.uk/files/58341345/1312.0158.pd.pdf",
"label": "Algebraic phase retrieval"
},
{
"url": "https://arxiv.org/abs/2607.27719",
"label": "Phase retrieval in dimension four"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/46 | null | null | null | Given a representation $\rho:G\to\operatorname{GL}(\mathbb F^d)$, characterize the subspaces $S\subseteq\mathbb F^d$ for which the orbit $\{\rho(g)z:g\in G\}$ determines almost every $z\in S$ up to the unavoidable scalar ambiguities. | Given a representation \rho:G\to GL(\mathbb F^d), characterize the subspaces S\subseteq\mathbb F^d such that the orbit \{\rho(g)z:g\in G\} uniquely determines almost every z\in S modulo trivial scalar ambiguities. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803 |
30,003,982 | OWR-16629-008 | Sharper Paulsen Bounds from Frame Potential Flows | Can the gradient flow of the frame potential prove a Paulsen bound of the form $$\|\Phi-\Psi\|_2^2\leq C\varepsilon d^{2-\alpha}$$ for some $0<\alpha<1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803](https://doi.org/10.4171/owr/2018/46)
##... | 3 | partially_solved | null | 2,018 | 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-16629-008",
"literature-status:partially-solved",
"owr-year:2018"
] | The qualitative Paulsen problem is solved and a deterministic squared-distance bound of order epsilon times d squared is known, but the stronger exponent improvement proposed in the record is not resolved in general. | [
{
"url": "https://doi.org/10.4230/LIPIcs.ITCS.2019.41",
"label": "A Proof of the Paulsen Problem"
},
{
"url": "https://arxiv.org/abs/2605.03867",
"label": "Geometric Perspective on Concentration Phenomena in Frame Theory"
},
{
"url": "https://doi.org/10.4171/owr/2018/46",
"label": "O... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/46 | null | null | null | Can the gradient flow of the frame potential prove a Paulsen bound of the form $$\|\Phi-\Psi\|_2^2\leq C\varepsilon d^{2-\alpha}$$ for some $0<\alpha<1$? | Determine whether an inequality of the form \|\Phi-\Psi\|_2\le C\epsilon^{d^2-\alpha}, with 0\le\alpha<1, follows from the gradient flow of the frame potential. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803 |
30,003,983 | OWR-16629-009 | Decomposition of Equiangular Tight Frames | If $\Phi$ is an equiangular tight frame, when can it be decomposed nontrivially into a disjoint union of equiangular tight frames for their respective spans? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803](https://doi.org/10.4171/owr/2018/46)
##... | 3 | partially_solved | null | 2,018 | 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,
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16629-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16629-009",
"literature-status:partially-solved",
"owr-year:2018"
] | The two-block decomposition is structurally characterized: the spans are either orthogonal or both full, and the equiangular special case is correspondingly restricted; the broader decomposition question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/46",
"label": "Oberwolfach Report 46/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/46 | null | null | null | If $\Phi$ is an equiangular tight frame, when can it be decomposed nontrivially into a disjoint union of equiangular tight frames for their respective spans? | If \Phi is an equiangular tight frame, can it be nontrivially decomposed into a disjoint union of equiangular tight frames for their spans? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803 |
30,003,984 | OWR-16629-010 | Finite-Field Constructions of Complex Equiangular Tight Frames | Can difficult existence problems for complex equiangular tight frames, including the Fickus and Zauner conjectures, be solved over finite fields, and can finite-field solutions be lifted back to the complex setting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803](https://doi.org/10.4171/owr/2018/46)
##... | 3 | partially_solved | null | 2,018 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16629-010",
"literature-status:partially-solved",
"owr-year:2018"
] | Finite-field equiangular-frame theory establishes substantial analogues and proves transfer from a complex equiangular tight frame to infinitely many finite fields, but the reverse transfer and the general existence questions in the record remain unresolved. | [
{
"url": "https://arxiv.org/abs/2012.12977",
"label": "Frames over Finite Fields: Basic Theory"
},
{
"url": "https://arxiv.org/abs/2012.13642",
"label": "Frames over Finite Fields: Orthogonal Geometry"
},
{
"url": "https://doi.org/10.4171/owr/2018/46",
"label": "Oberwolfach Report 46... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/46 | null | null | null | Can difficult existence problems for complex equiangular tight frames, including the Fickus and Zauner conjectures, be solved over finite fields, and can finite-field solutions be lifted back to the complex setting? | Can the difficult existence problems for complex equiangular tight frames, including the Fickus and Zauner conjectures, be solved over finite fields, and can finite-field solutions be transferred back to the complex setting? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/46, pp. 2769--2803 |
30,003,985 | OWR-16630-001 | Orbit Closures and Stationary Measures of Random Walks | For a random walk generated by a probability measure $\mu$ acting on $X$ with semigroup closure $\Gamma$, describe all orbit closures $\Gamma x_0$; determine whether the empirical measures $\nu_n$ converge and identify their limits; prove no escape of mass; describe all $\mu$-stationary measures; and describe the topol... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Rigidity of Stationary Measure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/47, pp. 2805--2858](https://doi.org/10.4171/owr/2018/47)
## Literature review (checked... | 3 | open | null | 2,018 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16630-001",
"literature-status:open",
"owr-year:2018"
