id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,416 | OWR-15216-022 | Embedding Interval Groups Without Thompson F into the G-Hierarchy | Does every finitely generated subgroup $G\leq\mathrm{PL}_+(I)$ that contains no copy of Thompson's group $F$ embed into $G_\xi$ for some $\xi<\varepsilon_0$? In particular, does every finitely generated elementary amenable subgroup of $F$ embed into some $G_\xi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589](https://doi.org/10.4171/owr/2017/11)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15216-022",
"literature-status:open",
"owr-year:2017"
] | The cited subgroup-classification paper states these bi-embeddability and embedding assertions as conjectures; its explicit families and structural theorems do not resolve the general claims. | [
{
"url": "https://research-repository.st-andrews.ac.uk/bitstream/10023/18600/1/fastgen_JCA_final.pdf",
"label": "Groups of fast homeomorphisms"
},
{
"url": "https://arxiv.org/abs/1711.10998",
"label": "Complexity among finitely generated subgroups of F"
},
{
"url": "https://ems.press/con... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/11 | null | null | null | Does every finitely generated subgroup $G\leq\mathrm{PL}_+(I)$ that contains no copy of Thompson's group $F$ embed into $G_\xi$ for some $\xi<\varepsilon_0$? In particular, does every finitely generated elementary amenable subgroup of $F$ embed into some $G_\xi$? | Conjecture: Every finitely generated subgroup G of \mathrm{PL}_{+}(I) that contains no copy of Thompson\textquotesingle s group F embeds into G_{\xi} for some \xi<\varepsilon_0; in particular, every finitely generated elementarily amenable subgroup of F embeds into some G_{\xi}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589 |
30,003,417 | OWR-15216-023 | Meager Ideal Equalities at Uncountable Regular Cardinals | For every uncountable regular cardinal $\kappa$ satisfying $2^{<\kappa}=\kappa$, are $$\operatorname{add}(\mathcal M_\kappa)=\mathfrak b_\kappa\qquad\text{and}\qquad\mathfrak d_\kappa=\operatorname{cof}(\mathcal M_\kappa)$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589](https://doi.org/10.4171/owr/2017/11)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15216-023",
"literature-status:open",
"owr-year:2017"
] | Brendle proved exact min and max formulas involving the meager ideal, not the two equalities conjectured here; equality is known in special compactness models but not for every regular uncountable cardinal under the stated arithmetic. | [
{
"url": "https://arxiv.org/abs/1907.03111",
"label": "Higher Cichoń diagram in the degenerate case"
},
{
"url": "https://doi.org/10.1007/s00153-025-00977-2",
"label": "Generalized cardinal invariants with compactness"
},
{
"url": "https://ems.press/content/serial-article-files/46674",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/11 | null | null | null | For every uncountable regular cardinal $\kappa$ satisfying $2^{<\kappa}=\kappa$, are $$\operatorname{add}(\mathcal M_\kappa)=\mathfrak b_\kappa\qquad\text{and}\qquad\mathfrak d_\kappa=\operatorname{cof}(\mathcal M_\kappa)$$? | For every uncountable regular cardinal \kappa with 2^{<\kappa}=\kappa, is it true that \operatorname{add}(\mathcal{M}_{\kappa})=\mathfrak b_{\kappa} and \mathfrak d_{\kappa}=\operatorname{cof}(\mathcal{M}_{\kappa})? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589 |
30,003,418 | OWR-15216-026 | Consistency Strength of Almost Effective Equivalence Reductions | What is the consistency strength of $E_{\omega_1}\leq_{a\Delta^1_1}F_{\omega_1}$? Does such an almost-$\Delta^1_1$ reduction imply the existence of a real whose admissibility spectrum is sufficiently sparse that its admissible ordinals are $L$-cardinals and $0^\#$ can be recovered? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589](https://doi.org/10.4171/owr/2017/11)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15216-026",
"literature-status:open",
"owr-year:2017"
] | Known results give non-reducibility in L and positive almost reductions from a measurable cardinal, but the exact consistency strength asked for this reduction is not determined. | [
{
"url": "https://arxiv.org/abs/1601.07924",
"label": "Countable admissible ordinal equivalence relation"
},
{
"url": "https://williamchan-math.github.io/papers/countable_admissible_ordinal_equivalence_relation.pdf",
"label": "Author version of the admissibility paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/11 | null | null | null | What is the consistency strength of $E_{\omega_1}\leq_{a\Delta^1_1}F_{\omega_1}$? Does such an almost-$\Delta^1_1$ reduction imply the existence of a real whose admissibility spectrum is sufficiently sparse that its admissible ordinals are $L$-cardinals and $0^\#$ can be recovered? | What is the consistency strength of E_{\omega_1}\leq_{a\Delta^1_1}F_{\omega_1}, and does such an almost \Delta^1_1 reduction imply the existence of a real whose admissibility spectrum is sufficiently spread out to make its admissible ordinals L-cardinals and recover 0^\#? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589 |
30,003,419 | OWR-15216-027 | Reducing Cardinal Invariants from Boolean Ultrapower Constructions | Can the Boolean-ultrapower consistency patterns for cardinal invariants be obtained without assuming a supercompact cardinal, or with the affected invariants assigned smaller values below the first ground-model supercompact above $\kappa$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589](https://doi.org/10.4171/owr/2017/11)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessmen... | 3 | open | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15216-027",
"literature-status:open",
"owr-year:2017"
] | The extracted passage is a broad collection of unresolved Boolean-ultrapower questions; later work supplies related consistency constructions but no general determination of the requested smaller invariant values. | [
{
"url": "https://ems.press/content/serial-article-files/46674",
"label": "OWR Set Theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/11 | null | null | null | Can the Boolean-ultrapower consistency patterns for cardinal invariants be obtained without assuming a supercompact cardinal, or with the affected invariants assigned smaller values below the first ground-model supercompact above $\kappa$? | Can the cardinal invariants occurring in the report\textquotesingle s Theorems 1--4 be consistently arranged to have smaller, more accessible values than the values produced by the Boolean-ultrapower constructions? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589 |
30,003,420 | OWR-15216-028 | Consistency Patterns Among Cardinal Characteristics | Are the consistency patterns $\mathfrak b<\mathfrak s<\mathfrak d$ and $\mathfrak b<\mathfrak a<\mathfrak s$ possible? Is $\mathfrak u(\omega_1)<2^{\aleph_1}$ consistent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589](https://doi.org/10.4171/owr/2017/11)
## Literature review (checked 2026-08-21)
**Status:** partially solved
... | 3 | partially_solved | null | 2,017 | 10 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15216-028",
"literature-status:partially-solved",
"owr-year:2017"
] | Forcing has produced several related separations among cardinal characteristics, including small ultrafilter numbers at higher cardinals, but the full list of three consistency questions in the extracted record is not settled as one theorem. | [
{
"url": "https://arxiv.org/abs/1812.05291",
"label": "Cardinal characteristics at aleph omega"
},
{
"url": "https://ems.press/content/serial-article-files/46674",
"label": "OWR Set Theory report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/11 | null | null | null | Are the consistency patterns $\mathfrak b<\mathfrak s<\mathfrak d$ and $\mathfrak b<\mathfrak a<\mathfrak s$ possible? Is $\mathfrak u(\omega_1)<2^{\aleph_1}$ consistent? | Are the consistency patterns \mathfrak b<\mathfrak s<\mathfrak d and \mathfrak b<\mathfrak a<\mathfrak s possible, and is \mathfrak u(\omega_1)<2^{\aleph_1} consistent? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Set Theory (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/11, pp. 527--589 |
30,003,421 | OWR-15217-001 | Support Ideals in Constructible-Function Convolution Algebras | For the convolution algebra of constructible functions associated with quiver data $\Pi$, is the direct sum of the homogeneous subspaces consisting of functions $f$ such that
$$
\dim\operatorname{supp}(f)<\dim G(d)-q_D^C(d/D)
$$
an ideal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681](https://doi.org/10.4171/owr/2017/12)
## Literature revi... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15217-001",
"literature-status:open",
"owr-year:2017"
] | The support conjecture remains the needed unproved premise for the stated Hall-algebra realization; later convolution and canonical-basis results give related support theorems but not this exact ideal assertion. | [
{
"url": "https://ems.press/content/serial-article-files/46676",
"label": "OWR Representation Theory report"
},
{
"url": "https://arxiv.org/abs/1311.5396",
"label": "Quivers with loops and Lagrangian subvarieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/12 | null | null | null | For the convolution algebra of constructible functions associated with quiver data $\Pi$, is the direct sum of the homogeneous subspaces consisting of functions $f$ such that
