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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,002,016 | OWR-11583-009 | Low-Degree Cohomology of Finite Groups of Lie Type | Compute the first and second cohomology groups of finite groups of Lie type with coefficients in simple modules whose highest weight is fundamental dominant. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-009",
"literature-status:partially-solved",
"owr-year:2012"
] | First and second cohomology are computed for broad ranges of groups, primes, and fundamental or small dominant weights, but no uniform answer for all fundamental weights and parameters is known. | [
{
"url": "https://arxiv.org/abs/1010.1203",
"label": "First cohomology"
},
{
"url": "https://arxiv.org/abs/1110.0228",
"label": "Second cohomology"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Compute the first and second cohomology groups of finite groups of Lie type with coefficients in simple modules whose highest weight is fundamental dominant. | Compute the first and second cohomology groups of finite groups of Lie type with coefficients in simple modules whose highest weight is fundamental dominant. | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,017 | OWR-11583-010 | Character Degrees, Group Algebras, and Nilpotent Blocks | Determine whether the set of irreducible character degrees determines solvability of a finite group, whether its complex group algebra determines the existence of a normal Sylow $p$-subgroup, and whether nilpotent blocks are exactly those whose height-zero characters all have the same degree. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,012 | 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-11583-010",
"literature-status:open",
"owr-year:2012"
] | The fragment invokes Dade's Projective Conjecture; reductions and broad special cases are known, but the conjecture is not proved for all finite groups. | [
{
"url": "https://ems.press/journals/jems/articles/14667",
"label": "Reduction theorem for Dade's projective conjecture"
},
{
"url": "https://arxiv.org/abs/2402.10632",
"label": "Character Triple reduction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Determine whether the set of irreducible character degrees determines solvability of a finite group, whether its complex group algebra determines the existence of a normal Sylow $p$-subgroup, and whether nilpotent blocks are exactly those whose height-zero characters all have the same degree. | Determine whether the set of irreducible character degrees determines solvability of a finite group, whether its complex group algebra determines the existence of a normal Sylow p-subgroup, and whether nilpotent blocks are exactly those whose height-zero characters all have the same degree. | 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 | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,018 | OWR-11583-011 | Perverse Deligne–Lusztig Equivalences for Abelian Defect Blocks | Prove that the Deligne–Lusztig-derived equivalence predicted by Broué's abelian-defect-group conjecture for suitable finite groups of Lie type is a perverse equivalence. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-011",
"literature-status:partially-solved",
"owr-year:2012"
] | Perverse equivalences have been constructed in cyclic and several noncyclic cases, but the general equivalences predicted from Deligne--Lusztig varieties are not established. | [
{
"url": "https://doi.org/10.1016/j.aim.2013.07.010",
"label": "Perverse equivalences and Broué's conjecture"
},
{
"url": "https://arxiv.org/abs/1207.0116",
"label": "Cyclic case"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Prove that the Deligne–Lusztig-derived equivalence predicted by Broué's abelian-defect-group conjecture for suitable finite groups of Lie type is a perverse equivalence. | Prove that the Deligne--Lusztig-derived equivalence predicted by Brou\acute e's abelian-defect-group conjecture for suitable finite groups of Lie type is a perverse equivalence. | 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 | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,019 | OWR-11583-012 | Inductive Proofs of Alperin Conjectures | Prove the Alperin–McKay and Alperin weight conjectures, including their blockwise versions, by verifying the corresponding inductive conditions on finite simple groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-012",
"literature-status:partially-solved",
"owr-year:2012"
] | The inductive Alperin--McKay program is complete for prime 2 and many families, but the all-prime conjecture remains unresolved. | [
{
"url": "https://annals.math.princeton.edu/2025/201-2/p02",
"label": "Alperin--McKay for prime 2"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869320300739",
"label": "Type-A Alperin--McKay result"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Prove the Alperin–McKay and Alperin weight conjectures, including their blockwise versions, by verifying the corresponding inductive conditions on finite simple groups. | Prove the Alperin--McKay and Alperin weight conjectures, including their blockwise versions, by verifying the corresponding inductive conditions on finite simple 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 | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,020 | OWR-11583-013 | Inductive Blockwise Alperin Weight Condition | Does the inductive blockwise Alperin weight condition hold for every finite simple group and every prime $p$, and hence imply the blockwise Alperin weight conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-013",
"literature-status:partially-solved",
"owr-year:2012"
] | The blockwise Alperin weight conjecture is proved for several families and block classes, including type-A cases, while the general all-group statement remains open. | [
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0021869325000857",
"label": "Blockwise Alperin weight conjecture"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0021869323002168",
"label": "Type-A inductive condition"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Does the inductive blockwise Alperin weight condition hold for every finite simple group and every prime $p$, and hence imply the blockwise Alperin weight conjecture? | Determine whether the inductive blockwise Alperin weight condition holds for every finite simple group and every prime p, and hence yields the blockwise Alperin weight conjecture. | 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 | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,021 | OWR-11583-014 | Simple Rational Modules in Positive Characteristic | Determine the dimensions and characters of simple rational modules for a split reductive group in positive characteristic, and give a uniform construction or description of them. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-11583-014",
"literature-status:partially-solved",
"owr-year:2012"
] | Dimensions and characters around the Steinberg weight are known in important ranges and computable cases, but the requested uniform description is not available in general. | [
{
"url": "https://people.mpim-bonn.mpg.de/geordie/GWilliamson-finitegroups.pdf",
"label": "Williamson's Steinberg-weight survey"
},
{
"url": "https://doi.org/10.1016/j.aim.2015.04.022",
"label": "Light leaves and Lusztig's conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Determine the dimensions and characters of simple rational modules for a split reductive group in positive characteristic, and give a uniform construction or description of them. | Determine the dimensions and characters of simple rational modules for a split reductive group in positive characteristic, and give a uniform construction or description of them. | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,022 | OWR-11583-017 | Affine Algebra Models for Principal Representation Blocks | Let $A$ be the integral algebra whose complex module category is equivalent to the principal block $\mathcal O_0$ of category $\mathcal O$ and whose reduction over a field $k$ models the corresponding modular category. Fiebig's affine analogue controls the full Lusztig conjecture. How is the module category of this aff... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019](https://doi.org/10.4171/owr/2012/16)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,012 | 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-11583-017",
"literature-status:open",
"owr-year:2012"
] | The record explicitly leaves unresolved how the affine version of the algebra relates to the whole principal block of rational representations; later work gives structural dualities but not this identification. | [
{
"url": "https://doi.org/10.4171/owr/2012/16",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1209.3760",
"label": "Modular Koszul duality"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/16 | null | null | null | Let $A$ be the integral algebra whose complex module category is equivalent to the principal block $\mathcal O_0$ of category $\mathcal O$ and whose reduction over a field $k$ models the corresponding modular category. Fiebig's affine analogue controls the full Lusztig conjecture. How is the module category of this aff... | How is the category controlled by the affine version of the algebra A, which is related to the full Lusztig conjecture, related to the whole principal block of \operatorname{Rep} G_k? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Representations of Finite Groups (2012), Oberwolfach Reports, DOI 10.4171/owr/2012/16, pp. 963--1019 |
30,002,023 | OWR-11779-002 | Renormalization Basins of Quasiperiodic Schrödinger Cocycles | For a one-frequency analytic quasiperiodic Schrödinger cocycle $(\alpha,A)$ over the rotation $x\mapsto x+\alpha$, what is the basin of the renormalization attractor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/17, pp. 1035--1106](https://doi.org/10.4171/owr/2012/17)
## Literature review (ch... | 3 | open | null | 2,012 | 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-11779-002",
"literature-status:open",
"owr-year:2012"
] | Renormalization and rigidity theory gives major classification results for one-frequency cocycles, but the basin of the renormalization attractor in the stated generality remains unresolved. | [
{
"url": "https://arxiv.org/abs/0905.3902",
"label": "Global theory I"
},
{
"url": "https://www.imj-prg.fr/wp-content/uploads/2020/prix/avila2010.pdf",
"label": "Avila ICM survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/17 | null | null | null | For a one-frequency analytic quasiperiodic Schrödinger cocycle $(\alpha,A)$ over the rotation $x\mapsto x+\alpha$, what is the basin of the renormalization attractor? | For a one-frequency analytic quasiperiodic Schrödinger cocycle (\alpha,A) over the rotation x\mapsto x+\alpha, what is the basin of the renormalization attractor? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Arbeitsgemeinschaft: Quasiperiodic Schrödinger Operators (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/17, pp. 1035--1106 |
30,002,024 | OWR-11780-003 | Real Orbit Counts on Wonderful Varieties | Let $X$ be a wonderful $G$-variety with canonical $\sigma$-equivariant real structure $\mu$, let $X(\mathbb{R})=\{x\in X:\mu(x)=x\}$, and let $G_0^\sigma$ be the identity component of the fixed-point group. What is the exact number of $G_0^\sigma$-orbits in $X(\mathbb{R})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148](https://doi.org/10.4171/owr/2012/18)
## Literature review (checked ... | 3 | open | null | 2,012 | 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-11780-003",
"literature-status:open",
"owr-year:2012"
] | The report asks for the exact number of G-sigma-zero orbits; subsequent structural work does not provide a general exact orbit count, so the broad question remains open. | [
{
"url": "https://doi.org/10.4171/OWR/2012/18",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1702.08426",
"label": "Kac--Moody symmetric spaces"
},
{
"url": "https://doi.org/10.1515/advgeom-2025-0036",
"label": "Köhl--Vock"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/18 | null | null | null | Let $X$ be a wonderful $G$-variety with canonical $\sigma$-equivariant real structure $\mu$, let $X(\mathbb{R})=\{x\in X:\mu(x)=x\}$, and let $G_0^\sigma$ be the identity component of the fixed-point group. What is the exact number of $G_0^\sigma$-orbits in $X(\mathbb{R})$? | For a wonderful variety X with canonical real structure and real part R X, what is the exact number of G^{\sigma}_0-orbits of R X? | corrected_verified | The official report confirms the orbit-count question and supplies the definitions omitted by the extraction. | null | null | null | null | null | Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148 |
30,002,025 | OWR-11780-004 | Nonspherical Orbit-Parameterization Report | For a non-spherical Kac--Moody group G with unitary form K, what orbit and double-coset structure replaces the spherical description of K\backslash G, in particular for B-orbits on K\backslash G? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148](https://doi.org/10.4171/owr/2012/18)
## Literature review (checked ... | 3 | partially_solved | null | 2,012 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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"
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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 | Unrecoverable OWR statement (The official contribution introduces the nonspherical orbit question and then states its orbit-parameterization theorem, so the extraction t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11780-004",
"literature-status:partially-solved",
"owr-year:2012"
] | Non-spherical double-coset and building parametrizations and refined Iwasawa decompositions are known, but a complete orbit and decomposition theory for the non-spherical case is not established. | [
{
"url": "https://ems.press/content/serial-article-files/46388",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1708.05566",
"label": "Horn on Kac--Moody decompositions"
},
{
"url": "https://doi.org/10.1515/advgeom-2025-0036",
"label": "Köhl--Vock"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/18 | null | null | null | null | For a non-spherical Kac--Moody group G with unitary form K, what orbit and double-coset structure replaces the spherical description of K\backslash G, in particular for B-orbits on K\backslash G? | unrecoverable | The official contribution introduces the nonspherical orbit question and then states its orbit-parameterization theorem, so the extraction turns an answered research aim into an apparent open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148 |
30,002,026 | OWR-11780-005 | Iwasawa Decompositions Without Borel Exchange | For a group $G$ with a twin $BN$-pair and involution $\theta$, how does the Iwasawa decomposition change when the hypothesis $\theta(B^+)=B^-$ is removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148](https://doi.org/10.4171/owr/2012/18)
## Literature review (checked ... | 3 | open | null | 2,012 | 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"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11780-005",
"literature-status:open",
"owr-year:2012"
] | Known polar and Iwasawa results rely on specific Cartan--Chevalley or twisted involution hypotheses; no general classification under the proposed relaxed condition theta of B plus equals B minus was found. | [
{
"url": "https://ems.press/content/serial-article-files/46388",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1708.05566",
"label": "Horn on Kac--Moody decompositions"
},
{
"url": "https://doi.org/10.1515/advgeom-2025-0036",
"label": "Köhl--Vock"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/18 | null | null | null | For a group $G$ with a twin $BN$-pair and involution $\theta$, how does the Iwasawa decomposition change when the hypothesis $\theta(B^+)=B^-$ is removed? | For a group G with twin BN-pair and involution \theta, what happens to the Iwasawa decomposition when the condition \theta(B^+)=B^- is relaxed? | corrected_verified | The official report explicitly asks for the theory after dropping the Borel-exchange hypothesis. | null | null | null | null | null | Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148 |
30,002,027 | OWR-11780-007 | Cartan and Polar Decompositions for Kac–Moody Groups | For a Kac–Moody group $G$ with unitary form $K$, when do Cartan or polar decompositions exist? Does $G=KAK$ imply that $G$ is spherical? Does $\operatorname{SL}_n(F[t,t^{-1}])$ admit a polar decomposition? If $U$ is the unipotent radical of a Borel subgroup, when does $G=KUK$ hold in the nonspherical case, particularly... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148](https://doi.org/10.4171/owr/2012/18)
## Literature review (checked ... | 3 | open | null | 2,012 | 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"
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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-11780-007",
"literature-status:open",
"owr-year:2012"
] | The source leaves G equals KUK unresolved; later Iwasawa decompositions do not prove this Kostant-type factorization, and no general proof or counterexample for the Laurent-polynomial case was located. | [
{
"url": "https://ems.press/content/serial-article-files/46388",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1708.05566",
"label": "Horn on Kac--Moody decompositions"
},
{
"url": "https://doi.org/10.1515/advgeom-2025-0036",
"label": "Köhl--Vock"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/18 | null | null | null | For a Kac–Moody group $G$ with unitary form $K$, when do Cartan or polar decompositions exist? Does $G=KAK$ imply that $G$ is spherical? Does $\operatorname{SL}_n(F[t,t^{-1}])$ admit a polar decomposition? If $U$ is the unipotent radical of a Borel subgroup, when does $G=KUK$ hold in the nonspherical case, particularly... | For the Chevalley involution on G=\operatorname{SL}_n(F[t,t^{-1}]), when do polar or Cartan decompositions exist; does G=KAK imply that G is spherical; does G admit a polar decomposition; and when does G=KUK hold in the non-spherical case, especially for this G? | corrected_verified | The official report lists these as four related open questions in its nonspherical Kac–Moody discussion. | null | null | null | null | null | Mini-Workshop: Generalizations of Symmetric Spaces (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/18, pp. 1107--1148 |
30,002,028 | OWR-11781-001 | Supersaturation Blow-Ups in Uniform Hypergraphs | For all positive integers $\ell$ and $r$ and every $c>0$, does there exist $\gamma>0$ such that every $r$-uniform hypergraph $H$ with at least $cn^\ell$ copies of the complete $r$-uniform hypergraph $K^r_\ell$ contains a complete $\ell$-partite $r$-uniform hypergraph with equal part size $t\geq\gamma(\log n)^{1/(r-1)}$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11781-001",
"literature-status:open",
"owr-year:2012"
] | The stronger conjectured logarithmic blowup exponent from a positive density of complete partite copies remains unresolved; recent algorithmic work reaches the Erdős-order exponent but not this copy-count conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/46390?nt=1",
"label": "Oberwolfach report"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0020019026000050",