] | The report proves orbit-closure, stationary-measure, and empirical-convergence statements in particular homogeneous settings, but the broad five questions in the extracted record have no general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2018/47",
"label": "Oberwolfach Report 47/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/47 | null | null | null | For a random walk generated by a probability measure $\mu$ acting on $X$ with semigroup closure $\Gamma$, describe all orbit closures $\Gamma x_0$; determine whether the empirical measures $\nu_n$ converge and identify their limits; prove no escape of mass; describe all $\mu$-stationary measures; and describe the topol... | For a random walk generated by a probability measure \mu acting on X with semigroup closure \Gamma, describe all orbit closures \Gamma x_0; determine whether the empirical measures \nu_n converge and identify their limits; prove no escape of mass; describe all \mu-stationary measures; and describe the topology of the s... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Rigidity of Stationary Measure (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/47, pp. 2805--2858 |
30,003,986 | OWR-16632-001 | Crystallization under Elastic Interaction Potentials | Can the crystallization and limiting results for the particle system be extended to more general interaction potentials that allow elastic deformations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967](https://doi.org/10.4171/owr/2018/49)
... | 3 | open | null | 2,018 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16632-001",
"literature-status:open",
"owr-year:2018"
] | Extensions from the rigid interaction models to general potentials and elastic deformations are not established in the record or in the cited primary literature; only special cases are available. | [
{
"url": "https://doi.org/10.4171/owr/2018/49",
"label": "Oberwolfach Report 49/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/49 | null | null | null | Can the crystallization and limiting results for the particle system be extended to more general interaction potentials that allow elastic deformations? | Can the crystallization and limiting results for the particle system be extended to more general interaction potentials that allow elastic deformations? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967 |
30,003,987 | OWR-16632-002 | Thermodynamic Fluid–Solid Phase Transitions | Can statistical mechanics prove the existence of a thermodynamic fluid-solid phase transition, for example in the hard-sphere model? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967](https://doi.org/10.4171/owr/2018/49)
... | 3 | open | null | 2,018 | 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-16632-002",
"literature-status:open",
"owr-year:2018"
] | A rigorous positive-temperature fluid-solid phase transition for hard spheres remains a longstanding open problem in statistical mechanics. | [
{
"url": "https://doi.org/10.4171/owr/2018/49",
"label": "Oberwolfach Report 49/2018"
},
{
"url": "https://link.springer.com/article/10.1007/s10955-024-03349-x",
"label": "Hard-Sphere Crystallization Review"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/49 | null | null | null | Can statistical mechanics prove the existence of a thermodynamic fluid-solid phase transition, for example in the hard-sphere model? | Can statistical mechanics prove the existence of a thermodynamic fluid-solid phase transition, for example in the hard-sphere model? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967 |
30,003,988 | OWR-16632-004 | Mean-Field Limits with Finite-Volume Effects | In the presence of finite-volume effects, can one rigorously justify the limiting passage from the microscopic particle system to the macroscopic mean-field system? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967](https://doi.org/10.4171/owr/2018/49)
... | 3 | open | null | 2,018 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16632-004",
"literature-status:open",
"owr-year:2018"
] | The general finite-volume passage from microscopic excluded-volume systems to macroscopic laws remains unresolved; later work treats selected weak, moderate, or strong scaling regimes rather than the full problem. | [
{
"url": "https://doi.org/10.4171/owr/2018/49",
"label": "Oberwolfach Report 49/2018"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4281/OWR_2025_23.pdf?isAllowed=y&sequence=4",
"label": "Macroscopic Limits of Systems with Excluded-Volume Interactions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/49 | null | null | null | In the presence of finite-volume effects, can one rigorously justify the limiting passage from the microscopic particle system to the macroscopic mean-field system? | In the presence of finite-volume effects, can one rigorously justify the limiting passage from the microscopic particle system to the macroscopic mean-field system? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Emergence of Structures in Particle Systems: Mechanics, Analysis and Computation (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/49, pp. 2915--2967 |
30,003,989 | OWR-16633-003 | Proximity and Sparsity of Optimal Integer Solutions | For integer linear optimization, given an optimal solution of the linear-programming relaxation, how close can an optimal integer solution be in the $\ell_1$ or $\ell_\infty$ norm, and for a system of linear equations with nonnegative variables and a linear objective, how sparse can an optimal integer solution be? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16633-003",
"literature-status:partially-solved",
"owr-year:2018"
] | Strong proximity and support-size bounds for integer optima are known, including improved and in some standard formulations optimal bounds, but the broad l1 and l-infinity closeness and sparsity questions in the record are not fully characterized. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
},
{
"url": "https://doi.org/10.1137/17M1162792",
"label": "The Support of Integer Optimal Solutions"
},
{
"url": "https://arxiv.org/abs/2606.13579",