$$
\dim\operatorname{supp}(f)<\dim G(d)-q_D^C(d/D)
$$
an ideal? | Support Conjecture: For the convolution algebra of constructible functions associated with the quiver data \Pi, the direct sum of the homogeneous subspaces consisting of functions f with \dim\operatorname{supp}(f)<\dim G(d)-q_D^C(d/D) is an ideal. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681 |
30,003,422 | OWR-15217-003 | DG Models for Higher Cluster Categories | Is there a natural differential graded category $B_m^{(d)}$ with one object, endomorphism algebra $B_m$, and perfect derived category equal to the higher cluster category $C_{\infty,m}^{(d)}$, preferably with a topological interpretation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681](https://doi.org/10.4171/owr/2017/12)
## Literature revi... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15217-003",
"literature-status:open",
"owr-year:2017"
] | The report presents the dg-category and topological-realization request as a question; higher Nakayama and topological Fukaya developments do not establish the exact requested construction for all parameters. | [
{
"url": "https://ems.press/content/serial-article-files/46676",
"label": "OWR Representation Theory report"
},
{
"url": "https://arxiv.org/abs/1604.03500",
"label": "Higher Nakayama algebras"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/12 | null | null | null | Is there a natural differential graded category $B_m^{(d)}$ with one object, endomorphism algebra $B_m$, and perfect derived category equal to the higher cluster category $C_{\infty,m}^{(d)}$, preferably with a topological interpretation? | Is there a nice differential graded category \mathcal B^{(d)}_m with one-object endomorphism algebra \mathcal B_m and whose perfect derived category is the higher cluster category \mathcal C^{(d)}_{\infty,m}, ideally with a topological interpretation? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681 |
30,003,423 | OWR-15217-004 | Smooth Moduli Spaces of Tame Algebras | Let $A$ be a tame finite-dimensional algebra, let $C\subseteq\operatorname{rep}(A,d)$ be a closed irreducible invariant subvariety with $\theta$-stable decomposition $C=m_1C_1\dotplus\cdots\dotplus m_rC_r$, and suppose no $C_i$ is an orbit closure. Is the natural finite birational surjection
$$
\Psi:\prod_{i=1}^r S^{m_... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681](https://doi.org/10.4171/owr/2017/12)
## Literature revi... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15217-004",
"literature-status:partially-solved",
"owr-year:2017"
] | The decomposition theorem gives the morphism and proves it is an isomorphism under normality; tame and special-biserial cases have strong positive results, but the all-tame and universal smoothness questions remain open. | [
{
"url": "https://arxiv.org/abs/1705.10255",
"label": "Decomposing moduli of representations"
},
{
"url": "https://arxiv.org/abs/1109.2915",
"label": "Invariant theory for tame tilted algebras"
},
{
"url": "https://ems.press/content/serial-article-files/46676",
"label": "OWR Represen... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/12 | null | null | null | Let $A$ be a tame finite-dimensional algebra, let $C\subseteq\operatorname{rep}(A,d)$ be a closed irreducible invariant subvariety with $\theta$-stable decomposition $C=m_1C_1\dotplus\cdots\dotplus m_rC_r$, and suppose no $C_i$ is an orbit closure. Is the natural finite birational surjection
$$
\Psi:\prod_{i=1}^r S^{m_... | For every tame algebra, is the morphism \Psi in the moduli-space construction an isomorphism, and are moduli spaces of tame algebras always smooth? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681 |
30,003,424 | OWR-15217-008 | Positivity of Kac-Type Polynomials for Concealed-Canonical Algebras | If $C$ is an almost concealed-canonical algebra, are all coefficients of the polynomial $P_{C,d}(T)$ nonnegative for every dimension vector $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681](https://doi.org/10.4171/owr/2017/12)
## Literature revi... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15217-008",
"literature-status:open",
"owr-year:2017"
] | The cited work establishes polynomiality and integrality for the relevant Kac-type polynomials, but the non-negativity of all coefficients for almost concealed-canonical algebras remains stated as a conjecture in the later primary literature. | [
{
"url": "https://arxiv.org/abs/1602.01207",
"label": "Plamondon--Schiffmann, Kac polynomials for canonical algebras"
},
{
"url": "https://ems.press/content/serial-article-files/46676?nt=1",
"label": "Oberwolfach primary report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/12 | null | null | null | If $C$ is an almost concealed-canonical algebra, are all coefficients of the polynomial $P_{C,d}(T)$ nonnegative for every dimension vector $d$? | If C is an almost concealed-canonical algebra, are all coefficients of the polynomial P_{C,d}(T) non-negative for every dimension vector d? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Representation Theory of Quivers and Finite Dimensional Algebras (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/12, pp. 591--681 |
30,003,425 | OWR-15218-001 | Volatility Smile Extrapolation and Latent Stochasticity | Can the volatility smile be extrapolated from observable strikes robustly enough to infer accurately the stochasticity of volatility from market data? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-001",
"literature-status:open",
"owr-year:2017"
] | Rough and path-dependent models improve smile fitting and extrapolation diagnostics, but no model-independent result shows that visible strikes robustly identify the latent stochasticity or determine accurate extrapolation. | [
{
"url": "https://arxiv.org/abs/1702.02777",
"label": "Gatheral--Jaisson--Rosenbaum, rough volatility evidence"
},
{
"url": "https://arxiv.org/abs/2401.03345",
"label": "Guyon--Lekeufack, volatility models in practice"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | Can the volatility smile be extrapolated from observable strikes robustly enough to infer accurately the stochasticity of volatility from market data? | Can the volatility smile be extrapolated from visible strikes robustly enough to determine accurately the stochasticity of volatility from market data? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,426 | OWR-15218-002 | Dependent Volatility Drivers in Tractable Pricing Models | How far can the assumption that the volatility process $\sigma$ is independent of the Brownian motion $W$ driving the stock price be relaxed while preserving tractable option-pricing models and allowing asymmetric implied-volatility smiles? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-002",
"literature-status:partially-solved",
"owr-year:2017"
] | The independence assumption has been relaxed in correlated, leverage, jump, and rough-volatility models, with Malliavin-calculus formulas for implied-volatility effects; a complete general theory for arbitrary dependence remains unavailable. | [
{
"url": "https://doi.org/10.1137/16M1086315",
"label": "Alos--Leon, curvature of the smile in stochastic volatility models"
},
{
"url": "https://doi.org/10.1016/j.physa.2008.10.012",
"label": "Alos--León--Vives, leverage effect in stochastic volatility"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | How far can the assumption that the volatility process $\sigma$ is independent of the Brownian motion $W$ driving the stock price be relaxed while preserving tractable option-pricing models and allowing asymmetric implied-volatility smiles? | How can the assumption that the volatility process \sigma is independent of the Brownian motion W driving the stock price be relaxed while retaining tractable option-pricing models and allowing asymmetric implied-volatility smiles? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,427 | OWR-15218-003 | Multiple-Maturity Consistency Under Bid–Ask Spreads | Given option prices at more than one maturity and a bound $\varepsilon$ on the discounted bid–ask spread of the underlying asset, characterize $\varepsilon$-consistency and determine the smallest admissible $\varepsilon$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-003",
"literature-status:partially-solved",
"owr-year:2017"
] | The one-maturity epsilon-consistency problem has necessary and sufficient conditions, while the multiple-maturity case has necessary conditions and equivalent semiexplicit criteria but no comparably explicit necessary-and-sufficient characterization. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC7155110/",
"label": "Gerhold--Gulum, consistency under bid-ask spreads"
},
{
"url": "https://doi.org/10.4171/owr/2017/13",
"label": "Oberwolfach quantitative-finance report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | Given option prices at more than one maturity and a bound $\varepsilon$ on the discounted bid–ask spread of the underlying asset, characterize $\varepsilon$-consistency and determine the smallest admissible $\varepsilon$. | Given option prices with more than one maturity and a bound \epsilon on the discounted bid--ask spread of the underlying, what are necessary and sufficient conditions for \epsilon-consistency, and what is the smallest such \epsilon? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,428 | OWR-15218-004 | Market Origins of Rough Volatility | What mathematical or market-microstructural mechanisms explain the apparently universal roughness of financial volatility, commonly modeled by fractional Brownian motion with a small Hurst parameter $H$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-004",