"label": "Finding partite hypergraphs efficiently"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | For all positive integers $\ell$ and $r$ and every $c>0$, does there exist $\gamma>0$ such that every $r$-uniform hypergraph $H$ with at least $cn^\ell$ copies of the complete $r$-uniform hypergraph $K^r_\ell$ contains a complete $\ell$-partite $r$-uniform hypergraph with equal part size $t\geq\gamma(\log n)^{1/(r-1)}$... | For all positive integers \ell and r and every c>0, does there exist \gamma>0 such that every r-uniform hypergraph H with at least c n^\ell copies of the complete r-uniform hypergraph K^r_\ell contains a complete \ell-partite r-uniform hypergraph with equal part size t\geq\gamma(\log n)^{1/(r-1)}? | 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: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,029 | OWR-11781-002 | Decidability of Hypergraph Turán Densities | Given a finite family $F$ of $r$-uniform hypergraphs and $\alpha\in\mathbb{Q}$, is it decidable whether the Turán density $\pi(F)$ satisfies $\pi(F)\leq\alpha$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11781-002",
"literature-status:open",
"owr-year:2012"
] | No algorithm deciding pi of F less than or equal to alpha for arbitrary finite hypergraph families has been proved; subsequent work on possible Turan densities and high algebraic degree does not resolve decidability. | [
{
"url": "https://ems.press/content/serial-article-files/46390?nt=1",
"label": "Oberwolfach report"
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{
"url": "https://doi.org/10.1007/s11856-014-0031-5",
"label": "Pikhurko on possible Turan densities"
},
{
"url": "https://wrap.warwick.ac.uk/174830/1/WRAP-hypergraph-turan-densities-ar... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | Given a finite family $F$ of $r$-uniform hypergraphs and $\alpha\in\mathbb{Q}$, is it decidable whether the Turán density $\pi(F)$ satisfies $\pi(F)\leq\alpha$? | Given a finite family F of r-uniform hypergraphs and \alpha\in\mathbb{Q}, is it decidable whether the Tur\'an density \pi(F) satisfies \pi(F)\leq\alpha? | 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: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,030 | OWR-11781-003 | Three-Color Edge-Folkman Numbers for Triangles | What are good bounds on the order of a graph $G$ such that every coloring of the edges of $G$ with three colors contains a monochromatic triangle, i.e. $G\longrightarrow(K_3)^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,012 | 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-11781-003",
"literature-status:open",
"owr-year:2012"
] | The three-color K4-free edge-Folkman question asking for good bounds remains unresolved; multicolor Ramsey results give related bounds but do not settle this host-restricted problem. | [
{
"url": "https://ems.press/content/serial-article-files/46390?nt=1",
"label": "Oberwolfach report"
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"url": "https://link.springer.com/article/10.1007/s40687-024-00463-w",
"label": "Multicolor Ramsey numbers of 3-graphs"
},
{
"url": "https://arxiv.org/abs/1302.5304",
"label": "Mu... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | What are good bounds on the order of a graph $G$ such that every coloring of the edges of $G$ with three colors contains a monochromatic triangle, i.e. $G\longrightarrow(K_3)^3$? | What are good bounds on the order of a graph G such that every coloring of the edges of G with three colors contains a monochromatic triangle, i.e. G\longrightarrow(K_3)^3? | 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: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,031 | OWR-11781-004 | Turán Densities of Hypergraph Daisies | Let $D_r$ be the $r$-daisy consisting of the six $r$-sets $A$ with $P\subset A\subset P\cup Q$ for an $(r-2)$-set $P$ and a disjoint $4$-set $Q$. How large can a family $\mathcal A$ of $r$-sets from an $n$-set be if it contains no copy of $D_r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-11781-004",
"literature-status:partially-solved",
"owr-year:2012"
] | Ellis, Ivan, and Leader disproved the conjecture that daisy Turan densities tend to zero, but the extremal function and exact density questions, including pi of D3, remain open. | [
{
"url": "https://arxiv.org/abs/2401.16289",
"label": "Ellis--Ivan--Leader"
},
{
"url": "https://api.repository.cam.ac.uk/server/api/core/bitstreams/11513fbb-eac3-4eaf-bed3-46228c0c6758/content",
"label": "Daisy density results"
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{
"url": "https://ems.press/content/serial-article-files... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | Let $D_r$ be the $r$-daisy consisting of the six $r$-sets $A$ with $P\subset A\subset P\cup Q$ for an $(r-2)$-set $P$ and a disjoint $4$-set $Q$. How large can a family $\mathcal A$ of $r$-sets from an $n$-set be if it contains no copy of $D_r$? | Let D_r be the r-daisy consisting of the six r-sets A with P\subset A\subset P\cup Q for an (r-2)-set P and a disjoint 4-set Q. How large can a family A of r-sets from an n-set be if it contains no copy of D_r? | 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: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,032 | OWR-11781-005 | Ramsey Numbers for Loose Triangles versus Complete Hypergraphs | For loose $3$-uniform hypergraph triangles $C_3$ and complete $3$-uniform hypergraphs $K^3_t$, does the Ramsey number satisfy $R(C_3,K^3_t)=o(t^{3/2})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,012 | 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-11781-005",
"literature-status:open",
"owr-year:2012"
] | The best known estimates remain between order t to the three halves divided by a logarithmic factor and order t to the three halves, so the conjectured little-o bound is still open. | [
{
"url": "https://doi.org/10.1016/j.jcta.2013.04.009",
"label": "Kostochka--Mubayi--Verstraete"
},
{
"url": "https://arxiv.org/abs/1707.04229",
"label": "Ramsey theory survey"
},
{
"url": "https://ems.press/content/serial-article-files/46390?nt=1",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | For loose $3$-uniform hypergraph triangles $C_3$ and complete $3$-uniform hypergraphs $K^3_t$, does the Ramsey number satisfy $R(C_3,K^3_t)=o(t^{3/2})$? | For loose 3-uniform hypergraph triangles C_3 and complete 3-uniform hypergraphs K^3_t, does the Ramsey number satisfy R(C_3,K^3_t)=o(t^{3/2})? | 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 | Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,033 | OWR-11781-006 | Monochromatic Structures below Random Density | Does an analogue of the quadratic-structure phenomenon for two-colorings with fewer than the random density of monochromatic $K_4$'s hold for graph colorings, and what is the asymptotically minimal number of monochromatic $3$-term arithmetic progressions in a two-coloring of $\{1,\ldots,n\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182](https://doi.org/10.4171/owr/2012/19)
## Literature review (checked 2026-08-21)... | 3 | open | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11781-006",
"literature-status:open",
"owr-year:2012"
] | The asymptotic minimum density of monochromatic three-term progressions in two-colorings is not determined; known bounds and restricted-class optimality results leave the general problem open. | [
{
"url": "https://doi.org/10.1016/j.jcta.2007.03.006",
"label": "Parrilo--Robertson--Saracino"
},
{
"url": "https://arxiv.org/abs/2301.00336",
"label": "Greenwood--Kariv--Williams"
},
{
"url": "https://ems.press/content/serial-article-files/46390?nt=1",
"label": "Oberwolfach report"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/19 | null | null | null | Does an analogue of the quadratic-structure phenomenon for two-colorings with fewer than the random density of monochromatic $K_4$'s hold for graph colorings, and what is the asymptotically minimal number of monochromatic $3$-term arithmetic progressions in a two-coloring of $\{1,\ldots,n\}$? | Does an analogue of the quadratic-structure phenomenon for two-colorings with fewer than the random density of monochromatic K_4's hold for graph colorings, and what is the asymptotically minimal number of monochromatic 3-term arithmetic progressions in a two-coloring of \{1,\ldots,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: Hypergraph Turán Problem (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/19, pp. 1149--1182 |
30,002,034 | OWR-11782-001 | Leavitt Path Algebra Isomorphisms and Graph $C^*$-Algebras | For arbitrary graphs $E$ and $F$, does a ring isomorphism $L_{\mathbb C}(E)\cong L_{\mathbb C}(F)$ imply $C^*(E)\cong C^*(F)$, and conversely? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Endomorphisms, Semigroups and C*-Algebras of Rings (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/20, pp. 1183--1229](https://doi.org/10.4171/owr/2012/20)
## Literature r... | 3 | open | null | 2,012 | 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-11782-001",
"literature-status:open",
"owr-year:2012"
] | Classification is known in special and diagonal-preserving or star-isomorphism settings, but the general ring-isomorphism versus graph-C-star-isomorphism question for Leavitt path algebras remains open. | [
{
"url": "https://arxiv.org/abs/0810.2569",
"label": "Abrams--Tomforde"
},
{
"url": "https://doi.org/10.1112/blms.13139",
"label": "Cortinas classification survey"
},
{
"url": "https://ems.press/content/serial-article-files/46391",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/20 | null | null | null | For arbitrary graphs $E$ and $F$, does a ring isomorphism $L_{\mathbb C}(E)\cong L_{\mathbb C}(F)$ imply $C^*(E)\cong C^*(F)$, and conversely? | For arbitrary graphs E and F, does a ring isomorphism between the Leavitt path algebras L_{\mathbb{C}}(E) and L_{\mathbb{C}}(F) imply an isomorphism between the graph C^*-algebras C^*(E) and C^*(F), and conversely? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Endomorphisms, Semigroups and C*-Algebras of Rings (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/20, pp. 1183--1229 |
30,002,035 | OWR-11782-002 | Cuntz Splices and Morita Equivalence of Leavitt Path Algebras | Is the determinant a Morita-equivalence invariant for Leavitt path algebras; in particular, does the Cuntz splice preserve Morita equivalence of Leavitt path algebras? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Endomorphisms, Semigroups and C*-Algebras of Rings (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/20, pp. 1183--1229](https://doi.org/10.4171/owr/2012/20)
## Literature r... | 3 | open | null | 2,012 | 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-11782-002",
"literature-status:open",
"owr-year:2012"
] | The determinant and Cuntz-splice Morita-equivalence question remains unresolved; available classification results cover special graph classes and do not prove the general algebraic Morita invariant claim. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2013.03.004",
"label": "Ruiz--Tomforde"
},
{
"url": "https://doi.org/10.1112/blms.13139",
"label": "Cortinas classification survey"
},
{
"url": "https://ems.press/content/serial-article-files/46391",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/20 | null | null | null | Is the determinant a Morita-equivalence invariant for Leavitt path algebras; in particular, does the Cuntz splice preserve Morita equivalence of Leavitt path algebras? | Is the determinant a Morita-equivalence invariant for Leavitt path algebras; in particular, does the Cuntz splice preserve Morita equivalence of Leavitt path algebras? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Mini-Workshop: Endomorphisms, Semigroups and C*-Algebras of Rings (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/20, pp. 1183--1229 |
30,002,036 | OWR-11783-002 | Property $N_{3d-3}$ for Veronese Embeddings | Does the $d$-uple Veronese embedding of projective space satisfy property $N_{3d-3}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11783-002",
"literature-status:partially-solved",
"owr-year:2012"
] | The Veronese syzygy conjecture is proved for degree three and several special cases but remains open in general, while toric hypersurface implicitization has substantial approximation-complex and syzygy progress without a complete general theory. | [
{
"url": "https://arxiv.org/abs/math/9811131",
"label": "Ottaviani--Paoletti"
},
{
"url": "https://arxiv.org/abs/1303.5532",
"label": "Vu on third Veronese embeddings"
},
{
"url": "https://arxiv.org/abs/2606.01415",
"label": "Recent syzygy implicitization"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | Does the $d$-uple Veronese embedding of projective space satisfy property $N_{3d-3}$? | Does the d-uple Veronese embedding of \mathbb{P}^n satisfy property N_{3d-3}; and, for a divisor D and basepoint-free subspace U\subset H^0(X,\mathcal{O}_X(D)) with \dim U=\dim X+2 and hypersurface image in \mathbb{P}(U), how can the implicit equation be efficiently determined from approximation complexes and multigrad... | corrected_verified | The official report poses this Veronese-syzygy question separately; the extracted implicitization material belongs to the next record. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,037 | OWR-11783-003 | Toric Hypersurface Implicitization from Syzygies | Let $X$ be a toric variety, $D$ a divisor, and $U\subseteq H^0(X,\mathcal O_X(D))$ a basepoint-free subspace with $\dim U=\dim X+2$ whose image is a hypersurface in $\mathbb P(U)$. How can its implicit equation be computed efficiently from an approximation complex, and how do the multigraded syzygies of $I_U$ control t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11783-003",
"literature-status:partially-solved",
"owr-year:2012"
] | Approximation-complex and syzygy methods solve broad surface and selected higher-dimensional cases, and recent work extends matrix constructions, but arbitrary toric hypersurface implicitization remains an active general problem. | [
{
"url": "https://doi.org/10.1016/j.jsc.2015.09.001",
"label": "Botbol--Dickenstein"
},
{
"url": "https://arxiv.org/abs/2606.01415",
"label": "Recent syzygy implicitization"
},
{
"url": "https://ems.press/content/serial-article-files/46392",
"label": "Toric Geometry report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | Let $X$ be a toric variety, $D$ a divisor, and $U\subseteq H^0(X,\mathcal O_X(D))$ a basepoint-free subspace with $\dim U=\dim X+2$ whose image is a hypersurface in $\mathbb P(U)$. How can its implicit equation be computed efficiently from an approximation complex, and how do the multigraded syzygies of $I_U$ control t... | For a divisor D and a basepoint-free subspace U\subset H^0(X,\mathcal{O}_X(D)) with \dim U=\dim X+2 whose image in \mathbb{P}(U) is a toric hypersurface, how can its implicit equation be determined efficiently, and how do the multigraded syzygies of the ideal of U control the geometry of that hypersurface? | corrected_verified | The official report supplies the toric variety, divisor, subspace, dimension, and hypersurface hypotheses omitted or distorted in the extraction. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,038 | OWR-11783-004 | Hamiltonian Displaceability of Toric Fibers | For a $2n$-dimensional toric symplectic manifold $(M,\omega)$ with moment map $\mu$ and Lagrangian torus fibers $T_u=\mu^{-1}(u)$, which fibers can be displaced by a Hamiltonian isotopy; equivalently, for which $u$ does there exist $\phi\in\operatorname{Ham}(M,\omega)$ with $\phi(T_u)\cap T_u=\varnothing$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11783-004",
"literature-status:partially-solved",
"owr-year:2012"
] | Floer-theoretic and probe methods give strong non-displaceability and equivalence criteria and settle multiple families, but a general classification of Hamiltonian-displaceable toric fibers is still open. | [
{
"url": "https://arxiv.org/abs/0802.1703",
"label": "Fukaya--Oh--Ohta--Ono"
},
{
"url": "https://doi.org/10.2140/agt.2025.25.1839",
"label": "Brendel toric fibers"
},
{
"url": "https://ems.press/content/serial-article-files/46392",
"label": "Toric Geometry report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | For a $2n$-dimensional toric symplectic manifold $(M,\omega)$ with moment map $\mu$ and Lagrangian torus fibers $T_u=\mu^{-1}(u)$, which fibers can be displaced by a Hamiltonian isotopy; equivalently, for which $u$ does there exist $\phi\in\operatorname{Ham}(M,\omega)$ with $\phi(T_u)\cap T_u=\varnothing$? | For a 2n-dimensional toric symplectic manifold (M,\omega) with moment map \mu and Lagrangian torus fibers T_u=\mu^{-1}(u), which fibers can be displaced by a Hamiltonian isotopy; equivalently, for which u does there exist \phi\in\operatorname{Ham}(M,\omega) with \phi(T_u)\cap T_u=\varnothing? | corrected_verified | The official report was checked and confirms the complete problem statement. TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,039 | OWR-11783-006 | Minimal Models Near Stable Surface Limits | For a nonisotrivial $\mathbb Q$-Gorenstein deformation of projective surfaces whose special fiber $X$ is an irreducible normal surface with $T$-singularities, what are the smooth minimal models of the singular and nonsingular surfaces in the moduli space near the stable limit of $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11783-006",
"literature-status:partially-solved",
"owr-year:2012"
] | Hacking--Tevelev--Urzúa give an algorithm and classify substantial classes of flips and antiflips, with later work treating N-resolutions, but the broad question about all smooth minimal models near an arbitrary stable limit is not completely classified. | [
{
"url": "https://arxiv.org/abs/1310.1580",
"label": "Hacking--Tevelev--Urzúa, Flipping surfaces"
},
{
"url": "https://arxiv.org/abs/2204.13225",
"label": "Tevelev--Urzúa, Categorical aspects of the KSB correspondence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | For a nonisotrivial $\mathbb Q$-Gorenstein deformation of projective surfaces whose special fiber $X$ is an irreducible normal surface with $T$-singularities, what are the smooth minimal models of the singular and nonsingular surfaces in the moduli space near the stable limit of $X$? | For a non-isotrivial Q-Gorenstein deformation of projective surfaces whose special fiber X is an irreducible normal surface with T-singularities, what are the smooth minimal models of the singular and nonsingular surfaces in the moduli space around the stable limit of X? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete mathematical question was preserved while the deformation and singularity notation was normalized. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,040 | OWR-11783-007 | Maps from Varieties to Okounkov Bodies | Does there exist, in general, a reasonable map from a variety $X$ to its Okounkov body $\Delta(X,L,\nu)$, and under what hypotheses can such a map be constructed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11783-007",
"literature-status:partially-solved",
"owr-year:2012"
] | Harada--Kaveh construct the requested map when a suitable toric degeneration or finitely generated Okounkov semigroup exists, and later work extends the construction, but no general construction for arbitrary varieties is established. | [
{
"url": "https://arxiv.org/abs/1205.5249",