"label": "Optimal Proximity Bound and Product Fu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | For integer linear optimization, given an optimal solution of the linear-programming relaxation, how close can an optimal integer solution be in the $\ell_1$ or $\ell_\infty$ norm, and for a system of linear equations with nonnegative variables and a linear objective, how sparse can an optimal integer solution be? | For integer linear optimization, given an optimal solution of the linear-programming relaxation, how close can an optimal integer solution be in the \ell_1 or \ell_\infty norm, and for a system of linear equations with nonnegative variables and a linear objective, how sparse can an optimal integer solution be? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,990 | OWR-16633-006 | Convergence Rates for Convex-Body Bounds | Let $p_{\min}$ be the minimum of a polynomial $p$ on a convex body $K$, and let $p(r)$ be the degree-$2r$ sum-of-squares-density upper bound obtained from a reference measure on $K$. What is the sharp asymptotic rate of $p(r)-p_{\min}$ for general convex bodies? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16633-006",
"literature-status:open",
"owr-year:2018"
] | Sharp rates are known for several special classes, but the exact convergence rate for the general convex-body setting remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Let $p_{\min}$ be the minimum of a polynomial $p$ on a convex body $K$, and let $p(r)$ be the degree-$2r$ sum-of-squares-density upper bound obtained from a reference measure on $K$. What is the sharp asymptotic rate of $p(r)-p_{\min}$ for general convex bodies? | What is the exact regime governing the rate of convergence of the bounds p(r) for general convex bodies? | corrected_verified | The official report was checked. The reconstruction restores the polynomial minimum and the sum-of-squares-density hierarchy whose convergence rate is open. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,991 | OWR-16633-008 | Topology and Limits in the Asymptotic Spectrum of Graphs | For finite graphs, let $\Delta$ be the compact space of graph parameters $f$ satisfying
$$f(G\sqcup H)=f(G)+f(H),\qquad f(G\boxtimes H)=f(G)f(H),$$
monotonicity under cohomomorphisms, and $f(K_1)=1$. Is $\Delta$ connected? Does some $f\in\Delta$ satisfy $f(C_7)=\Theta(C_7)$? As primes $p\to\infty$, do the Haemers bou... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "open",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **open, with a corrected statement**; the dataset currently labels it open. A. Schrijver (with S. Polak), OWR 50/2018, p. 3005, lists as open: whether Δ is connected; "Find f ∈ Δ with f(C₇) = Θ(C₇)"; whether lim_{p→∞} h∗_{𝔽_p} = h∗_ℚ (printed twice, both times for the frac... | [
"owr",
"oberwolfach-reports",
"OWR-16633-008",
"literature-status:open",
"owr-year:2018"
] | The entry contains several separate questions about connectivity, asymptotic limits, and continuity of theta-type parameters; at least these general questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | For finite graphs, let $\Delta$ be the compact space of graph parameters $f$ satisfying
$$f(G\sqcup H)=f(G)+f(H),\qquad f(G\boxtimes H)=f(G)f(H),$$
monotonicity under cohomomorphisms, and $f(K_1)=1$. Is $\Delta$ connected? Does some $f\in\Delta$ satisfy $f(C_7)=\Theta(C_7)$? As primes $p\to\infty$, do the Haemers bou... | Determine whether \Delta is connected; whether \lim_{p\to\infty}h_{F_p}^*=h_{\mathbb Q}^* and \lim_{p\to\infty}h_{F_p}=h_{\mathbb Q}; and whether the functions k\mapsto\Theta(C_{k,n}) and k\mapsto\vartheta(C_{k,n}) are continuous. | corrected_verified | The official report was checked. The reconstruction defines the asymptotic-spectrum space and circular graphs, restores the omitted problem of attaining the Shannon capacity of the seven-cycle, and retains the stated connectivity, field-limit, and continuity questions. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,992 | OWR-16633-009 | Fast Low-Rank Maximum-Weight Assignment | For the maximum-weight assignment problem on a complete bipartite graph with weight matrix $W\in\mathbb R^{n\times n}$ of rank $r$, can the optimum be computed in time $O(nr^2\log n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16633-009",
"literature-status:open",
"owr-year:2018"
] | The combined entry remains unresolved because the rank-two maximum weighted assignment question and the general linear k-cut integrality-gap question both lack a complete resolution. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | For the maximum-weight assignment problem on a complete bipartite graph with weight matrix $W\in\mathbb R^{n\times n}$ of rank $r$, can the optimum be computed in time $O(nr^2\log n)$? | For the maximum-weight assignment problem on a complete bipartite graph with weight matrix W\in\mathbb R^{n\times n} of rank r, can the optimum be computed in time O(nr^2\log n), in particular improving on the known rank-two case? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,993 | OWR-16633-010 | Integrality Gaps for Directed Linear k-Cut | For directed Linear-$k$-Cut, is the integrality gap of the natural linear-programming relaxation $O(1)$ for every $k$, or is it $\omega(1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16633-010",
"literature-status:open",
"owr-year:2018"
] | For general k, the linear k-cut relaxation has logarithmic upper bounds, but whether its integrality gap is bounded by an absolute constant or grows unboundedly remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
},
{
"url": "https://karthik.ise.illinois.edu/pubs/linear-3-cut.pdf",
"label": "Linear 3-Cut and General Linear k-Cut"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | For directed Linear-$k$-Cut, is the integrality gap of the natural linear-programming relaxation $O(1)$ for every $k$, or is it $\omega(1)$? | For directed Linear-k-Cut, is the integrality gap of the natural LP relaxation O(1) for every k, or is it \omega(1)? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,994 | OWR-16633-011 | The Polynomial Hirsch Conjecture | Is the diameter of the $1$-skeleton of every polyhedron bounded by a polynomial in its number $n$ of facets and its dimension $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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 | Duplicate of canonical problem CS-002 | [