"literature-status:open",
"owr-year:2017"
] | Microstructural and statistical models now generate rough volatility and reproduce several stylized facts, but the claimed universal origin of roughness across markets is not established. | [
{
"url": "https://arxiv.org/abs/1609.05177",
"label": "Benzaquen--Bouchaud--Mastromatteo, microstructural foundations"
},
{
"url": "https://arxiv.org/abs/1702.02777",
"label": "Gatheral--Jaisson--Rosenbaum, rough volatility evidence"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | What mathematical or market-microstructural mechanisms explain the apparently universal roughness of financial volatility, commonly modeled by fractional Brownian motion with a small Hurst parameter $H$? | What mathematical or market-microstructural mechanisms explain the apparently universal roughness of financial volatility, typically modeled by fractional Brownian motion with a small Hurst parameter? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,429 | OWR-15218-005 | Exact Smile Calibration in Path-Dependent Volatility Models | For a path-dependent volatility model, can the volatility function $\sigma$ and mean-reversion parameter $\lambda$ be chosen to fit the market volatility smile exactly? Does the calibrated model reproduce features such as large negative short-term forward skews? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-005",
"literature-status:partially-solved",
"owr-year:2017"
] | Path-dependent and stochastic-volatility models have achieved accurate numerical calibration, including recent joint smile calibration, and can generate negative skews; exact universal calibration with the requested dynamics is not proved. | [
{
"url": "https://doi.org/10.1016/j.csda.2008.10.042",
"label": "Foschi--Pascucci, path-dependent-volatility calibration"
},
{
"url": "https://arxiv.org/abs/2406.02319",
"label": "Guyon--Lekeufack, four-factor path-dependent volatility"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | For a path-dependent volatility model, can the volatility function $\sigma$ and mean-reversion parameter $\lambda$ be chosen to fit the market volatility smile exactly? Does the calibrated model reproduce features such as large negative short-term forward skews? | For a path-dependent volatility model, can the volatility function \sigma and mean-reversion parameter \lambda be chosen to fit the market volatility smile exactly, and does the calibrated model reproduce desired implied-volatility dynamics such as large negative short-term forward skews? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,430 | OWR-15218-006 | Performance Gains from Robust Mean–Variance Portfolios | How much can robust mean–variance portfolio strategies improve investor performance under uncertainty in volatility, correlation, and model specification? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-006",
"literature-status:partially-solved",
"owr-year:2017"
] | Robust mean-variance formulations and distributionally robust extensions are well developed and empirically evaluated, but performance gains depend on uncertainty sets, data, costs, and investor objectives; there is no universal improvement theorem. | [
{
"url": "https://doi.org/10.1287/moor.28.1.1.14260",
"label": "Goldfarb--Iyengar, robust portfolio selection"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC8224264/",
"label": "Robust portfolio optimization comparative analysis"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | How much can robust mean–variance portfolio strategies improve investor performance under uncertainty in volatility, correlation, and model specification? | How much can robust mean--variance portfolio strategies improve investor performance, especially under volatility, correlation, and model uncertainty? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,431 | OWR-15218-007 | Canonical Continuous-Time Martingale Transport | Given probability measures $\mu$ and $\nu$ with $\mu\prec_c\nu$, is there a canonical continuous Markov martingale with initial law $\mu$ and terminal law $\nu$? Is there a canonical continuous-time formulation of the martingale transport problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-007",
"literature-status:partially-solved",
"owr-year:2017"
] | Kellerer-type continuous martingales and canonical constructions such as the Bass martingale and martingale Benamou--Brenier solutions provide natural examples, but naturality is not a unique mathematically defined property and no universal canonical choice is known. | [
{
"url": "https://arxiv.org/abs/1708.04869",
"label": "Backhoff-Veraguas--Beiglbock--Pammer, martingale Benamou--Brenier"
},
{
"url": "https://doi.org/10.4171/owr/2017/13",
"label": "Oberwolfach martingale-transport report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | Given probability measures $\mu$ and $\nu$ with $\mu\prec_c\nu$, is there a canonical continuous Markov martingale with initial law $\mu$ and terminal law $\nu$? Is there a canonical continuous-time formulation of the martingale transport problem? | Given probability measures \mu and \nu with \mu\prec_c\nu, does there exist a natural continuous Markov martingale with initial law \mu and terminal law \nu, and is there a natural continuous-time version of the martingale transport problem? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,432 | OWR-15218-008 | Relaxing Endpoint Conditions in Affine Volatility Large Deviations | In the large-deviation principle for affine stochastic-volatility models, can the endpoint condition $w(u_+)=w(u_-)$ be weakened or removed, and which replacement hypotheses suffice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769](https://doi.org/10.4171/owr/2017/13)
## Literature review (checked 2026-08-21)
**St... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15218-008",
"literature-status:partially-solved",
"owr-year:2017"
] | Large-deviation results have been extended to broad affine and Volterra stochastic-volatility classes, but the specific endpoint matching condition in the extracted theorem remains restrictive and lacks a general necessary-and-sufficient relaxation. | [
{
"url": "https://arxiv.org/abs/1809.06153",
"label": "Grbac--Krief--Tankov, trajectorial large deviations"
},
{
"url": "https://doi.org/10.1137/17M116344X",
"label": "Gulisashvili, large deviations for Volterra volatility"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/13 | null | null | null | In the large-deviation principle for affine stochastic-volatility models, can the endpoint condition $w(u_+)=w(u_-)$ be weakened or removed, and which replacement hypotheses suffice? | For the large-deviation principle of affine stochastic-volatility models, can the restrictive endpoint condition w(u_+)=w(u_-) be weakened or removed, and under what replacement hypotheses? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematics of Quantitative Finance (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/13, pp. 683--769 |
30,003,433 | OWR-15219-001 | Optimal Degree Bounds for Sum-of-Squares Representations | Determine the best possible degree bounds for the polynomials in sum-of-squares representations of nonnegative polynomials, or equivalently in the associated rational-function representations. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | partially_solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-001",
"literature-status:partially-solved",
"owr-year:2017"
] | Constructive elementary-recursive degree bounds for Hilbert's seventeenth problem and Positivstellensatz are known, together with lower bounds in special settings, but best possible general bounds remain unresolved. | [
{
"url": "https://arxiv.org/abs/1404.2338",
"label": "Lombardi--Perrucci--Roy, effective Hilbert seventeenth problem"
},
{
"url": "https://doi.org/10.1016/j.jmaa.2006.05.028",
"label": "Representations of positive polynomials on semialgebraic sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Determine the best possible degree bounds for the polynomials in sum-of-squares representations of nonnegative polynomials, or equivalently in the associated rational-function representations. | What are the best possible degree bounds for the polynomials in a sum-of-squares representation of a non-negative polynomial, or equivalently in the associated rational-function representation? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,434 | OWR-15219-002 | Reducing the Exponential Tower in Constructive Degree Bounds | Is the tower of five exponentials in the constructive degree bound necessary, or can its height be substantially reduced? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-002",
"literature-status:open",
"owr-year:2017"
] | The five-exponential tower is an explicit upper bound produced by the constructive method, but the primary source explicitly gives no structural reason for that height and current lower bounds are far smaller; optimality is open. | [
{
"url": "https://arxiv.org/abs/1404.2338",
"label": "Lombardi--Perrucci--Roy, elementary-recursive bound"
