id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,616 | OWR-13102-002 | Generalized Kato Classes at Vanishing Artin-Twisted L-Values | For an elliptic curve $E$ over $\mathbb{Q}$ and an Artin representation $\rho$, assuming $L(E,\rho,1)=0$, does the generalized Kato class lie in $E(H)_\rho\otimes\mathbb{Q}_p$ and become trivial when the equivariant analytic rank is greater than $2$, with the rank-$2$ class given by the proposed $p$-adic-period formula... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800](https://doi.org/10.4171/owr/2014/32)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13102-002",
"literature-status:open",
"owr-year:2014"
] | The record truncates a Darmon--Rotger conjecture on generalized Kato classes for rank two elliptic curves and vanishing beyond rank two; the primary paper formulates the expected relation but gives no general proof. | [
{
"url": "https://doi.org/10.1186/s40687-016-0074-9",
"label": "Darmon--Rotger, elliptic curves and generalized Kato classes"
},
{
"url": "https://doi.org/10.4171/owr/2014/32",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/32 | null | null | null | For an elliptic curve $E$ over $\mathbb{Q}$ and an Artin representation $\rho$, assuming $L(E,\rho,1)=0$, does the generalized Kato class lie in $E(H)_\rho\otimes\mathbb{Q}_p$ and become trivial when the equivariant analytic rank is greater than $2$, with the rank-$2$ class given by the proposed $p$-adic-period formula... | For an elliptic curve E over \mathbb{Q} and an Artin representation \rho, assuming L(E,\rho,1)=0, does the generalized Kato class lie in E(H)_\rho\otimes\mathbb{Q}_p and become trivial when the equivariant analytic rank is greater than 2, with the rank-2 class given by the proposed p-adic-period formula? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800 |
30,002,617 | OWR-13102-005 | Canonical Plectic Lifts of Shimura-Variety Cohomology | Does the étale cohomology complex of a Shimura variety admit a canonical plectic lift with the indicated $\operatorname{Aut}(F\otimes\overline{\mathbb{Q}}/F)[\mu]$-action, compatible with products and the action of $G(\mathbb{Q})$, so that plectic $\ell$-adic étale cohomology can be defined by taking the corresponding ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800](https://doi.org/10.4171/owr/2014/32)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13102-005",
"literature-status:partially-solved",
"owr-year:2014"
] | The canonical plectic lift is proved in important special cases, including degree two under mild assumptions and global function fields, while the general number field conjecture remains unresolved. | [
{
"url": "https://arxiv.org/abs/2211.12078",
"label": "Loeffler--Zerbes, plectic structures"
},
{
"url": "https://arxiv.org/abs/2106.05382",
"label": "Li--Huerta, function field plectic conjecture"
},
{
"url": "https://webusers.imj-prg.fr/~jan.nekovar/pu/introplec.pdf",
"label": "Nek... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/32 | null | null | null | Does the étale cohomology complex of a Shimura variety admit a canonical plectic lift with the indicated $\operatorname{Aut}(F\otimes\overline{\mathbb{Q}}/F)[\mu]$-action, compatible with products and the action of $G(\mathbb{Q})$, so that plectic $\ell$-adic étale cohomology can be defined by taking the corresponding ... | Does the etale cohomology complex of a Shimura variety admit a canonical plectic lift with the indicated \operatorname{Aut}(F\otimes\overline{\mathbb{Q}}/F)[\mu]-action, compatible with products and the action of G(\mathbb{Q}), so that plectic l-adic etale cohomology can be defined by taking the corresponding group coh... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800 |
30,002,618 | OWR-13102-007 | Monodromy Exactness for Isocrystals on Semistable Curves | For an $F$-convergent isocrystal $E$ on a semistable curve, for which coefficient objects is the sequence $H^1_{\mathrm{rig}}(X_k,E)\to H^1_{\mathrm{log-cris}}(X_k,E)\xrightarrow{N_E}H^1_{\mathrm{log-cris}}(X_k,E)$ exact? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800](https://doi.org/10.4171/owr/2014/32)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13102-007",
"literature-status:open",
"owr-year:2014"
] | Non-exactness is known for general coefficients, but a classification of the coefficient systems for which the sequence is exact, especially those arising geometrically, remains open. | [
{
"url": "https://doi.org/10.1515/crelle-2013-0117",
"label": "Chiarellotto--Coleman--Di Proietto--Iovita, p-adic invariant cycles"
},
{
"url": "https://doi.org/10.4171/owr/2014/32",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/32 | null | null | null | For an $F$-convergent isocrystal $E$ on a semistable curve, for which coefficient objects is the sequence $H^1_{\mathrm{rig}}(X_k,E)\to H^1_{\mathrm{log-cris}}(X_k,E)\xrightarrow{N_E}H^1_{\mathrm{log-cris}}(X_k,E)$ exact? | For an F-convergent isocrystal E on a semistable curve, for which coefficient objects is the sequence H^1_{\mathrm{rig}}(X_k,E)\to H^1_{\mathrm{log-cris}}(X_k,E)\xrightarrow{N_E}H^1_{\mathrm{log-cris}}(X_k,E) exact? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Algebraische Zahlentheorie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/32, pp. 1747--1800 |
30,002,619 | OWR-13103-001 | Involutivity Obstructions for Normal Currents | Let $X(x,y,z)=(1,0,-x/2)$ and $Y(x,y,z)=(0,1,y/2)$ be the horizontal vector fields on the Heisenberg group $\mathbb H^1\cong\mathbb R^3$, and put $\xi=X\wedge Y$. If $T=\xi\wedge\mu$ is a normal $2$-current in $\mathbb R^3$, must $\mu$ be absolutely continuous with respect to Lebesgue measure? More generally, can norma... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860](https://doi.org/10.4171/owr/2014/33)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] keep **partially_solved**, but **statement fix: X = (1,0,−y/2), Y = (0,1,x/2)**. The source (p. 1808) and the record print X = (1,0,−x/2), Y = (0,1,y/2) as the Heisenberg horizontal fields, but these commute; the corrected ones have [X,Y] = ∂_z (our check). | [
"owr",
"oberwolfach-reports",
"OWR-13103-001",
"literature-status:partially-solved",
"owr-year:2014"
] | Later work proves substantial absolute-continuity and structure results for normal currents tangent to smooth distributions, but the weaker-regularity and weaker-involutivity variants explicitly remain unresolved. | [
{
"url": "https://doi.org/10.4310/jdg/1668186786",
"label": "Alberti--Massaccesi--Stepanov, currents tangent to distributions"
},
{
"url": "https://doi.org/10.4171/owr/2014/33",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/33 | null | null | null | Let $X(x,y,z)=(1,0,-x/2)$ and $Y(x,y,z)=(0,1,y/2)$ be the horizontal vector fields on the Heisenberg group $\mathbb H^1\cong\mathbb R^3$, and put $\xi=X\wedge Y$. If $T=\xi\wedge\mu$ is a normal $2$-current in $\mathbb R^3$, must $\mu$ be absolutely continuous with respect to Lebesgue measure? More generally, can norma... | Can all normal k-currents that fail the integral-current involutivity conclusion be reduced to a specified class; in particular, for the horizontal non-involutive field \xi=X\wedge Y on the Heisenberg group \mathbb{R}^3 and T=\xi\wedge\mu\in N_2(\mathbb{R}^3), must \mu be absolutely continuous with respect to Lebesgue ... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860 |
30,002,620 | OWR-13103-002 | Mass-Preserving Decomposition of Normal Currents | Given a normal $k$-current $T\in N_k(\mathbb{R}^d)$, does there exist a measure space $(L,\lambda)$ and integral currents $R_\lambda$ such that $T=\int_L R_\lambda\,d\lambda$, $M(T)=\int_L M(R_\lambda)\,d\lambda$, and $M(\partial T)=\int_L M(\partial R_\lambda)\,d\lambda$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860](https://doi.org/10.4171/owr/2014/33)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no; answered in the source)**. A. Massaccesi (OWR 33/2014, p. 1808) states F. Morgan's question (Problem 3.8, 1984 AMS Summer Institute), whether normal currents decompose into integral ones with additive mass and boundary mass, and answers no: for a non-involutiv... | [
"owr",
"oberwolfach-reports",
"OWR-13103-002",
"literature-status:partially-solved",
"owr-year:2014"
] | The specific horizontal absolute-continuity question is answered positively by a later tangent-current theorem, while Morgan's broader normal-current decomposition and stronger distribution questions are not fully resolved. | [
{
"url": "https://doi.org/10.4310/jdg/1668186786",
"label": "Alberti--Massaccesi--Stepanov, currents tangent to distributions"
},
{
"url": "https://doi.org/10.4171/owr/2014/33",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/33 | null | null | null | Given a normal $k$-current $T\in N_k(\mathbb{R}^d)$, does there exist a measure space $(L,\lambda)$ and integral currents $R_\lambda$ such that $T=\int_L R_\lambda\,d\lambda$, $M(T)=\int_L M(R_\lambda)\,d\lambda$, and $M(\partial T)=\int_L M(\partial R_\lambda)\,d\lambda$? | Given a normal k-current T\in N_k(\mathbb{R}^d), does there exist a measure space (L,\lambda) and integral currents R_\lambda such that T=\int_L R_\lambda d\lambda, M(T)=\int_L M(R_\lambda) d\lambda, and M(\partial T)=\int_L M(\partial R_\lambda) d\lambda? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860 |
30,002,621 | OWR-13103-003 | Stable Minimal Hypersurfaces and Entire Minimal Graphs | Are there complete stable minimal hypersurfaces in asymptotically flat manifolds, and are affine functions the only entire minimal graphs over $\mathbb{R}^{n-1}$ in $\mathbb{R}^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860](https://doi.org/10.4171/owr/2014/33)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,014 | 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-13103-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The Bernstein graph problem is settled through ambient dimension eight and disproved from dimension nine onward, while the existence and rigidity questions for stable minimal hypersurfaces in general asymptotically flat manifolds remain only partially understood. | [
{
"url": "https://eudml.org/doc/141966",
"label": "Bombieri--De Giorgi--Giusti, minimal cones and Bernstein problem"
},
{
"url": "https://doi.org/10.1007/s00526-016-0989-4",
"label": "Carlotto, stable minimal hypersurfaces"
},
{
"url": "https://doi.org/10.4171/owr/2014/33",
"label": ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/33 | null | null | null | Are there complete stable minimal hypersurfaces in asymptotically flat manifolds, and are affine functions the only entire minimal graphs over $\mathbb{R}^{n-1}$ in $\mathbb{R}^n$? | Are there complete stable minimal hypersurfaces in asymptotically flat manifolds, and are affine functions the only entire minimal graphs over \mathbb{R}^{n-1} in \mathbb{R}^n? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860 |
30,002,622 | OWR-13103-004 | Calibrations for Unoriented Minimum Matching | How much of the calibration and filling-minimization procedure survives for the unoriented minimum-matching problem after discarding the linear duality between currents and differential forms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860](https://doi.org/10.4171/owr/2014/33)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,014 | 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-13103-004",
"literature-status:open",
"owr-year:2014"
] | The extracted record is a vague fragment about how much of a matching procedure survives after discarding structure; no uniquely identifiable proposition or resolution can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2014/33",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/33 | null | null | null | How much of the calibration and filling-minimization procedure survives for the unoriented minimum-matching problem after discarding the linear duality between currents and differential forms? | How much of the calibration and filling-minimization procedure survives for the unoriented minimum-matching problem after discarding the linear duality between currents and differential forms? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860 |
30,002,623 | OWR-13103-005 | Integral Representatives of Normal Mod-Two Currents | Is every normal mod-2 current equivalent to a normal integral current? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860](https://doi.org/10.4171/owr/2014/33)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,014 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13852-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13103-005",
"literature-status:open",
"owr-year:2014"
] | The exact question whether every normal mod-2 current is equivalent to a normal integral current remains unresolved; related nonorientability and flat-chain results do not prove this stronger statement. | [
{
"url": "https://doi.org/10.4171/owr/2014/33",
"label": "original Oberwolfach report"
},
{
"url": "https://par.nsf.gov/servlets/purl/10054904",
"label": "related quantitative nonorientability work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/33 | null | null | null | Is every normal mod-2 current equivalent to a normal integral current? | Is every normal mod-2 current equivalent to a normal integral current? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Calculus of Variations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/33, pp. 1801--1860 |
30,002,624 | OWR-13104-004 | Square-Function Criterion for Higher-Dimensional Rectifiability | Let $\mu$ be a Radon measure on $\mathbb R^d$ such that $0<\Theta_{n,*}(x,\mu)<\infty$ for $\mu$-almost every $x$ and
$$\int_0^1\left(\frac{\mu(B(x,r))}{r^n}-\frac{\mu(B(x,2r))}{(2r)^n}\right)^2\frac{dr}{r}<\infty.$$
Must $\mu$ be $n$-rectifiable? In particular, if $\mu=\mathcal H^n\!\restriction E$, must $E$ be $n$-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/34, pp. 1861--1931](https://doi.org/10.4171/owr/2014/34)
## Literature review (checked 2... | 3 | partially_solved | null | 2,014 | 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-13104-004",
"literature-status:partially-solved",
"owr-year:2014"
] | The square-function criterion is proved to imply the desired rectifiability in dimension one, while the report leaves the analogous question in dimensions greater than one unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/34",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/34 | null | null | null | Let $\mu$ be a Radon measure on $\mathbb R^d$ such that $0<\Theta_{n,*}(x,\mu)<\infty$ for $\mu$-almost every $x$ and
$$\int_0^1\left(\frac{\mu(B(x,r))}{r^n}-\frac{\mu(B(x,2r))}{(2r)^n}\right)^2\frac{dr}{r}<\infty.$$
Must $\mu$ be $n$-rectifiable? In particular, if $\mu=\mathcal H^n\!\restriction E$, must $E$ be $n$-... | If a Radon measure \mu on \mathbb{R}^d satisfies 0<\Theta_{n,*}(x,\mu)<\infty for \mu-almost every x and \int_0^1\left(\frac{\mu(B(x,r))}{r^n}-\frac{\mu(B(x,2r))}{(2r)^n}\right)^2\frac{dr}{r}<\infty, does this imply that \mu, or E when \mu=\mathcal{H}^n|E, is n-rectifiable? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/34, pp. 1861--1931 |
30,002,625 | OWR-13105-002 | Hardness Amplification by Exponent Noise | Does adding noise to the exponent in a group-theoretic learning problem amplify computational intractability, as proposed by Learning with Errors in the Exponent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990](https://doi.org/10.4171/owr/2014/35)
## Literature review (checked 2026-08-21)
**Status:** partially sol... | 3 | partially_solved | null | 2,014 | 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-13105-002",
"literature-status:partially-solved",
"owr-year:2014"
] | Learning with Errors in the Exponent provides reductions and cryptographic constructions showing hardness under parameterized assumptions, but it does not establish a universal theorem that exponent noise always amplifies intractability. | [
{
"url": "https://eprint.iacr.org/2014/826.pdf",
"label": "Dagdelen--Gajek--Gopfert, Learning with Errors in the Exponent"
},
{
"url": "https://doi.org/10.1007/978-3-319-30840-1_5",
"label": "published LWEE paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/35 | null | null | null | Does adding noise to the exponent in a group-theoretic learning problem amplify computational intractability, as proposed by Learning with Errors in the Exponent? | Does adding noise to the exponent in a group-theoretic learning problem amplify computational intractability, as proposed by Learning with Errors in the Exponent? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990 |
30,002,626 | OWR-13105-003 | Optimal Fair Multiparty Coin Flipping | Does there exist a fair three-party coin-flipping protocol without the $O(\log^2 m)$ factor? More generally, does there exist a fair protocol for any number of parties against any number of corrupted parties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990](https://doi.org/10.4171/owr/2014/35)
## Literature review (checked 2026-08-21)
**Status:** open
**Asses... | 3 | open | null | 2,014 | 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-13105-003",
"literature-status:open",
"owr-year:2014"
] | The optimal three-party protocol without the logarithmic loss remains open, and current many-party results cover restricted corruption regimes rather than any number of parties and corruptions. | [
{
"url": "https://epubs.siam.org/doi/10.1137/15M1009147",
"label": "Haitner--Tsfadia, fair coin flipping"
},
{
"url": "https://link.springer.com/article/10.1007/s00145-025-09561-6",
"label": "2025 many-party coin-flipping bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/35 | null | null | null | Does there exist a fair three-party coin-flipping protocol without the $O(\log^2 m)$ factor? More generally, does there exist a fair protocol for any number of parties against any number of corrupted parties? | Does there exist a fair three-party coin-flipping protocol without the O(\log^2 m) factor, or more generally a fair coin-flipping protocol for any number of parties against any number of corrupted parties? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990 |