"CS-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-011",
"literature-status:open",
"owr-year:2018"
] | The polynomial Hirsch conjecture remains open; current general diameter bounds are quasi-polynomial rather than polynomial in the number of facets and dimension. | [
{
"url": "https://link.springer.com/article/10.1007/s10107-024-02107-x",
"label": "On Circuit Diameter Bounds via Circuit Imbalances"
},
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Is the diameter of the $1$-skeleton of every polyhedron bounded by a polynomial in its number $n$ of facets and its dimension $d$? | Is the diameter of the 1-skeleton of every polyhedron bounded by a polynomial in its number n of facets and dimension d, as asserted by the polynomial Hirsch conjecture? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,995 | OWR-16633-012 | Average Normal-Cone Width and Random Polytope Diameters | Can a notion of normal cones being wide on average yield useful polyhedral-diameter bounds, including a bound for random Gaussian polytopes $\{x:Ax\leq\mathbf1\}$ when the entries of $A$ are independent standard normal variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16633-012",
"literature-status:open",
"owr-year:2018"
] | The extracted entry only says that an unspecified notion should be derived and omits the mathematical object and conclusion; because the claim is unresolved and unclear, it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Can a notion of normal cones being wide on average yield useful polyhedral-diameter bounds, including a bound for random Gaussian polytopes $\{x:Ax\leq\mathbf1\}$ when the entries of $A$ are independent standard normal variables? | Can one derive a notion of normal cones being wide on average that yields useful diameter bounds, in particular a diameter bound for random Gaussian polytopes of the form Ax\le 1 with independent standard-normal entries in A? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,996 | OWR-16633-013 | Hardness of Root-Dependent Spanning-Tree Optimization | Given an undirected graph $G=(V,E)$ and, for each root $r\in V$, an arc-cost vector $c_r$, prove that it is NP-hard to find a spanning tree $T$ minimizing
$$\sum_{r\in V}c_r(T^r),$$
where $T^r$ is the arborescence rooted at $r$ induced by $T$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | solved | null | 2,018 | 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": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (NP-hard)**. V. Kaibel (OWR 50/2018, pp. 3014–3015) asks whether, and why, integer optimization over Martin's extended formulation of the spanning tree polytope (Problem 1) is NP-hard, in the combinatorial form the record states. We found no published proof; the sh... | [
"owr",
"oberwolfach-reports",
"OWR-16633-013",
"literature-status:open",
"owr-year:2018"
] | No primary source located by the cutoff resolves the exact aggregate rooted-arborescence cost problem stated in the record; related hardness results do not establish this precise claim. | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Given an undirected graph $G=(V,E)$ and, for each root $r\in V$, an arc-cost vector $c_r$, prove that it is NP-hard to find a spanning tree $T$ minimizing
$$\sum_{r\in V}c_r(T^r),$$
where $T^r$ is the arborescence rooted at $r$ induced by $T$. | Why is the following optimization problem NP-hard: given an undirected graph G=(V,E) and a cost vector c_r for each root r, find a spanning tree T minimizing the sum over r\in V of c_r(T^r), where T^r is the arborescence rooted at r induced by T? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,997 | OWR-16633-014 | Hardness of Path-Cost Arborescence Optimization | Given a directed graph $D=(V,A)$, a root $r\in V$, and a cost vector $c^v$ for every $v\neq r$, prove that it is NP-hard to find an arborescence $T$ minimizing
$$\sum_{v\in V\setminus\{r\}}c^v(P^v),$$
where $P^v$ is the path from $r$ to $v$ in $T$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | solved | null | 2,018 | 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... | [
"OWR-16633-015"
] | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (NP-hard)**. This is Problem 2 of the same abstract, for Wong's formulation. | [
"owr",
"oberwolfach-reports",
"OWR-16633-014",
"literature-status:open",
"owr-year:2018"
] | The 2018 problem asks whether the root-dependent cost optimization over spanning trees is NP-hard; the current literature search found no proof of hardness or polynomial algorithm for this exact formulation. | [
{
"url": "https://ems.press/content/serial-article-files/46772",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Given a directed graph $D=(V,A)$, a root $r\in V$, and a cost vector $c^v$ for every $v\neq r$, prove that it is NP-hard to find an arborescence $T$ minimizing
$$\sum_{v\in V\setminus\{r\}}c^v(P^v),$$
where $P^v$ is the path from $r$ to $v$ in $T$. | Why is the following optimization problem NP-hard: given a directed graph D=(V,A), a root r, and a cost vector c^v for each v\ne r, find an arborescence T minimizing the sum over v\ne r of c^v(P^v), where P^v is the r-to-v path in T? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,998 | OWR-16633-015 | Duplicate Path-Cost Arborescence Problem | Why is the following optimization problem NP-hard: given a directed graph D=(V,A), a root r, and a cost vector c^v for each v\ne r, find an arborescence T minimizing the sum over v\ne r of c^v(P^v), where P^v is the r-to-v path in T? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | solved | null | 2,018 | 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 | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | Duplicate/merged OWR extraction (The official problem session contains one path-cost arborescence hardness problem, represented canonically by OWR-16633-014. This extraction) | [
"OWR-16633-014"