},
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Oberwolfach effective real-algebra report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Is the tower of five exponentials in the constructive degree bound necessary, or can its height be substantially reduced? | Is the tower of five exponentials in the constructive degree bound necessary, or can it be substantially reduced? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,435 | OWR-15219-003 | Infinite-Dimensional K-Moment Problems in Quantum Field Theory | Develop existence, determinacy, and support criteria for representing measures in infinite-dimensional $K$-moment problems arising in quantum field theory and stochastic analysis. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-003",
"literature-status:open",
"owr-year:2017"
] | Important full moment results exist for broad infinite-dimensional semialgebraic settings, but the requested systematic treatment of the K-moment problem in the report's field-theoretic settings remains an explicitly unresolved research program. | [
{
"url": "https://doi.org/10.1016/j.jfa.2014.06.012",
"label": "Infusino--Kuna--Rota, infinite-dimensional moment problem"
},
{
"url": "https://arxiv.org/abs/1610.01659",
"label": "Infusino--Kuhlmann, open questions in infinite-dimensional moments"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Develop existence, determinacy, and support criteria for representing measures in infinite-dimensional $K$-moment problems arising in quantum field theory and stochastic analysis. | How can the K-moment problem be studied systematically in the quantum-field-theoretic and infinite-dimensional stochastic settings described in the report? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,436 | OWR-15219-005 | Expected Degrees of Random Real Grassmannians | Is there a convex body naturally associated with the lines on a random cubic surface, analogous to the convex-geometric objects used to study expected degrees of random real Grassmannians? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-005",
"literature-status:partially-solved",
"owr-year:2017"
] | The Kostlan random cubic expectation is exactly 6 square-root-of-2 minus 3, an explicit special-function or elliptic-integral formula is known for delta-1-3, and fixed-k asymptotics are proved; the convex-body question remains open. | [
{
"url": "https://arxiv.org/abs/1610.01205",
"label": "Basu--Lerario--Lundberg--Peterson, random cubic lines"
},
{
"url": "https://arxiv.org/abs/1912.08291",
"label": "Lerario--Mathis, probabilistic Schubert asymptotics"
},
{
"url": "https://doi.org/10.1007/s40598-021-00182-y",
"labe... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Is there a convex body naturally associated with the lines on a random cubic surface, analogous to the convex-geometric objects used to study expected degrees of random real Grassmannians? | For the expected degree \delta_{k,n} of the Grassmannian of k-flats in random real projective space \mathbb{RP}^{n}, (i) is there an explicit special-function formula for \delta_{1,3}, (ii) for fixed k what is the asymptotic behavior of \delta_{k,n} as n\to\infty, and (iii) is there a convex body naturally associated w... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,437 | OWR-15219-006 | Certificates of Global Optimality for Thomson Configurations | For Thomson's problem of minimizing $$\sum_{1\leq i<j\leq N}\frac{1}{\lVert x_i-x_j\rVert}$$ over $N$ distinct points on $S^2$, and for its Riesz-energy variants, develop rigorous certificates that a candidate configuration attains the global minimum. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-006",
"literature-status:open",
"owr-year:2017"
] | Semidefinite hierarchies and high-precision dual certificates prove or strongly certify several small-particle cases, but a general method proving global optimality for arbitrary Thomson or Riesz configurations is not known. | [
{
"url": "https://arxiv.org/abs/1503.07228",
"label": "de Laat, moment methods in energy minimization"
},
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Oberwolfach energy-minimization report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | For Thomson's problem of minimizing $$\sum_{1\leq i<j\leq N}\frac{1}{\lVert x_i-x_j\rVert}$$ over $N$ distinct points on $S^2$, and for its Riesz-energy variants, develop rigorous certificates that a candidate configuration attains the global minimum. | For the Thomson problem of minimizing \sum_{1\le i<j\le N}\lVert x_i-x_j\rVert^{-1} over N distinct points on the unit sphere S^2 (and its Riesz-energy variants), how can one prove that a given configuration attains the global minimum? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,438 | OWR-15219-007 | Universal Sharpness of Second-Level Five-Point Energy Relaxations | Is the second-level relaxation $E_2$ sharp for the energy minimization problem of five points on $S^2$ for every pair potential in the prescribed class? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-007",
"literature-status:open",
"owr-year:2017"
] | For five points on the sphere, numerical semidefinite bounds and exact results for selected Riesz exponents are available, but universal sharpness of the four-point bound for every completely monotone potential remains a conjecture. | [
{
"url": "https://arxiv.org/abs/1503.07228",
"label": "de Laat, moment methods in energy minimization"
},
{
"url": "https://arxiv.org/abs/math/0607446",
"label": "Cohn--Kumar, universally optimal distributions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Is the second-level relaxation $E_2$ sharp for the energy minimization problem of five points on $S^2$ for every pair potential in the prescribed class? | Conjecture: the second-level relaxation E_2 is universally sharp for energy minimization of five particles on S^2, meaning it is sharp for the relevant broad class of pair-potential functions. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,439 | OWR-15219-008 | Negatively Curved Barriers Beyond Hyperbolicity Cones | Does there exist an algebraic convex cone, defined by homogeneous multivariate polynomial inequalities, that admits a normal barrier of negative curvature but is not a hyperbolicity cone? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-008",
"literature-status:open",
"owr-year:2017"
] | Hyperbolicity cones supply logarithmic barriers with negative curvature and related Helton--Nie statements have counterexamples, but the narrower existence question for an algebraic non-hyperbolicity cone with such a barrier remains unresolved. | [
{
"url": "https://arxiv.org/abs/1208.0441",
"label": "Netzer--Sanyal, smooth hyperbolicity cones"
},
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Oberwolfach hyperbolicity-cone report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Does there exist an algebraic convex cone, defined by homogeneous multivariate polynomial inequalities, that admits a normal barrier of negative curvature but is not a hyperbolicity cone? | Does there exist an algebraic convex cone, defined by homogeneous multivariate polynomial inequalities, that admits a normal barrier with negative curvature but is not a hyperbolicity cone? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,440 | OWR-15219-009 | Bounding Generic Completion Rank by Maximum-Likelihood Threshold | Does there exist a function $f:\mathbb N\to\mathbb N$ such that, for every finite simple graph $G$, the generic completion rank of $G$ is at most $f(\operatorname{mlt}(G))$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-009",
"literature-status:open",
"owr-year:2017"
] | The inequality maximum-likelihood-threshold at most generic-completion-rank is established, and many graph families are understood, but no function of the former invariant is known that uniformly bounds the latter for all finite simple graphs. | [
{
"url": "https://doi.org/10.1007/s00454-018-9990-3",
"label": "Blekherman--Sinn, MLT and generic completion rank"
},
{
"url": "https://arxiv.org/abs/2108.02185",
"label": "Bernstein et al., maximum-likelihood thresholds via rigidity"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Does there exist a function $f:\mathbb N\to\mathbb N$ such that, for every finite simple graph $G$, the generic completion rank of $G$ is at most $f(\operatorname{mlt}(G))$? | Does there exist a function f:\mathbb{N}\to\mathbb{N} such that, for every finite simple graph G, f(\operatorname{mlt}(G)) is an upper bound for the generic completion rank of G? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,441 | OWR-15219-010 | Atomic Measures on Irreducible Truncated Moment Varieties | Let $V=Z(p)$ be an irreducible real algebraic set. Must every recursively generated truncated moment matrix $M^{(n)}$ associated with $V$ admit a representing measure with $\operatorname{rank}M^{(n)}$ atoms? How can the variety change when $M^{(n)}$ is extended to $M^{(n+1)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-010",
"literature-status:open",
"owr-year:2017"
] | Flat-extension and extremal cases give necessary and sufficient criteria in important regimes, but the irreducible-variety questions about an r-to-the-n-atomic measure and the evolution of the variety under extension remain open in general. | [
{
"url": "https://arxiv.org/abs/math/0610882",