"label": "Harada--Kaveh, Integrable systems, toric degenerations and Okounkov bodies"
},
{
"url": "https://arxiv.org/abs/2210.13137",
"label": "Murata--Bossinger, Maps to toric varieties and toric degenerations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | Does there exist, in general, a reasonable map from a variety $X$ to its Okounkov body $\Delta(X,L,\nu)$, and under what hypotheses can such a map be constructed? | Does there exist, in general, a reasonable map from a variety X to its Okounkov body \Delta(X,L,\nu), and under what hypotheses can such a map be constructed? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete mathematical question was preserved while undelimited notation was repaired. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,041 | OWR-11783-008 | Cellular Resolutions for Consistent Toric Algebras | Let $X$ be an $n$-dimensional Gorenstein affine toric variety, let $\mathcal E=(E_0,\ldots,E_r)$ be rank-one reflexive sheaves, and set $A=\operatorname{End}_{\mathcal O_X}(\bigoplus_i E_i)$. If $A$ is a consistent toric algebra of global dimension $n$, does its higher quiver exist, and is the minimal projective $(A,A)... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11783-008",
"literature-status:open",
"owr-year:2012"
] | Craw--Quintero-Vélez prove the cellular resolution only in specified dimension-three and dimension-four families and explicitly leave the all-consistent-toric-algebra extension as a conjecture; no general proof was found. | [
{
"url": "https://eprints.gla.ac.uk/41620/1/41620.pdf",
"label": "Craw--Quintero-Vélez, Cellular resolutions of noncommutative toric algebras"
},
{
"url": "https://doi.org/10.4171/owr/2012/21",
"label": "Oberwolfach report, Toric Geometry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | Let $X$ be an $n$-dimensional Gorenstein affine toric variety, let $\mathcal E=(E_0,\ldots,E_r)$ be rank-one reflexive sheaves, and set $A=\operatorname{End}_{\mathcal O_X}(\bigoplus_i E_i)$. If $A$ is a consistent toric algebra of global dimension $n$, does its higher quiver exist, and is the minimal projective $(A,A)... | For every consistent toric algebra A of global dimension n=\dim X, does the higher-quiver construction exist and does the minimal projective A-bimodule resolution have the cellular form asserted by Theorem 0.2? | corrected_verified | The official report supplies the geometric and algebraic data omitted by the source-dependent extraction and states the higher-quiver and cellular-resolution questions. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,042 | OWR-11783-009 | Degrees and Finiteness of Stringy $E$-Polynomials | For a Gorenstein polytope $P$ of index $r$, is the degree of its stringy $E$-function $E_{\mathrm{st}}(P,t)$ equal to $\dim(P)+1-2r$, and are there, up to multiples, only finitely many such stringy $E$-polynomials with fixed value of $\dim(P)+1-2r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11783-009",
"literature-status:open",
"owr-year:2012"
] | Polynomiality of the stringy E-function is proved, and finiteness is known for special smooth classes, but the expected-degree and general finiteness questions for arbitrary Gorenstein polytopes remain unresolved. | [
{
"url": "https://doi.org/10.1007/s00208-012-0792-2",
"label": "Nill--Schepers, Gorenstein polytopes and their stringy E-functions"
},
{
"url": "https://www.jstage.jst.go.jp/article/tmj/67/4/67_513/_pdf/-char/en",
"label": "Nill--Schepers, On smooth Gorenstein polytopes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | For a Gorenstein polytope $P$ of index $r$, is the degree of its stringy $E$-function $E_{\mathrm{st}}(P,t)$ equal to $\dim(P)+1-2r$, and are there, up to multiples, only finitely many such stringy $E$-polynomials with fixed value of $\dim(P)+1-2r$? | For a Gorenstein polytope P of index r, is the degree of its stringy E-function E_{\mathrm{st}}(P,t) equal to the expected degree \dim(P)+1-2r, and are there, up to multiples, only finitely many such stringy E-polynomials with fixed \dim(P)+1-2r? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete two-part question was preserved while all polytope and degree notation was normalized. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,043 | OWR-11783-010 | Combinatorial Nonnegativity for Polytope $S$-Polynomials | Does every lattice polytope $P$ have a combinatorial proof that its $S$-polynomial has nonnegative coefficients? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11783-010",
"literature-status:open",
"owr-year:2012"
] | The cited S-polynomial identities and nonnegativity are established, but the extracted request for a genuinely combinatorial proof is still posed as an open methodological question and no authoritative resolution was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/21",
"label": "Oberwolfach report, Toric Geometry"
},
{
"url": "https://www.researchgate.net/publication/2207724_Combinatorial_aspects_of_mirror_symmetry",
"label": "Batyrev--Nill, Combinatorial aspects of mirror symmetry"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | Does every lattice polytope $P$ have a combinatorial proof that its $S$-polynomial has nonnegative coefficients? | Does every lattice polytope P have a combinatorial proof that its S-polynomial has non-negative coefficients? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete statement was preserved while mathematical notation was normalized. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,044 | OWR-11783-011 | Geometry of Cones of $q$-Ample Line Bundles | What is a useful geometric description of the generally nonconvex cone of $q$-ample line bundles on a variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306](https://doi.org/10.4171/owr/2012/21)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11783-011",
"literature-status:open",
"owr-year:2012"
] | Toric varieties admit substantial polyhedral descriptions of q-ample cones, but Totaro identifies a general numerical characterization of q-ampleness as open; the broad cone-description problem therefore remains open. | [
{
"url": "https://ems.press/content/serial-article-files/31884?nt=1",
"label": "Totaro, Line bundles with partially vanishing cohomology"
},
{
"url": "https://arxiv.org/abs/1202.3065",
"label": "Broomhead--Ottem--Prendergast-Smith, Partially ample line bundles on toric varieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/21 | null | null | null | What is a useful geometric description of the generally nonconvex cone of $q$-ample line bundles on a variety? | What is a good description of the, generally non-convex, cone of q-ample line bundles on a variety? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete question was preserved while the mathematical parameter was delimited and vague wording was tightened without changing scope. | null | null | null | null | null | Toric Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/21, pp. 1231--1306 |
30,002,045 | OWR-11784-002 | Effective Thue–Mahler Equations over Finitely Generated Domains | Let $F\in A[X,Y]$ be a binary form of degree at least $3$ without multiple factors over a finitely generated domain $A$. Given that $F(x,y)\in A^*$ has only finitely many solution classes under simultaneous multiplication by units, can representatives $(x_i,y_i)$ of every class be determined effectively? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | partially_solved | null | 2,012 | 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-11784-002",
"literature-status:partially-solved",
"owr-year:2012"
] | Effective algorithms are known for unit, Thue, hyperelliptic, and superelliptic equations over finitely generated domains, but the exact effective determination of representatives for the general Thue--Mahler problem in the record remains open. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/1fd6cbc9-1093-41b9-8def-fe335e6bf581/content",
"label": "Oberwolfach report, Diophantische Approximationen"
},
{
"url": "https://doi.org/10.4064/aa163-1-6",
"label": "Bérczes--Evertse--Győry, Effective results for Diophantine equation... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | Let $F\in A[X,Y]$ be a binary form of degree at least $3$ without multiple factors over a finitely generated domain $A$. Given that $F(x,y)\in A^*$ has only finitely many solution classes under simultaneous multiplication by units, can representatives $(x_i,y_i)$ of every class be determined effectively? | Given a binary form F in A[X,Y] of degree at least 3 without multiple factors and an arbitrary finitely generated domain A, the Thue--Mahler equation F(x,y) in A^* for x,y in A has finitely many solution classes under multiplication by units; can representatives (x_i,y_i) of all classes be determined effectively? | corrected_verified | The official report explicitly asks for an effective determination of representatives after stating the finiteness theorem. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,046 | OWR-11784-003 | Real Fixed Points of the Minkowski Question-Mark Function | How many real fixed points does Minkowski’s question-mark function have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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-11784-003",
"literature-status:open",
"owr-year:2012"
] | The fixed-point count for Minkowski's question-mark function is not known: the literature proves several fixed points and studies their arithmetic, but does not determine whether further irrational fixed points exist. | [
{
"url": "https://arxiv.org/abs/1811.10139",
"label": "Gayfulin--Shulga, Diophantine properties of fixed points of Minkowski question mark function"
},
{
"url": "https://m.mathnet.ru/php/archive.phtml?jrnid=acta&option_lang=rus&paperid=6&wshow=paper",
"label": "Acta Arithmetica version of the fi... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | How many real fixed points does Minkowski’s question-mark function have? | How many real solutions does the Minkowski question-mark equation ?(x)=x have? | corrected_verified | The official report poses this fixed-point question; the extraction had corrupted the function notation into ungrammatical prose. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,047 | OWR-11784-005 | Littlewood Conjecture | For every $(\alpha,\beta)\in\mathbb R^2$, is $\liminf_{q\to\infty}q\lVert q\alpha\rVert\,\lVert q\beta\rVert=0$, where $\lVert\cdot\rVert$ denotes distance to the nearest integer? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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-11784-005",
"literature-status:open",
"owr-year:2012"
] | Littlewood's conjecture remains unresolved; Einsiedler--Katok--Lindenstrauss show that any exceptional set has Hausdorff dimension zero, which is substantial progress but not a proof for every pair. | [
{
"url": "https://annals.math.princeton.edu/wp-content/uploads/annals-v164-n2-p04.pdf",
"label": "Einsiedler--Katok--Lindenstrauss, Invariant measures and the set of exceptions to Littlewood's conjecture"
},
{
"url": "https://numdam.org/articles/10.5802/pmb.1/",
"label": "Bugeaud, Around the Lit... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | For every $(\alpha,\beta)\in\mathbb R^2$, is $\liminf_{q\to\infty}q\lVert q\alpha\rVert\,\lVert q\beta\rVert=0$, where $\lVert\cdot\rVert$ denotes distance to the nearest integer? | Littlewood conjecture: for every (\alpha,\beta) in R^2, lim inf as q tends to infinity of q times ||q\alpha|| times ||q\beta|| equals 0, where ||.|| is distance to the nearest integer. | corrected_verified | The official report states the Littlewood Conjecture in this form. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,048 | OWR-11784-007 | Exceptional-Unit Bounds by Algebraic Degree | Let $E_0(\alpha)$ be the largest $n$ such that $\alpha^j-1$ is a unit for every $1\leq j\leq n$, or $0$ if $\alpha-1$ is not a unit, and let $e(d)=\max E_0(\alpha)$ over algebraic integers $\alpha$ of degree $d$. Is $e(d)<d$ for every $d\geq7$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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-11784-007",
"literature-status:open",
"owr-year:2012"
] | The exceptional-unit literature still records e(d)<d for d at least 7 as a conjecture; the known small-degree computations and lower bounds do not establish it in all degrees. | [
{
"url": "https://www.impan.pl/shop/publication/transaction/download/product/82792",
"label": "Hare--Mossinghoff, Exceptional units and cyclic resultants"
},
{
"url": "https://uwaterloo.ca/pure-mathematics/sites/default/files/uploads/documents/exceptional_units-5_0.pdf",
"label": "Hare--Mossingh... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | Let $E_0(\alpha)$ be the largest $n$ such that $\alpha^j-1$ is a unit for every $1\leq j\leq n$, or $0$ if $\alpha-1$ is not a unit, and let $e(d)=\max E_0(\alpha)$ over algebraic integers $\alpha$ of degree $d$. Is $e(d)<d$ for every $d\geq7$? | Let E_0(\alpha) be the largest n such that \alpha^j-1 is a unit for every 1 less than or equal to j less than or equal to n, or 0 if \alpha-1 is not a unit, and let e(d)=max E_0(\alpha) over algebraic integers \alpha of degree d; conjecture e(d)<d for every d greater than or equal to 7. | corrected_verified | The official report states this definition and question with the same degree threshold. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,049 | OWR-11784-008 | Zilber Conjecture for Torsion-Anomalous Intersections | For every algebraic subset $W\subseteq\mathbb G_m^N$, is there a finite collection $\mathcal U_W$ of codimension-one torsion cosets such that, for every torsion coset $T_0$ and every irreducible component $Y$ of $W\cap T_0$ with $\dim Y>\dim W-\operatorname{codim}T_0$, some $T\in\mathcal U_W$ satisfies $Y\subseteq W\ca... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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-11784-008",
"literature-status:open",
"owr-year:2012"
] | The record concerns Zilber's unlikely-intersection conjecture for algebraic tori; the cited sparse-equation algorithm is conditional on an effective form, and the general conjecture remains open despite many special cases. | [
{
"url": "https://arxiv.org/abs/1307.5788",
"label": "Amoroso--Leroux--Sombra, Overdetermined systems of sparse polynomial equations"
},
{
"url": "https://doi.org/10.1112/jlms.70536",
"label": "Capuano, Exploring Zilber's conjecture on atypical intersections"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | For every algebraic subset $W\subseteq\mathbb G_m^N$, is there a finite collection $\mathcal U_W$ of codimension-one torsion cosets such that, for every torsion coset $T_0$ and every irreducible component $Y$ of $W\cap T_0$ with $\dim Y>\dim W-\operatorname{codim}T_0$, some $T\in\mathcal U_W$ satisfies $Y\subseteq W\ca... | Zilber conjecture: for every algebraic subset W of G_m^N there is a finite collection U_W of codimension-one torsion cosets such that, for every torsion coset T_0 and every irreducible component Y of W intersect T_0 with dim Y greater than dim W minus codim T_0, some T in U_W satisfies Y is contained in W intersect T. | corrected_verified | The official report states this version of Zilber’s conjecture with the ambient torus and exceptional family made explicit. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,050 | OWR-11784-009 | Conditional Sparse-Decomposition Theorem | Assuming Zilber's conjecture, if V is a subvariety of G_m^n over a number field K defined by a bounded number of bounded-height equations of degree at most d and with bounded monomial support, one can find in O(log d) arithmetic operations a finite collection of sequences (P_1,...,P_L,Q), with L at most n, of Laurent p... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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 (a conditional theorem, not a problem)) | null | null | [Discussion #4 literature review, 2026-09-30] **solved (a conditional theorem, not a problem)**. The record is Theorem 2 of F. Amoroso's abstract (joint with L. Leroux and M. Sombra; OWR 22/2012, p. 1340): assuming Zilber's conjecture, a sparse system over a number field with bounded data can be split in O(log d) opera... | [
"owr",
"oberwolfach-reports",
"OWR-11784-009",
"literature-status:open",
"owr-year:2012"
] | The displayed decomposition theorem is conditional on an effective Zilber conjecture; since that premise is unresolved in general, the extracted unconditional claim is not settled. | [
{
"url": "https://arxiv.org/abs/1307.5788",
"label": "Amoroso--Leroux--Sombra, Overdetermined systems of sparse polynomial equations"
},
{
"url": "https://doi.org/10.1112/jlms.70536",
"label": "Capuano, Exploring Zilber's conjecture on atypical intersections"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | null | Assuming Zilber's conjecture, if V is a subvariety of G_m^n over a number field K defined by a bounded number of bounded-height equations of degree at most d and with bounded monomial support, one can find in O(log d) arithmetic operations a finite collection of sequences (P_1,...,P_L,Q), with L at most n, of Laurent p... | unrecoverable | The official contribution states the sparse-decomposition claim as a theorem conditional on Zilber’s conjecture; it is not an additional open problem beyond the conjecture retained in the preceding record. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,051 | OWR-11784-010 | Mixed Littlewood Conjecture for Pseudo-Absolute Values | For a pseudo-absolute-value sequence $D=(n_k)$ with $n_0=1$ and $n_k\mid n_{k+1}$, define $|q|_D=\min\{n_k^{-1}:q\in n_k\mathbb Z\}$. Is $\inf_{q\geq1}|q|_D\,\lVert qx\rVert=0$ for every such $D$ and every $x\in\mathbb R$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359](https://doi.org/10.4171/owr/2012/22)
## Literature review (checked 2026-08-21)
**Status... | 3 | open | null | 2,012 | 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-11784-010",
"literature-status:open",
"owr-year:2012"
] | Mixed Littlewood statements for special p-adic or pseudo-absolute sequences and for almost every parameter are known, but the universal assertion for every pseudo-absolute-value sequence remains a conjecture. | [
{
"url": "https://arxiv.org/abs/1012.0191",
"label": "Harrap--Haynes, The mixed Littlewood conjecture for pseudo-absolute values"
},
{
"url": "https://doi.org/10.1017/S1446788718000198",
"label": "Liu, Some refined results on the mixed Littlewood conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/22 | null | null | null | For a pseudo-absolute-value sequence $D=(n_k)$ with $n_0=1$ and $n_k\mid n_{k+1}$, define $|q|_D=\min\{n_k^{-1}:q\in n_k\mathbb Z\}$. Is $\inf_{q\geq1}|q|_D\,\lVert qx\rVert=0$ for every such $D$ and every $x\in\mathbb R$? | For a pseudo-absolute value sequence D=(n_k) with n_0=1 and n_k dividing n_{k+1}, define |q|_D=min{n_k^{-1}:q is in n_k Z}; mixed Littlewood conjecture: for every such D and every x in R, inf over positive integers q of |q|_D ||qx|| equals 0. | corrected_verified | The official report states the mixed Littlewood Conjecture in this form. | null | null | null | null | null | Diophantische Approximationen (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/22, pp. 1307--1359 |