30,002,627 | OWR-13105-006 | Witness Pseudorandom Functions from Witness Encryption | Can witness pseudorandom functions be constructed generically from any witness encryption scheme? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990](https://doi.org/10.4171/owr/2014/35)
## Literature review (checked 2026-08-21)
**Status:** open
**Asses... | 3 | open | null | 2,014 | 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-13105-006",
"literature-status:open",
"owr-year:2014"
] | Witness PRFs were constructed from multilinear-map assumptions and used to build witness encryption, but no generic construction from an arbitrary witness-encryption scheme is established. | [
{
"url": "https://eprint.iacr.org/2014/301",
"label": "Zhandry witness PRF paper"
},
{
"url": "https://doi.org/10.1007/978-3-662-49099-0_16",
"label": "TCC 2016 witness PRFs"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/35 | null | null | null | Can witness pseudorandom functions be constructed generically from any witness encryption scheme? | Can witness pseudorandom functions be constructed generically from any witness encryption scheme? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990 |
30,002,628 | OWR-13105-007 | Reusable Garbled RAM under Weaker Assumptions | Can reusable garbled RAM, including schemes with persistent memory, be constructed under assumptions weaker than indistinguishability obfuscation, functional encryption for circuits, or the stronger obfuscation assumptions used by the known constructions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990](https://doi.org/10.4171/owr/2014/35)
## Literature review (checked 2026-08-21)
**Status:** open
**Asses... | 3 | open | null | 2,014 | 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-13105-007",
"literature-status:open",
"owr-year:2014"
] | Reusable garbled RAM has constructions with differing efficiency and security tradeoffs, including one-way-function garbled RAM, but the requested best-of-both-worlds reusable construction under weaker assumptions remains unresolved. | [
{
"url": "https://ieee-focs.org/FOCS-2014-Papers/6517a404.pdf",
"label": "FOCS 2014 reusable garbled RAM"
},
{
"url": "https://eprint.iacr.org/2014/941.pdf",
"label": "Garbled RAM from one-way functions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/35 | null | null | null | Can reusable garbled RAM, including schemes with persistent memory, be constructed under assumptions weaker than indistinguishability obfuscation, functional encryption for circuits, or the stronger obfuscation assumptions used by the known constructions? | Can one construct reusable garbled RAM achieving the best of both stated worlds, and can solutions be obtained under weaker assumptions? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990 |
30,002,629 | OWR-13105-008 | Depth-Independent Attribute-Based Encryption | Can attribute-based encryption be constructed with parameters independent of circuit depth? What applications does fully key-homomorphic encryption have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990](https://doi.org/10.4171/owr/2014/35)
## Literature review (checked 2026-08-21)
**Status:** partially sol... | 3 | partially_solved | null | 2,014 | 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-13105-008",
"literature-status:partially-solved",
"owr-year:2014"
] | Fully key-homomorphic encryption has yielded several applications and attribute-based homomorphic encryption supports bounded-depth computation, but depth-independent parameters for the general requested ABE setting and a complete application theory are not established. | [
{
"url": "https://www.iacr.org/archive/eurocrypt2014/84410298/84410298.pdf",
"label": "Eurocrypt 2014 fully key-homomorphic encryption"
},
{
"url": "https://www.iacr.org/archive/crypto2013/80420297/80420297.pdf",
"label": "Crypto 2013 identity and attribute-based FHE"
},
{
"url": "https:... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/35 | null | null | null | Can attribute-based encryption be constructed with parameters independent of circuit depth? What applications does fully key-homomorphic encryption have? | Can attribute-based encryption be constructed with parameters independent of circuit depth, and what interesting applications does fully-key homomorphic encryption have? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Cryptography (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/35, pp. 1933--1990 |
30,002,630 | OWR-13106-003 | Positive Mass on Simply Connected Nonspin Manifolds | For every $n\geq 8$, does there exist a closed simply connected nonspin $n$-manifold $M$ such that every admissible metric on $M$ has nonnegative mass? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | solved | null | 2,014 | 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/10.1016/j.aim.2016.03.008",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes, given the positive mass theorem in all dimensions)**. A. Hermann (joint with E. Humbert; OWR 36/2014, p. 2001) asks whether for every n ≥ 8 some closed simply connected non-spin n-manifold has nonnegative mass for all metrics with positive conformal Laplacian... | [
"owr",
"oberwolfach-reports",
"OWR-13106-003",
"literature-status:open",
"owr-year:2014"
] | The proposed simply connected non-spin manifolds in dimensions at least eight would provide the missing non-spin high-dimensional positive-mass theorem; the general problem remains unresolved, although candidate families were identified. | [
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1401.1614",
"label": "mass of elliptic operators"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | For every $n\geq 8$, does there exist a closed simply connected nonspin $n$-manifold $M$ such that every admissible metric on $M$ has nonnegative mass? | For every n\geq8, does there exist a closed simply-connected non-spin n-manifold M such that every admissible metric on M has non-negative mass? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,631 | OWR-13106-004 | Vanishing of the $hat A$-Genus Under Nonnegative Curvature | Does the $\hat A$-genus vanish for every spin manifold that admits a metric of nonnegative sectional curvature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-004",
"literature-status:open",
"owr-year:2014"
] | The question is Lott's vanishing problem for the A-hat genus under abstract nonnegative sectional curvature; known vanishing results cover stronger or additional hypotheses, but the stated general conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1112/blms.12695",
"label": "nonnegative curvature spin manifolds"
},
{
"url": "https://arxiv.org/abs/2209.11951",
"label": "almost nonnegative Ricci curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | Does the $\hat A$-genus vanish for every spin manifold that admits a metric of nonnegative sectional curvature? | Does the \hat A-genus of every abstract non-negatively curved spin manifold vanish? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,632 | OWR-13106-005 | Infinite Values of the $kappa$-Invariant | For a closed manifold $M$, define $\kappa(M)$ to be the least integer $k$ such that, for every $\varepsilon>0$, there is a Riemannian metric $g_\varepsilon$ whose Dirac eigenvalues satisfy $\mu_k(g_\varepsilon)=1$ and $|\mu_i(g_\varepsilon)|<\varepsilon$ for $0\leq i<k$; set $\kappa(M)=\infty$ if no such $k$ exists. Ca... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-005",
"literature-status:open",
"owr-year:2014"
] | The kappa-invariant is known to be finite for simply connected manifolds of dimension at least five and has surgery and genus bounds, but no example with kappa equal to infinity or proof excluding all such examples is known. | [
{
"url": "https://doi.org/10.1007/s00039-003-0419-6",
"label": "Bär--Dahl conformal Laplacian paper"
},
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | For a closed manifold $M$, define $\kappa(M)$ to be the least integer $k$ such that, for every $\varepsilon>0$, there is a Riemannian metric $g_\varepsilon$ whose Dirac eigenvalues satisfy $\mu_k(g_\varepsilon)=1$ and $|\mu_i(g_\varepsilon)|<\varepsilon$ for $0\leq i<k$; set $\kappa(M)=\infty$ if no such $k$ exists. Ca... | For the invariant \kappa(M) considered in the report, can the value \kappa(M)=\infty occur? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,633 | OWR-13106-006 | Sharp $hat A$-Genus Bound for the $kappa$-Invariant | For a compact spin manifold $M$ of dimension $4m$, the known estimate is $|\hat A(M)|\leq 2^{2m-1}\kappa(M)$. Can the factor $2^{2m-1}$ be replaced by $2^m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-006",
"literature-status:open",
"owr-year:2014"
] | The primary source proves the bound with the factor two raised to two m minus one and explicitly poses replacement by two raised to m as an open question; no later proof of the sharper universal bound was located. | [
{
"url": "https://doi.org/10.1007/s00039-003-0419-6",
"label": "Bär--Dahl conformal Laplacian paper"
},
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | For a compact spin manifold $M$ of dimension $4m$, the known estimate is $|\hat A(M)|\leq 2^{2m-1}\kappa(M)$. Can the factor $2^{2m-1}$ be replaced by $2^m$? | Can the factor 2^{2m-1} in Theorem 4 be replaced by 2^m? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,634 | OWR-13106-007 | Lichnerowicz Conjecture for Conformal Isometry Groups | Let $(M,g)$ be a compact Riemannian $n$-manifold, $n\geq 3$, that is not conformal to the round sphere. Does its conformal class contain a constant-scalar-curvature metric $\widetilde g$ satisfying $\operatorname{Isom}(M,\widetilde g)=\operatorname{Conf}(M,g)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | partially_solved | null | 2,014 | 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-13106-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The Lichnerowicz conclusion follows in the cases where the equivariant Yamabe inequality is proved, including the established low-dimensional and special-action cases, but the all-dimensional minimization route remains conditional on the general positive-mass input. | [
{
"url": "https://doi.org/10.1016/j.crma.2012.10.004",
"label": "Madani equivariant Yamabe results"
},
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | Let $(M,g)$ be a compact Riemannian $n$-manifold, $n\geq 3$, that is not conformal to the round sphere. Does its conformal class contain a constant-scalar-curvature metric $\widetilde g$ satisfying $\operatorname{Isom}(M,\widetilde g)=\operatorname{Conf}(M,g)$? | Lichnerowicz conjecture: for every compact Riemannian n-manifold (M,g) with n\geq3 not conformal to the round sphere, there is a conformal metric \tilde g with constant scalar curvature and \operatorname{Isom}(M,\tilde g)=\operatorname{Conf}(M,g). | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,635 | OWR-13106-008 | Equivariant Yamabe Minimizers for Isometric Group Actions | Given $G\subseteq\operatorname{Isom}(M,g)$, does the $G$-invariant conformal class $[g]_G$ contain a $G$-invariant metric that minimizes the Yamabe functional among all metrics in $[g]_G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | partially_solved | null | 2,014 | 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-13106-008",
"literature-status:partially-solved",
"owr-year:2014"
] | The equivariant Yamabe minimizer exists in broad classes such as nonpositive Yamabe cases, free actions, and proved low-dimensional or nondegenerate-action cases, while the fully general positive case is not established unconditionally. | [
{
"url": "https://doi.org/10.1016/j.crma.2012.10.004",
"label": "Madani equivariant Yamabe results"
},
{
"url": "https://doi.org/10.1007/s00526-021-02154-8",
"label": "equivariant Yamabe with boundary"
},
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | Given $G\subseteq\operatorname{Isom}(M,g)$, does the $G$-invariant conformal class $[g]_G$ contain a $G$-invariant metric that minimizes the Yamabe functional among all metrics in $[g]_G$? | Given a subgroup G of \operatorname{Isom}(M,g), does there exist a G-invariant metric minimizing the Yamabe functional over the G-invariant conformal class [g]_G? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,636 | OWR-13106-009 | Yamabe Solutions on Products of Spheres | For $n,m\geq 2$ and $T>0$, consider the conformal class $[g_0^n+Tg_0^m]$ on $S^n\times S^m$. As $T$ varies, is the full space of solutions of the Yamabe equation connected? Does every solution lie on a branch bifurcating from a constant solution? Are there solutions that depend nontrivially on both sphere variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-009",
"literature-status:open",
"owr-year:2014"
] | For products of round spheres, bifurcation theory gives many branches and multiplicity results, but connectedness of the full solution space and existence of solutions depending nontrivially on both variables remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s00526-014-0748-3",
"label": "related bifurcation work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | For $n,m\geq 2$ and $T>0$, consider the conformal class $[g_0^n+Tg_0^m]$ on $S^n\times S^m$. As $T$ varies, is the full space of solutions of the Yamabe equation connected? Does every solution lie on a branch bifurcating from a constant solution? Are there solutions that depend nontrivially on both sphere variables? | Is the solution space parametrized by T connected, do all solutions arise from the constant solution through bifurcations, and are there solutions depending non-trivially on both variables? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,637 | OWR-13106-010 | Instability of Nontrivial Compact Ricci Solitons | For every nontrivial compact Ricci soliton, does the second variation of Perelman's $\nu$-entropy have a positive eigenvalue? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-010",
"literature-status:open",
"owr-year:2014"
] | All known nontrivial compact Ricci solitons were reported to be unstable, but whether every nontrivial Ricci soliton has this instability property remains an open problem. | [
{
"url": "https://doi.org/10.1007/s00526-014-0748-3",
"label": "Kröncke stability paper"
},
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | For every nontrivial compact Ricci soliton, does the second variation of Perelman's $\nu$-entropy have a positive eigenvalue? | Do all nontrivial compact Ricci solitons have the instability property that the second variation of Perelman's \nu-entropy has a positive eigenvalue? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,638 | OWR-13106-011 | Gromov Macroscopic Dimension Conjecture | If a closed $n$-manifold $M$ admits a metric of positive scalar curvature, must the macroscopic dimension of its universal cover satisfy $\dim_{\mathrm{mc}}(\widetilde M)\leq n-2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | open | null | 2,014 | 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-13106-011",
"literature-status:open",
"owr-year:2014"
] | The extracted record is an overview containing Gromov's macroscopic-dimension positive-scalar-curvature conjecture and examples consistent with it; the general conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/1408.0372",
"label": "macroscopic dimension examples"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | If a closed $n$-manifold $M$ admits a metric of positive scalar curvature, must the macroscopic dimension of its universal cover satisfy $\dim_{\mathrm{mc}}(\widetilde M)\leq n-2$? | Gromov macroscopic-dimension conjecture: if a closed n-manifold M admits a Riemannian metric of positive scalar curvature, then the macroscopic dimension of its universal cover satisfies \operatorname{dim}_{\mathrm{mc}}(\widetilde M)\leq n-2. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,639 | OWR-13106-014 | Invariant Positive-Scalar-Curvature Metrics | Let a compact connected Lie group $G$ act effectively on a closed manifold $M$. Must $M$ admit a $G$-invariant Riemannian metric of positive scalar curvature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046](https://doi.org/10.4171/owr/2014/36)
## Literatur... | 3 | partially_solved | null | 2,014 | 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-13106-014",
"literature-status:partially-solved",
"owr-year:2014"
] | Invariant positive-scalar-curvature metrics are known for nonabelian actions and several circle-action classes, while explicit circle-action obstructions and examples without invariant metrics show that the unrestricted existence question has no uniform affirmative answer. | [
{
"url": "https://doi.org/10.4171/owr/2014/36",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1090/tran/6666",
"label": "circle actions and scalar curvature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/36 | null | null | null | Let a compact connected Lie group $G$ act effectively on a closed manifold $M$. Must $M$ admit a $G$-invariant Riemannian metric of positive scalar curvature? | Does M admit an invariant metric of positive scalar curvature? | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/36, pp. 1991--2046 |
30,002,640 | OWR-13108-001 | Algebraicity of Perturbative Fiber-Knot Invariants | For any Seifert space $M$ with $\chi(M)>0$, does there exist a finite-degree extension $L(M)$ of $\mathbb Q(e^u)$ containing all genus-$g$ $A$-series perturbative invariants of fiber knots in $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13108-001",
"literature-status:open",
"owr-year:2014"
] | The finite-extension statement is proved for important spherical Seifert examples, but the general claim for all Seifert spaces and all stated perturbative invariants remains a conjecture in the later primary treatment. | [
{
"url": "https://doi.org/10.1007/s00029-016-0266-6",
"label": "Borot--Eynard--Weisse"
},