"label": "Curto--Fialkow--Moeller, extremal truncated moments"
},
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Oberwolfach truncated-moment report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $V=Z(p)$ be an irreducible real algebraic set. Must every recursively generated truncated moment matrix $M^{(n)}$ associated with $V$ admit a representing measure with $\operatorname{rank}M^{(n)}$ atoms? How can the variety change when $M^{(n)}$ is extended to $M^{(n+1)}$? | For an irreducible algebraic set V=Z(p) in the truncated moment problem, must a recursively generated moment matrix M^{(n)} admit a representing measure with rank(M^{(n)}) atoms, and how is V affected when passing from M^{(n)} to M^{(n+1)}? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,442 | OWR-15219-012 | Largest Roots of Doubly Stochastic Stable Polynomials | Let $D_{m,d}$ consist of the doubly stochastic stable homogeneous polynomials of degree $d$, let $\lambda_1(P)$ be the largest zero of the mixed characteristic polynomial $\chi_P$, and set $P_\infty=(x_1+\cdots+x_m)^d/m^d$. Is $\lambda_1(P)\leq\lambda_1(P_\infty)$ for every $P\in D_{m,d}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-012",
"literature-status:partially-solved",
"owr-year:2017"
] | The largest-root bound is proved for symmetric stable doubly stochastic polynomials, while the unrestricted conjecture remains unresolved; thus the available theorem covers a substantial but proper subclass. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Branden, van der Waerden and Kadison--Singer with symmetries"
},
{
"url": "https://annals.math.princeton.edu/2015/182-1/p08",
"label": "Marcus--Spielman--Srivastava, mixed characteristic polynomials"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $D_{m,d}$ consist of the doubly stochastic stable homogeneous polynomials of degree $d$, let $\lambda_1(P)$ be the largest zero of the mixed characteristic polynomial $\chi_P$, and set $P_\infty=(x_1+\cdots+x_m)^d/m^d$. Is $\lambda_1(P)\leq\lambda_1(P_\infty)$ for every $P\in D_{m,d}$? | Let D_{m,d} be the doubly stochastic stable homogeneous degree-d polynomials, let \lambda_1(P) be the largest zero of the mixed characteristic polynomial \chi_P, and let P_\infty=(x_1+\cdots+x_m)^d/m^d. Conjecture: if P\in D_{m,d}, then \lambda_1(P)\leq\lambda_1(P_\infty). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,443 | OWR-15219-013 | Root Vector Majorization for Doubly Stochastic Stable Polynomials | Let $D_{m,d}$, $P_\infty$, and $\lambda(P)=(\lambda_1(P),\ldots,\lambda_d(P))$ be as in the doubly stochastic stable-polynomial setting. Is $\lambda(P)$ majorized by $\lambda(P_\infty)$ for every $P\in D_{m,d}$? Moreover, if $P\in D_{m,d}\cap\operatorname{Sym}_m$, $0\leq r\leq s$, and $\Psi_s=\exp(s(I-T))$, is $\lambda... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-013",
"literature-status:open",
"owr-year:2017"
] | Majorization of the full zero vector remains conjectural; only the largest-root inequality is obtained in the symmetric subclass, so the stated strong Van der Waerden conjecture is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Branden, stable-polynomial conjectures"
},
{
"url": "https://arxiv.org/abs/1606.03140",
"label": "Slofstra, related Kadison--Singer background"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $D_{m,d}$, $P_\infty$, and $\lambda(P)=(\lambda_1(P),\ldots,\lambda_d(P))$ be as in the doubly stochastic stable-polynomial setting. Is $\lambda(P)$ majorized by $\lambda(P_\infty)$ for every $P\in D_{m,d}$? Moreover, if $P\in D_{m,d}\cap\operatorname{Sym}_m$, $0\leq r\leq s$, and $\Psi_s=\exp(s(I-T))$, is $\lambda... | With the notation above and \lambda(P)=(\lambda_1(P),\ldots,\lambda_d(P)), Conjecture: \lambda(P) is majorized by \lambda(P_\infty) for every P\in D_{m,d}; moreover, for P\in D_{m,d}\cap\operatorname{Sym}_m and 0\leq r\leq s, \lambda(\Psi_r(P)) is majorized by \lambda(\Psi_s(P)), where \Psi_s=\exp(s(I-T)). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,444 | OWR-15219-014 | Representing Measures for Finite-Dimensional Function Spaces | Let $S$ be a topological space, let $V$ be a finite-dimensional vector space of continuous real-valued functions on $S$, and let $L\in V^*$. Characterize when there exists a Borel measure $\mu$ on $S$ such that $$L(f)=\int_S f\,d\mu\qquad\text{for every }f\in V$$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-014",
"literature-status:open",
"owr-year:2017"
] | The truncated moment question has complete criteria in one-dimensional, compact, extremal, and several special algebraic settings, but no general necessary-and-sufficient characterization for arbitrary finite-dimensional V and L is known. | [
{
"url": "https://arxiv.org/abs/math/0610882",
"label": "Curto--Fialkow--Moeller, extremal truncated moments"
},
{
"url": "https://doi.org/10.1016/j.jfa.2014.06.012",
"label": "Infusino--Kuna--Rota, moment representation"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $S$ be a topological space, let $V$ be a finite-dimensional vector space of continuous real-valued functions on $S$, and let $L\in V^*$. Characterize when there exists a Borel measure $\mu$ on $S$ such that $$L(f)=\int_S f\,d\mu\qquad\text{for every }f\in V$$. | Let S be a topological space, V a finite-dimensional space of continuous real-valued functions on S, and L\in V^*. Does there exist a Borel measure \mu on S such that L(f)=\int_S f d\mu for every f\in V? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,445 | OWR-15219-015 | Minimal Flat Extension Orders for Truncated Moments | Given a truncated moment sequence $\beta^{(2d)}$, estimate the smallest $k\geq0$ for which the moment matrix $M_{d+k}$ has a flat extension $M_{d+k+1}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | partially_solved | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-015",
"literature-status:partially-solved",
"owr-year:2017"
] | Flat-extension theorems reduce the problem to finding a finite extension, and sharp worst-case extension-degree bounds are now known in general moment spaces, but a good instance-sensitive estimate for the smallest k remains unavailable. | [
{
"url": "https://arxiv.org/abs/1903.00598",
"label": "di Dio--Kummer, Caratheodory numbers and flat extensions"
},
{
"url": "https://arxiv.org/abs/1105.0410",
"label": "Helton--Nie, semidefinite truncated K-moments"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Given a truncated moment sequence $\beta^{(2d)}$, estimate the smallest $k\geq0$ for which the moment matrix $M_{d+k}$ has a flat extension $M_{d+k+1}$. | Given a truncated moment sequence \beta^{(2d)}, find a good estimate for the smallest k\geq0 such that the moment matrix M_{d+k} admits a flat extension M_{d+k+1}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,446 | OWR-15219-016 | Shortest Moment Extensions and Minimal Atomic Measures | Does a shortest convergent extension sequence for a truncated moment sequence $\beta^{(2d)}$ always produce a representing measure with the minimum possible number of atoms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-016",
"literature-status:open",
"owr-year:2017"
] | Bounds on the length of convergent extension sequences and algorithms for special finite-variety cases are known, but the shortest-sequence versus fewest-atoms implication remains an explicit open question. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Oberwolfach truncated-moment report"
},
{
"url": "https://jot.theta.ro/jot/archive/2008-060-002/2008-060-002-007.pdf",
"label": "Fialkow, truncated moment algorithms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Does a shortest convergent extension sequence for a truncated moment sequence $\beta^{(2d)}$ always produce a representing measure with the minimum possible number of atoms? | Does the shortest convergent extension sequence for a truncated moment sequence \beta^{(2d)} always yield a representing measure with the fewest atoms? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,447 | OWR-15219-017 | Positivity and Closure of Flat Moment Matrices | Give concrete conditions on a truncated moment sequence $\beta^{(m)}$ that ensure positivity of its Riesz functional $L_\beta$, and characterize the closure $F_{n,d}$ of the cone of flat positive $n$-dimensional moment matrices of degree $2d$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | partially_solved | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-017",
"literature-status:partially-solved",
"owr-year:2017"
] | Concrete characterizations of the flat positive moment-matrix cone are known in several low-dimensional cases, and rank-based positivity criteria are known, but a general concrete characterization of F remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1090/S0002-9939-2014-12253-2",
"label": "Positive Gorenstein ideals"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Give concrete conditions on a truncated moment sequence $\beta^{(m)}$ that ensure positivity of its Riesz functional $L_\beta$, and characterize the closure $F_{n,d}$ of the cone of flat positive $n$-dimensional moment matrices of degree $2d$. | What concrete conditions on a truncated moment sequence \beta^{(m)} ensure that its Riesz functional L_\beta is positive, and can one give a concrete characterization of the closure F_{n,d} of the flat positive n-dimensional moment matrices of degree 2d? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,448 | OWR-15219-018 | Sum of Squares Symmetric Quartics in Higher Dimensions | For the symmetric quartic form 8M_1(x)M_3(x)+nM_4(x), known to be positive definite and a sum of squares for n=2,3, is it a sum of squares for larger n? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | solved | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "resolution",