30,002,052 | OWR-11785-001 | Hodge Structures on Periodic Cyclic Homology | For a smooth complex algebraic variety $X$, does $\operatorname{Perf}(X)$ remember any part of the mixed Hodge structure on its de Rham cohomology? More generally, does the periodic cyclic homology of every differential graded category carry a functorial Hodge-like structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularity Theory and Integrable Systems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/23, pp. 1361--1403](https://doi.org/10.4171/owr/2012/23)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,012 | 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-11785-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Noncommutative Hodge structures and Hodge-to-de Rham type results provide functorial Hodge-like structures for broad classes of dg categories, but a general canonical recovery of the mixed Hodge structure of every Perf(X) is not established. | [
{
"url": "https://arxiv.org/abs/1107.3156",
"label": "Shklyarov, Non-commutative Hodge structures"
},
{
"url": "https://arxiv.org/abs/1510.03795",
"label": "Sheridan, Formulae in noncommutative Hodge theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/23 | null | null | null | For a smooth complex algebraic variety $X$, does $\operatorname{Perf}(X)$ remember any part of the mixed Hodge structure on its de Rham cohomology? More generally, does the periodic cyclic homology of every differential graded category carry a functorial Hodge-like structure? | Does Perf(X) remember any part of the mixed Hodge structure on the de Rham cohomology of an algebraic variety X? More generally, does periodic cyclic homology of every differential graded category carry a functorial Hodge-like structure? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Singularity Theory and Integrable Systems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/23, pp. 1361--1403 |
30,002,053 | OWR-11786-001 | Open Problems in Triangulation Theory | Determine the following: (1) all facets of the secondary polytope of the $d$-cube; (2) whether a graph of triangulations can be disconnected in dimensions $3$ or $4$; (3) the complexity of counting triangulations and a method for uniformly random generation; (4) whether every smooth polytope has a regular unimodular tr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-001",
"literature-status:partially-solved",
"owr-year:2012"
] | The collection is mixed: regular unimodular triangulations of matroid base polytopes are now constructed, while the smooth-polytope, Hamiltonian-dual-graph, enumeration, and sharp-diameter questions remain open or only partly resolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4147/OWR_2023_58.pdf?isAllowed=y&sequence=6",
"label": "Liu--Backman, A regular unimodular triangulation of the matroid base polytope"
},
{
"url": "https://arxiv.org/abs/1405.1687",
"label": "Haase--Paffenholz--Piechnik--Santos, Existenc... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Determine the following: (1) all facets of the secondary polytope of the $d$-cube; (2) whether a graph of triangulations can be disconnected in dimensions $3$ or $4$; (3) the complexity of counting triangulations and a method for uniformly random generation; (4) whether every smooth polytope has a regular unimodular tr... | Open questions: (1) Can all facets of the secondary polytope of the d-cube be found? (2) Are there disconnected 3-dimensional or 4-dimensional graphs of triangulations? (3) What is the computational complexity of counting triangulations, and how can one generate a triangulation uniformly at random? (4) Do all smooth po... | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,054 | OWR-11786-002 | Additivity of Triangulation Complexity under Connected Sum | Let $M$ be a compact $(d-1)$-dimensional manifold with boundary, where $d\geq4$, and define
$$\Gamma(M)=\min_{|\Delta|=M}\bigl(h_2(\Delta)-h_{d-1}(\Delta)-d h_d(\Delta)\bigr)=\min_{|\Delta|=M}\bigl(h_2(\Delta)-f_0^{\mathrm{int}}(\Delta)\bigr).$$
For a closed manifold, set $\Gamma(M)=\Gamma(M\setminus B^{d-1})$. Is $\Ga... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-002",
"literature-status:open",
"owr-year:2012"
] | The proposed additivity of the triangulation complexity Gamma under connected sum is still an unresolved general question; no proof or counterexample for the stated invariant was located. | [
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "Oberwolfach report, Triangulations"
},
{
"url": "https://link.springer.com/book/10.1007/978-3-642-12971-1",
"label": "De Loera--Rambau--Santos, Triangulations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Let $M$ be a compact $(d-1)$-dimensional manifold with boundary, where $d\geq4$, and define
$$\Gamma(M)=\min_{|\Delta|=M}\bigl(h_2(\Delta)-h_{d-1}(\Delta)-d h_d(\Delta)\bigr)=\min_{|\Delta|=M}\bigl(h_2(\Delta)-f_0^{\mathrm{int}}(\Delta)\bigr).$$
For a closed manifold, set $\Gamma(M)=\Gamma(M\setminus B^{d-1})$. Is $\Ga... | For the invariant Gamma(M) defined for a manifold M with boundary by the report's minimum h-vector formula, is Gamma(M_1 connected-sum M_2)=Gamma(M_1)+Gamma(M_2)? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,055 | OWR-11786-008 | Diameter Bounds for Connected Layer Families | For connected layer families on $d$-element multisets from $n$ symbols, is $\widetilde f(d,n)=d(n-1)$? In particular, can this be proved or refuted for $d=3$? For layer families arising from triangulated surfaces, are the upper bounds $2n$ with boundary and $n$ without boundary tight? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11786-008",
"literature-status:partially-solved",
"owr-year:2012"
] | The polynomial Hirsch conjecture remains open, while the Hirsch bound is proved for normal flag complexes and related flag cases; the general superstrongly-connected family is not settled. | [
{
"url": "https://doi.org/10.1007/s00454-026-00844-8",
"label": "current diameter paper"
},
{
"url": "https://doi.org/10.1287/moor.2014.0661",
"label": "flag-complex theorem"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | For connected layer families on $d$-element multisets from $n$ symbols, is $\widetilde f(d,n)=d(n-1)$? In particular, can this be proved or refuted for $d=3$? For layer families arising from triangulated surfaces, are the upper bounds $2n$ with boundary and $n$ without boundary tight? | For connected layer families on d-element multisets from n symbols, conjecture that f-tilde(d,n)=d(n-1); in particular, can this be proved or refuted for d=3, and for layer families arising from triangulated surfaces are the upper bounds 2n with boundary and n without boundary tight? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,056 | OWR-11786-009 | Wedge-of-Spheres Homotopy Type of Random Flag Complexes | Let $X\in X(n,p)$ be a random flag complex. For $d\geq6$ and
$$n^{-2/d}\ll p\ll n^{-2/(d+1)},$$
is $X$ asymptotically almost surely homotopy equivalent to a wedge of $\lfloor d/2\rfloor$-dimensional spheres? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-009",
"literature-status:partially-solved",
"owr-year:2012"
] | Integer-homology vanishing thresholds are known in important random-complex models, but the extracted torsion-vanishing conjecture has no specified p-range and the corresponding torsion-free behavior remains unresolved. | [
{
"url": "https://doi.org/10.1007/s00454-017-9863-1",
"label": "integer-homology threshold"
},
{
"url": "https://arxiv.org/abs/1301.7165",
"label": "random-complex survey"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Let $X\in X(n,p)$ be a random flag complex. For $d\geq6$ and
$$n^{-2/d}\ll p\ll n^{-2/(d+1)},$$
is $X$ asymptotically almost surely homotopy equivalent to a wedge of $\lfloor d/2\rfloor$-dimensional spheres? | If X is the random flag complex X(n,p) with n^{-2/d} much less than p much less than n^{-2/(d+1)} and d is at least 6, then with high probability X is homotopy equivalent to a wedge of floor(d/2)-spheres. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,057 | OWR-11786-010 | Highly Ramified Figure-Eight Covers of Hyperbolic 3-Manifolds | For a closed hyperbolic $3$-manifold $M$ and every $L>0$, does there exist a finite cover $\widetilde M\to M$ and a branched covering $p:\widetilde M\to S^3$ whose branch locus is the figure-eight knot and whose ramification index along every component over the knot exceeds $L$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-010",
"literature-status:open",
"owr-year:2012"
] | Francaviglia--Frigerio--Martelli identify this arbitrarily high ramification question as open in dimension three; universality of the figure-eight knot and results for special covers do not prove it for every closed hyperbolic manifold. | [
{
"url": "https://doi.org/10.1112/jtopol/jts026",
"label": "stable-complexity paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | For a closed hyperbolic $3$-manifold $M$ and every $L>0$, does there exist a finite cover $\widetilde M\to M$ and a branched covering $p:\widetilde M\to S^3$ whose branch locus is the figure-eight knot and whose ramification index along every component over the knot exceeds $L$? | For a closed hyperbolic 3-manifold M and every L>0, does there exist a finite cover M-tilde of M and a branched covering p:M-tilde to S^3 with branch locus the figure-eight knot, such that every component over the knot has ramification index greater than L? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,058 | OWR-11786-011 | Finite-Ring Solutions of Thurston Equations | Let $M$ be a compact $3$-manifold. For every nontrivial $\gamma\in\pi_1(M)$, is there a finite commutative ring $R$ with identity and a homomorphism $\pi_1(M)\to\operatorname{PSL}(2,R)$ that does not send $\gamma$ to the identity? If $M$ is closed, oriented, and not $S^3$, does some one-vertex triangulation of $M$ have... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-011",
"literature-status:open",
"owr-year:2012"
] | The extraction names conjectures and a weaker Conjecture 2 but omits their mathematical statements, so no precise claim can be verified or classified as solved or disproved. | [
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Let $M$ be a compact $3$-manifold. For every nontrivial $\gamma\in\pi_1(M)$, is there a finite commutative ring $R$ with identity and a homomorphism $\pi_1(M)\to\operatorname{PSL}(2,R)$ that does not send $\gamma$ to the identity? If $M$ is closed, oriented, and not $S^3$, does some one-vertex triangulation of $M$ have... | Conjectures on Thurston equations: (1) If M is a compact 3-manifold and nontrivial gamma is in pi_1(M), there is a finite commutative ring R with identity and a homomorphism pi_1(M) to PSL(2,R) sending gamma to a non-identity element. (2) If M is a closed oriented 3-manifold other than S^3, some one-vertex triangulatio... | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,059 | OWR-11786-012 | Quillen's $p$-Subgroup Conjecture | Let $G$ be a finite group and $p$ a prime. If the order complex of the poset of nontrivial $p$-subgroups of $G$ is contractible, is it strongly collapsible, equivalently, does $G$ have a nontrivial normal $p$-subgroup? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-012",
"literature-status:partially-solved",
"owr-year:2012"
] | Quillen's p-subgroup conjecture remains unresolved in general: Aschbacher--Smith proved major cases for p greater than 5, later work covers p equal to 3 and 5, and substantial cases of p equal to 2 remain open. | [
{
"url": "https://annals.math.princeton.edu/1993/137-3/p02",
"label": "Aschbacher--Smith"
},
{
"url": "https://doi.org/10.4171/JCA/95",
"label": "Piterman--Smith"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Let $G$ be a finite group and $p$ a prime. If the order complex of the poset of nontrivial $p$-subgroups of $G$ is contractible, is it strongly collapsible, equivalently, does $G$ have a nontrivial normal $p$-subgroup? | Quillen conjecture: if G is a finite group and the order complex of the poset of nontrivial p-subgroups of G is contractible, then that complex is strongly collapsible (equivalently, G has a nontrivial normal p-subgroup). | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,060 | OWR-11786-015 | Collapsibility of Linear Triangulations of Convex Balls | Is every linear triangulation of a convex ball in Euclidean space collapsible? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-015",
"literature-status:partially-solved",
"owr-year:2012"
] | Lickorish's question is proved in dimensions below four and after at most one barycentric subdivision for linear subdivisions of polytopes, but collapsibility of every original linear triangulation in arbitrary dimension remains open. | [
{
"url": "https://doi.org/10.1007/s00454-019-00137-3",
"label": "barycentric-subdivision theorem"
},
{
"url": "https://arxiv.org/abs/1709.07930",
"label": "published theorem preprint"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Is every linear triangulation of a convex ball in Euclidean space collapsible? | If C is a linear triangulation (subdivision) of a convex ball in Euclidean space, is C collapsible? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,061 | OWR-11786-016 | Collapse Preservation under Subdivision | If a simplicial complex $C$ collapses to a subcomplex $C'$, and $D$ is a subdivision of $C$ restricting to a subdivision $D'$ of $C'$, must $D$ collapse to $D'$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-016",
"literature-status:partially-solved",
"owr-year:2012"
] | The subdivision question is open in its stated form, but a barycentric subdivision of D is proved to collapse to the corresponding barycentric subdivision of D-prime, with further low-dimensional positive cases. | [
{
"url": "https://arxiv.org/abs/1709.07930",
"label": "Adiprasito--Benedetti"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | If a simplicial complex $C$ collapses to a subcomplex $C'$, and $D$ is a subdivision of $C$ restricting to a subdivision $D'$ of $C'$, must $D$ collapse to $D'$? | If a simplicial complex C collapses to a subcomplex C-prime, and D is a subdivision of C restricting to a subdivision D-prime of C-prime, does D collapse to D-prime? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,062 | OWR-11786-017 | Polynomial Hirsch Conjecture for Superstrongly Connected Complexes | Does there exist a polynomial $P(n,d)$ that bounds the dual-graph diameter of every superstrongly connected $d$-dimensional simplicial complex on $n$ vertices? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-017",
"literature-status:partially-solved",
"owr-year:2012"
] | The polynomial Hirsch conjecture is proved for flag complexes and the Hirsch bound for normal flag complexes, but the general superstrongly-connected family in the record remains open. | [
{
"url": "https://doi.org/10.1287/moor.2014.0661",
"label": "flag-complex theorem"
},
{
"url": "https://doi.org/10.1007/s00454-026-00844-8",
"label": "current status paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Does there exist a polynomial $P(n,d)$ that bounds the dual-graph diameter of every superstrongly connected $d$-dimensional simplicial complex on $n$ vertices? | Polynomial Hirsch conjecture: for the family of superstrongly connected d-dimensional simplicial complexes with n vertices, there is a polynomial P in n and d that bounds the diameter of the dual graph of every member by P(n,d). | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,063 | OWR-11786-019 | Decomposability Thresholds for Simplicial Polytopes | What is the least $k=k(d)$ such that every simplicial $d$-polytope is weakly $k$-decomposable, respectively $k$-decomposable, while some simplicial $d$-polytope is not weakly $(k-1)$-decomposable, respectively $(k-1)$-decomposable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11786-019",
"literature-status:partially-solved",
"owr-year:2012"
] | There are counterexamples to weak k-decomposability for every fixed k when dimension is allowed to grow, but the exact minimum k as a function of fixed dimension d is not known. | [
{
"url": "https://doi.org/10.1090/S0002-9939-2014-12101-0",
"label": "Hah nle--Klee--Pilaud"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | What is the least $k=k(d)$ such that every simplicial $d$-polytope is weakly $k$-decomposable, respectively $k$-decomposable, while some simplicial $d$-polytope is not weakly $(k-1)$-decomposable, respectively $(k-1)$-decomposable? | What is the least k=k(d) such that every simplicial d-polytope is weakly k-decomposable (respectively k-decomposable), while some simplicial d-polytope is not weakly (k-1)-decomposable (respectively (k-1)-decomposable)? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,064 | OWR-11786-020 | Matveev–Jaco–Rubinstein Lens-Space Complexity Conjecture | For coprime integers $p>q>0$ with $p>3$, is the complexity of the lens space $L(p,q)$ equal to $E(p,q)-3$, where $E(p,q)$ is the sum of the partial denominators in the continued-fraction expansion of $p/q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-020",
"literature-status:partially-solved",
"owr-year:2012"
] | The Matveev--Jaco--Rubinstein formula is proved for infinite families of lens spaces and many small cases, but the general exact-complexity conjecture for all lens spaces remains unresolved. | [
{
"url": "https://arxiv.org/abs/0805.2425",
"label": "minimal lens triangulations"
},
{
"url": "https://doi.org/10.1112/jtopol/jts026",
"label": "stable-complexity literature"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | For coprime integers $p>q>0$ with $p>3$, is the complexity of the lens space $L(p,q)$ equal to $E(p,q)-3$, where $E(p,q)$ is the sum of the partial denominators in the continued-fraction expansion of $p/q$? | Matveev--Jaco--Rubinstein conjecture: for coprime integers p>q>0 with p>3, the complexity of the lens space L(p,q) is E(p,q)-3, where E(p,q) is the sum of the partial denominators in the continued-fraction expansion of p/q. | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,065 | OWR-11786-021 | Complexity of Random Morse Functions on Simplex Boundaries | What is the expected complexity of a random Morse function on the boundary of a $d$-simplex, and how does it behave under repeated barycentric subdivision? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** partially s... | 3 | partially_solved | null | 2,012 | 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-11786-021",
"literature-status:partially-solved",
"owr-year:2012"
] | The record's repeated-barycentric-subdivision subquestion has an exponential lower-bound answer, but the expected complexity for random Morse functions on simplex boundaries is not determined in general. | [
{
"url": "https://doi.org/10.1007/s00454-017-9860-4",
"label": "Adiprasito--Benedetti--Lutz"
},
{
"url": "https://arxiv.org/abs/1303.6422",
"label": "random discrete Morse theory"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | What is the expected complexity of a random Morse function on the boundary of a $d$-simplex, and how does it behave under repeated barycentric subdivision? | What is the expected complexity (complicatedness) of a random Morse function on the boundary of a d-simplex, and how does this quantity behave under repeated barycentric subdivisions? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,066 | OWR-11786-022 | Random Triangulations and Exchangeable Clique Complexes | Is there a polynomial-time algorithm that samples uniformly from closed $3$-manifold triangulations with $N$ tetrahedra, including under the restriction to triangulations of the $3$-sphere? Separately, for clique complexes of exchangeable random graphs, determine their homotopy groups and whether this random model is u... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-022",