] | null | [Discussion #4 literature review, 2026-09-29] **solved (NP-hard)**. This is Problem 2 of the same abstract, for Wong's formulation. | [
"owr",
"oberwolfach-reports",
"OWR-16633-015",
"literature-status:open",
"owr-year:2018"
] | The exact path-cost arborescence problem, motivated by Wong's spanning-tree formulation, remains posed as an unresolved complexity question; no exact hardness proof or polynomial algorithm was located. | [
{
"url": "https://ems.press/content/serial-article-files/46772",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | null | Why is the following optimization problem NP-hard: given a directed graph D=(V,A), a root r, and a cost vector c^v for each v\ne r, find an arborescence T minimizing the sum over v\ne r of c^v(P^v), where P^v is the r-to-v path in T? | unrecoverable | The official problem session contains one path-cost arborescence hardness problem, represented canonically by OWR-16633-014. This extraction repeats it verbatim. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,003,999 | OWR-16633-016 | Polynomial-Time Comparison of Sparse Algebraic Power Sums | Given integers $r_1,\ldots,r_n$, is there an algorithm polynomial in
$$\sum_{i=1}^n\log(\lvert r_i\rvert+1)$$
that decides whether $\sum_{i=1}^n2^{r_i/3}>1$? More generally, for fixed $\alpha\in\mathbb Q$ and input coefficients $\beta_i\in\mathbb Q$, decide whether $\sum_i\beta_i\alpha^{r_i}>0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16633-016",
"literature-status:open",
"owr-year:2018"
] | The succinct-input sign problem for sums of powers of the cube root of two is still presented as an open algorithmic question; the search found no demonstrated polynomial-time decision procedure or hardness classification for this exact form. | [
{
"url": "https://ems.press/content/serial-article-files/46772",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Given integers $r_1,\ldots,r_n$, is there an algorithm polynomial in
$$\sum_{i=1}^n\log(\lvert r_i\rvert+1)$$
that decides whether $\sum_{i=1}^n2^{r_i/3}>1$? More generally, for fixed $\alpha\in\mathbb Q$ and input coefficients $\beta_i\in\mathbb Q$, decide whether $\sum_i\beta_i\alpha^{r_i}>0$. | Given integers r_1,\ldots,r_n, is there a polynomial-time algorithm in the input size O(\sum_i\log(|r_i|+1)) to decide whether \sum_{i=1}^n 2^{r_i/3}>1? More generally, for fixed rational \alpha and input rationals \beta_i, determine whether \sum_i\beta_i\alpha^{r_i}>0. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,000 | OWR-16633-017 | Degree-Utility Optimization in Graphs | Given $n,m$ and univariate functions $f_1,\ldots,f_n$, what is the complexity of finding an $m$-edge graph on $[n]$ that maximizes
$$\sum_{i=1}^nf_i(d_i),$$
where $d_i$ is the degree of vertex $i$ and the functions need not be identical? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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... | [
"OWR-16633-018"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-017",
"literature-status:partially-solved",
"owr-year:2018"
] | Later work proves polynomial algorithms for several graph/function regimes and NP-hardness for others, while explicitly leaving the general arbitrary-function problem, especially on complete graphs, open. | [
{
"url": "https://arxiv.org/abs/1908.09278",
"label": "Optimization over Degree Sequences of Graphs"
},
{
"url": "https://arxiv.org/abs/1706.03951",
"label": "Optimization over Degree Sequences"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Given $n,m$ and univariate functions $f_1,\ldots,f_n$, what is the complexity of finding an $m$-edge graph on $[n]$ that maximizes
$$\sum_{i=1}^nf_i(d_i),$$
where $d_i$ is the degree of vertex $i$ and the functions need not be identical? | Given k,n,m and univariate functions f_1,\ldots,f_n, find an k-uniform hypergraph on [n] with m edges maximizing \sum_{i=1}^n f_i(d_i), where d_i is the degree of vertex i. What is the complexity for graphs (k=2) when the functions are not necessarily identical? | corrected_verified | The official report was checked. The source uses uniform hypergraphs as setup but asks the unresolved complexity question specifically for graphs with nonidentical vertex functions. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,001 | OWR-16633-018 | Duplicate Degree-Utility Graph Optimization Problem | For graphs, given n,m and vertex functions f_1,\ldots,f_n, what is the complexity of finding an m-edge graph maximizing \sum_{i=1}^n f_i(d_i) when the functions are not necessarily identical? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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 | Duplicate/merged OWR extraction (This record repeats the graph-complexity question represented canonically and with its objective by OWR-16633-017. No separate clean stateme) | [
"OWR-16633-017"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-018",
"literature-status:partially-solved",
"owr-year:2018"
] | The extracted question is the non-identical-functions graph case; subsequent results settle important convex, monotonic, and restricted-graph cases and prove hardness in mixed-curvature cases, but retain broad unresolved cases. | [
{
"url": "https://arxiv.org/abs/1908.09278",
"label": "Optimization over Degree Sequences of Graphs"
},
{
"url": "https://arxiv.org/abs/1706.03951",
"label": "Optimization over Degree Sequences"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | null | For graphs, given n,m and vertex functions f_1,\ldots,f_n, what is the complexity of finding an m-edge graph maximizing \sum_{i=1}^n f_i(d_i) when the functions are not necessarily identical? | unrecoverable | This record repeats the graph-complexity question represented canonically and with its objective by OWR-16633-017. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,002 | OWR-16633-020 | Rainbow Paths in Properly Edge-Colored Regular Graphs | Does every simple $k$-regular graph with a proper $k$-edge-coloring contain a rainbow path of length $k-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-020",
"literature-status:partially-solved",
"owr-year:2018"