"evidence": "published"
} | Unrecoverable OWR statement (The official report answers the higher-dimensional sum-of-squares question immediately by displaying an identity valid for every dimension, ) | null | null | [Discussion #4 literature review, 2026-10-14] **solved (yes)**; the dataset currently labels it open. B. Reznick, OWR 14/2017, p. 843: is the symmetric quartic 8M₁M₃ + nM₄ (M_k the power sums) a sum of squares for every n? The same paragraph answers with n³(8M₁M₃ + nM₄) = Σ_{j=1}^{n} (n²x_j² + 4n x_j M₁ − 8M₁²)², which... | [
"owr",
"oberwolfach-reports",
"OWR-15219-018",
"literature-status:open",
"owr-year:2017"
] | The extracted record is only the question `What about larger n?' and does not state a standalone mathematical claim whose resolution can be verified; it therefore remains open under the triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | null | For the symmetric quartic form 8M_1(x)M_3(x)+nM_4(x), known to be positive definite and a sum of squares for n=2,3, is it a sum of squares for larger n? | unrecoverable | The official report answers the higher-dimensional sum-of-squares question immediately by displaying an identity valid for every dimension, so this extraction is not an unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,449 | OWR-15219-019 | Rank-One Kernel Boundary Points of Free Spectrahedra | Let $L$ be a Hermitian monic linear pencil and let $D(L)$ be its free spectrahedron. Must there exist a boundary point $X$ satisfying $\dim\ker L(X)=1$; equivalently, is $\partial^1D(L)$ nonempty? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-019",
"literature-status:open",
"owr-year:2017"
] | The record says that a free-spectrahedron boundary question is related to Kippenhahn's conjecture, but does not state an equivalence; the classical Kippenhahn conjecture is disproved by Laffey, while the extracted boundary question is not thereby settled. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/0024-3795(83)90159-3",
"label": "Laffey counterexample to Kippenhahn's conjecture"
},
{
"url": "https://arxiv.org/abs/1512.02648",
"label": "Free loci of matrix... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $L$ be a Hermitian monic linear pencil and let $D(L)$ be its free spectrahedron. Must there exist a boundary point $X$ satisfying $\dim\ker L(X)=1$; equivalently, is $\partial^1D(L)$ nonempty? | For a hermitian monic pencil L and its free spectrahedron D(L), is the set of boundary points X with \dim\ker L(X)=1 nonempty; equivalently, does \partial^1D(L)\neq\varnothing? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,450 | OWR-15219-020 | Positive Radon Measures for Truncated Moment Data | Let $X$ be locally compact, let $V\subseteq C(X,\mathbb R)$ have basis $a_1,\ldots,a_m$, and let $s_1,\ldots,s_m\in\mathbb R$. Characterize when there is a positive Radon measure $\mu$ on $X$ such that $$s_j=\int_X a_j(x)\,d\mu(x)\qquad(1\leq j\leq m)$$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-020",
"literature-status:open",
"owr-year:2017"
] | General truncated moment existence has positivity, extension, and flatness criteria in important special settings, but the arbitrary positive Radon-measure existence question as extracted is not resolved without further hypotheses on X and the data. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1090/memo/0568",
"label": "Solution of the truncated complex moment problem for flat data"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | Let $X$ be locally compact, let $V\subseteq C(X,\mathbb R)$ have basis $a_1,\ldots,a_m$, and let $s_1,\ldots,s_m\in\mathbb R$. Characterize when there is a positive Radon measure $\mu$ on $X$ such that $$s_j=\int_X a_j(x)\,d\mu(x)\qquad(1\leq j\leq m)$$. | Given a locally compact space X, a finite-dimensional function space with basis a_1,\ldots,a_m, and real numbers s_1,\ldots,s_m, does there exist a positive Radon measure \mu on X such that s_j=\int_X a_j(x) d\mu for every j=1,\ldots,m? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,451 | OWR-15219-021 | Carathéodory Bounds and Independent Evaluation Vectors | For $d\geq3$, are the Carathéodory number $C_{2d}$ and the maximal finite projective-zero count $\beta(2d)$ related by $$\beta(2d)\leq C_{2d}\leq\beta(2d)+1?$$ If $f\in B_{n,2d}$ is nonnegative on $\mathbb R^n$ and has projective zero set $\{z_1,\ldots,z_k\}$, must the evaluation vectors $\{s_{B_{n,2d}}(z_i):1\leq i\le... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-021",
"literature-status:open",
"owr-year:2017"
] | The report establishes upper bounds and examples relating the Caratheodory number to the maximal finite projective-zero count, but the displayed two-sided conjecture and the accompanying general open problem remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1203.3775",
"label": "Positive Gorenstein ideals"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | For $d\geq3$, are the Carathéodory number $C_{2d}$ and the maximal finite projective-zero count $\beta(2d)$ related by $$\beta(2d)\leq C_{2d}\leq\beta(2d)+1?$$ If $f\in B_{n,2d}$ is nonnegative on $\mathbb R^n$ and has projective zero set $\{z_1,\ldots,z_k\}$, must the evaluation vectors $\{s_{B_{n,2d}}(z_i):1\leq i\le... | Conjecture: \beta(2d)\leq C_{2d}\leq\beta(2d)+1 for d\geq3. Open problem: if f\in B_{n,2d} is nonnegative on \mathbb{R}^n and its projective zero set is \{z_1,\ldots,z_k\}, are the evaluation vectors \{s_{B_{n,2d}}(z_i):1\leq i\leq k\} linearly independent? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,452 | OWR-15219-022 | Bianalytic Free Spectrahedron Maps Without Genericity | In the partial converse classifying bianalytic maps between bounded free spectrahedra, can the genericity hypothesis on the coefficient tuples $A$ and $B$ be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862](https://doi.org/10.4171/owr/2017/14)
## Lite... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15219-022",
"literature-status:open",
"owr-year:2017"
] | The extracted conjecture removes a genericity hypothesis from the classification of bianalytic free-spectrahedron maps; published results still require genericity or related irreducibility assumptions, so the stated generalization remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/14",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00208-017-1630-3",
"label": "Bianalytic maps between free spectrahedra"
},
{
"url": "https://arxiv.org/abs/1711.09459",
"label": "Free bianalytic maps in a gen... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/14 | null | null | null | In the partial converse classifying bianalytic maps between bounded free spectrahedra, can the genericity hypothesis on the coefficient tuples $A$ and $B$ be removed? | In the partial converse for bianalytic maps between bounded free spectrahedra, is the genericity hypothesis on the coefficient tuples A and B unnecessary? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Real Algebraic Geometry With a View Toward Moment Problems and Optimization (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/14, pp. 771--862 |
30,003,453 | OWR-15221-002 | Bayesian Bias Correction in Support-Boundary Models | In the irregular nonparametric support-boundary model, does a Bayesian procedure automatically produce the finite-sample correction to the maximum-likelihood estimator given by the number of support points on the MLE divided by the sample size? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Recovery of Discrete, Geometric and Invariant Structures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/16, pp. 949--999](https://doi.org/10.4171/owr/2017/16)
## Literature ... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 update, 2026-10-14] Scoped preprint for OWR-15221-002: A Sharp Prior-Sensitivity Threshold for Fixed-Partition Support Boundaries. | [
"owr",
"oberwolfach-reports",
"OWR-15221-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Bayesian support-boundary analyses prove automatic bias correction for compound-Poisson priors in specified classes and also exhibit failures for linear boundaries; no universal automatic correction theorem is known. | [
{
"url": "https://doi.org/10.4171/owr/2017/16",
"label": "Original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1809.04140",
"label": "Nonparametric Bayesian analysis of the compound Poisson prior"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/16 | null | null | null | In the irregular nonparametric support-boundary model, does a Bayesian procedure automatically produce the finite-sample correction to the maximum-likelihood estimator given by the number of support points on the MLE divided by the sample size? | In the irregular nonparametric support-boundary model, does a Bayesian procedure automatically produce the finite-sample correction to the maximum-likelihood estimator given by the number of support points on the MLE divided by the sample size? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Statistical Recovery of Discrete, Geometric and Invariant Structures (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/16, pp. 949--999 |