"literature-status:open",
"owr-year:2012"
] | The excerpt combines unresolved sampling, 3-sphere, homotopy-group, and universality questions for random triangulations and exchangeable random graph clique complexes; no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1016/j.disc.2008.11.012",
"label": "random-clique-complex literature"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Is there a polynomial-time algorithm that samples uniformly from closed $3$-manifold triangulations with $N$ tetrahedra, including under the restriction to triangulations of the $3$-sphere? Separately, for clique complexes of exchangeable random graphs, determine their homotopy groups and whether this random model is u... | Is there a polynomial-time algorithm to sample uniformly from closed 3-manifold triangulations with N tetrahedra, including when restricted to 3-spheres? How do the homotopy groups of clique complexes of exchangeable random graphs behave, and are these random objects universal in any respect? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the stated hypotheses, notation, and open target. | null | null | null | null | null | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,067 | OWR-11786-023 | Dual-Diameter Bounds for Triangulated Surfaces | If $\overline f(2,n)$ is the maximal dual diameter of a triangulated surface with boundary and $n$ vertices, is $\overline f(2,n)\leq n-3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23072344",
"checked_at": "2026-09-30",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **A Negative Answer to a Question of Santos on the Dual Diameter of Surfaces with Boundary** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23072344) | [
"owr",
"oberwolfach-reports",
"OWR-11786-023",
"literature-status:open",
"owr-year:2012"
] | The extraction is an incomplete work-in-progress paragraph about Lagrangian structures and the Novikov conjecture, not a complete claim whose truth can be checked; under the stated rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2012/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | If $\overline f(2,n)$ is the maximal dual diameter of a triangulated surface with boundary and $n$ vertices, is $\overline f(2,n)\leq n-3$? | If f-bar(2,n) is the maximal dual diameter of a triangulated surface with boundary and n vertices, is f-bar(2,n) less than or equal to n-3? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,068 | OWR-11786-024 | Unimodular Triangulations of Smooth Lattice Polytopes | Does every smooth lattice polytope have a unimodular triangulation? For the specified smooth reflexive $7$-polytope with facets $x_2-2x_6-x_7\leq 1$, $2x_6-x_1-x_2\leq 1$, $2x_1-x_2-x_3-x_4-x_5+x_6\leq 1$, $x_2-x_6\leq 1$, and $x_i\leq 1$ for $i=1,\ldots,7$, does it have a regular unimodular triangulation, and is its t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-024",
"literature-status:open",
"owr-year:2012"
] | The extraction begins with a technical problem and states a heat-kernel setting but ends before the requested criterion or theorem is specified, so the mathematical claim is unresolved and unclear. | [
{
"url": "https://doi.org/10.2140/apde.2013.6.221",
"label": "Lesch analytic-torsion paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Does every smooth lattice polytope have a unimodular triangulation? For the specified smooth reflexive $7$-polytope with facets $x_2-2x_6-x_7\leq 1$, $2x_6-x_1-x_2\leq 1$, $2x_1-x_2-x_3-x_4-x_5+x_6\leq 1$, $x_2-x_6\leq 1$, and $x_i\leq 1$ for $i=1,\ldots,7$, does it have a regular unimodular triangulation, and is its t... | Does every smooth lattice polytope have a unimodular triangulation? For the specified smooth reflexive 7-polytope with facets x_2-2x_6-x_7≤1, 2x_6-x_1-x_2≤1, 2x_1-x_2-x_3-x_4-x_5+x_6≤1, x_2-x_6≤1, and x_i≤1 for i=1,...,7, does it have a regular unimodular triangulation, and is its toric ideal generated by quadrics? | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,069 | OWR-11786-025 | Universal Triangulations with Prescribed Boundary | For a simplicial $(d-1)$-sphere $T$ linearly embedded in $\mathbb{R}^d$, characterize universal triangulations, construct algorithmically a universal $d$-ball $U$ with prescribed boundary $T$, and bound the size of $U$. The case $d=2$ is known, but higher dimensions remain open. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-025",
"literature-status:open",
"owr-year:2012"
] | Lesch's published singular-space gluing formula still assumes product structure near the cutting hypersurface; later non-product formulas for compact manifolds do not establish the conjectured singular result. | [
{
"url": "https://doi.org/10.2140/apde.2013.6.221",
"label": "Lesch analytic-torsion paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | For a simplicial $(d-1)$-sphere $T$ linearly embedded in $\mathbb{R}^d$, characterize universal triangulations, construct algorithmically a universal $d$-ball $U$ with prescribed boundary $T$, and bound the size of $U$. The case $d=2$ is known, but higher dimensions remain open. | For a simplicial (d-1)-sphere T linearly embedded in R^d, characterize universal triangulations, construct a universal d-ball U with prescribed boundary T algorithmically, and bound the size of U; the case d=2 is known but higher dimensions are open. | 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 | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,070 | OWR-11786-027 | Triangulations of 3-Manifolds with Edge Valences Five and Six | Can every orientable 3-manifold be triangulated using only edge valences 5 and 6, improving the known construction with valences in the set 4,5,6? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486](https://doi.org/10.4171/owr/2012/24)
## Literature review (checked 2026-08-21)
**Status:** open
**Ass... | 3 | open | null | 2,012 | 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-11786-027",
"literature-status:open",
"owr-year:2012"
] | The 4--5--6 edge-degree theorem is established, but the stronger assertion that every closed orientable 3-manifold has a triangulation using only degrees 5 and 6 remains an open TCP-triangulation problem. | [
{
"url": "https://doi.org/10.2307/1194005",
"label": "Brady--McCammond--Meier"
},
{
"url": "https://doi.org/10.4171/owr/2012/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/24 | null | null | null | Can every orientable 3-manifold be triangulated using only edge valences 5 and 6, improving the known construction with valences in the set 4,5,6? | Can every orientable 3-manifold be triangulated using only edge valences 5 and 6, improving the known construction with valences in the set 4,5,6? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Triangulations (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/24, pp. 1405--1486 |
30,002,071 | OWR-11787-002 | Heat-Trace Asymptotics on Singular and Noncompact Manifolds | For an elliptic operator $P$ on a possibly noncompact or singular manifold, give criteria ensuring that $e^{-tP}$ is trace class and that its heat trace has an asymptotic expansion $\sum_{\alpha,k}a_{\alpha,k}t^\alpha(\log t)^k$ as $t\to0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562](https://doi.org/10.4171/owr/2012/25)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-11787-002",
"literature-status:open",
"owr-year:2012"
] | The extraction is a technical setup for analytic-torsion heat asymptotics and stops before a precise criterion is stated; no complete claim can be assessed beyond the open problem context. | [
{
"url": "https://doi.org/10.2140/apde.2013.6.221",
"label": "Lesch analytic-torsion paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/25 | null | null | null | For an elliptic operator $P$ on a possibly noncompact or singular manifold, give criteria ensuring that $e^{-tP}$ is trace class and that its heat trace has an asymptotic expansion $\sum_{\alpha,k}a_{\alpha,k}t^\alpha(\log t)^k$ as $t\to0$. | For an elliptic operator P on a possibly noncompact or singular manifold, give criteria ensuring that e^{-tP} is trace class and that its heat trace has an asymptotic expansion of the form sum of a_{alpha,k} t^alpha log^k t as t tends to 0. | corrected_verified | The official report explicitly identifies these trace-class and heat-expansion criteria as open. | null | null | null | null | null | Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562 |
30,002,072 | OWR-11787-003 | Cheeger–Müller Gluing Without Product Structures | In the Cheeger–Müller theorem for singular manifolds, can the assumption that all structures are products near the gluing boundary be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562](https://doi.org/10.4171/owr/2012/25)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-11787-003",
"literature-status:open",
"owr-year:2012"
] | The conjecture that the product assumption can be removed from the singular-space gluing theorem remains unresolved; the published theorem explicitly retains that assumption. | [
{
"url": "https://doi.org/10.2140/apde.2013.6.221",
"label": "Lesch analytic-torsion paper"
},
{
"url": "https://doi.org/10.4171/owr/2012/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/25 | null | null | null | In the Cheeger–Müller theorem for singular manifolds, can the assumption that all structures are products near the gluing boundary be removed? | In the Cheeger-Muller theorem for singular manifolds, can the assumption that all structures are product near the gluing boundary be removed? | corrected_verified | The official report poses exactly this removal of the product-near-boundary hypothesis. | null | null | null | null | null | Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562 |
30,002,073 | OWR-11787-004 | $L^2$-Cohomology of Strongly Centered Monopole Moduli Spaces | Determine the dimension of the $L^2$-cohomology of the moduli space of strongly centered $\operatorname{SU}(2)$-monopoles on $\mathbb R^3$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562](https://doi.org/10.4171/owr/2012/25)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,012 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11787-004",
"literature-status:partially-solved",
"owr-year:2012"
] | The Sen conjecture for strongly centered SU(2) monopoles has substantial partial results: Fritzsch, Kottke, and Singer prove the coprime case and part of the predicted L2-cohomology statement, but the full charge-general claim is not established. | [
{
"url": "https://arxiv.org/abs/1811.00601",
"label": "Fritzsch--Kottke--Singer, Monopoles and the Sen Conjecture: Part I"
},
{
"url": "https://doi.org/10.1007/BF02099547",
"label": "Segal--Selby, The cohomology of the space of magnetic monopoles"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/25 | null | null | null | Determine the dimension of the $L^2$-cohomology of the moduli space of strongly centered $\operatorname{SU}(2)$-monopoles on $\mathbb R^3$. | Sen conjecture: determine the dimension of the L^2-cohomology of the moduli space of strongly centred SU(2)-monopoles on R^3. | corrected_verified | The official report says that Sen predicts this dimension but does not state a formula; the clean statement therefore retains only the determination problem supported by the source. | null | null | null | null | null | Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562 |
30,002,074 | OWR-11787-005 | Asymptotic Metrics for Higher-Rank Monopoles | For $\operatorname{SU}(N)$-monopoles with maximal symmetry breaking, establish the quasi-isometric asymptotics of the monopole metric on the analogous compactification and determine whether they agree qualitatively with the $\operatorname{SU}(2)$ case. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562](https://doi.org/10.4171/owr/2012/25)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11787-005",
"literature-status:open",
"owr-year:2012"
] | Asymptotic metrics for maximally broken SU(N) monopoles are known, but the proposed compactification and the claimed global quasi-isometric control for arbitrary charges remain unresolved; the record itself describes this as work in progress. | [
{
"url": "https://arxiv.org/abs/hep-th/9801092",
"label": "Bielawski, Asymptotic metrics for SU(N)-monopoles with maximal symmetry breaking"
},
{
"url": "https://arxiv.org/abs/1512.02979",
"label": "Kottke--Singer, Partial compactification of monopoles and metric asymptotics"
},
{
"url":... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/25 | null | null | null | For $\operatorname{SU}(N)$-monopoles with maximal symmetry breaking, establish the quasi-isometric asymptotics of the monopole metric on the analogous compactification and determine whether they agree qualitatively with the $\operatorname{SU}(2)$ case. | For SU(N)-monopoles with maximal symmetry breaking, establish the quasi-isometric asymptotics of the monopole metric on the analogous compactification and determine whether they agree qualitatively with the SU(2) case. | corrected_verified | The official report describes this higher-rank extension as work in progress and states the same asymptotic comparison goal. | null | null | null | null | null | Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562 |
30,002,075 | OWR-11787-006 | Transfer Index Conjecture in Differential Algebraic $K$-Theory | For a proper submersion $\pi:W\to B$ equipped with a Riemannian structure and a geometrized local system $[V,h^V]$, does the topological differential-algebraic $K$-theory index $\operatorname{ind}_{\mathrm{top}}[V,h^V]$ equal the analytic index $\operatorname{ind}_{\mathrm{an}}[V,h^V]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562](https://doi.org/10.4171/owr/2012/25)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-11787-006",
"literature-status:open",
"owr-year:2012"
] | The transfer index conjecture is still presented in the primary Bunke--Gepner work as a conjectural equality; that paper proves only consequences and special cases, not the general statement. | [
{
"url": "https://arxiv.org/abs/1306.0247",
"label": "Bunke--Gepner, Differential function spectra and the differential Becker--Gottlieb transfer"
},
{
"url": "https://ems.press/content/serial-article-files/46396",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/25 | null | null | null | For a proper submersion $\pi:W\to B$ equipped with a Riemannian structure and a geometrized local system $[V,h^V]$, does the topological differential-algebraic $K$-theory index $\operatorname{ind}_{\mathrm{top}}[V,h^V]$ equal the analytic index $\operatorname{ind}_{\mathrm{an}}[V,h^V]$? | Transfer index conjecture: for a proper submersion pi: W to B with the relevant geometric and coefficient data, prove that the topological differential-algebraic K-theory index ind_top equals the analytic index ind_an. | corrected_verified | The official report supplies the proper-submersion, geometric, and coefficient data and states the equality of the two indices as the transfer index conjecture. | null | null | null | null | null | Analysis and Geometric Singularities (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/25, pp. 1487--1562 |
30,002,076 | OWR-11788-002 | Global Regularity and Uniqueness of Three-Dimensional Navier–Stokes | For the three-dimensional Navier–Stokes equations on $\mathbb R^3$, are Leray–Hopf solutions globally regular and unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-11788-009"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11788-002",
"literature-status:open",
"owr-year:2012"
] | The three-dimensional Navier--Stokes global regularity and uniqueness problem remains unresolved; the Clay Mathematics Institute still lists the basic existence and uniqueness questions as lacking a proof. | [
{
"url": "https://www.claymath.org/millennium/navier-stokes-equation/",
"label": "Clay Mathematics Institute, Navier--Stokes Equation"
},
{
"url": "https://www.claymath.org/wp-content/uploads/2022/02/MPPc.pdf",
"label": "Fefferman, official Millennium problem statement"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | For the three-dimensional Navier–Stokes equations on $\mathbb R^3$, are Leray–Hopf solutions globally regular and unique? | For the three-dimensional Navier-Stokes equations on R^3, determine whether Leray-Hopf solutions are globally regular and unique. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,077 | OWR-11788-003 | Nonlinear Stability of Subextremal Kerr Black Holes | Black-hole stability conjecture: do sufficiently small perturbations of sub-extremal Kerr initial data for the vacuum Einstein equations evolve toward a nearby Kerr black hole? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.4310/pamq.2023.v19.n3.a1",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (the slowly rotating case is proved). M. Dafermos (joint with G. Holzegel and I. Rodnianski; OWR 26/2012, p. 1573) states the black hole stability conjecture: small perturbations of subextremal Kerr initial data converge to a nearby Kerr solution. Klain... | [
"owr",
"oberwolfach-reports",
"OWR-11788-003",
"literature-status:open",
"owr-year:2012"
] | The extracted text is only a continuation around an unspecified conjecture and gives no complete mathematical claim; under the triage rule the unresolved and non-identifiable record is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2012/26",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | Black-hole stability conjecture: do sufficiently small perturbations of sub-extremal Kerr initial data for the vacuum Einstein equations evolve toward a nearby Kerr black hole? | Black-hole stability conjecture: do sufficiently small perturbations of sub-extremal Kerr initial data for the vacuum Einstein equations evolve toward a nearby Kerr black hole? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,078 | OWR-11788-004 | Scattering for the Quintic Resonant System | For a sequence $\vec u=(u_j)_{j\in\mathbb Z^2}$ governed by the quintic resonant system
$$i\partial_tu_j+\partial_{xx}u_j=\sum_{(j_1,\ldots,j_5)\in\mathcal R(j)}u_{j_1}\overline{u}_{j_2}u_{j_3}\overline{u}_{j_4}u_{j_5},$$
where
$$\mathcal R(j)=\left\{(j_1,\ldots,j_5)\in(\mathbb Z^2)^5:\ j_1-j_2+j_3-j_4+j_5=j,\ |j_1|... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-11788-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11788-004",
"literature-status:partially-solved",
"owr-year:2012"
] | The conjecture for the quintic resonant NLS system is not resolved in full generality, but the two-discrete-component case singled out in the Hani--Pausader program was later proved by Cheng, Guo, and Zhao. | [
{
"url": "https://arxiv.org/abs/1205.6136",
"label": "Hani--Pausader, On scattering for the quintic defocusing NLS on R times T2"
},
{
"url": "https://arxiv.org/abs/1809.01527",
"label": "Cheng--Guo--Zhao, On scattering for the quintic defocusing NLS on the two-dimensional cylinder"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | For a sequence $\vec u=(u_j)_{j\in\mathbb Z^2}$ governed by the quintic resonant system
$$i\partial_tu_j+\partial_{xx}u_j=\sum_{(j_1,\ldots,j_5)\in\mathcal R(j)}u_{j_1}\overline{u}_{j_2}u_{j_3}\overline{u}_{j_4}u_{j_5},$$
where