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For any Seifert space $M$ with $\chi(M)>0$, does there exist a finite-degree extension $L(M)$ of $\mathbb Q(e^u)$ containing all genus-$g$ $A$-series perturbative invariants of fiber knots in $M$? | For any Seifert space M with \chi(M)>0, does there exist a finite-degree extension L(M) of \mathbb Q(e^u) containing all genus-g A-series perturbative invariants of fiber knots in M? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,641 | OWR-13108-002 | The L-Space and Left-Orderability Conjecture | An irreducible rational homology $3$-sphere $W$ is not an L-space if and only if $\pi_1(W)$ is left-orderable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13108-002",
"literature-status:open",
"owr-year:2014"
] | The L-space equivalence with left-orderability is proved for graph manifolds and other special classes, but the irreducible rational-homology-sphere conjecture remains widely open in general. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original OWR report"
},
{
"url": "https://ems.press/content/serial-article-files/48584?nt=1",
"label": "2024 primary treatment"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | An irreducible rational homology $3$-sphere $W$ is not an L-space if and only if $\pi_1(W)$ is left-orderable. | An irreducible rational homology 3-sphere W is not an L-space if and only if \pi_1(W) is left-orderable. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,642 | OWR-13108-003 | Bounded Negativity and Infinite Families of Negative Curves | Bounded-negativity conjecture: for every smooth projective surface $X$ over $\mathbb C$, the self-intersections of reduced irreducible curves on $X$ are bounded below; additionally, for every $g>1$, does some $X$ have infinitely many curves with $C^2=-1$ and arithmetic genus $g$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13108-003",
"literature-status:open",
"owr-year:2014"
] | Bounded negativity over complex smooth projective surfaces remains a central open conjecture; substantial weak forms and results for special surfaces or bounded genus do not settle the stated claim. | [
{
"url": "https://doi.org/10.1515/advgeom-2023-0027",
"label": "recent bounded-negativity paper"
},
{
"url": "https://arxiv.org/1708.09463",
"label": "weak bounded negativity"
},
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | Bounded-negativity conjecture: for every smooth projective surface $X$ over $\mathbb C$, the self-intersections of reduced irreducible curves on $X$ are bounded below; additionally, for every $g>1$, does some $X$ have infinitely many curves with $C^2=-1$ and arithmetic genus $g$? | Bounded-negativity conjecture: for every smooth projective surface X over \mathbb C, the self-intersections of reduced irreducible curves on X are bounded below; additionally, for every g>1, does some X have infinitely many curves with C^2=-1 and arithmetic genus g? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,643 | OWR-13108-005 | Determinant Bounds in Terms of Knot-Crossing Number | For a knot or link $K \subset S^3$, let $\det(K) = |\Delta_K(-1)|$ be its determinant, let $c(K)$ be its crossing number, and let $v_8 \approx 3.66386$ denote the volume of the regular ideal hyperbolic octahedron. For every knot or link $K$, does the upper bound
$$
\frac{2\pi \log \det(K)}{c(K)} \leq v_8
$$
hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13108-005",
"literature-status:open",
"owr-year:2014"
] | The determinant-density upper bound equivalent to Kenyon's planar-graph conjecture has been verified for broad families and finite crossing ranges, but the universal knot-and-link statement remains conjectural. | [
{
"url": "https://arxiv.org/1506.05841",
"label": "density spectra for knots"
},
{
"url": "https://doi.org/10.1112/jlms/jdw062",
"label": "geometrically maximal knots"
},
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For a knot or link $K \subset S^3$, let $\det(K) = |\Delta_K(-1)|$ be its determinant, let $c(K)$ be its crossing number, and let $v_8 \approx 3.66386$ denote the volume of the regular ideal hyperbolic octahedron. For every knot or link $K$, does the upper bound
$$
\frac{2\pi \log \det(K)}{c(K)} \leq v_8
$$
hold? | For every knot or link K, does \frac{2\pi\log\det(K)}{c(K)}\leq v_8 hold? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,644 | OWR-13108-006 | Diagrammatic and Geometric Maximality | For a sequence of knots or links $K_n$ with crossing number $c(K_n)\to\infty$, call it geometrically maximal if $\operatorname{vol}(K_n)/c(K_n)\to v_8$ and diagrammatically maximal if $2\pi\log\det(K_n)/c(K_n)\to v_8$, where $v_8$ is the volume of the regular ideal octahedron. Is every diagrammatically maximal sequence... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13108-006",
"literature-status:open",
"owr-year:2014"
] | The two notions coincide for important alternating and weaving families, but the primary paper states the equivalence for arbitrary diagrammatically or geometrically maximal sequences as an open question. | [
{
"url": "https://doi.org/10.1112/jlms/jdw062",
"label": "geometrically and diagrammatically maximal knots"
},
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For a sequence of knots or links $K_n$ with crossing number $c(K_n)\to\infty$, call it geometrically maximal if $\operatorname{vol}(K_n)/c(K_n)\to v_8$ and diagrammatically maximal if $2\pi\log\det(K_n)/c(K_n)\to v_8$, where $v_8$ is the volume of the regular ideal octahedron. Is every diagrammatically maximal sequence... | Is every diagrammatically maximal sequence of knots or links geometrically maximal, and conversely? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,645 | OWR-13108-009 | Nonsimple Deformation Varieties and Geometrically Isolated Cusps | Let $X$ be a $k$-cusped hyperbolic $3$-manifold. If the deformation variety of $X$ is not simple, then $X$ has a set of cusps strongly geometrically isolated from the rest. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 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-13108-009",
"literature-status:partially-solved",
"owr-year:2014"
] | Jeon proves the strong-isolation conclusion for holonomy varieties under rationally independent cusp shapes and related hypotheses; the unrestricted higher-cusped formulation in the record is not established. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2005.02481",
"label": "Jeon, anomalous holonomy subvarieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | Let $X$ be a $k$-cusped hyperbolic $3$-manifold. If the deformation variety of $X$ is not simple, then $X$ has a set of cusps strongly geometrically isolated from the rest. | Let X be a k-cusped hyperbolic 3-manifold. If its deformation variety is not simple, then X has a set of cusps strongly geometrically isolated from the rest. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,646 | OWR-13108-010 | The Bounded-Height Conjecture for Hyperbolic Dehn Fillings | For every $k$-cusped hyperbolic $3$-manifold $M$, are the heights of all Dehn fillings of $M$ uniformly bounded? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-13108-011"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13108-010",
"literature-status:partially-solved",
"owr-year:2014"
] | Uniform bounded height is proved for one cusp and important two-cusp cases, including rationally independent cusp shapes, but no general theorem for all k-cusped manifolds was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1409.2069",
"label": "Jeon, bounded height theorem"
},
{
"url": "https://doi.org/10.1112/plms.70017",
"label": "Jeon, hyperbolic Dehn fillings"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For every $k$-cusped hyperbolic $3$-manifold $M$, are the heights of all Dehn fillings of $M$ uniformly bounded? | Bounded-height conjecture: for every k-cusped hyperbolic 3-manifold M, the heights of all Dehn fillings of M are uniformly bounded. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,647 | OWR-13108-011 | Duplicate Hyperbolic Dehn-Filling Bounded-Height Question | Is the bounded-height conjecture for hyperbolic 3-manifolds true, and would it yield a complete positive answer to the associated finiteness question for hyperbolic 3-manifolds with bounded volume and trace-field degree? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report contains one bounded-height conjecture for Dehn fillings, represented canonically by OWR-13108-010. This record repeats ) | [
"OWR-13108-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13108-011",
"literature-status:open",
"owr-year:2014"
] | The record only refers to an above conjecture and does not state a complete mathematical claim; the extracted item is therefore unresolved and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | null | Is the bounded-height conjecture for hyperbolic 3-manifolds true, and would it yield a complete positive answer to the associated finiteness question for hyperbolic 3-manifolds with bounded volume and trace-field degree? | unrecoverable | The official report contains one bounded-height conjecture for Dehn fillings, represented canonically by OWR-13108-010. This record repeats that conjecture and adds only its stated consequence for a preceding finiteness question. No separate clean statement is promoted; the original record remains publicly visible and ... | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,648 | OWR-13108-012 | Hyperbolic-Volume Decay of Partition Functions | For the quantum-Teichmüller TQFT state-integral $Z_b(X)$ associated with a triangulated hyperbolic $3$-manifold $X$ whose edges may carry conical singularities, is
$$\lvert Z_b(X)\rvert\sim\exp\left(-\frac{\operatorname{vol}(X)}{2\pi b^2}\right)$$
as $b\to0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 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-13108-012",
"literature-status:partially-solved",
"owr-year:2014"
] | Exponential decay with the hyperbolic-volume rate is proved for generalized FAMED semi-geometric triangulations, while the broader model-wide claim in the record remains unproved. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2512.23198",
"label": "Wong, Teichmuller TQFT asymptotics"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For the quantum-Teichmüller TQFT state-integral $Z_b(X)$ associated with a triangulated hyperbolic $3$-manifold $X$ whose edges may carry conical singularities, is
$$\lvert Z_b(X)\rvert\sim\exp\left(-\frac{\operatorname{vol}(X)}{2\pi b^2}\right)$$
as $b\to0$? | Does the partition function of the model decay exponentially, with decay rate given by the hyperbolic volume of the corresponding 3-manifold with conical singularities? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,649 | OWR-13108-013 | Positive Bases for Surface Skein Algebras | Let $S(\Sigma)$ be the Kauffman bracket skein algebra of a surface $\Sigma$ over $\mathbb Z[t^{\pm1}]$. For an integer lamination $\mu=\{(a_i,C_i)\}$, set $b_T(\mu)=\prod_i T_{a_i}(C_i)$ using the Chebyshev polynomials $T_j$. Is $b_T=\{b_T(\mu)\}$ a positive basis of $S(\Sigma)$, meaning that all multiplication structu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 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-13108-013",
"literature-status:partially-solved",
"owr-year:2014"
] | Quantum bracelet positivity is proved for broad unpunctured marked-surface settings, but the full compact-surface formulation in the record is not covered in every case. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2301.11101",
"label": "Mandel and Qin, bracelet bases"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | Let $S(\Sigma)$ be the Kauffman bracket skein algebra of a surface $\Sigma$ over $\mathbb Z[t^{\pm1}]$. For an integer lamination $\mu=\{(a_i,C_i)\}$, set $b_T(\mu)=\prod_i T_{a_i}(C_i)$ using the Chebyshev polynomials $T_j$. Is $b_T=\{b_T(\mu)\}$ a positive basis of $S(\Sigma)$, meaning that all multiplication structu... | For the stated skein algebra S(\Sigma), is b_T a positive basis, with structure constants that are Laurent polynomials in t having non-negative coefficients? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,650 | OWR-13108-014 | Knot Volume Conjecture | For every knot $K$, does the volume conjecture hold in the form
$$\lim_{N\to\infty}\frac{\log\left\lvert J_N\!\left(K;\exp(2\pi i/N)\right)\right\rvert}{N}=\frac{\operatorname{Vol}(S^3\setminus K)}{2\pi},$$
where $J_N$ is the $N$-colored Jones polynomial and $\operatorname{Vol}$ is the simplicial volume of the knot c... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176](https://doi.org/10.4171/owr/2014/38)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 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-13108-014",
"literature-status:partially-solved",
"owr-year:2014"
] | The colored-Jones volume formula is proved for several families and special cases, but the asserted formula for every knot remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/38",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/BF02392716",
"label": "Murakami and Murakami, colored Jones and simplicial volume"
},
{
"url": "https://arxiv.org/abs/math/0502163",
"label": "Garoufalidis and ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/38 | null | null | null | For every knot $K$, does the volume conjecture hold in the form
$$\lim_{N\to\infty}\frac{\log\left\lvert J_N\!\left(K;\exp(2\pi i/N)\right)\right\rvert}{N}=\frac{\operatorname{Vol}(S^3\setminus K)}{2\pi},$$
where $J_N$ is the $N$-colored Jones polynomial and $\operatorname{Vol}$ is the simplicial volume of the knot c... | For every knot K, the Volume Conjecture asserts that \lim_{N\to\infty}\frac{\log J_N(K;\exp(2\pi\sqrt{-1}/N))}{N}=\frac{\operatorname{Vol}(S^3\setminus K)}{2\pi}, where \operatorname{Vol} is the simplicial volume of the knot complement. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Low-dimensional Topology and Number Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/38, pp. 2115--2176 |
30,002,651 | OWR-13109-001 | Abundance Conjecture for Projective Minimal Models | If $X$ is a projective minimal model with nef canonical divisor $K_X$, is $K_X$ semiample; equivalently, is $mK_X$ globally generated for some $m>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate of canonical problem AG-002 | [
"AG-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13109-001",
"literature-status:open",
"owr-year:2014"
] | The extracted passage is meeting prose about the abundance conjecture and a threefold result, not a complete mathematical claim; no claim can be triaged beyond open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | If $X$ is a projective minimal model with nef canonical divisor $K_X$, is $K_X$ semiample; equivalently, is $mK_X$ globally generated for some $m>0$? | Abundance conjecture: if X is a projective minimal model with nef canonical divisor K_X, then K_X is semi-ample, i.e. some positive multiple mK_X is globally generated. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,652 | OWR-13109-003 | Rational Curves on Compact Kähler Manifolds | Let $X$ be a compact Kähler manifold. Is $X$ covered by rational curves if and only if $K_X$ is not pseudoeffective? If $K_X$ is pseudoeffective but not nef, must $X$ contain a rational curve? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,014 | 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-13109-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The projective equivalence is known and the Kähler statements are established through dimension three, but the higher-dimensional compact-Kähler formulation remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1502.03936",
"label": "Cao and Hoering, rational curves on compact Kähler manifolds"
},
{
"url": "https://doi.org/10.24033/asens.2301",
"label": "Campana, Hoering... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | Let $X$ be a compact Kähler manifold. Is $X$ covered by rational curves if and only if $K_X$ is not pseudoeffective? If $K_X$ is pseudoeffective but not nef, must $X$ contain a rational curve? | (1) If X is a compact K\ddot{a}hler manifold, then X is covered by rational curves if and only if K_X is not pseudoeffective. (2) If X is a compact K\ddot{a}hler manifold with K_X pseudoeffective but not nef, then X contains a rational curve. | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,653 | OWR-13109-004 | Indeterminacy Locus of the Perfect Cone Prym Map | For the extension $P_g^{\mathrm{Perf}}$ of the Prym map to the perfect-cone compactification, is its indeterminacy locus exactly $FS_2\cup FS_3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-004",
"literature-status:open",
"owr-year:2014"
] | The perfect-cone Prym indeterminacy locus is known only between established inclusions in general; equality with the two Friedman-Smith loci remains unresolved in higher genus. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4171/JEMS/678",
"label": "Casalaina-Martin et al., Prym compactifications"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | For the extension $P_g^{\mathrm{Perf}}$ of the Prym map to the perfect-cone compactification, is its indeterminacy locus exactly $FS_2\cup FS_3$? | For the Prym map P_g^{Perf} to the perfect-cone compactification, is the indeterminacy locus exactly FS_2\cup FS_3? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,654 | OWR-13109-005 | K-Moduli and Minimal Fano Fillings | Consider families of Fano varieties with log-terminal singularities and a fibre-tangent holomorphic vector field $V$, with every pair $(X_t,V_t)$ modified K-semistable. Does their moduli functor admit a proper coarse algebraic moduli space $M$ parametrizing modified K-polystable Fano varieties, with Kähler connected co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-005",
"literature-status:open",
"owr-year:2014"