30,003,454 | OWR-15222-001 | Sampling Complexity of Hyperbolic-Cross Approximation | Can better sampling measures lower the sample complexity of hyperbolic-cross polynomial approximation, and can sample-complexity estimates be proved for domains that are not unions of rectangles with nonvanishing volume, including triangles, simplices, and spheres? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiscale and High-Dimensional Problems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/17, pp. 1001--1051](https://doi.org/10.4171/owr/2017/17)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,017 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15222-001",
"literature-status:open",
"owr-year:2017"
] | The report explicitly leaves both improved sampling measures and sample-complexity estimates for irregular domains such as simplices and spheres as open problems; later approximation results do not establish these exact goals. | [
{
"url": "https://doi.org/10.4171/owr/2017/17",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/17 | null | null | null | Can better sampling measures lower the sample complexity of hyperbolic-cross polynomial approximation, and can sample-complexity estimates be proved for domains that are not unions of rectangles with nonvanishing volume, including triangles, simplices, and spheres? | Can better sampling measures lower the sample complexity of hyperbolic-cross polynomial approximation, and can sample-complexity estimates be proved for domains that are not unions of rectangles with nonvanishing volume, including triangles, simplices, and spheres? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Multiscale and High-Dimensional Problems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/17, pp. 1001--1051 |
30,003,455 | OWR-15222-006 | Multivariate Smoothness Classes and Their Approximation | What is a natural multivariate analogue of univariate smoothness classes, and how should functions in those classes be approximated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiscale and High-Dimensional Problems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/17, pp. 1001--1051](https://doi.org/10.4171/owr/2017/17)
## Literature review (checked 2026-08-21... | 3 | open | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15222-006",
"literature-status:open",
"owr-year:2017"
] | The record asks for natural multivariate smoothness classes and optimal approximation methods; mixed-smoothness approximation and associated n-width questions remain active open problems rather than a single settled theorem. | [
{
"url": "https://doi.org/10.4171/owr/2017/17",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/17 | null | null | null | What is a natural multivariate analogue of univariate smoothness classes, and how should functions in those classes be approximated? | What is a natural multivariate analogue of univariate smoothness classes, and how should functions in those classes be approximated? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Multiscale and High-Dimensional Problems (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/17, pp. 1001--1051 |
30,003,456 | OWR-15426-001 | Higher Central-Derivative Formulas for L-Functions | Develop formulas for higher-order central derivatives of automorphic $L$-functions that extend the Waldspurger and Gross–Zagier formulas over number fields and function fields. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134](https://doi.org/10.4171/owr/2017/18)
## Literature review (checked 2... | 3 | partially_solved | null | 2,017 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15426-001",
"literature-status:partially-solved",
"owr-year:2017"
] | Higher central-derivative formulas are proved over function fields by Yun and Zhang, including arbitrary orders in their stated setting, while the analogous general number-field geometric theory remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2017/18",
"label": "Original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1712.08026",
"label": "Shtukas and the Taylor expansion of L-functions II"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/18 | null | null | null | Develop formulas for higher-order central derivatives of automorphic $L$-functions that extend the Waldspurger and Gross–Zagier formulas over number fields and function fields. | What formulas express higher-order central derivatives of L-functions, generalizing the Waldspurger and Gross--Zagier formulas, in the relevant automorphic and function-field settings? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134 |
30,003,457 | OWR-15426-002 | Frame Bundles as Stack Fiber Products | Given a rank-n vector bundle E on S with classifying map f_E:S\to BGL_n, how should the fiber product S\times_{BGL_n}\mathrm{pt} be interpreted geometrically, namely as the frame bundle of E? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134](https://doi.org/10.4171/owr/2017/18)
## Literature review (checked 2... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report immediately identifies the displayed fiber product with the frame bundle of the vector bundle; this is an answered clari) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15426-002",
"literature-status:open",
"owr-year:2017"
] | The extracted item is the meta-question `How to make this geometric?' in a discussion of stacks, not a complete mathematical claim; no definite resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2017/18",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/18 | null | null | null | null | Given a rank-n vector bundle E on S with classifying map f_E:S\to BGL_n, how should the fiber product S\times_{BGL_n}\mathrm{pt} be interpreted geometrically, namely as the frame bundle of E? | unrecoverable | The official report immediately identifies the displayed fiber product with the frame bundle of the vector bundle; this is an answered clarification question, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134 |
30,003,458 | OWR-15426-003 | Shtuka Strata as Automorphism Torsors | For r=0, how should the decomposition \mathrm{Sht}^{\mu}_n=\coprod_E[\operatorname{Spec}\mathbb{F}_q/\operatorname{Aut}(E)] be interpreted concretely as describing \operatorname{Aut}(E)-torsors on S? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134](https://doi.org/10.4171/owr/2017/18)
## Literature review (checked 2... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report immediately explains the stratum as an automorphism-group torsor and a twisted form; this is an answered clarification q) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15426-003",
"literature-status:open",
"owr-year:2017"
] | The extracted item is only the clarification question `What exactly does this mean?' and does not contain a standalone proposition to test; it remains open under the triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2017/18",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/18 | null | null | null | null | For r=0, how should the decomposition \mathrm{Sht}^{\mu}_n=\coprod_E[\operatorname{Spec}\mathbb{F}_q/\operatorname{Aut}(E)] be interpreted concretely as describing \operatorname{Aut}(E)-torsors on S? | unrecoverable | The official report immediately explains the stratum as an automorphism-group torsor and a twisted form; this is an answered clarification question, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134 |
30,003,459 | OWR-15426-004 | Multiplicity One in Cuspidal Automorphic Decompositions | For the decomposition A_{G,\mathrm{cusp},\chi}=\bigoplus_{\pi\in\Pi_{G,\mathrm{cusp},\chi}}\pi, does each irreducible cuspidal automorphic representation occur as an honest subrepresentation with multiplicity one, rather than merely as a subquotient? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134](https://doi.org/10.4171/owr/2017/18)
## Literature review (checked 2... | 3 | open | null | 2,017 | 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 | Unrecoverable OWR statement (The official report states and proves the multiplicity-one assertion in the surrounding theorem; this extraction is an answered expository q) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15426-004",
"literature-status:open",
"owr-year:2017"
] | The extracted item asks for the content of a displayed definition-and-corollary passage rather than posing a complete unresolved theorem; its intended target is unclear, so it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2017/18",
"label": "Original Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/18 | null | null | null | null | For the decomposition A_{G,\mathrm{cusp},\chi}=\bigoplus_{\pi\in\Pi_{G,\mathrm{cusp},\chi}}\pi, does each irreducible cuspidal automorphic representation occur as an honest subrepresentation with multiplicity one, rather than merely as a subquotient? | unrecoverable | The official report states and proves the multiplicity-one assertion in the surrounding theorem; this extraction is an answered expository question, not an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Higher Gross Zagier Formulas (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/18, pp. 1067--1134 |