$$\mathcal R(j)=\left\{(j_1,\ldots,j_5)\in(\mathbb Z^2)^5:\ j_1-j_2+j_3-j_4+j_5=j,\ |j_1|... | For every E>0 and every smooth initial datum for the quintic system (5) with Els(initial datum) less than or equal to E, does there exist a global solution conserving Els that scatters as t tends to both positive and negative infinity? | corrected_verified | The numbered system and its conserved energy were restored from the official report, eliminating the unresolved equation reference while preserving Conjecture 2. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,079 | OWR-11788-005 | Duplicate Quintic Resonant-System Scattering Problem | For every E>0 and every smooth initial datum for the quintic system (5) with Els(initial datum) less than or equal to E, does there exist a global solution conserving Els that scatters as t tends to both positive and negative infinity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record exactly repeats the same-report resonant-system conjecture represented canonically by OWR-11788-004. No separate clean statement) | [
"OWR-11788-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11788-005",
"literature-status:partially-solved",
"owr-year:2012"
] | The conditional scattering theorem for NLS on R times T2 remains conditional on the full resonant-system conjecture, while later work settles only special resonant components; therefore the extracted all-energy statement is not fully solved. | [
{
"url": "https://arxiv.org/abs/1205.6136",
"label": "Hani--Pausader, On scattering for the quintic defocusing NLS on R times T2"
},
{
"url": "https://arxiv.org/abs/1809.01527",
"label": "Cheng--Guo--Zhao, two-component resonant-system result"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | null | For every E>0 and every smooth initial datum for the quintic system (5) with Els(initial datum) less than or equal to E, does there exist a global solution conserving Els that scatters as t tends to both positive and negative infinity? | unrecoverable | This record exactly repeats the same-report resonant-system conjecture represented canonically by OWR-11788-004. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,080 | OWR-11788-006 | Mass-Decreasing Flows and the Positive Mass Theorem | Can the mass-decreasing flow on asymptotically flat three-manifolds be used to give an independent proof of the positive mass theorem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 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-11788-006",
"literature-status:open",
"owr-year:2012"
] | The mass-decreasing flow was proved to eliminate the mass only under an a priori inequality, and the proposed independent proof of the positive mass theorem is stated as a question with no general proof found. | [
{
"url": "https://arxiv.org/abs/1107.3220",
"label": "Haslhofer, A mass-decreasing flow in dimension three"
},
{
"url": "https://www.math.utoronto.ca/roberth/papers/Haslhofer_owr_mdf.pdf",
"label": "Haslhofer, Oberwolfach report on the mass-decreasing flow"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | Can the mass-decreasing flow on asymptotically flat three-manifolds be used to give an independent proof of the positive mass theorem? | Can the mass-decreasing flow on asymptotically flat three-manifolds be used to give an independent proof of the positive mass theorem? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,081 | OWR-11788-007 | Asymptotic Symmetry of Geometric PDE Singularities | How should the folklore conjecture that finite-time singularities of parabolic geometric PDE become asymptotically as symmetric as their topology permits be formulated and interpreted? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 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-11788-007",
"literature-status:open",
"owr-year:2012"
] | The extracted record consists only of the question `How should this be interpreted?' and does not identify a definite proposition or conjecture whose truth can be checked; it is therefore unresolved by rule. | [
{
"url": "https://doi.org/10.4171/owr/2012/26",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | How should the folklore conjecture that finite-time singularities of parabolic geometric PDE become asymptotically as symmetric as their topology permits be formulated and interpreted? | How should the folklore conjecture that finite-time singularities of parabolic geometric PDE become asymptotically as symmetric as their topology permits be formulated and interpreted? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,082 | OWR-11788-008 | Uniqueness of Tangent Flows in Mean Curvature Flow | Do mean-curvature-flow singularities have unique tangent flows, and more generally can the full asymptotic-symmetry conjecture for finite-time geometric PDE singularities be proved? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 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-11788-008",
"literature-status:partially-solved",
"owr-year:2012"
] | Uniqueness of tangent flows is proved for several important classes, including compact smooth multiplicity-one shrinkers and asymptotically conical flows, but the general conjecture remains open. | [
{
"url": "https://arxiv.org/abs/1107.4643",
"label": "Schulze, Uniqueness of compact tangent flows in mean curvature flow"
},
{
"url": "https://doi.org/10.1215/00127094-2020-0098",
"label": "Chodosh--Schulze, Uniqueness of asymptotically conical tangent flows"
},
{
"url": "https://doi.or... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | Do mean-curvature-flow singularities have unique tangent flows, and more generally can the full asymptotic-symmetry conjecture for finite-time geometric PDE singularities be proved? | Do mean-curvature-flow singularities have unique tangent flows, and more generally can the full asymptotic-symmetry conjecture for finite-time geometric PDE singularities be proved? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,083 | OWR-11788-009 | Duplicate Three-Dimensional Navier–Stokes Problem | For the three-dimensional Navier-Stokes equations, is the global well-posedness and regularity problem true? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This record restates the same-report three-dimensional Navier–Stokes global regularity and uniqueness problem represented canonically by OWR) | [
"OWR-11788-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11788-009",
"literature-status:open",
"owr-year:2012"
] | The global regularity and uniqueness problem for three-dimensional incompressible Navier--Stokes remains open in the Clay formulation. | [
{
"url": "https://www.claymath.org/millennium/navier-stokes-equation/",
"label": "Clay Mathematics Institute, Navier--Stokes Equation"
},
{
"url": "https://www.claymath.org/wp-content/uploads/2022/02/MPPc.pdf",
"label": "Fefferman, official Millennium problem statement"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | null | For the three-dimensional Navier-Stokes equations, is the global well-posedness and regularity problem true? | unrecoverable | This record restates the same-report three-dimensional Navier–Stokes global regularity and uniqueness problem represented canonically by OWR-11788-002. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,084 | OWR-11788-010 | Large-Data Scattering for Energy-Critical Schrödinger Maps | For Schrödinger maps from $\mathbb R^{2+1}$ to $S^2$ with zero homotopy class and energy below $2E(Q_1)=8\pi$, do global well-posedness and scattering hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637](https://doi.org/10.4171/owr/2012/26)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 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-11788-010",
"literature-status:partially-solved",
"owr-year:2012"
] | Small critical-data global well-posedness and scattering, and some low-energy equivariant cases, are known; the large-data Schrödinger-map problem described in the record remains unresolved. | [
{
"url": "https://arxiv.org/abs/0807.0265",
"label": "Bejenaru--Ionescu--Kenig--Tataru, Global Schrödinger maps"
},
{
"url": "https://arxiv.org/abs/1112.6122",
"label": "Bejenaru--Ionescu--Kenig--Tataru, Equivariant Schrödinger maps in two spatial dimensions"
},
{
"url": "https://eudml.o... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/26 | null | null | null | For Schrödinger maps from $\mathbb R^{2+1}$ to $S^2$ with zero homotopy class and energy below $2E(Q_1)=8\pi$, do global well-posedness and scattering hold? | For Schrödinger maps from R^{2+1} to S^2 with zero homotopy class and energy below 2E(Q_1)=8pi, do global well-posedness and scattering hold? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Nonlinear Evolution Problems (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/26, pp. 1563--1637 |
30,002,085 | OWR-11789-006 | Classification of Ricci-Flat ALE Four-Manifolds | Do Ricci-flat ALE four-manifolds exist beyond Kronheimer’s gravitational instantons and their known finite quotients? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686](https://doi.org/10.4171/owr/2012/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,012 | 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-11789-006",
"literature-status:open",
"owr-year:2012"
] | Kronheimer's classification covers hyperkähler ALE 4-manifolds and important extra hypotheses are known, but whether every simply connected Ricci-flat ALE 4-manifold is hyperkähler remains open. | [
{
"url": "https://arxiv.org/abs/2304.01609",
"label": "Li, On 4-dimensional Ricci-flat ALE manifolds"
},
{
"url": "https://arxiv.org/abs/2606.10443",
"label": "Li--Sun, Geometry of gravitational instantons"
},
{
"url": "https://doi.org/10.4171/owr/2012/27",
"label": "original Oberwol... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/27 | null | null | null | Do Ricci-flat ALE four-manifolds exist beyond Kronheimer’s gravitational instantons and their known finite quotients? | Are there Ricci-flat ALE 4-manifolds other than Kronheimer gravitational instantons and the known finite quotients? | corrected_verified | The official report explicitly says that the existence of any other Ricci-flat ALE four-manifolds is an important open question. | null | null | null | null | null | Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686 |
30,002,086 | OWR-11789-007 | Gradient Lower Bounds for Shrinking Ricci Solitons | For a complete shrinking Ricci soliton $(M,g,f)$ with basepoint $p$ minimizing $f$, does there exist $C>0$ such that $|\nabla f|(x)\geq C^{-1}$ whenever $d(x,p)\geq C$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686](https://doi.org/10.4171/owr/2012/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,012 | 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-11789-007",
"literature-status:open",
"owr-year:2012"
] | The record identifies an unresolved technical condition for four-dimensional Ricci shrinkers and asks for a proof that it always holds; no general proof was found. | [
{
"url": "https://www.math.utoronto.ca/roberth/papers/Haslhofer_owr_singularities.pdf",
"label": "Haslhofer, Singularities in 4d Ricci flow"
},
{
"url": "https://doi.org/10.4171/owr/2012/27",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/27 | null | null | null | For a complete shrinking Ricci soliton $(M,g,f)$ with basepoint $p$ minimizing $f$, does there exist $C>0$ such that $|\nabla f|(x)\geq C^{-1}$ whenever $d(x,p)\geq C$? | For shrinking Ricci solitons, can one prove that the technical condition |nabla f|(x) is bounded below by a positive constant outside a sufficiently large compact set? | corrected_verified | The official report displays this technical condition and explicitly says that proving it for every shrinker remains open. | null | null | null | null | null | Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686 |
30,002,087 | OWR-11789-008 | Shrinking-Soliton Degeneration Report | Given Gromov-Hausdorff limits X of sequences of shrinking Ricci solitons, what geometric and singularity structure can the metric space X have? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686](https://doi.org/10.4171/owr/2012/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,012 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official contribution uses a broad question about Gromov–Hausdorff limits as motivation and then states its compactness and singular-loc) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11789-008",
"literature-status:open",
"owr-year:2012"
] | The extracted question gives no definition or properties of the metric space X, so it is not a determinate claim for which a solved status can be justified; it remains open under the stated rule. | [
{
"url": "https://doi.org/10.4171/owr/2012/27",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/27 | null | null | null | null | Given Gromov-Hausdorff limits X of sequences of shrinking Ricci solitons, what geometric and singularity structure can the metric space X have? | unrecoverable | The official contribution uses a broad question about Gromov–Hausdorff limits as motivation and then states its compactness and singular-locus theorem under the relevant volume and diameter bounds; the extraction omits those hypotheses and does not preserve a determinate residual open claim. No separate clean statement... | null | null | null | null | null | Geometrie (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/27, pp. 1639--1686 |
30,002,088 | OWR-11790-001 | Weak Injectivity of the Whitehead-Double Concordance Operator | Is the Whitehead-double satellite operator weakly injective on the smooth knot concordance group; equivalently, does $\operatorname{Wh}(K)=\operatorname{Wh}(U)$ imply $K=U$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758](https://doi.org/10.4171/owr/2012/28)
## Literature review (chec... | 3 | open | null | 2,012 | 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-11790-001",
"literature-status:open",
"owr-year:2012"
] | The weak injectivity question for the Whitehead-double operator on smooth knot concordance remains open; known injectivity results are conditional on the smooth four-dimensional Poincare conjecture or apply to other satellite operators. | [
{
"url": "https://arxiv.org/abs/1205.5058",
"label": "Cochran--Davis--Ray, Injectivity of satellite operators in knot concordance"
},
{
"url": "https://doi.org/10.4171/owr/2012/28",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/28 | null | null | null | Is the Whitehead-double satellite operator weakly injective on the smooth knot concordance group; equivalently, does $\operatorname{Wh}(K)=\operatorname{Wh}(U)$ imply $K=U$? | Is the Whitehead double satellite operator weakly injective on the smooth knot concordance group; equivalently, does Wh(K)=Wh(U) imply K=U? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758 |
30,002,089 | OWR-11790-003 | Categorification and Higher-Dimensional Extensions of Parity Brackets | How can one construct a homological complex whose Euler characteristic is the parity bracket, and how can parity theory and a bracket be generalized to higher-dimensional objects such as surfaces in 4-space? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758](https://doi.org/10.4171/owr/2012/28)
## Literature review (chec... | 3 | open | null | 2,012 | 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-11790-003",
"literature-status:open",
"owr-year:2012"
] | The questions about categorifying the parity bracket and extending parity theory to higher-dimensional objects are posed as research directions, and no general construction resolving them was identified. | [
{
"url": "https://arxiv.org/abs/0912.5348",
"label": "Manturov, Free Knots and Parity"
},
{
"url": "https://doi.org/10.4171/owr/2012/28",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/28 | null | null | null | How can one construct a homological complex whose Euler characteristic is the parity bracket, and how can parity theory and a bracket be generalized to higher-dimensional objects such as surfaces in 4-space? | How can one construct a homological complex whose Euler characteristic is the parity bracket, and how can parity theory and a bracket be generalized to higher-dimensional objects such as surfaces in 4-space? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758 |
30,002,090 | OWR-11790-004 | Group-Valued Parity and Knots in Three-Manifolds | For parity theory, how can group information be encoded at crossings and a group bracket defined; does a parity theory exist for knots in arbitrary 3-manifolds; and are there applications to link homotopy theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758](https://doi.org/10.4171/owr/2012/28)
## Literature review (chec... | 3 | open | null | 2,012 | 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-11790-004",
"literature-status:open",
"owr-year:2012"
] | The questions about parity for knots in arbitrary 3-manifolds and applications to link homotopy remain open-ended research questions; the cited free-knot results do not resolve these extensions. | [
{
"url": "https://arxiv.org/abs/0912.5348",
"label": "Manturov, Free Knots and Parity"
},
{
"url": "https://doi.org/10.4171/owr/2012/28",
"label": "original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/28 | null | null | null | For parity theory, how can group information be encoded at crossings and a group bracket defined; does a parity theory exist for knots in arbitrary 3-manifolds; and are there applications to link homotopy theory? | For parity theory, how can group information be encoded at crossings and a group bracket defined; does a parity theory exist for knots in arbitrary 3-manifolds; and are there applications to link homotopy theory? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758 |
30,002,091 | OWR-11790-006 | Vanishing Exceptional Curves in Class-VII Surface Degenerations | In the study of complex surfaces (such as minimal class $\mathrm{VII}$ surfaces with small $b_2$), consider a holomorphic deformation family $X \to D$ over the unit disk whose general fibers $X_t$ ($t \neq 0$) contain exceptional curves $E_{i,t}$, whereas the central fiber $X_0$ does not. What is the geometric limiting... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758](https://doi.org/10.4171/owr/2012/28)
## Literature review (chec... | 3 | partially_solved | null | 2,012 | 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-11790-006",
"literature-status:partially-solved",
"owr-year:2012"
] | Donaldson and Teleman methods establish substantial class VII results, including curves and classification information for small second Betti number, but the extracted limiting behavior of the exceptional curves as the parameter tends to zero is not resolved in full generality. | [
{
"url": "https://arxiv.org/abs/0704.2634",
"label": "Teleman, Instantons and curves on class VII surfaces"
},
{
"url": "https://doi.org/10.4171/owr/2012/28",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/28 | null | null | null | In the study of complex surfaces (such as minimal class $\mathrm{VII}$ surfaces with small $b_2$), consider a holomorphic deformation family $X \to D$ over the unit disk whose general fibers $X_t$ ($t \neq 0$) contain exceptional curves $E_{i,t}$, whereas the central fiber $X_0$ does not. What is the geometric limiting... | In a deformation X to D whose fibers X_t contain exceptional curves E_{i,t} for t not equal to 0 while X_0 does not, what happens to E_{i,t} as t tends to 0 and why do they disappear? In the reported example their areas diverge to infinity. | corrected_verified | The official report confirms the qualitative degeneration question, but its notation depends on a preceding construction and does not provide enough local definitions for a fully self-contained statement. | null | null | null | null | null | Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758 |