] | The conjecture is proved for bounded degree and asymptotically in full generality: every properly edge-coloured d-regular graph has a rainbow path of length (1-o(1))d; the exact d-1 assertion remains unresolved. | [
{
"url": "https://arxiv.org/abs/2503.01825",
"label": "Towards Graham's Rearrangement Conjecture via Rainbow Paths"
},
{
"url": "https://homepages.cwi.nl/~lex/files/rainbowpath.pdf",
"label": "Rainbow Paths in Edge-Coloured Regular Graphs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Does every simple $k$-regular graph with a proper $k$-edge-coloring contain a rainbow path of length $k-1$? | Conjecture: every simple k-regular properly k-edge-coloured graph has a rainbow path of length k-1, where all path edges have distinct colours. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,003 | OWR-16633-021 | Clique-Sequence Rank and Generic Rigidity Matroids | For $F\subseteq E(K_n)$, define
$$r_t(F)=\min_{(C_1,\ldots,C_k)}\left(\left\lvert F\cup\bigcup_{i=1}^kC_i\right\rvert-k\right),$$
where the minimum ranges over proper $K_t$-sequences in $K_n$. Is $r_t$ submodular, so that $(E(K_n),r_t)$ is a matroid? In particular, is $(E(K_n),r_5)$ the generic $3$-rigidity matroid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16633-022"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-021",
"literature-status:partially-solved",
"owr-year:2018"
] | The longest K_t-sequence problem and matroid conjecture are settled for t=3 and t=4, with substantial 3-rigidity/cofactor progress, but the general conjecture and the highlighted t=5 case are not settled. | [
{
"url": "https://ems.press/content/serial-article-files/46772",
"label": "Oberwolfach Report 50/2018"
},
{
"url": "https://arxiv.org/abs/1911.00207",
"label": "Abstract 3-Rigidity and Bivariate C2-1-Splines II"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | For $F\subseteq E(K_n)$, define
$$r_t(F)=\min_{(C_1,\ldots,C_k)}\left(\left\lvert F\cup\bigcup_{i=1}^kC_i\right\rvert-k\right),$$
where the minimum ranges over proper $K_t$-sequences in $K_n$. Is $r_t$ submodular, so that $(E(K_n),r_t)$ is a matroid? In particular, is $(E(K_n),r_5)$ the generic $3$-rigidity matroid? | For a proper K_t-sequence (C_1,\ldots,C_k) in K_n, define r_t(F)=\min\{\lvert F\cup\bigcup_i C_i\rvert-k\}. Conjecture: r_t is submodular and (E(K_n),r_t) is a matroid; in particular, (E(K_n),r_5) is conjectured to be the generic 3-rigidity matroid. | corrected_verified | The official problem session was checked. The definition of the longest-clique-sequence rank and both conjectural conclusions were restored. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,004 | OWR-16633-022 | Duplicate Clique-Sequence Submodularity Conjecture | For the longest K_t-sequence rank function r_t on E(K_n), is r_t submodular, so that (E(K_n),r_t) forms a matroid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (This extraction repeats the submodularity clause represented canonically and more completely by OWR-16633-021. No separate clean statement i) | [
"OWR-16633-021"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-022",
"literature-status:partially-solved",
"owr-year:2018"
] | Duplicate extraction; the canonical question is OWR-16633-021. This extraction repeats the submodularity clause represented canonically and more completely by OWR-16633-021. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance.
**What remains.** Consult the ... | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | null | For the longest K_t-sequence rank function r_t on E(K_n), is r_t submodular, so that (E(K_n),r_t) forms a matroid? | unrecoverable | This extraction repeats the submodularity clause represented canonically and more completely by OWR-16633-021. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,005 | OWR-16633-023 | Fast Submodular Minimization for Represented Matroid Ranks | Let $r$ be the rank function of a matroid on ground set $V$, supplied by an explicit linear representation over a field, and let $z:V\to\mathbb R$. Can
$$\min_{S\subseteq V}\bigl(r(S)-z(S)\bigr)$$
be computed more efficiently by exploiting the representation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-16633-024"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-023",
"literature-status:partially-solved",
"owr-year:2018"
] | The special objective is covered by strongly polynomial submodular-minimization algorithms, with later work improving the general SFM bounds; a representation-specific improvement beyond those algorithms remains unresolved. | [
{
"url": "https://arxiv.org/abs/2304.03426",
"label": "Convex Minimization with Integer Minima in O-tilde(n4) Time"
},
{
"url": "https://ems.press/content/serial-article-files/46772",
"label": "Oberwolfach Report 50/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Let $r$ be the rank function of a matroid on ground set $V$, supplied by an explicit linear representation over a field, and let $z:V\to\mathbb R$. Can
$$\min_{S\subseteq V}\bigl(r(S)-z(S)\bigr)$$
be computed more efficiently by exploiting the representation? | Let r be the rank function of a linearly represented matroid on V and let z:V\to\mathbb R. Can the problem \min_{S\subseteq V}(r(S)-z(S)) be solved more efficiently by using the linear representation? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,006 | OWR-16633-024 | Duplicate Represented-Matroid Minimization Problem | Given an explicit linear representation of a matroid rank function r on V and z:V\to\mathbb R, is there a more efficient algorithm for computing \min_{S\subseteq V}(r(S)-z(S))? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | Duplicate/merged OWR extraction (This record repeats the represented-matroid submodular-minimization problem represented canonically by OWR-16633-023. No separate clean stat) | [
"OWR-16633-023"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-024",
"literature-status:open",
"owr-year:2018"
] | Duplicate extraction; the canonical question is OWR-16633-023. This record repeats the represented-matroid submodular-minimization problem represented canonically by OWR-16633-023. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance.