] | The record is an incomplete fragment referring to Odaka-type K-moduli and filling-in conjectures; the precise asserted statement is not recoverable and is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | Consider families of Fano varieties with log-terminal singularities and a fibre-tangent holomorphic vector field $V$, with every pair $(X_t,V_t)$ modified K-semistable. Does their moduli functor admit a proper coarse algebraic moduli space $M$ parametrizing modified K-polystable Fano varieties, with Kähler connected co... | Conjecturally, the moduli functor of Fano families with a fibrewise holomorphic vector field and K-semistable pairs admits a proper coarse algebraic moduli space M parametrizing modified K-polystable Fano varieties, with K\ddot{a}hler connected components; the limiting classes L_{T,k} should exist and the K-polystable ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,655 | OWR-13109-007 | Ascending Chain Condition for Log Discrepancies | Fix a dimension $n$, a descending-chain-condition set $I\subseteq[0,1]$, and a descending-chain-condition set $J\subseteq\mathbb R_{\geq 0}$. Does there exist a finite subset $J_0\subseteq J$ such that, whenever $(X,\Delta)$ is an $n$-dimensional log canonical pair whose coefficients lie in $I$ and whose log discrepanc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-007",
"literature-status:open",
"owr-year:2014"
] | The extracted item names Shokurov's ACC-for-log-discrepancy conjecture without resolving it; only special dimensions or singularity classes are known, so the general claim remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1112/jlms.70510",
"label": "Kawakita, smooth-threefold ACC result"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | Fix a dimension $n$, a descending-chain-condition set $I\subseteq[0,1]$, and a descending-chain-condition set $J\subseteq\mathbb R_{\geq 0}$. Does there exist a finite subset $J_0\subseteq J$ such that, whenever $(X,\Delta)$ is an $n$-dimensional log canonical pair whose coefficients lie in $I$ and whose log discrepanc... | ACC for log discrepancies: for fixed n and DCC subsets I\subset[0,1] and J\subset[0,\infty), there is a finite set J_0 such that every n-dimensional log canonical pair (X,\Delta) with coefficients of \Delta in I and log discrepancy in J has log discrepancy in J_0. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,656 | OWR-13109-008 | Economical Toroidal Resolutions of Log Canonical Pairs | For every $n>0$, does there exist $s=s(n)$ such that each $n$-dimensional log canonical pair $(X,\Delta)$ admits a projective birational morphism $\pi:Y\to X$ with the following properties? Writing $\Gamma=\widetilde\Delta+E$, the pair $(Y,\Gamma)$ is quotient-dlt near the generic point of every non-klt center, $\pi$ h... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-008",
"literature-status:open",
"owr-year:2014"
] | The extracted sentence gives only a numerical interpretation of an economical-resolution conjecture and omits the conjecture itself; the claim is therefore unclear and normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | For every $n>0$, does there exist $s=s(n)$ such that each $n$-dimensional log canonical pair $(X,\Delta)$ admits a projective birational morphism $\pi:Y\to X$ with the following properties? Writing $\Gamma=\widetilde\Delta+E$, the pair $(Y,\Gamma)$ is quotient-dlt near the generic point of every non-klt center, $\pi$ h... | For every positive integer n there is an integer s such that every n-dimensional log canonical pair (X,\Delta) admits a projective birational morphism \pi:Y\to X for which (Y,\Gamma), with \Gamma=\widetilde{\Delta}+E, is toroidal near the generic point of every non-kawamata-log-terminal centre, has at most s exceptiona... | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,657 | OWR-13109-009 | Rationally Connected Cycles on Hyperkähler Manifolds | Let $X$ be a projective hyperkähler manifold of dimension $2n$. Does $X$ contain a rationally connected subscheme of pure dimension $n$? If $Y_1,Y_2\subset X$ are rationally connected subschemes of dimension $n$, do arbitrary points $y_i\in Y_i$ determine the same class $c_X\in CH_0(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-009",
"literature-status:open",
"owr-year:2014"
] | There are positive constructions in special hyperkähler deformation types and dimensions, but the existence and universal CH0-class assertions for arbitrary projective hyperkähler manifolds remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1401.4071",
"label": "Charles and Pacienza, rational curves and zero-cycles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | Let $X$ be a projective hyperkähler manifold of dimension $2n$. Does $X$ contain a rationally connected subscheme of pure dimension $n$? If $Y_1,Y_2\subset X$ are rationally connected subschemes of dimension $n$, do arbitrary points $y_i\in Y_i$ determine the same class $c_X\in CH_0(X)$? | If X is a projective hyperK\ddot{a}hler manifold of dimension 2n, (i) does X contain a rationally connected subscheme Y of pure dimension n, and (ii) do any two points on any two rationally connected n-dimensional subschemes determine the same class c_X\in CH_0(X)? | corrected_verified | The mathematical content is unchanged; notation, typography, and wording were normalized into a self-contained publication form. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,658 | OWR-13109-010 | Yau–Tian–Donaldson Conjecture for Polarized Varieties | Let $(X,L)$ be a smooth polarized complex projective variety with finite automorphism group. Does $c_1(L)$ contain a constant-scalar-curvature Kähler metric if and only if $(X,L)$ is K-stable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234](https://doi.org/10.4171/owr/2014/39)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13109-010",
"literature-status:open",
"owr-year:2014"
] | The extracted statement is only the word conjecture followed by established theorems and a corollary, so it does not identify an unresolved standalone claim; under the queue rule it is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2014/39",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/39 | null | null | null | Let $(X,L)$ be a smooth polarized complex projective variety with finite automorphism group. Does $c_1(L)$ contain a constant-scalar-curvature Kähler metric if and only if $(X,L)$ is K-stable? | Yau--Tian--Donaldson conjecture: for a smooth polarized projective complex variety (X,L) with finite automorphism group, c_1(L) contains a constant-scalar-curvature K\ddot{a}hler metric if and only if (X,L) is K-stable. | corrected_verified | Checked against the official Oberwolfach report; the clean statement restores the source's hypotheses and notation while preserving its open questions. | null | null | null | null | null | Komplexe Analysis (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/39, pp. 2177--2234 |
30,002,659 | OWR-13110-001 | Shortest Billiard Trajectories in Constant Width Bodies | A shortest closed billiard trajectory in a Euclidean convex body of constant width 1 in the plane has period 2; does the same period-2 conclusion hold for constant-width bodies in every higher dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-001",
"literature-status:open",
"owr-year:2014"
] | The planar period-two result is known, but whether every shortest billiard trajectory in a higher-dimensional Euclidean constant-width body has period two remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/40",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s10711-009-9353-6",
"label": "Bezdek and Bezdek, shortest billiard trajectories"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | A shortest closed billiard trajectory in a Euclidean convex body of constant width 1 in the plane has period 2; does the same period-2 conclusion hold for constant-width bodies in every higher dimension? | A shortest closed billiard trajectory in a Euclidean convex body of constant width 1 in the plane has period 2; does the same period-2 conclusion hold for constant-width bodies in every higher dimension? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,660 | OWR-13110-002 | Shortest Billiards Beyond Euclidean Convex Bodies | Can the Bezdek–Bezdek approach to shortest billiard trajectories be extended from Euclidean convex bodies to hyperbolic or spherical geometry, or to Riemannian and Finsler manifolds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-002",
"literature-status:open",
"owr-year:2014"
] | The extracted statement contains no mathematical question beyond the words Open Question, so its content is unclear and is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2014/40",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Can the Bezdek–Bezdek approach to shortest billiard trajectories be extended from Euclidean convex bodies to hyperbolic or spherical geometry, or to Riemannian and Finsler manifolds? | Can the Bezdek--Bezdek approach to shortest billiard trajectories be extended from Euclidean convex bodies to hyperbolic or spherical geometry, or to Riemannian and Finsler manifolds? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,661 | OWR-13110-004 | Bang Plank Conjecture for Nonsymmetric Convex Bodies | If a convex body $K\subset\mathbb{R}^n$ is covered by planks $P_1,\ldots,P_m$, must the sum of their relative widths, measured in the norm whose unit ball is $K-K$, be at least $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-004",
"literature-status:open",
"owr-year:2014"
] | The record explicitly says that the non-symmetric-body version remains open; no later general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/40",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4310/JSG.2019.v17.n6.a1",
"label": "Akopyan, Karasev, and Petrov, symplectic invariants"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | If a convex body $K\subset\mathbb{R}^n$ is covered by planks $P_1,\ldots,P_m$, must the sum of their relative widths, measured in the norm whose unit ball is $K-K$, be at least $1$? | Bang's conjecture for nonsymmetric bodies: if a convex body K\subset\mathbb{R}^n is covered by planks P_1,\ldots,P_m, then the sum of their relative widths, measured in the norm with unit ball K-K, is at least 1. | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,662 | OWR-13110-005 | Displacement-Energy Bound for Plank Coverings | Let $K$ be a convex body covered by finitely many planks whose relative widths sum to $w$, and let $B^\circ$ be the polar of the unit ball for the norm used to measure those widths. Must the displacement energy satisfy $e(K\times B^\circ)\leq 2w$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-005",
"literature-status:open",
"owr-year:2014"
] | The displacement-energy plank inequality is proved only in special configurations; the full conjecture remains open together with the general non-symmetric Bang problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/40",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1404.0871",
"label": "Akopyan, Karasev, and Petrov, Bang problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Let $K$ be a convex body covered by finitely many planks whose relative widths sum to $w$, and let $B^\circ$ be the polar of the unit ball for the norm used to measure those widths. Must the displacement energy satisfy $e(K\times B^\circ)\leq 2w$? | If a convex body K is covered by finitely many planks whose sum of relative widths is w, then the displacement energy satisfies e(K\times B^\circ)\le 2w, where B^\circ is the polar body used in the symplectic formulation. | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,663 | OWR-13110-006 | Subadditivity of Symplectic Capacities Under Convex Covers | If a convex body $X\subset\mathbb{R}^{2n}$ is covered by finitely many convex bodies $X_i$, is there a symplectic capacity $c$ for which $\sum_i c(X_i)\geq c(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-006",
"literature-status:open",
"owr-year:2014"
] | The subadditivity principle is presented as a conjectural symplectic ingredient for Bang's problem, and no general proof or disproof was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/40",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1404.0871",
"label": "Akopyan, Karasev, and Petrov, Bang problem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | If a convex body $X\subset\mathbb{R}^{2n}$ is covered by finitely many convex bodies $X_i$, is there a symplectic capacity $c$ for which $\sum_i c(X_i)\geq c(X)$? | Subadditivity conjecture: if a convex body X\subset\mathbb{R}^{2n} is covered by finitely many convex bodies X_i, then there is a symplectic capacity c such that \sum_i c(X_i)\ge c(X). | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,664 | OWR-13110-010 | Planar Regions Avoiding Prescribed Interior Lattice Point Counts | Does there exist, for each natural number n, a planar region of area n such that no congruent copy of the region contains exactly n interior lattice points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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-13110-010",
"literature-status:open",
"owr-year:2014"
] | Known positive results cover compact, strictly convex, algebraic, and polygonal regions, but the stated question for arbitrary planar regions remains explicitly unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46530",
"label": "Oberwolfach report on the Steinhaus lattice-point problem"
},
{
"url": "https://doi.org/10.1007/s00454-017-9869-8",
"label": "Maehara, lattice points on polyhedra"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Does there exist, for each natural number n, a planar region of area n such that no congruent copy of the region contains exactly n interior lattice points? | Does there exist, for each natural number n, a planar region of area n such that no congruent copy of the region contains exactly n interior lattice points? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,665 | OWR-13110-013 | Uniform Cover Decomposition Bounds for Convex Polygons | For every integer $n>3$, does there exist an integer $m(n)$ such that every convex n-gon Q satisfies $m(Q)\leq m(n)$, where $m(Q)$ is the least multiplicity for which every m-fold covering of the plane by translates of Q decomposes into two coverings? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] - The note's "survey" (I. Kovács's 2015 thesis summary) already reports the refutation, and `OWR-13110-013` cites the same paper. | [
"owr",
"oberwolfach-reports",
"OWR-13110-013",
"literature-status:open",
"owr-year:2014"
] | The supremum of the covering multiplicity over convex polygons is unbounded, while the proposed uniform bound is still unresolved even for quadrilaterals. | [
{
"url": "https://ems.press/content/serial-article-files/46530",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.aim.2016.07.011",
"label": "Pach--Pálvölgyi, unsplittable coverings in the plane"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | For every integer $n>3$, does there exist an integer $m(n)$ such that every convex n-gon Q satisfies $m(Q)\leq m(n)$, where $m(Q)$ is the least multiplicity for which every m-fold covering of the plane by translates of Q decomposes into two coverings? | For every integer n>3, does there exist an integer m(n) such that every convex n-gon Q satisfies m(Q)\le m(n), where m(Q) is the least multiplicity for which every m-fold covering of the plane by translates of Q decomposes into two coverings? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,666 | OWR-13110-015 | Embedding Triangular 2-Complexes in 3-Space | Given a two-dimensional complex $K$ formed from triangular faces by identifying edges or vertices, does $K$ embed in $\mathbb{R}^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (decidable; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (decidable; answered in the source)**. The statement is the problem that opens E. Sedgwick's abstract (OWR 40/2014, p. 2277): does a given 2-complex made of triangles embed in R³? Its main result: this is decidable (Matoušek–Sedgwick–Tancer–Wagner, [J. ACM 65 (2018... | [
"owr",
"oberwolfach-reports",
"OWR-13110-015",
"literature-status:open",
"owr-year:2014"
] | Embeddability of arbitrary two-complexes in three-space is decidable, but the extracted record does not specify the pictured complex, so its particular yes-or-no instance cannot be assessed. | [
{
"url": "https://ems.press/content/serial-article-files/46530",
"label": "Sedgwick, Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1402.0815",
"label": "Matoušek--Sedgwick--Tancer--Wagner, embeddability decision theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Given a two-dimensional complex $K$ formed from triangular faces by identifying edges or vertices, does $K$ embed in $\mathbb{R}^3$? | Given a 2-dimensional complex K formed from triangular faces by identifying edges and/or vertices, does K embed in \mathbb{R}^3? | corrected_verified | The supplied statement explicitly identifies the mathematical question; notation and publication prose were repaired without changing its substance. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,667 | OWR-13110-016 | Kühnel Conjecture for Embedded Simplicial Skeletons | Kühnel's conjecture: if the k-skeleton $\Delta_n^{(k)}$ embeds in a compact $(k-1)$-connected 2k-manifold with kth Betti number b over $\mathbb{Z}_2$, then $\binom{n-k-1}{k+1}\leq\binom{2k+1}{k+1}b$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,014 | 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-13110-016",
"literature-status:partially-solved",
"owr-year:2014"
] | The Kühnel bound remains unproved, but successive van Kampen--Flores, quadratic, and linear bounds give substantial partial progress. | [
{
"url": "https://arxiv.org/abs/1610.09063",
"label": "Goaoc--Mabillard--Paták--Tancer--Wagner, generalized Heawood inequalities"
},
{
"url": "https://doi.org/10.1007/s00454-023-00595-w",
"label": "Paták--Tancer, embeddings of complexes into manifolds"
},
{
"url": "https://arxiv.org/abs/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Kühnel's conjecture: if the k-skeleton $\Delta_n^{(k)}$ embeds in a compact $(k-1)$-connected 2k-manifold with kth Betti number b over $\mathbb{Z}_2$, then $\binom{n-k-1}{k+1}\leq\binom{2k+1}{k+1}b$. | K\ddot{u}hnel's conjecture: if the k-skeleton \Delta_n^{(k)} embeds in a compact (k-1)-connected 2k-manifold with kth Betti number b over \mathbb{Z}_2, then \binom{n-k-1}{k+1}\le\binom{2k+1}{k+1}b. | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,668 | OWR-13110-017 | Long Alternating Paths in Colored Line Arrangements | Given n red, n blue, and n green lines in general position in the plane, does the dual graph of the arrangement always contain an alternating path of length $\Theta(n^2)$, where consecutive crossed edges cannot have the same color? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 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"