30,002,092 | OWR-11790-007 | Kirby’s Whitehead-Double Sliceness Conjecture | Is the Whitehead double of a knot $K$ slice if and only if $K$ is slice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758](https://doi.org/10.4171/owr/2012/28)
## Literature review (chec... | 3 | open | null | 2,012 | 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-11790-007",
"literature-status:open",
"owr-year:2012"
] | The smooth Whitehead-double sliceness conjecture remains explicitly conjectural; untwisted Whitehead doubles are all topologically slice, so the corresponding unrestricted topological statement is false rather than a solution of the smooth problem. | [
{
"url": "https://arxiv.org/abs/1009.5361",
"label": "Knot concordance and Whitehead doubling"
},
{
"url": "https://arxiv.org/abs/math/0606094",
"label": "Hedden, Knot Floer homology of Whitehead doubles"
},
{
"url": "https://doi.org/10.4171/owr/2012/28",
"label": "original OWR repor... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/28 | null | null | null | Is the Whitehead double of a knot $K$ slice if and only if $K$ is slice? | Kirby's conjecture asserts that the Whitehead double of a knot K is slice if and only if K is slice. | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Invariants in Low-Dimensional Topology and Knot Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/28, pp. 1687--1758 |
30,002,093 | OWR-11791-001 | Minimizers for Banach-Space Subspace Segmentation | For the subspace-segmentation problem of minimizing the approximation error over $M$-tuples of closed subspaces of a Banach space, what are necessary and sufficient conditions for a minimizer to exist when the exponent $p\ne2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843](https://doi.org/10.4171/owr/2012/29)
## Literature review (checked ... | 3 | open | null | 2,012 | 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",
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] | Necessary and sufficient existence conditions are known for the quadratic case p equals 2, while the cited survey and subsequent literature still do not provide a general characterization for p not equal to 2. | [
{
"url": "https://onlinelibrary.wiley.com/doi/10.1155/2013/417492",
"label": "Aldroubi et al., review of subspace segmentation"
},
{
"url": "https://doi.org/10.4171/owr/2012/29",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/29 | null | null | null | For the subspace-segmentation problem of minimizing the approximation error over $M$-tuples of closed subspaces of a Banach space, what are necessary and sufficient conditions for a minimizer to exist when the exponent $p\ne2$? | For the subspace-segmentation problem of minimizing the approximation error over M-tuples of closed subspaces of a Banach space, what are necessary and sufficient conditions for a minimizer to exist when the exponent p\ne 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 | Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843 |
30,002,094 | OWR-11791-002 | Stable Oversampling Approximations of Linear Systems | Which linear time-invariant systems can be stably approximated by approximation processes that use oversampling? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843](https://doi.org/10.4171/owr/2012/29)
## Literature review (checked ... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-11791-002",
"literature-status:open",
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] | Later work gives stable approximation under broader measurement models and in selected sampling schemes, but a general characterization of all systems stably approximable by oversampling remains unresolved. | [
{
"url": "https://arxiv.org/abs/1402.1092",
"label": "Signal and system approximation from general measurements"
},
{
"url": "https://doi.org/10.4171/owr/2012/29",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/29 | null | null | null | Which linear time-invariant systems can be stably approximated by approximation processes that use oversampling? | Which linear time-invariant systems can be stably approximated by approximation processes that use oversampling? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843 |
30,002,095 | OWR-11791-004 | Super-Resolution Accuracy beyond the Cutoff Scale | Given noisy low-pass measurements of a signal $x$, how accurately can super-resolution recover features below the cutoff scale? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843](https://doi.org/10.4171/owr/2012/29)
## Literature review (checked ... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
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"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11791-004",
"literature-status:open",
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] | The extracted sentence is a context-free question about recovering finer features and does not specify the model, observations, or target theorem; no determinate solved or disproved claim can be identified. | [
{
"url": "https://doi.org/10.4171/owr/2012/29",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/29 | null | null | null | Given noisy low-pass measurements of a signal $x$, how accurately can super-resolution recover features below the cutoff scale? | Given noisy low-pass measurements of a signal x, how accurately can its finer features be recovered by super-resolution as the desired resolution becomes finer than the cutoff resolution? | 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 | Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843 |
30,002,096 | OWR-11791-005 | Frame Sets of General Gabor Windows | For which triples $(g,\alpha,\beta)$, with $g\in L^2(\mathbb R)$ and $\alpha,\beta>0$, is the Gabor system $\{e^{2\pi i\beta lt}g(t-\alpha k):k,l\in\mathbb Z\}$ a frame for $L^2(\mathbb R)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843](https://doi.org/10.4171/owr/2012/29)
## Literature review (checked ... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
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"order_index": 8,
"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.",
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"owr",
"oberwolfach-reports",
"OWR-11791-005",
"literature-status:open",
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] | The frame set is known for several important windows, but current literature still describes determining the frame set of a general window as an open problem, including unresolved cases among standard windows. | [
{
"url": "https://arxiv.org/abs/2310.01141",
"label": "Obstructions for Gabor frames of the second-order B-spline"
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{
"url": "https://arxiv.org/abs/2205.06479",
"label": "Frame set for Gabor systems with Haar window"
},
{
"url": "https://doi.org/10.4171/owr/2012/29",
"label": "orig... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/29 | null | null | null | For which triples $(g,\alpha,\beta)$, with $g\in L^2(\mathbb R)$ and $\alpha,\beta>0$, is the Gabor system $\{e^{2\pi i\beta lt}g(t-\alpha k):k,l\in\mathbb Z\}$ a frame for $L^2(\mathbb R)$? | For which triples (g,\alpha,\beta), with g\in L^2(\mathbb R) and \alpha,\beta>0, is the Gabor system \{e^{2\pi i\beta lt}g(t-\alpha k):k,l\in\mathbb Z\} a frame for L^2(\mathbb R)? | 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 | Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843 |
30,002,097 | OWR-11791-006 | Restricted Isometries for Random Scattering Matrices | Does the random scattering matrix used for sparse recovery satisfy a restricted isometry property in a parameter regime strong enough to yield uniform recovery of all sparse signals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843](https://doi.org/10.4171/owr/2012/29)
## Literature review (checked ... | 3 | open | null | 2,012 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
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"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-11791-006",
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] | Nonuniform sparse-recovery results and numerical damping methods are available, but the RIP estimate for the specific scattering matrix in the extracted problem remains unestablished and the matrix model is not generalized enough for a theorem covering the claim. | [
{
"url": "https://doi.org/10.4171/owr/2012/29",
"label": "original OWR report"
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{
"url": "https://repository.kaust.edu.sa/items/6801b3b7-0d36-44f0-84fd-cdeee9e0a8c3",
"label": "modified CoSaMP electromagnetic imaging"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/29 | null | null | null | Does the random scattering matrix used for sparse recovery satisfy a restricted isometry property in a parameter regime strong enough to yield uniform recovery of all sparse signals? | Does the random scattering matrix used for sparse recovery satisfy a restricted isometry property in a parameter regime strong enough to yield uniform recovery of all sparse signals? | exact | Manual review confirmed that the exact extracted statement is self-contained, mathematically coherent, and free of LaTeX or report-layout artifacts. | null | null | null | null | null | Applied Harmonic Analysis and Sparse Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/29, pp. 1759--1843 |
30,002,098 | OWR-11792-001 | Pure Resolutions of Paracanonical Level Curves | For a general level-$\ell$ curve $[C,\eta]$ of even genus $g\geq6$, does the paracanonically embedded curve $C\hookrightarrow\mathbb P^{g-2}$ have a pure homogeneous coordinate-ring resolution; equivalently, is $K_{g/2-2,1}(C,K_C\otimes\eta)=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebraic_geometry",
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"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-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",
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"OWR-11792-001",
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] | The level-syzygy conjecture is verified in low genus and special levels, with exceptional genera identified, but no general proof covering the stated conjectural pattern was found. | [
{
"url": "https://www2.mathematik.hu-berlin.de/~farkas/nivel3.pdf",
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{
"url": "https://doi.org/10.4171/owr/2012/30",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | For a general level-$\ell$ curve $[C,\eta]$ of even genus $g\geq6$, does the paracanonically embedded curve $C\hookrightarrow\mathbb P^{g-2}$ have a pure homogeneous coordinate-ring resolution; equivalently, is $K_{g/2-2,1}(C,K_C\otimes\eta)=0$? | For a general level-\ell curve [C,\eta] of even genus g\ge 6, does the paracanonically embedded curve C\hookrightarrow\mathbb P^{g-2} have a pure homogeneous coordinate-ring resolution, equivalently K_{g/2-2,1}(C,K_C\otimes\eta)=0? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,099 | OWR-11792-002 | Exceptional Dynamics of Polarized Surface Endomorphisms | For regular polarized self-maps of smooth projective surfaces over a number field, can the exceptional cases with no periodic point having multiplicatively independent derivative eigenvalues be classified, and can the resulting invariant algebraic curves be naturally parameterized by elements of $\overline{\mathbb Q}$ ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "algebraic_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 | [
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] | The extracted question does not identify Zhang's conjecture or the precise class of invariant curves well enough to test a theorem; the record therefore remains unresolved under the required normalization. | [
{
"url": "https://doi.org/10.4171/owr/2012/30",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | For regular polarized self-maps of smooth projective surfaces over a number field, can the exceptional cases with no periodic point having multiplicatively independent derivative eigenvalues be classified, and can the resulting invariant algebraic curves be naturally parameterized by elements of $\overline{\mathbb Q}$ ... | For regular polarized self-maps of smooth projective surfaces over a number field, can the exceptional cases with no periodic point having multiplicatively independent derivative eigenvalues be classified, and can the resulting invariant algebraic curves be naturally parameterized by elements of \overline{\mathbb Q} ra... | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,100 | OWR-11792-003 | The Minimal Model Program for Stable-Curve Moduli | Can the minimal model program be run on $\overline{\mathcal M}_g$, the moduli space of Deligne–Mumford stable curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"slug": "algebraic-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",
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] | The Hassett--Keel program has constructed and interpreted initial log canonical models and flips, but running the full minimal model program on the moduli space of stable curves remains incomplete in general. | [
{
"url": "https://annals.math.princeton.edu/2013/177-3/p03",
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{
"url": "https://arxiv.org/abs/1006.1094",
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"url": "https://doi.org/10.4171/owr/2012/30",
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | Can the minimal model program be run on $\overline{\mathcal M}_g$, the moduli space of Deligne–Mumford stable curves? | Can the minimal model program be run on \overline{\mathcal M}_g, the moduli space of Deligne--Mumford stable curves? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,101 | OWR-11792-004 | Modular Interpretations of Log Canonical Curve-Moduli Models | Does the log canonical model $\overline{\mathcal M}_g(\alpha)$ inherit a moduli interpretation as a moduli space of singular curves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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-11792-004",
"literature-status:partially-solved",
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] | Several early log canonical models have modular descriptions through pseudostable and related singular curves, and genus four has recently been completed, but a uniform modular description for all alpha and genus is not known. | [
{
"url": "https://arxiv.org/abs/0806.3444",
"label": "Hassett and Hyeon, first flip"
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{
"url": "https://arxiv.org/abs/2504.20312",
"label": "Hassett--Keel program in genus four"
},
{
"url": "https://doi.org/10.4171/owr/2012/30",
"label": "original OWR report"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | Does the log canonical model $\overline{\mathcal M}_g(\alpha)$ inherit a moduli interpretation as a moduli space of singular curves? | Does the log canonical model \overline{\mathcal M}_g(\alpha) inherit a moduli interpretation as a moduli space of singular curves? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,102 | OWR-11792-005 | Functorial Chow Rings for Singular Varieties | For a projective variety $X$ over an algebraically closed field, can one define a Chow ring $CH^*(X)$ with the expected contravariant functoriality and cycle-class and Chern-class properties, including a rational Chern-character isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
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"slug": "algebraic-geometry",
"order_index": 5,
"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-11792-005",
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] | The record is an incomplete prompt about Chern classes and cycles supported in a given codimension; the surrounding text exhibits failures of the naive formula but does not state a replacement theorem that settles the extracted problem. | [
{
"url": "https://doi.org/10.4171/owr/2012/30",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | For a projective variety $X$ over an algebraically closed field, can one define a Chow ring $CH^*(X)$ with the expected contravariant functoriality and cycle-class and Chern-class properties, including a rational Chern-character isomorphism? | For a projective variety X over an algebraically closed field, can one define a Chow ring CH^*(X) with the expected contravariant functoriality, cycle-class and Chern-class properties, including a rational Chern-character isomorphism? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,103 | OWR-11792-006 | Leray–Hodge Filtrations and Chern Classes on Singular Varieties | For a singular complex projective variety $X$, is the Leray filtration on $H^n(X,\mathbb Z)$ a filtration by sub-mixed-Hodge structures, and does the image of the $p$th Chern class map
$$K_0(X)\otimes\mathbb Q\to H^{2p}(X,\mathbb Q)$$
equal
$$\operatorname{Hom}_{\mathrm{MHS}}(\mathbb Z(-p),L^pH^{2p}(X,\mathbb Z))\ot... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,012 | 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-11792-006",
"literature-status:open",
"owr-year:2012"
] | The singular cohomological Hodge conjecture has partial results and active modern work, but the stated Chern-class characterization is not proved in general, including the broad singular threefold setting described in the record. | [
{
"url": "https://arxiv.org/abs/2509.25273",
"label": "Hodge conjecture via singular varieties"
},
{
"url": "https://doi.org/10.4171/owr/2012/30",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | For a singular complex projective variety $X$, is the Leray filtration on $H^n(X,\mathbb Z)$ a filtration by sub-mixed-Hodge structures, and does the image of the $p$th Chern class map
$$K_0(X)\otimes\mathbb Q\to H^{2p}(X,\mathbb Q)$$
equal
$$\operatorname{Hom}_{\mathrm{MHS}}(\mathbb Z(-p),L^pH^{2p}(X,\mathbb Z))\ot... | For a singular complex projective variety X, is the Leray filtration on H^n(X,\mathbb Z) a filtration by sub-mixed-Hodge structures, and does the image of the p-th Chern class map K_0(X)\otimes\mathbb Q\to H^{2p}(X,\mathbb Q) equal \operatorname{Hom}_{MHS}(\mathbb Z(-p),L^pH^{2p}(X,\mathbb Z))\otimes\mathbb Q? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,104 | OWR-11792-007 | The Zariski Multiplicity Problem | Do hypersurfaces with topologically equivalent isolated singularities necessarily have the same multiplicities at their singular points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893](https://doi.org/10.4171/owr/2012/30)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,012 | 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-11792-007",
"literature-status:partially-solved",
"owr-year:2012"
] | This is the Zariski multiplicity problem: positive results cover quasihomogeneous, Newton-nondegenerate, and other special classes, but equality of multiplicity for arbitrary topologically equivalent hypersurface singularities remains open. | [
{
"url": "https://doi.org/10.1016/j.crma.2007.04.005",
"label": "Lefschetz, multiplicity and Zariski's problem"