**What remains.** Consu... | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | null | Given an explicit linear representation of a matroid rank function r on V and z:V\to\mathbb R, is there a more efficient algorithm for computing \min_{S\subseteq V}(r(S)-z(S))? | unrecoverable | This record repeats the represented-matroid submodular-minimization problem represented canonically by OWR-16633-023. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,007 | OWR-16633-025 | Decomposition of Representable Polymatroids into Matroid Ranks | Let $f$ be a polymatroid function on a ground set $V$ that is linearly representable over a field $F$: there are subspaces $T_v$ such that
$$f(S)=\operatorname{rk}\!\left(\bigcup_{v\in S}T_v\right).$$
Is $f$ always a nonnegative linear combination of linear-matroid rank functions over $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-025",
"literature-status:open",
"owr-year:2018"
] | An elementary counterexample works over every field: take $T_0=F^2$, $T_1=\langle e_1\rangle$, $T_2=\langle e_2\rangle$, $T_3=\langle e_1+e_2\rangle$. Its rank sum cannot be a nonnegative combination of any matroid ranks. Equality in $f(0i)\ge f(0)$ and $f(ij)\le f(i)+f(j)$ forces each positive summand to have 1,2,3 in... | [
{
"url": "https://doi.org/10.4171/owr/2018/50",
"label": "Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023"
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedMath discussion #4 — Alper Ferudun, status... | 2026-09-28T00:00:00 | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023: https://doi.org/10.4171/owr/2018/50 | https://doi.org/10.4171/owr/2018/50 | null | null | null | Let $f$ be a polymatroid function on a ground set $V$ that is linearly representable over a field $F$: there are subspaces $T_v$ such that
$$f(S)=\operatorname{rk}\!\left(\bigcup_{v\in S}T_v\right).$$
Is $f$ always a nonnegative linear combination of linear-matroid rank functions over $F$? | If a polymatroid function f(S)=\operatorname{rk}(\bigcup_{v\in S}T_v) is linearly representable over a field F, is f always a nonnegative linear combination of linear matroid rank functions over F? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,008 | OWR-16633-026 | Rainbow Arborescences Across Arc Partitions | Let a directed graph $G=(V,A)$ with $\lvert V\rvert=k+1$ have its arc set partitioned into $k$ arborescences $F_1,\ldots,F_k$, each having $k$ arcs. Must there be an arborescence $F^*\subseteq A$ such that $\lvert F^*\cap F_i\rvert=1$ for every $i$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023](https://doi.org/10.4171/owr/2018/50)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16633-026",
"literature-status:partially-solved",
"owr-year:2018"
] | The rainbow-arborescence existence conjecture remains open, but fixed-root existence testing is NP-complete and the conjecture is proved for several cases, including cyclic underlying graphs and common roots. | [
{
"url": "https://arxiv.org/abs/2412.15457",
"label": "Rainbow Arborescence Conjecture"
},
{
"url": "https://arxiv.org/abs/2511.04953",
"label": "The Rainbow Arborescence Problem on Cycles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/50 | null | null | null | Let a directed graph $G=(V,A)$ with $\lvert V\rvert=k+1$ have its arc set partitioned into $k$ arborescences $F_1,\ldots,F_k$, each having $k$ arcs. Must there be an arborescence $F^*\subseteq A$ such that $\lvert F^*\cap F_i\rvert=1$ for every $i$? | Let a directed graph on k+1 vertices have its arcs partitioned into k arborescences F_1,\ldots,F_k, each with k arcs. Must there always be an arborescence F^*\subseteq A such that |F^*\cap F_i|=1 for every i? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Combinatorial Optimization (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/50, pp. 2969--3023 |
30,004,009 | OWR-16634-002 | Real Tau Conjecture for Depth-Four Circuits | Is the number of distinct real zeros of every univariate real polynomial represented by a depth-four arithmetic circuit, consisting of a sum of products of sparse polynomials, bounded by a polynomial in the circuit size? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,018 | 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-16634-002",
"literature-status:partially-solved",
"owr-year:2018"
] | The average-case Real Tau Conjecture and a deterministic PTAS for bounded-degree algebraic rank are established results, but the unrestricted Real Tau Conjecture and the broader exact rank problem are not thereby resolved. | [
{
"url": "https://arxiv.org/abs/1806.00417",
"label": "The Real Tau-Conjecture Is True on Average"
},
{
"url": "https://ems.press/content/serial-article-files/46773",
"label": "Oberwolfach Report 51/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | Is the number of distinct real zeros of every univariate real polynomial represented by a depth-four arithmetic circuit, consisting of a sum of products of sparse polynomials, bounded by a polynomial in the circuit size? | The Real Tau Conjecture claims that the number of real zeros of a univariate real polynomial represented by a depth-four circuit (a sum of products of sparse polynomials) is polynomially bounded in the circuit size; the report records an average-case result for independent standard-Gaussian coefficients. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,010 | OWR-16634-003 | Karchmer–Raz–Wigderson Composition Conjecture | For nonconstant Boolean functions $f$ and $g$, is the circuit-depth complexity of their composition equal, up to lower-order terms, to the sum of their individual depth complexities? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,018 | 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-16634-003",
"literature-status:partially-solved",
"owr-year:2018"
] | Explicit lossless dimension expanders have advanced, and the KRW program has proved important restricted and related composition theorems, but the KRW Conjecture itself remains open. | [
{
"url": "https://eccc.weizmann.ac.il/report/2024/086/download",
"label": "ECCC Report 2024/086"
},
{
"url": "https://doi.org/10.1137/23M158615X",
"label": "Toward Better Depth Lower Bounds: A KRW-like Theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | For nonconstant Boolean functions $f$ and $g$, is the circuit-depth complexity of their composition equal, up to lower-order terms, to the sum of their individual depth complexities? | KRW Conjecture: for two nonconstant Boolean functions, the depth complexity of their composition is approximately the sum of their individual depth complexities. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,011 | OWR-16634-004 | Defining High-Dimensional Expanders Through Local Spectra | What is a high-dimensional expander; in particular, which local or spectral expansion conditions on the links of a bounded-dimensional simplicial complex should define this notion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,018 | 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 uses this sentence as an expository heading, immediately supplies a local-spectral definition, and lists different concr) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16634-004",