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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-13110-017",
"literature-status:open",
"owr-year:2014"
] | Quadratic dual paths exist in uncolored arrangements, but known colored results give counterexamples or weaker bounds and do not settle the stated balanced three-color alternating-path question. | [
{
"url": "https://ems.press/content/serial-article-files/46530",
"label": "Oberwolfach report"
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{
"url": "https://arxiv.org/abs/1506.03728",
"label": "Hoffmann--Kleist--Miltzow, long dual paths"
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{
"url": "https://doi.org/10.46298/dmtcs.2088",
"label": "Aichholzer et al., cell pa... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Given n red, n blue, and n green lines in general position in the plane, does the dual graph of the arrangement always contain an alternating path of length $\Theta(n^2)$, where consecutive crossed edges cannot have the same color? | Given n red, n blue, and n green lines in general position in the plane, does the dual graph of the arrangement always contain an alternating path of length \Theta(n^2), where consecutive crossed edges cannot have the same color? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,669 | OWR-13110-018 | Minimum Volume of Bodies with Unit Width | What is the minimum volume among all convex sets in $\mathbb{R}^d$ whose width is at least 1 in every direction? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "geometry",
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"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": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13110-018",
"literature-status:open",
"owr-year:2014"
] | The minimum-width volume problem is solved in dimension two by the equilateral triangle, but the exact higher-dimensional problem remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46530",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1112/jlms.12982",
"label": "Codenotti, lattice-reduced and complete convex bodies"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | What is the minimum volume among all convex sets in $\mathbb{R}^d$ whose width is at least 1 in every direction? | What is the minimum volume among all convex sets in \mathbb{R}^d whose width is at least 1 in every direction? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,670 | OWR-13110-019 | Contractibility of Convex-Position Polygon Spaces | Call a convex polygon with at most $k$ vertices a $k$-gon. Is the space of ordered arrangements of $n$ such $k$-gons in convex position, modulo affine transformations, contractible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "geometry",
"display_name": "Geometry",
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"created_at": "2026-07-31T15:26:25.671Z"
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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-13110-019",
"literature-status:open",
"owr-year:2014"
] | Realization spaces of unrestricted convex-body arrangements are understood, but bounded-vertex polygon realization spaces can have complicated topology and the convex-position k-gon contractibility question remains open. | [
{
"url": "https://doi.org/10.1007/s00454-017-9869-8",
"label": "Dobbins--Holmsen--Hubard, convex-body realization spaces"
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{
"url": "https://ems.press/content/serial-article-files/46530",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Call a convex polygon with at most $k$ vertices a $k$-gon. Is the space of ordered arrangements of $n$ such $k$-gons in convex position, modulo affine transformations, contractible? | Is the space of n k-gons in convex position, modulo affine transformations, contractible? | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,671 | OWR-13110-020 | Sharpness of the One-Round Voronoi Game Bound | In the one-round Voronoi game in which the first player places t facilities and the second places one, is the bound $VR_{t:1}\leq\frac{t-1}{t+1}$ sharp? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13110-020",
"literature-status:open",
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] | The discrete Voronoi-game bounds are established, but the exact sharpness of the stated bound remains an open problem in the cited primary literature and current search. | [
{
"url": "https://doi.org/10.7155/jgaa.00331",
"label": "Gerbner et al., advantage in the discrete Voronoi game"
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{
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | In the one-round Voronoi game in which the first player places t facilities and the second places one, is the bound $VR_{t:1}\leq\frac{t-1}{t+1}$ sharp? | In the one-round Voronoi game in which the first player places t facilities and the second places one, is the bound VR_{t:1}\le\frac{t-1}{t+1} sharp? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,672 | OWR-13110-021 | Line Discrepancy Centers and Orthic-Triangle Coverings | Two independent questions are posed. First, for every $\alpha>0$, does there exist $\beta<\alpha$ such that every two-colored $n$-point set $P\subset\mathbb{R}^2$ with line discrepancy at most $\alpha n$ has a point $q$ through which every line has discrepancy at most $\beta n$? Second, if an acute triangle $T$ is cove... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296](https://doi.org/10.4171/owr/2014/40)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,014 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13110-021",
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] | The record combines two distinct questions, a line-discrepancy assertion and an orthic-triangle covering inequality; no authoritative source located resolves either exact statement. | [
{
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"label": "Oberwolfach report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/40 | null | null | null | Two independent questions are posed. First, for every $\alpha>0$, does there exist $\beta<\alpha$ such that every two-colored $n$-point set $P\subset\mathbb{R}^2$ with line discrepancy at most $\alpha n$ has a point $q$ through which every line has discrepancy at most $\beta n$? Second, if an acute triangle $T$ is cove... | (1) For every \alpha>0, does there exist \beta<\alpha such that every two-colored n-point set P\subset\mathbb{R}^2 with line discrepancy D(l)\le\alpha n for every line has a point q through which every line has discrepancy at most \beta n? (2) If an acute triangle T is covered by acute triangles S_1,\ldots,S_N, must th... | corrected_verified | The official Oberwolfach report passage was checked directly; the mathematical question, definitions, and notation were restored without adding a stronger claim. | null | null | null | null | null | Discrete Geometry (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/40, pp. 2235--2296 |
30,002,673 | OWR-13111-003 | Estimating Probabilities of Unobserved Species | Given a multinomial database sample $X\sim\operatorname{Multinom}(n,p)$ over a very large species set and an unobserved species $s$ with $X_s=0$, develop a statistically sound estimate of $p_s$ (or $-\log_{10}p_s$) and quantify its uncertainty. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Horizons in Statistical Decision Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/41, pp. 2297--2352](https://doi.org/10.4171/owr/2014/41)
## Literature review (checked 2026-08... | 3 | open | null | 2,014 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
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"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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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-13111-003",
"literature-status:open",
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] | The extracted text identifies a forensic-statistics research theme rather than a determinate proposition; no exact claim is available to classify as proved or false. | [
{
"url": "https://doi.org/10.4171/owr/2014/41",
"label": "Oberwolfach Report 41/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/41 | null | null | null | Given a multinomial database sample $X\sim\operatorname{Multinom}(n,p)$ over a very large species set and an unobserved species $s$ with $X_s=0$, develop a statistically sound estimate of $p_s$ (or $-\log_{10}p_s$) and quantify its uncertainty. | Given a multinomial database sample X\sim\operatorname{Multinom}(n,p) over a very large species set and an unobserved species s with X_s=0, develop a statistically sound estimate of p_s (or -\log_{10}p_s) and quantify its uncertainty. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | New Horizons in Statistical Decision Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/41, pp. 2297--2352 |
30,002,674 | OWR-13111-004 | Multipartite Quantum Data Hiding with Separable States | For multipartite quantum systems with more than two parties, can the bipartite data-hiding results for separable states be generalized, including asymptotically optimal information efficiency and the best hiding-quality scaling? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Horizons in Statistical Decision Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/41, pp. 2297--2352](https://doi.org/10.4171/owr/2014/41)
## Literature review (checked 2026-08... | 3 | open | null | 2,014 | 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",
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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",
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"OWR-13111-004",
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] | The record states a broad multipartite-data-hiding generalization question; multiparty protocols exist, but optimal separable-state efficiency and the stated general extension remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/41",
"label": "Oberwolfach Report 41/2014"
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{
"url": "https://doi.org/10.1103/PhysRevA.71.062339",
"label": "Hayden--Leung--Smith, multiparty data hiding"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/41 | null | null | null | For multipartite quantum systems with more than two parties, can the bipartite data-hiding results for separable states be generalized, including asymptotically optimal information efficiency and the best hiding-quality scaling? | For multipartite quantum systems with more than two parties, can the bipartite data-hiding results for separable states be generalized, including asymptotically optimal information efficiency and the best hiding-quality scaling? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | New Horizons in Statistical Decision Theory (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/41, pp. 2297--2352 |
30,002,675 | OWR-13112-001 | Solvability of Group Equations and Surjectivity of Word Maps | Can every nonsingular equation $w\in\Gamma*F_n$ with coefficients in a group $\Gamma$ be solved over $\Gamma$? Also, for every nontrivial word $w\in F_2$, does there exist $n_0$ such that the word map $w:\operatorname{PU}(n)\times\operatorname{PU}(n)\to\operatorname{PU}(n)$ is surjective for every $n\geq n_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/42, pp. 2353--2407](https://doi.org/10.4171/owr/2014/42)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,014 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://ems.press/content/serial-article-files/46531",
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"url": "https://arxiv.org/abs/1207.5596",
"label": "Elkasapy--Thom, surjectivity of word maps"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/42 | null | null | null | Can every nonsingular equation $w\in\Gamma*F_n$ with coefficients in a group $\Gamma$ be solved over $\Gamma$? Also, for every nontrivial word $w\in F_2$, does there exist $n_0$ such that the word map $w:\operatorname{PU}(n)\times\operatorname{PU}(n)\to\operatorname{PU}(n)$ is surjective for every $n\geq n_0$? | Conjecture A: every non-singular equation w\in\Gamma*F_n with coefficients in a group \Gamma can be solved over \Gamma. Conjecture B: for every non-trivial w\in F_2 there is n_0 such that the word map w:\operatorname{PU}(n)\times\operatorname{PU}(n)\to\operatorname{PU}(n) is surjective for all n\ge n_0. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Topologie (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/42, pp. 2353--2407 |
30,002,676 | OWR-13113-001 | Gradient Flows for $N$-Species Reactive Cahn–Hilliard Systems | Extend the generalized gradient-flow formulation, well-posedness theory, and energy-dissipation theory from the two-component reactive Cahn–Hilliard model to reactive Cahn–Hilliard systems with an arbitrary number $N$ of species. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reactive Flows in Deformable, Complex Media (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/43, pp. 2409--2468](https://doi.org/10.4171/owr/2014/43)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,014 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13113-001",
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] | General thermodynamically consistent reactive n-species models and numerical schemes now exist, but a general rigorous theory matching the stated extension remains incomplete. | [
{
"url": "https://doi.org/10.1016/j.cam.2018.10.007",
"label": "Clavijo et al., reactive n-species Cahn--Hilliard model"
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{
"url": "https://doi.org/10.1007/s00161-021-01045-9",
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{
"url": "https://doi.org/10.4171/owr/2014/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/43 | null | null | null | Extend the generalized gradient-flow formulation, well-posedness theory, and energy-dissipation theory from the two-component reactive Cahn–Hilliard model to reactive Cahn–Hilliard systems with an arbitrary number $N$ of species. | Extend the generalized gradient-flow formulation and its well-posedness and energy-dissipation theory from the two-component reactive Cahn--Hilliard model to general N-species reactive Cahn--Hilliard systems. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Reactive Flows in Deformable, Complex Media (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/43, pp. 2409--2468 |
30,002,677 | OWR-13346-002 | Parallel Transport Along Sticky Principal Components | How can parallel transport be defined along sticky principal components in stratified spaces such as BHV tree space, so that second principal components and related manifold-statistical techniques can be defined? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | partially_solved | null | 2,014 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"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 | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13346-002",
"literature-status:partially-solved",
"owr-year:2014"
] | Barycentric subspace analysis and multiple-component procedures provide workable stratified-space analogues, but there is no general canonical parallel transport across strata. | [
{
"url": "https://arxiv.org/abs/1607.02833",
"label": "Pennec, barycentric subspace analysis"
},
{
"url": "https://ems.press/content/serial-article-files/46534",
"label": "BHV principal components report"
},
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach report... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | How can parallel transport be defined along sticky principal components in stratified spaces such as BHV tree space, so that second principal components and related manifold-statistical techniques can be defined? | How can parallel transport be defined along sticky principal components in stratified spaces such as BHV tree space, so that second principal components and related manifold-statistical techniques can be defined? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,678 | OWR-13346-003 | Circuits and Thresholds in Rank-Two Matrix Completion | In rank-$2$ low-rank matrix completion, characterize circuits and circuit polynomials; moreover, if $N=n$ and the observed positions are the edges of a uniformly random $2r$-regular graph, determine whether all entries are completable with high probability as $n=N\to\infty$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | open | null | 2,014 | 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-13346-003",
"literature-status:open",
"owr-year:2014"
] | Rank-two algebraic-matroid structure and circuit-based completion have advanced, but the requested full circuit-polynomial characterization and random-regular-graph completability asymptotic remain unresolved. | [
{
"url": "https://doi.org/10.1016/j.laa.2017.07.016",
"label": "Bernstein, completion of rank-two matrices"
},
{
"url": "https://jmlr.csail.mit.edu/papers/volume16/kiraly15a/kiraly15a.html",
"label": "Király--Theran--Tomioka, low-rank matrix completion"
},
{
"url": "https://doi.org/10.41... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | In rank-$2$ low-rank matrix completion, characterize circuits and circuit polynomials; moreover, if $N=n$ and the observed positions are the edges of a uniformly random $2r$-regular graph, determine whether all entries are completable with high probability as $n=N\to\infty$. | In rank-2 low-rank matrix completion, characterize circuits and circuit polynomials; moreover, if N=n and the observed positions are the edges of a uniformly random 2r-regular graph, determine whether all entries are completable with high probability as n=N\to\infty. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,679 | OWR-13346-004 | Landmark Kernel Approximation on Algebraic Manifolds | Let $\mathcal M\subset\mathbb R^n$ be an algebraic manifold of dimension $D$ and let $k$ be a degree-$d$ polynomial kernel. For fixed $x,y\in\mathcal M$ and i.i.d. standard-normal landmark points $z_1,\ldots,z_m$ with $m\geq\lambda Dd\log n$, prove an asymptotic bound of compressed-sensing type for $k(x,y)-K(x,Z)K(Z,Z)... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | open | null | 2,014 | 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-13346-004",