},
{
"url": "https://arxiv.org/abs/math/0609093",
"label": "Nohara and Ueda, Newton non-degenerate singularities"
},
{
"url": "https://doi.org/10.4171/owr/2012/30",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/30 | null | null | null | Do hypersurfaces with topologically equivalent isolated singularities necessarily have the same multiplicities at their singular points? | Do hypersurfaces with topologically equivalent isolated singularities necessarily have the same multiplicities at their singular points? | exact | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Classical Algebraic Geometry (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/30, pp. 1845--1893 |
30,002,105 | OWR-11793-003 | Density and Geometry Recovery from Nearest-Neighbor Graphs | Let $X_1,\ldots,X_n$ be i.i.d. samples from a density $p$ on $\mathbb R^d$, and let $A$ be the adjacency matrix of their unweighted $k$-nearest-neighbor graph. Can $p(X_i)$ be estimated up to constant factors from $A$ alone, and can the sample locations be approximately reconstructed up to translation, rotation, and re... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Learning Theory and Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/31, pp. 1895--1948](https://doi.org/10.4171/owr/2012/31)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,012 | 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-11793-003",
"literature-status:partially-solved",
"owr-year:2012"
] | The density can be estimated from an unweighted directed k-nearest-neighbor graph under the paper's sampling assumptions, and point localization has synchronization-based results, but general reconstruction up to the stated similarities is not fully solved. | [
{
"url": "https://proceedings.neurips.cc/paper/2013/hash/eae27d77ca20db309e056e3d2dcd7d69-Abstract.html",
"label": "von Luxburg et al., density estimation from unweighted kNN graphs"
},
{
"url": "https://arxiv.org/abs/1504.00722",
"label": "point localization and density estimation from ordinal ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/31 | null | null | null | Let $X_1,\ldots,X_n$ be i.i.d. samples from a density $p$ on $\mathbb R^d$, and let $A$ be the adjacency matrix of their unweighted $k$-nearest-neighbor graph. Can $p(X_i)$ be estimated up to constant factors from $A$ alone, and can the sample locations be approximately reconstructed up to translation, rotation, and re... | Given only the adjacency matrix of an unweighted random k-nearest-neighbor graph built from i.i.d. samples of a density p on \mathbb R^d, can one estimate p(X_i) up to constant factors and approximately reconstruct the sample locations up to translation, rotation, and rescaling? | corrected_verified | The official report lists precisely these two open problems and says that no final answers were known. | null | null | null | null | null | Learning Theory and Approximation (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/31, pp. 1895--1948 |
30,002,106 | OWR-12004-001 | Perverse Intermediate Extensions at Parahoric Level | If $\pi_v$ is an irreducible cuspidal representation of $GL_g(F_v)$ whose mod-$\ell$ reduction is supercuspidal, does the conjectured isomorphism
$${}^pj_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg]\simeq{}^{p+}j_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg]$$
hold for every $1\leq t\leq\lflo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011](https://doi.org/10.4171/owr/2012/32)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-12004-001",
"literature-status:partially-solved",
"owr-year:2012"
] | The relevant nearby-cycles and local-model conjectural framework has been proved in important cases, including character-type representations and several parahoric settings, but the extracted record does not support a general proof for arbitrary local representation. | [
{
"url": "https://arxiv.org/abs/1110.5588",
"label": "Pappas and Zhu, local models and Kottwitz's conjecture"
},
{
"url": "https://arxiv.org/abs/math/0103047",
"label": "Gaitsgory and Haines, nearby cycles"
},
{
"url": "https://doi.org/10.4171/owr/2012/32",
"label": "original OWR rep... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/32 | null | null | null | If $\pi_v$ is an irreducible cuspidal representation of $GL_g(F_v)$ whose mod-$\ell$ reduction is supercuspidal, does the conjectured isomorphism
$${}^pj_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg]\simeq{}^{p+}j_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg]$$
hold for every $1\leq t\leq\lflo... | If \pi_v is an irreducible cuspidal representation of GL_g(F_v) whose mod-\ell reduction is supercuspidal, does the conjectured isomorphism {}^pj_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg]\simeq{}^{p+}j_{!*}\mathcal F_{\overline{\mathbb F}_\ell}(\pi_v,t)[d-tg] hold for every 1\le t\le\lfloor d/g\rfloor? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011 |
30,002,107 | OWR-12004-002 | Tannakian Lattice Chains for Bruhat–Tits Buildings | For a connected reductive group $G$ over a complete discretely valued field and a representation $V$, what lattice chains in $V\otimes K$ should be used to construct a Tannakian description of the Bruhat–Tits building and parahoric group schemes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011](https://doi.org/10.4171/owr/2012/32)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,012 | 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-12004-002",
"literature-status:open",
"owr-year:2012"
] | The extracted sentence is only a request to choose the lattice chains and does not specify a mathematical assertion; the underlying general parahoric construction is therefore unresolved or unclear from this record. | [
{
"url": "https://doi.org/10.4171/owr/2012/32",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/32 | null | null | null | For a connected reductive group $G$ over a complete discretely valued field and a representation $V$, what lattice chains in $V\otimes K$ should be used to construct a Tannakian description of the Bruhat–Tits building and parahoric group schemes? | For a connected reductive group G over a complete discretely valued field and a representation V, what lattice chains in V\otimes K should be used to construct a Tannakian description of the Bruhat--Tits building and parahoric group schemes? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011 |
30,002,108 | OWR-12004-003 | Local-Model Diagrams for Parahoric Shimura Varieties | Does every Shimura variety with parahoric level admit a local-model diagram
$$S_K\longleftarrow\widetilde S_K\longrightarrow M^{\mathrm{loc}}$$
in which the left map is a $K$-torsor and the right map is $K$-equivariant and smooth? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011](https://doi.org/10.4171/owr/2012/32)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,012 | 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-12004-003",
"literature-status:partially-solved",
"owr-year:2012"
] | Integral models and local-model diagrams are now constructed for broad Hodge- and abelian-type classes with parahoric level, and Kottwitz nearby-cycles statements hold under additional hypotheses, but the fully general conjectural diagram remains conditional in the literature. | [
{
"url": "https://pmihes.centre-mersenne.org/articles/10.1007/s10240-018-0100-0/",
"label": "Kisin and Pappas, integral models with parahoric level"
},
{
"url": "https://arxiv.org/abs/2010.10496",
"label": "Hamacher and Kim, mod p points at parahoric level"
},
{
"url": "https://doi.org/1... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/32 | null | null | null | Does every Shimura variety with parahoric level admit a local-model diagram
$$S_K\longleftarrow\widetilde S_K\longrightarrow M^{\mathrm{loc}}$$
in which the left map is a $K$-torsor and the right map is $K$-equivariant and smooth? | Does every Shimura variety with parahoric level admit a local-model diagram S_K\leftarrow\widetilde S_K\rightarrow M^{\mathrm{loc}} in which the left map is a K-torsor and the right map is K-equivariant and smooth? | corrected_verified | The mathematical content was checked against the cited official Oberwolfach report; notation, context, and question form were normalized without changing the source-level claim. | null | null | null | null | null | Reductions of Shimura Varieties (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/32, pp. 1961--2011 |
30,002,109 | OWR-12005-001 | Singular Coalescence Limits in Plasmonic Problems | As two domains in a plasmonic boundary-value problem coalesce with separation parameter $a\to0$, do solutions exist at $a=0$, how should the equations be modified there, and do qualitatively different branches such as localized or hybridized solutions occur? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,012 | 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-12005-001",
"literature-status:partially-solved",
"owr-year:2012"
] | Plasmonic eigenvalue asymptotics and blow-up methods resolve important smooth and nearly singular geometries, but the general singular limiting equations and all qualitatively different branches requested in the record remain unsettled. | [
{
"url": "https://arxiv.org/abs/1208.3120",
"label": "Helsing and Perfekt, the plasmonic eigenvalue problem"
},
{
"url": "https://academic.oup.com/imamat/article-abstract/84/4/813/5536913",
"label": "geometric quantization of localized surface plasmons"
},
{
"url": "https://doi.org/10.41... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | As two domains in a plasmonic boundary-value problem coalesce with separation parameter $a\to0$, do solutions exist at $a=0$, how should the equations be modified there, and do qualitatively different branches such as localized or hybridized solutions occur? | As two domains in the plasmonic boundary-value problem coalesce in the singular limit a\to0, do solutions exist at a=0, how should the equations be modified there, and are there qualitatively different branches such as localized or hybridized solutions? | corrected_verified | The official report asks these existence, formulation, and branch questions in the singular coalescence limit. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,110 | OWR-12005-002 | Hexagonal Asymptotics for Spectral Minimal Partitions | For a bounded planar domain $\Omega$, does the minimal $k$-partition energy satisfy the hexagonal asymptotic $\lim_{k\to\infty}L_k(\Omega)/k=\lambda(\mathrm{Hexa}_1)A(\Omega)^{-1}$, where $\mathrm{Hexa}_1$ is the regular unit-area hexagon? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12005-002",
"literature-status:open",
"owr-year:2012"
] | The hexagonal conjecture for planar spectral minimal partitions remains a stated open problem; lower bounds, numerical evidence, and proofs for restricted convex or related partition classes do not establish the full spectral asymptotic claimed here. | [
{
"url": "https://arxiv.org/abs/1509.04501",
"label": "Bonnaillie-Noel and Helffer, large k spectral partitions"
},
{
"url": "https://doi.org/10.1007/s00020-021-02635-7",
"label": "spectral minimal partitions and open problems"
},
{
"url": "https://doi.org/10.4171/owr/2012/33",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For a bounded planar domain $\Omega$, does the minimal $k$-partition energy satisfy the hexagonal asymptotic $\lim_{k\to\infty}L_k(\Omega)/k=\lambda(\mathrm{Hexa}_1)A(\Omega)^{-1}$, where $\mathrm{Hexa}_1$ is the regular unit-area hexagon? | For a bounded planar domain \Omega, does the minimal k-partition energy satisfy the hexagonal asymptotic \lim_{k\to\infty}L_k(\Omega)/k=\lambda(\mathrm{Hexa}_1)A(\Omega)^{-1}, where \mathrm{Hexa}_1 is the regular unit-area hexagon? | corrected_verified | The official report was checked and confirms the complete problem statement. TeX notation was enclosed in math delimiters without changing the mathematical content. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,111 | OWR-12005-003 | Spectral Determination of Toric Moment Polytopes | For a compact symplectic toric manifold $(M,g)$ with toric metric, does the Laplace spectrum determine its moment (Delzant) polytope and hence its symplectomorphism type? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | partially_solved | null | 2,012 | 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-12005-003",
"literature-status:partially-solved",
"owr-year:2012"
] | The ordinary-spectrum question remains open, while equivariant and generic toric variants and line-bundle cases have been proved by Dryden, Guillemin, and Sena-Dias. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
},
{
"url": "https://www.ams.org/journals/tran/2012-364-02/S0002-9947-2011-05412-7/",
"label": "Dryden Guillemin Sena-Dias"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For a compact symplectic toric manifold $(M,g)$ with toric metric, does the Laplace spectrum determine its moment (Delzant) polytope and hence its symplectomorphism type? | For a compact symplectic toric manifold (M,g) with toric metric, does the Laplace spectrum determine its moment (Delzant) polytope and hence its symplectomorphism type? | corrected_verified | The official report was checked and confirms the complete problem statement. The manifold and metric pair was placed in a math delimiter without changing the question. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,112 | OWR-12005-004 | Additive Eigenvalue Bounds for Domain Boundaries | For every dimension $m$, can the eigenvalue estimate for a smooth bounded domain $\Omega\subset\mathbb{R}^{m+1}$ with boundary $\Sigma$ be improved to $\lambda_k(\Sigma)\operatorname{Vol}(\Sigma)^{2/m}\leq A_m I(\Omega)^{1+2/m}+B_m k^{2/m}$, with constants $A_m,B_m$ depending only on $m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12005-004",
"literature-status:open",
"owr-year:2012"
] | The proposed additive eigenvalue estimate was posed as open in the report; the cited primary work proves a different multiplicative isoperimetric bound, and no resolution of this additive form was found. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1515/crelle-2012-0008",
"label": "Colbois El Soufi Girouard"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For every dimension $m$, can the eigenvalue estimate for a smooth bounded domain $\Omega\subset\mathbb{R}^{m+1}$ with boundary $\Sigma$ be improved to $\lambda_k(\Sigma)\operatorname{Vol}(\Sigma)^{2/m}\leq A_m I(\Omega)^{1+2/m}+B_m k^{2/m}$, with constants $A_m,B_m$ depending only on $m$? | For every dimension m, can one improve the eigenvalue estimate for a smooth bounded domain \Omega\subset\mathbb R^{m+1} with boundary \Sigma to \lambda_k(\Sigma)\operatorname{Vol}(\Sigma)^{2/m}\le A_m I(\Omega)^{1+2/m}+B_m k^{2/m} with constants A_m,B_m depending only on m? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete statement was preserved while previously undelimited mathematical notation was normalized into readable prose. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,113 | OWR-12005-005 | Maximal Normalized Steklov Eigenvalues | For a fixed $k$, how large can the $k$th Steklov eigenvalue $\sigma_k$ be when boundary measure is normalized; equivalently, what is the maximum of $\sigma_k(g)|\Sigma|_g^{1/n}$ over smooth Riemannian metrics? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12005-005",
"literature-status:open",
"owr-year:2012"
] | The extracted record is only the heading asking how large the Steklov eigenvalues can be, so it does not identify one precise claim; the report gives bounds and extremal examples but no complete general answer. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For a fixed $k$, how large can the $k$th Steklov eigenvalue $\sigma_k$ be when boundary measure is normalized; equivalently, what is the maximum of $\sigma_k(g)|\Sigma|_g^{1/n}$ over smooth Riemannian metrics? | For a fixed k, how large can the k-th Steklov eigenvalue \sigma_k be when the boundary measure is normalized, equivalently when maximizing \sigma_k(g)|\Sigma|_g^{1/n} over smooth Riemannian metrics? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete optimization question was preserved while the index and normalization notation were repaired. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,114 | OWR-12005-007 | Sharp Shape-Dependent Bounds for Dirichlet Eigenvalues | How does the shape of a bounded planar starlike domain affect the eigenvalues of its Dirichlet Laplacian, and what geometrically sharp shape-dependent upper bounds hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12005-007",
"literature-status:open",
"owr-year:2012"
] | The extracted record is a broad fragment about how domain shape affects eigenvalues and does not state a unique theorem or conjecture; the report describes this as a long standing difficult problem. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | How does the shape of a bounded planar starlike domain affect the eigenvalues of its Dirichlet Laplacian, and what geometrically sharp shape-dependent upper bounds hold? | How does the shape of a bounded planar starlike domain affect the eigenvalues of its Dirichlet Laplacian, and what geometrically sharp shape-dependent upper bounds hold? | exact | The official report was checked and confirms the complete problem statement. The statement is internally readable; retained byte-for-byte. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
30,002,115 | OWR-12005-008 | Harmonic Test Inequalities Above the First Eigenvalue | For every bounded sufficiently smooth domain $\Omega\subset\mathbb{R}^m$ and every $\lambda>\lambda_1(\Omega)$, does there exist a harmonic function $h$ such that $\sum_{j=1}^{\infty}\frac{\lambda_j}{\lambda_j-\lambda}|\langle h,u_j\rangle|^2<0$, where the $u_j$ are Dirichlet eigenfunctions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076](https://doi.org/10.4171/owr/2012/33)
## Literature review (checked 2026-08-21)
*... | 3 | open | null | 2,012 | 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-12005-008",
"literature-status:open",
"owr-year:2012"
] | The harmonic and lambda harmonic inequalities are stated as conjectures, with only a one dimensional failure noted; no proof in the stated higher dimensional setting was found. | [
{
"url": "https://ems.press/content/serial-article-files/46403",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2012/33 | null | null | null | For every bounded sufficiently smooth domain $\Omega\subset\mathbb{R}^m$ and every $\lambda>\lambda_1(\Omega)$, does there exist a harmonic function $h$ such that $\sum_{j=1}^{\infty}\frac{\lambda_j}{\lambda_j-\lambda}|\langle h,u_j\rangle|^2<0$, where the $u_j$ are Dirichlet eigenfunctions? | For every bounded sufficiently smooth domain \Omega\subset\mathbb R^m and every \lambda>\lambda_1(\Omega), does there exist a harmonic function h such that \sum_{j=1}^{\infty}\frac{\lambda_j}{\lambda_j-\lambda}|\langle h,u_j\rangle|^2<0, where u_j are Dirichlet eigenfunctions? | corrected_verified | The official report was checked and confirms the complete problem statement. The complete statement was preserved while previously undelimited mathematical notation was normalized into readable prose. | null | null | null | null | null | Geometric Aspects of Spectral Theory (2013), Oberwolfach Reports, DOI 10.4171/owr/2012/33, pp. 2013--2076 |
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