"literature-status:open",
"owr-year:2018"
] | This is an underspecified extracted question rather than a single formal conjecture; high-dimensional expansion has multiple competing definitions and no uniquely stated claim here is settled by the cited passage. | [
{
"url": "https://ems.press/content/serial-article-files/46773",
"label": "Oberwolfach Report 51/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | null | What is a high-dimensional expander; in particular, which local or spectral expansion conditions on the links of a bounded-dimensional simplicial complex should define this notion? | unrecoverable | The official report uses this sentence as an expository heading, immediately supplies a local-spectral definition, and lists different concrete research directions afterward; it is not a distinct unresolved claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,012 | OWR-16634-005 | Explicit Equations Separating Matrix Multiplication from Low-Rank Tensors | Given the variety of tensors of border rank at most r, how can one find explicit polynomials in its ideal that vanish on all such tensors but do not vanish on the matrix-multiplication tensor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,018 | 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 poses this as a rhetorical transition and immediately answers it by introducing representation-theoretic methods for fin) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16634-005",
"literature-status:open",
"owr-year:2018"
] | The extracted sentence is a context fragment asking how to construct polynomials in a matrix-multiplication/tensor setting; it gives no precise formal claim, and the corresponding construction problem remains unresolved in this record. | [
{
"url": "https://ems.press/content/serial-article-files/46773",
"label": "Oberwolfach Report 51/2018"
},
{
"url": "https://doi.org/10.1137/1.9781611978322.63",
"label": "More Asymmetry Yields Faster Matrix Multiplication"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | null | Given the variety of tensors of border rank at most r, how can one find explicit polynomials in its ideal that vanish on all such tensors but do not vanish on the matrix-multiplication tensor? | unrecoverable | The official report poses this as a rhetorical transition and immediately answers it by introducing representation-theoretic methods for finding equations in the border-rank ideal. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,013 | OWR-16634-006 | $d$-to-$1$ Games Conjecture | For every integer $d\geq2$ and every $s>0$, does there exist an alphabet size $k$ such that it is NP-hard to distinguish satisfiable $d$-to-$1$ Label-Cover instances from instances of value at most $s$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,018 | 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-16634-006",
"literature-status:partially-solved",
"owr-year:2018"
] | The d-to-1 program has major proved special and imperfect-completeness variants, but the general d-to-1 Games Conjecture in the extracted form is not fully proved; a 2025 route remains conditional on an additional hypothesis. | [
{
"url": "https://doi.org/10.4086/toc.2025.v021a011",
"label": "Towards a Proof of the 2-to-1 Games Conjecture"
},
{
"url": "https://eccc.weizmann.ac.il/report/2019/141/download",
"label": "ECCC Report 2019/141"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | For every integer $d\geq2$ and every $s>0$, does there exist an alphabet size $k$ such that it is NP-hard to distinguish satisfiable $d$-to-$1$ Label-Cover instances from instances of value at most $s$? | For every d\ge2 and s>0, does there exist an alphabet size k such that distinguishing satisfiable d-to-1 Label-Cover instances from instances of value at most s is NP-hard? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,014 | OWR-16634-007 | Unique Games Conjecture | For every $\varepsilon>0$, does there exist an alphabet size $k$ such that it is NP-hard to distinguish Unique-Games instances of value at least $1-\varepsilon$ from instances of value at most $\varepsilon$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,018 | 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 | Duplicate of canonical problem CS-001 | [
"CS-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16634-007",
"literature-status:open",
"owr-year:2018"
] | The Unique-Games Conjecture remains unresolved; current work proves related 2-to-2 results and conditional or restricted variants but not the conjecture itself. | [
{
"url": "https://toc.cs.uchicago.edu/articles/v021a011/v021a011.pdf",
"label": "Theory of Computing 2025 survey discussion"
},
{
"url": "https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.76",
"label": "A Quantum Unique Games Conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | For every $\varepsilon>0$, does there exist an alphabet size $k$ such that it is NP-hard to distinguish Unique-Games instances of value at least $1-\varepsilon$ from instances of value at most $\varepsilon$? | For every \varepsilon>0, does there exist an alphabet size k such that distinguishing Unique-Games instances of value at least 1-\varepsilon from those of value at most \varepsilon is NP-hard? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
30,004,015 | OWR-16634-008 | Subquadratic Approximation for Longest Common Subsequences | Does there exist, for some $\varepsilon>0$, a $1.1$-approximation algorithm for the longest common subsequence of two length-$n$ strings that runs in time $O(n^{2-\varepsilon})$ for every alphabet size? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080](https://doi.org/10.4171/owr/2018/51)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,018 | 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-16634-008",
"literature-status:partially-solved",
"owr-year:2018"
] | The exact 1.1-approximation in truly subquadratic time remains open, while later work gives substantially improved subquadratic approximation algorithms and conditional quadratic-time barriers. | [
{
"url": "https://ieee-focs.org/FOCS-2017-Papers/3464a025.pdf",
"label": "New Frameworks for Hardness of Approximation"
},
{
"url": "https://epubs.siam.org/doi/10.1137/20M1316500",
"label": "Approximation Algorithms for LCS and LIS"
},
{
"url": "https://arxiv.org/abs/2105.03028",
"la... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/51 | null | null | null | Does there exist, for some $\varepsilon>0$, a $1.1$-approximation algorithm for the longest common subsequence of two length-$n$ strings that runs in time $O(n^{2-\varepsilon})$ for every alphabet size? | Is there a 1.1-approximation algorithm for the longest common subsequence of two strings running in time O(n^{2-\varepsilon}) for some \varepsilon>0, for every alphabet size? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Complexity Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/51, pp. 3025--3080 |
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