"literature-status:open",
"owr-year:2014"
] | Nyström theory supplies error bounds under specified landmark sampling and regularity assumptions, but the extracted Gaussian-kernel asymptotic claim is unqualified and remains unresolved as stated. | [
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1605.07583",
"label": "Recursive sampling for the Nyström method"
},
{
"url": "https://doi.org/10.1137/21M1424627",
"label": "Cai--Nagy--Xi, deterministic Nyström approxim... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | Let $\mathcal M\subset\mathbb R^n$ be an algebraic manifold of dimension $D$ and let $k$ be a degree-$d$ polynomial kernel. For fixed $x,y\in\mathcal M$ and i.i.d. standard-normal landmark points $z_1,\ldots,z_m$ with $m\geq\lambda Dd\log n$, prove an asymptotic bound of compressed-sensing type for $k(x,y)-K(x,Z)K(Z,Z)... | Let \mathcal M\subset\mathbb R^n be an algebraic manifold of dimension D and let k be a degree-d polynomial kernel. For fixed x,y\in\mathcal M and i.i.d. standard-normal landmark points z_1,\ldots,z_m with m\ge\lambda Dd\log n, prove an asymptotic bound of compressed-sensing type for k(x,y)-K(x,Z)K(Z,Z)^{-1}K(Z,y), suc... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,680 | OWR-13346-005 | Nyström Approximation Bounds for Gaussian Kernels | For the Gaussian kernel $k(x,y)=\exp\bigl(-\lVert x-y\rVert^2/(2\sigma^2)\bigr)$, prove an asymptotic-in-$m$ approximation result, with explicit dependence on $m,X,Z$, of the form $K(X,X)\approx K(X,Z)K(Z,Z)^{-1}K(Z,X)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | partially_solved | null | 2,014 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13346-005",
"literature-status:partially-solved",
"owr-year:2014"
] | Nyström and related kernel-matrix literature gives general low-rank constructions and error analyses for Gaussian kernels, but the requested asymptotic statement with the report's specific M, X, and Z hypotheses was not identified as a complete theorem. | [
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach Report 44/2014"
},
{
"url": "https://jmlr.csail.mit.edu/papers/volume18/15-025/15-025.pdf",
"label": "Memory Efficient Kernel Approximation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | For the Gaussian kernel $k(x,y)=\exp\bigl(-\lVert x-y\rVert^2/(2\sigma^2)\bigr)$, prove an asymptotic-in-$m$ approximation result, with explicit dependence on $m,X,Z$, of the form $K(X,X)\approx K(X,Z)K(Z,Z)^{-1}K(Z,X)$. | For the Gaussian kernel k(x,y)=\exp\bigl(-\lVert x-y\rVert^2/(2\sigma^2)\bigr), prove an asymptotic-in-m approximation result, with explicit dependence on m,X,Z, of the form K(X,X)\approx K(X,Z)K(Z,Z)^{-1}K(Z,X). | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,681 | OWR-13346-006 | Tensor-Bundle Parametrization of Diffusion Densities | For diffusion PCA on a Riemannian manifold, prove or disprove the conjecture that the family $\Gamma$ of point-sourced diffusion densities can be parametrized by the bundle of symmetric positive-definite covariant tensors of order $2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | open | null | 2,014 | 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-13346-006",
"literature-status:open",
"owr-year:2014"
] | Diffusion PCA has subsequent work on anisotropic distributions and most-probable paths, but the precise topology and geometric parametrization of the density family Gamma by positive-definite covariant tensors remains an explicitly unresolved identification problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach Report 44/2014"
},
{
"url": "https://doi.org/10.1007/978-3-319-19992-4_15",
"label": "Sommer, Anisotropic Distributions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | For diffusion PCA on a Riemannian manifold, prove or disprove the conjecture that the family $\Gamma$ of point-sourced diffusion densities can be parametrized by the bundle of symmetric positive-definite covariant tensors of order $2$. | For diffusion PCA on a Riemannian manifold, prove or disprove the conjecture that the family \Gamma of point-sourced diffusion densities can be parametrized by the bundle of symmetric positive-definite covariant tensors of order 2. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,682 | OWR-13346-007 | Smeariness, Stability, and Strong Consistency on Manifolds | Determine whether a non-positively curved manifold can exhibit only non-positive $k$-smeariness; determine how manifold stability and stickiness are related on a non-Hausdorff Lie-group quotient; and determine whether the inclusion in Ziezold's strong consistency result, $\bigcup_{n=1}^{\infty}\bigcap_{k=n}^{\infty}\wi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | partially_solved | null | 2,014 | 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-13346-007",
"literature-status:partially-solved",
"owr-year:2014"
] | Sticky means now have rigorous laws of large numbers and central limit theorems in open books, cones, treespaces, and broader stratified settings, but the listed curvature, quotient-stability, and strong-consistency questions are not settled in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach Report 44/2014"
},
{
"url": "https://doi.org/10.1214/12-AAP899",
"label": "Sticky Central Limit Theorems on Open Books"
},
{
"url": "https://doi.org/10.48550/arXiv.2311.09455",
"label": "Central Limit Theorems for ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | Determine whether a non-positively curved manifold can exhibit only non-positive $k$-smeariness; determine how manifold stability and stickiness are related on a non-Hausdorff Lie-group quotient; and determine whether the inclusion in Ziezold's strong consistency result, $\bigcup_{n=1}^{\infty}\bigcap_{k=n}^{\infty}\wi... | Determine whether a non-positively curved manifold can exhibit only non-positive k-smeariness; determine how manifold stability and stickiness are related on a non-Hausdorff Lie-group quotient; and determine whether the inclusion in Ziezold's strong consistency result, \bigcup_{n=1}^{\infty}\bigcap_{k=n}^{\infty}\wideh... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,683 | OWR-13346-008 | Geometric Characterization and Removal of Stickiness | Find descriptors for the degree of full stickiness. Can stickiness always be removed by changing the geometry, and which classes cannot be so treated? Can only subsets of $Q_0$ be sticky? Characterize when stickiness is possible, for example in terms of the tangent cone. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527](https://doi.org/10.4171/owr/2014/44)
## Literature review (c... | 3 | partially_solved | null | 2,014 | 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-13346-008",
"literature-status:partially-solved",
"owr-year:2014"
] | Later work supplies topological definitions, degree measures, and sticky limit theorems for several model stratified spaces, but no general characterization of the degree, removability, sticky subsets, or tangent-cone conditions listed in the record is known. | [
{
"url": "https://doi.org/10.4171/owr/2014/44",
"label": "Oberwolfach Report 44/2014"
},
{
"url": "https://doi.org/10.48550/arXiv.2311.08846",
"label": "Sticky Flavors"
},
{
"url": "https://doi.org/10.48550/arXiv.2304.05025",
"label": "Types of Stickiness in BHV Treespaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/44 | null | null | null | Find descriptors for the degree of full stickiness. Can stickiness always be removed by changing the geometry, and which classes cannot be so treated? Can only subsets of $Q_0$ be sticky? Characterize when stickiness is possible, for example in terms of the tangent cone. | Find descriptors for the degree of full stickiness; determine whether stickiness can always be removed by changing the geometry and which classes cannot be so removed; determine whether only subsets of Q_0 can be sticky; and characterize when stickiness is possible, for example in terms of the tangent cone. | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for publication. | null | null | null | null | null | Mini-Workshop: Asymptotic Statistics on Stratified Spaces (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/44, pp. 2481--2527 |
30,002,684 | OWR-13347-001 | Non-Kähler Ricci Solitons and Broader Existence Methods | Can Hermitian non-Kähler Ricci solitons be constructed using methods successful in the Kähler setting? Can partial differential equation methods establish existence on more general Fano varieties? Are there other special geometries that yield nontrivial Ricci solitons? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-001",
"literature-status:open",
"owr-year:2014"
] | The record asks for broad existence results beyond the known Kähler and symmetric constructions; current literature still describes compact non-Einstein Ricci soliton examples as Kähler, so the non-Kähler existence and general Fano/PDE questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1007/s12220-024-01554-4",
"label": "Equivariant Solutions to the Prescribed Q-Curvature Equation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Can Hermitian non-Kähler Ricci solitons be constructed using methods successful in the Kähler setting? Can partial differential equation methods establish existence on more general Fano varieties? Are there other special geometries that yield nontrivial Ricci solitons? | Can Hermitian non-Kaehler examples of nontrivial Ricci solitons be found using these or related techniques, can PDE methods establish existence on more general Fano varieties, and do other special geometries yield nontrivial solitons? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,685 | OWR-13347-002 | Non-Kähler Shrinking Ricci Solitons | Do compact non-Kähler shrinking Ricci solitons exist? Do complete noncompact non-Kähler shrinkers exist that are not of Gaussian type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-002",
"literature-status:open",
"owr-year:2014"
] | Nontrivial compact and complete noncompact Kähler shrinkers are known, and product constructions give degenerate examples, but a non-Kähler shrinker of the requested genuinely non-Gaussian type has not been established as a general solution to this problem. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1016/j.crma.2011.11.004",
"label": "Lower Bounds for Scalar Curvatures of Noncompact Shrinkers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Do compact non-Kähler shrinking Ricci solitons exist? Do complete noncompact non-Kähler shrinkers exist that are not of Gaussian type? | Do there exist compact non-Kaehler Ricci shrinkers, or complete noncompact non-Kaehler shrinkers that are not of Gaussian type? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,686 | OWR-13347-003 | Classification of Noncompact Homogeneous Einstein Spaces | Classify the noncompact, nonflat homogeneous spaces $G/K$ that admit a $G$-invariant Einstein metric. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-003",
"literature-status:partially-solved",
"owr-year:2014"
] | The Alekseevskii conjecture now forces every negative-scalar-curvature homogeneous Einstein space into the Euclidean-topology and Einstein-solvmanifold framework, but classifying all such spaces reduces to the still-wide classification of nilsolitons and is not complete. | [
{
"url": "https://doi.org/10.1090/jams/1022",
"label": "Bohm--Lafuente, Non-compact Einstein Manifolds with Symmetry"
},
{
"url": "https://annals.math.princeton.edu/2010/172-3/p09",
"label": "Lauret, Einstein Solvmanifolds are Standard"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Classify the noncompact, nonflat homogeneous spaces $G/K$ that admit a $G$-invariant Einstein metric. | Classify the noncompact, non-flat homogeneous spaces G/K that admit G-invariant Einstein metrics. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,687 | OWR-13347-004 | Einstein Solvable Factors and Orthogonal Levi Orbits | For a noncompact nonflat homogeneous Einstein space $G/K$ with Levi decomposition $G=G_1\ltimes G_2$ and $G_2=AN$, is the geometry induced on $G_2$ as a subspace of $G/K$ Einstein? If $G_1=H_1\cdots H_k$ is a product of simple subgroups, are the $H_i$-orbits through $[e]$ pairwise orthogonal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-004",
"literature-status:open",
"owr-year:2014"
] | The embedded passage contains auxiliary open questions about the geometry of the Levi and solvable factors, including orthogonality of their orbits; later progress on the main Alekseevskii conjecture does not provide a general resolution of these auxiliary assertions. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1090/jams/1022",
"label": "Bohm--Lafuente, Non-compact Einstein Manifolds with Symmetry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | For a noncompact nonflat homogeneous Einstein space $G/K$ with Levi decomposition $G=G_1\ltimes G_2$ and $G_2=AN$, is the geometry induced on $G_2$ as a subspace of $G/K$ Einstein? If $G_1=H_1\cdots H_k$ is a product of simple subgroups, are the $H_i$-orbits through $[e]$ pairwise orthogonal? | For a noncompact non-flat homogeneous Einstein space G/K with Levi decomposition G=G_1\ltimes G_2 and G_2=AN, is the geometry induced on G_2 as a subspace of G/K Einstein? If G_1=H_1\cdots H_k is a product of simple subgroups, are the H_i-orbits through [e] pairwise orthogonal? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,688 | OWR-13347-005 | Self-Adjointness of the Isotropy Action on Nilradicals | For a group $U$ acting on $\operatorname{Lie}(N)$, is the restricted adjoint action $\operatorname{Ad}(U)|_{\operatorname{Lie}(N)}$ closed under transpose; equivalently, is the action self-adjoint? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-005",
"literature-status:open",
"owr-year:2014"
] | The self-adjointness of the U-action on the nilradical is posed as a structural step toward the strong Alekseevskii conjecture, and no general theorem resolving this exact action property was found. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1090/jams/1022",
"label": "Bohm--Lafuente, Non-compact Einstein Manifolds with Symmetry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | For a group $U$ acting on $\operatorname{Lie}(N)$, is the restricted adjoint action $\operatorname{Ad}(U)|_{\operatorname{Lie}(N)}$ closed under transpose; equivalently, is the action self-adjoint? | For U acting on \operatorname{Lie}N, is the restricted adjoint action \operatorname{Ad}(U)|_{\operatorname{Lie}N} closed under transpose, i.e. is the action self-adjoint? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,689 | OWR-13347-007 | Homogeneous Einstein Metrics on Flag and Stiefel Manifolds | Find all homogeneous Einstein metrics on generalized flag manifolds $G/K$ and on Stiefel manifolds $V_k\mathbb R^n=\operatorname{SO}(n)/\operatorname{SO}(n-k)$; and determine whether the number of homogeneous Einstein metrics is finite for homogeneous spaces with nonequivalent irreducible isotropy components and for co... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-007",
"literature-status:partially-solved",
"owr-year:2014"
] | Many generalized flag-manifold families and low-isotropy cases have been classified, but the requested all-metrics classifications for arbitrary flag manifolds, Stiefel manifolds, and compact simple groups remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1016/j.bulsci.2013.11.002",
"label": "Classification of Einstein Metrics on Flag Manifolds"
},
{
"url": "https://doi.org/10.48550/arXiv.1207.2897",
"label": "Flag Man... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Find all homogeneous Einstein metrics on generalized flag manifolds $G/K$ and on Stiefel manifolds $V_k\mathbb R^n=\operatorname{SO}(n)/\operatorname{SO}(n-k)$; and determine whether the number of homogeneous Einstein metrics is finite for homogeneous spaces with nonequivalent irreducible isotropy components and for co... | Find all homogeneous Einstein metrics on generalized flag manifolds G/K and on Stiefel manifolds V_k\mathbb R^n=\operatorname{SO}(n)/\operatorname{SO}(n-k); and determine whether the number of homogeneous Einstein metrics is finite for homogeneous spaces with non-equivalent irreducible isotropy components and for compa... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,690 | OWR-13347-008 | Non-Naturally Reductive Einstein Metrics on Compact Lie Groups | Find further non-naturally reductive Einstein metrics on compact simple Lie groups $G$ by using homogeneous spaces $G/H$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-008",
"literature-status:partially-solved",
"owr-year:2014"
] | Subsequent work has produced and classified additional non-Kahler and non-naturally reductive homogeneous Einstein metrics in several families, but finding and classifying all such metrics on compact simple groups remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.48550/arXiv.1207.2897",
"label": "Flag Manifolds with Five Isotropy Summands"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Find further non-naturally reductive Einstein metrics on compact simple Lie groups $G$ by using homogeneous spaces $G/H$. | Find more non-naturally reductive Einstein metrics on compact simple Lie groups G using homogeneous spaces G/H. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,691 | OWR-13347-010 | Convergence and Curvature of Homogeneous Ricci Flows | For a general solvable Lie group, does the bracket flow converge after suitable normalization to a Ricci soliton, and is the limit unique? If a homogeneous space admits homogeneous metrics with positive scalar curvature, must the scalar curvature of every homogeneous Ricci-flow solution on that space eventually become ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-010",
"literature-status:partially-solved",
"owr-year:2014"
] | Bracket-flow fixed points and several convergence results are known for important solvable and nilpotent classes, but convergence and uniqueness for arbitrary solvable groups and the stated scalar-curvature behavior for every homogeneous Ricci flow remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.1093/qmath/hat028",
"label": "On Homogeneous Ricci Solitons"
},
{
"url": "https://arxiv.org/abs/1212.6558",
"label": "Scalar Curvature Behavior of Homogeneous Ricci F... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | For a general solvable Lie group, does the bracket flow converge after suitable normalization to a Ricci soliton, and is the limit unique? If a homogeneous space admits homogeneous metrics with positive scalar curvature, must the scalar curvature of every homogeneous Ricci-flow solution on that space eventually become ... | For a general solvable Lie group, does the bracket flow converge after suitable normalization to a Ricci soliton, and is the limit unique? If a homogeneous space admits homogeneous metrics with positive scalar curvature, must the scalar curvature of every homogeneous Ricci-flow solution on that space eventually become ... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,692 | OWR-13347-011 | Hyperbolic Conformal Boundaries of Poincaré–Einstein Manifolds | Does there exist a complete conformally compactifiable Poincaré–Einstein manifold whose boundary at infinity is a compact connected manifold of constant sectional curvature $-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | solved | null | 2,014 | 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/10.4310/ATMP.2000.v4.n4.a5",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; classical)**. E. Woolgar (OWR 45/2014, p. 2550) asks for a complete, conformally compactifiable Poincaré–Einstein manifold whose boundary at infinity is a compact connected manifold of curvature −1, or a proof that none exists. Hyperbolic examples exist: in b... | [
"owr",
"oberwolfach-reports",
"OWR-13347-011",
"literature-status:open",
"owr-year:2014"
] | The extracted statement does not include the mathematical question being posed, so no definite claim can be tested; under the required uncertainty rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Does there exist a complete conformally compactifiable Poincaré–Einstein manifold whose boundary at infinity is a compact connected manifold of constant sectional curvature $-1$? | Does there exist a complete conformally compactifiable Poincare--Einstein manifold whose boundary at infinity is a compact connected manifold of constant sectional curvature -1, or is no such manifold possible? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,693 | OWR-13347-012 | Canonical Left-Invariant Metrics on Lie Groups | Does there exist a best left-invariant Riemannian metric on a given Lie group, and if so, how is its geometry related to the Lie-group structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-012",
"literature-status:open",
"owr-year:2014"
] | The phrase best metric is not defined precisely enough to yield a single theorem; uniqueness and maximal-symmetry results exist for selected solvable Ricci-soliton classes, but no general canonical metric principle is established. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://arxiv.org/abs/2112.09733",
"label": "Infinitesimal Maximal Symmetry and Ricci Solitons"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Does there exist a best left-invariant Riemannian metric on a given Lie group, and if so, how is its geometry related to the Lie-group structure? | Does there exist a best left-invariant Riemannian metric on a given Lie group, and if so, how is its geometry related to the Lie-group structure? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,694 | OWR-13347-013 | Curvature-Derivative Invariants of Homogeneous Spaces | For a homogeneous Riemannian manifold, let $k_o$ denote its constant Jacobi osculating rank, let $k_t$ be the least $k\geq0$ for which the completely traceless Cartan component $Y_0^{(k+3,2)}R$ vanishes, and let $k_S$ be its Singer invariant. Determine $k_t$ for $\operatorname{Sp}(2)/\operatorname{SU}(2)$, $(\operatorn... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-013",
"literature-status:partially-solved",
"owr-year:2014"
] | Several listed invariants have been computed for important homogeneous examples and special nearly Kahler spaces, but the universal finiteness, converse, and equality questions in the record remain open. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.48550/arXiv.1207.2897",
"label": "Flag Manifolds with Five Isotropy Summands"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | For a homogeneous Riemannian manifold, let $k_o$ denote its constant Jacobi osculating rank, let $k_t$ be the least $k\geq0$ for which the completely traceless Cartan component $Y_0^{(k+3,2)}R$ vanishes, and let $k_S$ be its Singer invariant. Determine $k_t$ for $\operatorname{Sp}(2)/\operatorname{SU}(2)$, $(\operatorn... | Determine the values of k_t for the listed examples; compute k_o,k_t,k_S for further homogeneous spaces; determine whether every naturally reductive, geodesic-orbit, or general homogeneous Riemannian space has k_t<\infty and whether the converse holds; determine whether every homogeneous Einstein manifold has k_o<\inft... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,695 | OWR-13347-014 | Parity and Ricci-Flow Evolution of Curvature Invariants | With $k_o$, $k_t$, and $k_S$ as the curvature-derivative, traceless-curvature, and Singer invariants of a homogeneous Riemannian manifold, is finite $k_o$ always even? If $k_t=1$, what can be deduced about the rough-Laplacian eigenvalue equation $\nabla^*\nabla R=\lambda R$? How do the defining traceless-curvature equa... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-014",
"literature-status:open",
"owr-year:2014"
] | The record asks for general information on an additional inequality and on the Ricci-flow evolution of several geometric invariants; no general resolution of these questions was identified. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | With $k_o$, $k_t$, and $k_S$ as the curvature-derivative, traceless-curvature, and Singer invariants of a homogeneous Riemannian manifold, is finite $k_o$ always even? If $k_t=1$, what can be deduced about the rough-Laplacian eigenvalue equation $\nabla^*\nabla R=\lambda R$? How do the defining traceless-curvature equa... | If k_t=1, what can be said about the equation \nabla^{*}\nabla R=\lambda R? How do Equation (5) and the invariants k_t,k_o,k_S evolve under the Ricci flow? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,696 | OWR-13347-015 | Geometric Invariant Theory for Homogeneous Spaces | What other tools from Geometric Invariant Theory can be applied to obtain new information about the geometry of homogeneous spaces? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | open | null | 2,014 | 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-13347-015",
"literature-status:open",
"owr-year:2014"
] | Geometric invariant theory has yielded major structural results for Einstein solvmanifolds and homogeneous solitons, but the open-ended request for further tools and new geometric consequences has no complete answer. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://annals.math.princeton.edu/2010/172-3/p09",
"label": "Lauret, Einstein Solvmanifolds are Standard"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | What other tools from Geometric Invariant Theory can be applied to obtain new information about the geometry of homogeneous spaces? | What other tools from Geometric Invariant Theory can be applied to obtain new information about the geometry of homogeneous spaces? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,697 | OWR-13347-016 | Maximal Isometry Groups of Solvable Ricci Solitons | To what extent do the maximal-isometry-group results for Einstein metrics extend to Ricci soliton metrics on general solvable Lie groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-016",
"literature-status:partially-solved",
"owr-year:2014"
] | The general homogeneous-Ricci-soliton theory now proves algebraicity relative to a suitable transitive isometry group, and expanding solvable solitons have strong maximal-symmetry and uniqueness results, but the full analogue of the Einstein maximal-isometry theorem is not completely uniform. | [
{
"url": "https://msp.org/gt/2014/18-4/gt-v18-n4-p12-s.pdf",
"label": "Every Semialgebraic Ricci Soliton is Algebraic"
},
{
"url": "https://arxiv.org/abs/2112.09733",
"label": "Infinitesimal Maximal Symmetry and Ricci Solitons"
},
{
"url": "https://doi.org/10.4171/owr/2014/45",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | To what extent do the maximal-isometry-group results for Einstein metrics extend to Ricci soliton metrics on general solvable Lie groups? | To what extent do the maximal-isometry-group results for Einstein metrics extend to Ricci soliton metrics on general solvable Lie groups? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,698 | OWR-13347-017 | Ricci-Tensor Fibrations for Generalized Flag Manifolds | Let $K\subset L\subset G$ define a fibration $G/K\to G/L$ with fiber $L/K$, where $G/K$ and $G/L$ are generalized flag manifolds. A Kähler–Einstein metric and the homogeneous-fibration Ricci-tensor formula determine the Ricci tensor when $b_2(G/K)=2$, $b_2(G/L)=1$, and the isotropy decomposition has at most six summand... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-017",
"literature-status:partially-solved",
"owr-year:2014"
] | The fibration and Riemannian-submersion method has classified numerous flag-manifold families, including five-isotropy-summand cases, but it has not yielded a complete method or classification for every generalized flag manifold. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://doi.org/10.48550/arXiv.1207.2897",
"label": "Flag Manifolds with Five Isotropy Summands"
},
{
"url": "https://doi.org/10.1016/j.bulsci.2013.11.002",
"label": "Classification of ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Let $K\subset L\subset G$ define a fibration $G/K\to G/L$ with fiber $L/K$, where $G/K$ and $G/L$ are generalized flag manifolds. A Kähler–Einstein metric and the homogeneous-fibration Ricci-tensor formula determine the Ricci tensor when $b_2(G/K)=2$, $b_2(G/L)=1$, and the isotropy decomposition has at most six summand... | Does the fibration method using K\"ahler--Einstein metrics and Lemma 2 work for every generalized flag manifold? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,699 | OWR-13347-018 | Negative Ricci Curvature on Solvable Lie Algebras | Let $\mathfrak{g}$ be a solvable Lie algebra with nilradical $\mathfrak{n}$. Does $\mathfrak{g}$ admit an inner product with $\operatorname{Ric}<0$ if and only if some $X\in\mathfrak{g}\setminus\mathfrak{n}$ has $\left.\operatorname{ad}X\right|_{\mathfrak{n}}$ satisfying linear inequalities determined solely by $\mathf... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | partially_solved | null | 2,014 | 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-13347-018",
"literature-status:partially-solved",
"owr-year:2014"
] | Necessary and sufficient criteria are known for abelian, Heisenberg, and several filiform nilradicals, and moment-map convex cones describe broad families, but the proposed characterization for arbitrary nilradicals remains open. | [
{
"url": "https://doi.org/10.48550/arXiv.1312.6803",
"label": "Solvable Lie Groups of Negative Ricci Curvature"
},
{
"url": "https://doi.org/10.1002/mana.201500019",
"label": "Solvable Extensions of Filiform Lie Groups"
},
{
"url": "https://doi.org/10.48550/arXiv.1912.06204",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Let $\mathfrak{g}$ be a solvable Lie algebra with nilradical $\mathfrak{n}$. Does $\mathfrak{g}$ admit an inner product with $\operatorname{Ric}<0$ if and only if some $X\in\mathfrak{g}\setminus\mathfrak{n}$ has $\left.\operatorname{ad}X\right|_{\mathfrak{n}}$ satisfying linear inequalities determined solely by $\mathf... | For a solvable Lie algebra g with nilradical n, does g admit an inner product with \operatorname{Ric}<0 if and only if some X\in g\setminus n has \operatorname{ad}X|_n satisfying linear inequalities determined solely by n? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,700 | OWR-13347-019 | Compactness of Positively Curved Shrinking Ricci Solitons | Must every gradient shrinking Ricci soliton with bounded positive curvature operator be compact? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568](https://doi.org/10.4171/owr/2... | 3 | solved | null | 2,014 | 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/10.4310/jdg/1500084024",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. W. Wylie (OWR 45/2014, p. 2563, Conjecture 2) conjectures that a gradient shrinking Ricci soliton with bounded positive curvature operator is compact. Munteanu–Wang, [J. Differential Geom. 106 (2017)](https://doi.org/10.4310/jdg/1500084024), Theorem 2 ([ar... | [
"owr",
"oberwolfach-reports",
"OWR-13347-019",
"literature-status:open",
"owr-year:2014"
] | Compactness is proved in dimensions three and four and under additional curvature, pinching, or volume-growth hypotheses, but the stated all-dimensional bounded-positive-curvature-operator conjecture is not resolved by the available results. | [
{
"url": "https://doi.org/10.4171/owr/2014/45",
"label": "Oberwolfach Report 45/2014"
},
{
"url": "https://cvgmt.sns.it/media/doc/paper/2295/CDM-SHRINKERS_3apr.pdf",
"label": "Rigidity of Asymptotically Cylindrical Shrinkers"
},
{
"url": "https://arxiv.org/abs/math/0601599",
"label":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/45 | null | null | null | Must every gradient shrinking Ricci soliton with bounded positive curvature operator be compact? | Every gradient shrinking Ricci soliton with bounded positive curvature operator is compact. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Mini-Workshop: Einstein Metrics, Ricci Solitons and Ricci Flow under Symmetry Assumptions (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/45, pp. 2529--2568 |
30,002,701 | OWR-13348-002 | Unstable Invariance of Multiple-Correlation Limits | Are all weak-$L^2$ accumulation points of the multiple-correlation sequence $\varphi_1\circ f^{n_1}\,\varphi_2\circ f^{n_1+n_2}\cdots\varphi_k\circ f^{n_1+\cdots+n_k}$, as all $n_i\to\infty$, also $W^u$-invariant, given that they are $W^s$-invariant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/46, pp. 2569--2617](https://doi.org/10.4171/owr/2014/4... | 3 | open | null | 2,014 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13348-002",
"literature-status:open",
"owr-year:2014"
] | For the multiple-mixing accumulation points in the record, stable invariance is proved but unstable invariance is explicitly posed as an open question; later weak-hyperbolicity results give mixing under extra assumptions rather than a general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2014/46",
"label": "Oberwolfach Report 46/2014"
},
{
"url": "https://doi.org/10.1017/S0143385706000733",
"label": "Coudene, On Invariant Distributions and Mixing"
},
{
"url": "https://arxiv.org/abs/1406.4015",
"label": "Multiple Mixing from Weak ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/46 | null | null | null | Are all weak-$L^2$ accumulation points of the multiple-correlation sequence $\varphi_1\circ f^{n_1}\,\varphi_2\circ f^{n_1+n_2}\cdots\varphi_k\circ f^{n_1+\cdots+n_k}$, as all $n_i\to\infty$, also $W^u$-invariant, given that they are $W^s$-invariant? | Are all weak-L^2 accumulation points of the multiple-correlation sequence \varphi_1\circ f^{n_1} \varphi_2\circ f^{n_1+n_2}\cdots\varphi_k\circ f^{n_1+\cdots+n_k}, as all n_i\to\infty, also W^u-invariant, given that they are W^s-invariant? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/46, pp. 2569--2617 |
30,002,702 | OWR-13348-003 | Kaplan–Yorke Equality for Coupled Baker's Maps | For bidirectionally coupled skinny baker's maps, does the Kaplan–Yorke equality hold for a prevalent set of coupling functions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/46, pp. 2569--2617](https://doi.org/10.4171/owr/2014/4... | 3 | open | null | 2,014 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13348-003",
"literature-status:open",
"owr-year:2014"
] | The cited work proves the Kaplan--Yorke equality for one-way coupling in a prevalent set of cases and proves failure in others, but explicitly leaves the bidirectional-coupling conjecture unresolved. | [
{
"url": "https://arxiv.org/abs/1303.0030",
"label": "Gröger--Hunt, Coupled skinny baker's maps"
},
{
"url": "https://doi.org/10.4171/owr/2014/46",
"label": "Oberwolfach Report 46/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/46 | null | null | null | For bidirectionally coupled skinny baker's maps, does the Kaplan–Yorke equality hold for a prevalent set of coupling functions? | For bi-directionally coupled skinny baker's maps, does the Kaplan--Yorke equality hold for a prevalent set of coupling functions? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Mini-Workshop: Differentiable Ergodic Theory, Dimension Theory and Stable Foliations (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/46, pp. 2569--2617 |
30,002,703 | OWR-13349-004 | Periodic Topologically Simple Locally Compact Groups | Does there exist a compactly generated totally disconnected locally compact group that is topologically simple, non-discrete, and periodic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Totally Disconnected Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/47, pp. 2619--2665](https://doi.org/10.4171/owr/2014/47)
## Literature review (checked 20... | 3 | open | null | 2,014 | 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-13349-004",
"literature-status:open",
"owr-year:2014"
] | The existence of a compactly generated, nondiscrete, topologically simple, periodic t.d.l.c. group is still presented as an open topological-Tarski-monster question, with no authoritative construction found. | [
{
"url": "https://doi.org/10.4171/owr/2014/47",
"label": "Oberwolfach Report 47/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/47 | null | null | null | Does there exist a compactly generated totally disconnected locally compact group that is topologically simple, non-discrete, and periodic? | Does there exist a compactly generated totally disconnected locally compact group that is topologically simple, non-discrete, and periodic? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Arbeitsgemeinschaft: Totally Disconnected Groups (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/47, pp. 2619--2665 |
30,002,704 | OWR-13350-001 | Quasi-Invariant Random Measures and Associated Diffusions | Let a group $G$ act on the space $\mathcal M(X)$ of Radon measures on $X$. Which laws of random measures are quasi-invariant under $G$ and support an associated analysis, such as a Laplace operator or a diffusion on $\mathcal M(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756](https://doi.org/10.4171/owr/2014/48)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13350-001",
"literature-status:open",
"owr-year:2014"
] | The record asks for a general theory of quasi-invariant laws of random measures and associated analysis, but gives no precise class or theorem; the broad problem remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2014/48",
"label": "Oberwolfach Report 48/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/48 | null | null | null | Let a group $G$ act on the space $\mathcal M(X)$ of Radon measures on $X$. Which laws of random measures are quasi-invariant under $G$ and support an associated analysis, such as a Laplace operator or a diffusion on $\mathcal M(X)$? | For a group G acting on the space M(X) of Radon measures on X, which laws of random measures are quasi-invariant under G and support associated analysis such as a Laplace operator or diffusion on M(X)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756 |
30,002,705 | OWR-13350-003 | Occupation Times of Manifold Brownian Motion | Let $W$ be Brownian motion on a Riemannian manifold $M$ starting at $o$, and let a hypersurface $N$ locally separate $M$ into $M^+$ and $M^-$. Describe the total time $T$ that $W$ spends in $M^+$ up to time $t$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756](https://doi.org/10.4171/owr/2014/48)
## Literature review (checked 2026-08-... | 3 | partially_solved | null | 2,014 | 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-13350-003",
"literature-status:partially-solved",
"owr-year:2014"
] | Hsu and Ouyang obtain a rigorous short-time expansion for the occupation time, including the arcsine term and the mean-curvature/local-time correction; a complete distributional description for arbitrary time is not supplied. | [
{
"url": "https://arxiv.org/abs/2004.10039",
"label": "Hsu--Ouyang, Geometric Deviation from Levys Law"
},
{
"url": "https://doi.org/10.4171/owr/2014/48",
"label": "Oberwolfach Report 48/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/48 | null | null | null | Let $W$ be Brownian motion on a Riemannian manifold $M$ starting at $o$, and let a hypersurface $N$ locally separate $M$ into $M^+$ and $M^-$. Describe the total time $T$ that $W$ spends in $M^+$ up to time $t$. | Let W be Brownian motion on a Riemannian manifold M starting at o, and let a hypersurface N locally divide M into M^+ and M^-. How can one describe the total time T that W spends in M^+ up to time t? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756 |
30,002,706 | OWR-13350-005 | Semigroup Uniqueness for Dirichlet Operators | Is the Friedrichs extension the only closed extension of $L_0$ generating a $C_0$-semigroup on $L^p(\mu)$ for $p\geq1$, equivalently, is $L_0$ essentially self-adjoint when $p=2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756](https://doi.org/10.4171/owr/2014/48)
## Literature review (checked 2026-08-... | 3 | open | null | 2,014 | 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-13350-005",
"literature-status:open",
"owr-year:2014"
] | Essential self-adjointness and Lp-uniqueness are proved for important concrete Gibbs and Dirichlet-operator classes, but the general uniqueness question stated here remains a fundamental open problem. | [
{
"url": "https://bibos.math.uni-bielefeld.de/preprints/06-05-211.pdf",
"label": "Albeverio--Kondratiev--Rockner, Essential self-adjointness"
},
{
"url": "https://doi.org/10.4171/owr/2014/48",
"label": "Oberwolfach Report 48/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/48 | null | null | null | Is the Friedrichs extension the only closed extension of $L_0$ generating a $C_0$-semigroup on $L^p(\mu)$ for $p\geq1$, equivalently, is $L_0$ essentially self-adjoint when $p=2$? | Is the Friedrichs extension the only closed extension of L_0 generating a C_0-semigroup on L^p(\mu) for p\geq1, equivalently is L_0 essentially self-adjoint when p=2? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Dirichlet Form Theory and its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/48, pp. 2667--2756 |
30,002,707 | OWR-13351-004 | Kontsevich–Zagier Equivalence of Real Period Integrals | Let $X_1,X_2\subset\mathbb R^n$ be semialgebraic sets and let $f_1,f_2$ be semialgebraic functions for which the integrals converge. If
$$\int_{X_1}f_1=\int_{X_2}f_2,$$
can one pass from one integral to the other using additivity, semialgebraic changes of variables, and Stokes' formula? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-004",
"literature-status:open",
"owr-year:2014"
] | For the real Kontsevich--Zagier period question, the implication that equal integral values are connected by the standard rules remains open; the report's p-adic discussion does not settle the real claim. | [
{
"url": "https://numdam.org/articles/10.5802/jtnb.1204/",
"label": "Kontsevich--Zagier period conjecture overview"
},
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach Report 49/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Let $X_1,X_2\subset\mathbb R^n$ be semialgebraic sets and let $f_1,f_2$ be semialgebraic functions for which the integrals converge. If
$$\int_{X_1}f_1=\int_{X_2}f_2,$$
can one pass from one integral to the other using additivity, semialgebraic changes of variables, and Stokes' formula? | If \int_{X_1}f_1=\int_{X_2}f_2, does it follow that one integral can be transformed into the other by standard integral-transformation rules? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,708 | OWR-13351-005 | Motivic Kontsevich–Zagier Equivalence | Does equality of two Cluckers–Loeser motivic integrals imply that they are related by the motivic analogues of additivity, semialgebraic change of variables, and Stokes' formula? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-005",
"literature-status:partially-solved",
"owr-year:2014"
] | The broad real period problem remains open, while Cluckers and Halupczok prove a positive p-adic semialgebraic analogue using basic integral transformation rules. | [
{
"url": "https://arxiv.org/abs/2003.01500",
"label": "Cluckers--Halupczok, p-adic Kontsevich--Zagier rules"
},
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach Report 49/2014"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Does equality of two Cluckers–Loeser motivic integrals imply that they are related by the motivic analogues of additivity, semialgebraic change of variables, and Stokes' formula? | For specified classes of sets X_i, functions f_i, and allowed transformation rules, does equality \int_{X_1}f_1=\int_{X_2}f_2 imply that the two integrals are related by those rules? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,709 | OWR-13351-007 | Essential Finite Generation of Valuation Rings | For a finite valued-field extension $(F|L,v)$, do there exist $a_1,\ldots,a_r\in O_F$ such that $O_F=O_L[a_1,\ldots,a_r]_{O_L[a_1,\ldots,a_r]\cap\mathfrak m_F}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"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/10.1002/mana.202100190",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (Knaf's criterion)**. J. Novacoski (joint with F.-V. Kuhlmann; OWR 49/2014, pp. 2799–2800) asks when O_F is essentially finitely generated over O_L for a finite extension (F|L, v), and records H. Knaf's necessary condition e₁ = ε₁, d₁ = 1, known to be sufficient in... | [
"owr",
"oberwolfach-reports",
"OWR-13351-007",
"literature-status:partially-solved",
"owr-year:2014"
] | The general essential-finite-generation question is not completely settled, but a necessary condition and a theorem characterizing finite generation of the integral closure are known, with sufficiency for henselian or normal extensions. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3439/OWR_2014_49.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://arxiv.org/abs/1311.6155",
"label": "Kuhlmann--Novacoski, Henselian elements"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | For a finite valued-field extension $(F|L,v)$, do there exist $a_1,\ldots,a_r\in O_F$ such that $O_F=O_L[a_1,\ldots,a_r]_{O_L[a_1,\ldots,a_r]\cap\mathfrak m_F}$? | For a finite valued-field extension (F|L,v), does there exist a_1,\ldots,a_r\in O_F such that O_F=O_L[a_1,\ldots,a_r]_{ O_L[a_1,\ldots,a_r]\cap\mathfrak m_F}? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,710 | OWR-13351-009 | Characteristic-Zero Lifts of Local Galois Extensions | Given an algebraically closed field $k$ of characteristic $p$ and a $G$-Galois extension $k[[z]]/k[[t]]$, does there exist a complete characteristic-zero discrete valuation ring $(R,\pi)$ with residue field $k$ and a $G$-Galois extension $R[[Z]]/R[[T]]$ reducing to $k[[z]]/k[[t]]$ modulo $\pi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-009",
"literature-status:open",
"owr-year:2014"
] | The local lifting problem is solved for cyclic groups, but no general theorem covers arbitrary finite Galois groups; the extracted universal question therefore remains open. | [
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://arxiv.org/abs/1502.07623",
"label": "Obus, A generalization of the Oort conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Given an algebraically closed field $k$ of characteristic $p$ and a $G$-Galois extension $k[[z]]/k[[t]]$, does there exist a complete characteristic-zero discrete valuation ring $(R,\pi)$ with residue field $k$ and a $G$-Galois extension $R[[Z]]/R[[T]]$ reducing to $k[[z]]/k[[t]]$ modulo $\pi$? | Given an algebraically closed field k of characteristic p and a G-Galois extension k[[z]]/k[[t]], does there exist a complete characteristic-zero discrete valuation ring (R,\pi) with residue field k and a G-Galois extension R[[Z]]/R[[T]] reducing to k[[z]]/k[[t]] modulo \pi? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,711 | OWR-13351-010 | Minimal Coefficient Rings for Cyclic Local Lifts | Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $k[[z]] / k[[t]]$ be a cyclic $G$-Galois extension of power-series rings. In the local lifting problem for cyclic groups $G$ (which asks for a complete discrete valuation ring $R$ of characteristic $0$ with residue field $k$ and a $G$-Galois ex... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-010",
"literature-status:open",
"owr-year:2014"
] | The existence of a cyclic lift is known, but the stronger assertion that the coefficient ring can always be chosen as W(k) with the indicated roots of unity remains an open question for the wild cyclic cases. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3439/OWR_2014_49.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://arxiv.org/abs/1502.07623",
"label": "Obus, A generalization of the Oort conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $k[[z]] / k[[t]]$ be a cyclic $G$-Galois extension of power-series rings. In the local lifting problem for cyclic groups $G$ (which asks for a complete discrete valuation ring $R$ of characteristic $0$ with residue field $k$ and a $G$-Galois ex... | For cyclic groups G not covered by the known construction, can the local lifting problem be solved with R=W(k)(\zeta_{|G|})? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,712 | OWR-13351-011 | Classification of Local Oort Groups | What is the complete list of local Oort groups, namely groups for which every local G-extension lifts to characteristic zero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-011",
"literature-status:open",
"owr-year:2014"
] | Cyclic groups are local Oort groups and several additional cases are known, but a complete classification of local Oort groups remains unresolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3439/OWR_2014_49.pdf?isAllowed=y&sequence=1",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://www2.math.upenn.edu/~harbater/oortpaper3.pdf",
"label": "Chinburg--Guralnick--Harbater, Global Oort groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | What is the complete list of local Oort groups, namely groups for which every local G-extension lifts to characteristic zero? | What is the complete list of local Oort groups, namely groups for which every local G-extension lifts to characteristic zero? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,713 | OWR-13351-012 | Odd Dihedral Groups as Oort Groups | For odd primes p, are the dihedral groups $D_{p^n}$ of order $2p^n$ Oort groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-13351-012",
"literature-status:partially-solved",
"owr-year:2014"
] | The conjecture that all odd-prime-power dihedral groups are local Oort groups has substantial special cases, including D_p and D_9, but remains open in general. | [
{
"url": "https://ems.press/content/serial-article-files/46540",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://arxiv.org/abs/1502.07623",
"label": "Obus, A generalization of the Oort conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | For odd primes p, are the dihedral groups $D_{p^n}$ of order $2p^n$ Oort groups? | For odd primes p, are the dihedral groups D_{p^n} of order 2p^n Oort groups? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,714 | OWR-13351-013 | Complete Integral Closures of Total Blow-Up Rings | Let $(R, v)$ be a valuation domain (or local Noetherian domain dominated by a valuation $v$), and let $S = B_\infty(R, v)$ be the total blow-up ring obtained as the union of the local blow-ups of $R$ along $v$. Is the complete integral closure of $S = B_\infty(R, v)$ always a valuation ring? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | open | null | 2,014 | 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-13351-013",
"literature-status:open",
"owr-year:2014"
] | For total blow-up rings S the question whether the complete integral closure is always a valuation ring is explicitly left open, and no later general resolution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46540",
"label": "Oberwolfach Report 49/2014"
},
{
"url": "https://doi.org/10.1017/S1446788700007230",
"label": "Heinzer, Some remarks on complete integral closure"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | Let $(R, v)$ be a valuation domain (or local Noetherian domain dominated by a valuation $v$), and let $S = B_\infty(R, v)$ be the total blow-up ring obtained as the union of the local blow-ups of $R$ along $v$. Is the complete integral closure of $S = B_\infty(R, v)$ always a valuation ring? | If S=B_{\infty}(R,v) is a total blow-up ring, is the complete integral closure of S a valuation ring? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that this meaning-preserving cleanup is self-contained and adds no unsupported source-dependent content. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
30,002,715 | OWR-13351-014 | Birational Anabelian Reconstruction over Finitely Generated Fields | For varieties $X$ and $Y$ of dimension at least $1$ over a finitely generated field $K$, are the canonical maps from $K$-isomorphisms of their function fields to $K$-birational isomorphisms and then to the corresponding outer Galois-group isomorphisms bijective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823](https://doi.org/10.4171/owr/2014/49)
## Literature review (checked 2026-08-21)
... | 3 | partially_solved | null | 2,014 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (yes; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; answered in the source)**. The record is item (4), the birational anabelian conjecture, of the list of Grothendieck's conjectures in A. M. Silberstein's abstract (OWR 49/2014, pp. 2807–2811); p. 2808 says Pop solved it. Pop, [Ann. of Math. 139 (1994)](https:/... | [
"owr",
"oberwolfach-reports",
"OWR-13351-014",
"literature-status:partially-solved",
"owr-year:2014"
] | Pop proved the birational anabelian conjecture over finitely generated fields, but the broader anabelian-variety and generic-point assertions in the record are not all known in this generality. | [
{
"url": "https://annals.math.princeton.edu/1994/139-1/p05",
"label": "Pop, birational anabelian geometry"
},
{
"url": "https://doi.org/10.4171/owr/2014/49",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2014/49 | null | null | null | For varieties $X$ and $Y$ of dimension at least $1$ over a finitely generated field $K$, are the canonical maps from $K$-isomorphisms of their function fields to $K$-birational isomorphisms and then to the corresponding outer Galois-group isomorphisms bijective? | Birational anabelian conjecture: for varieties X and Y of dimension at least 1 over a finitely generated field K, the canonical maps from K-isomorphisms of function fields to K-birational isomorphisms and then to the corresponding outer Galois-group isomorphisms are all isomorphisms. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Valuation Theory and Its Applications (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/49, pp. 2757--2823 |
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