30,003,460 | OWR-15427-002 | Piercing Line Families with the (p,3)-Property | Let $p\geq3$, and let $\mathcal F$ be a finite family of lines with the $(p,3)$-property: among every $p$ lines of $\mathcal F$, some three are concurrent. Must there be a set $U$ of at most $p-2$ points such that every line in $\mathcal F$ contains a point of $U$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no, for all sufficiently large p)**. V. Dol'nikov (joint with M. Didin and M. Grigorev; OWR 19/2017, p. 1154, Conjecture 1) conjectures that lines with the (p,3)-property can be pierced by p−2 points. The least failing p is open, as far as we found. | [
"owr",
"oberwolfach-reports",
"OWR-15427-002",
"literature-status:open",
"owr-year:2017"
] | The line-piercing conjecture is proved in small cases such as p at most 6, but the all-p conjecture that p minus 2 points pierce every line remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "Original Oberwolfach report"
},
{
"url": "https://www.renyi.hu/conferences/hunrus18/abstracts/grigoriev_abstract.pdf",
"label": "Ramsey type problems for lines and points"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $p\geq3$, and let $\mathcal F$ be a finite family of lines with the $(p,3)$-property: among every $p$ lines of $\mathcal F$, some three are concurrent. Must there be a set $U$ of at most $p-2$ points such that every line in $\mathcal F$ contains a point of $U$? | Suppose p\geq 3 is an integer and a family of straight lines F has the (p,3)-property. Then there exists a point set U with |U|\leq p-2 such that every line ell in F meets U. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,461 | OWR-15427-003 | Binomial Bounds for Gamma Vectors of Flag Spheres | Let $\Delta$ be a flag homology sphere with gamma-vector $(\gamma_0,\gamma_1,\ldots)$ and $\gamma_1=\ell$. Must $$0\leq\gamma_i\leq\binom{\ell}{i}\qquad\text{for every }i\geq2$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | partially_solved | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1137/17M1110298",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. The same abstract (pp. 1167–1168) states Conjecture 0.2: a flag homology sphere with γ₁ = ℓ has 0 ≤ γ_i ≤ C(ℓ, i). Its Theorem 0.3 (in Labbé–Nevo, [SIAM J. Discrete Math. 31 (2017)](https://doi.org/10.1137/17M1110298)) gives γ₂ ≤ C(ℓ, 2), γ_j = 0 for j... | [
"owr",
"oberwolfach-reports",
"OWR-15427-003",
"literature-status:open",
"owr-year:2017"
] | Known Ramsey-number formulas and finite-case structure theorems give partial information, but the assertion that every sufficiently large point set with the (2k plus 1,3)-property lies on k lines remains a conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "Original Oberwolfach report"
},
{
"url": "https://www.renyi.hu/conferences/hunrus18/abstracts/grigoriev_abstract.pdf",
"label": "Ramsey type problems for lines and points"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $\Delta$ be a flag homology sphere with gamma-vector $(\gamma_0,\gamma_1,\ldots)$ and $\gamma_1=\ell$. Must $$0\leq\gamma_i\leq\binom{\ell}{i}\qquad\text{for every }i\geq2$$? | Let Delta be a flag homology sphere. The gamma-vector of Delta is the f-vector of a flag simplicial complex. If gamma_1=ell, then for every i\geq2, 0\leq gamma_i\leq {ell\choose i}. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,462 | OWR-15427-004 | Flag Sphere Gamma Vectors Beyond Simplicial Polytopes | Does there exist a vector that is the gamma-vector of a flag homology sphere but is not the gamma-vector of any flag simplicial polytope? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15427-007"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-004",
"literature-status:open",
"owr-year:2017"
] | The even-parameter point-covering conjecture has partial bounds and exact Ramsey values in large finite regimes, but the claimed all-but-one-points-on-(k minus 1)-lines conclusion is not proved in general. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "Original Oberwolfach report"
},
{
"url": "https://www.renyi.hu/conferences/hunrus18/abstracts/grigoriev_abstract.pdf",
"label": "Ramsey type problems for lines and points"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Does there exist a vector that is the gamma-vector of a flag homology sphere but is not the gamma-vector of any flag simplicial polytope? | For any flag simplicial complex Gamma, does there exist a flag homology sphere Delta, of any dimension, whose gamma-vector equals the f-vector of Gamma? Does there exist a vector that is the gamma-vector of a flag homology sphere but not the gamma-vector of a flag simplicial polytope? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,463 | OWR-15427-005 | Complete Graph Minors from Homological Graph Dimension | For a finite graph $G$, let $\gamma(G)$ be the largest integer $q$ for which some connected family of induced subgraphs of $G$ has a nerve with nonzero $q$-dimensional homology. For every positive integer $d$, is $\gamma(G)\geq d$ equivalent to the existence of a $K_{d+2}$ minor in $G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-005",
"literature-status:open",
"owr-year:2017"
] | The homological dimension detects K3, K4, and K5 minors, but the proposed equivalence for every complete minor has only these low-dimensional cases established and remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1006/jctb.1995.1056",
"label": "On a minor-monotone graph invariant"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | For a finite graph $G$, let $\gamma(G)$ be the largest integer $q$ for which some connected family of induced subgraphs of $G$ has a nerve with nonzero $q$-dimensional homology. For every positive integer $d$, is $\gamma(G)\geq d$ equivalent to the existence of a $K_{d+2}$ minor in $G$? | For every positive integer d and finite graph G, K_{d+2} is a minor of G if and only if gamma(G)\geq d, where gamma(G) is the largest integer q for which some connected family of induced subgraphs of G has nerve with nonzero H_q. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,464 | OWR-15427-006 | Flag-Complex Realization of Gamma Vectors | Is the gamma-vector of every flag homology sphere the face vector of a flag simplicial complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-006",
"literature-status:open",
"owr-year:2017"
] | The extracted statement is truncated to `conjecture'; the contextual flag-sphere gamma conjectures have substantial partial bounds, but their general nonnegativity and flag-complex realization assertions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "Original Oberwolfach report"
},
{
"url": "https://doi.org/10.1137/17M1110298",
"label": "Bounds for entries of gamma-vectors of flag homology spheres"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Is the gamma-vector of every flag homology sphere the face vector of a flag simplicial complex? | For every d-dimensional flag homology sphere Delta with gamma_1=ell, the gamma-vector is constrained by 0\leq gamma_i\leq {ell\choose i} for i\geq2, and the gamma-vector is the f-vector of a flag simplicial complex. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,465 | OWR-15427-007 | Flag Sphere Gamma Vectors and Polytope Separation | Does there exist, for every flag simplicial complex Gamma, a flag homology sphere Delta of any dimension whose gamma-vector equals the f-vector of Gamma? Does some vector occur as the gamma-vector of a flag homology sphere but not as the gamma-vector of a flag simplicial polytope? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | partially_solved | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1137/17M1110298",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | Duplicate/merged OWR extraction (The official report shows that this record duplicates the flag-sphere gamma-vector problem retained as OWR-15427-004. No separate clean stat) | [
"OWR-15427-004"
] | null | [Discussion #4 literature review, 2026-09-30] **partially_solved** (first question: no, in the source). E. Nevo (joint with J.-P. Labbé; OWR 19/2017, p. 1168) asks whether the f-vector of every flag complex is the γ-vector of some flag homology sphere, and (Problem 1) whether some γ-vector of a flag homology sphere is ... | [
"owr",
"oberwolfach-reports",
"OWR-15427-007",
"literature-status:open",
"owr-year:2017"
] | The requested flag realization of gamma vectors remains unresolved in general; known results cover special cases such as low dimensions and barycentric subdivisions, not arbitrary flag homology spheres. | [
{
"url": "https://doi.org/10.1137/17M1110298",
"label": "Labbé and Nevo on gamma-vector bounds"
},
{
"url": "https://arxiv.org/abs/2410.08139",
"label": "Park on balanced realizations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | null | Does there exist, for every flag simplicial complex Gamma, a flag homology sphere Delta of any dimension whose gamma-vector equals the f-vector of Gamma? Does some vector occur as the gamma-vector of a flag homology sphere but not as the gamma-vector of a flag simplicial polytope? | unrecoverable | The official report shows that this record duplicates the flag-sphere gamma-vector problem retained as OWR-15427-004. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,466 | OWR-15427-008 | Proper Three-Colorings for Homothets of Convex Sets | For every plane convex body $D$, does there exist an integer $m$ such that every finite point set admits a three-coloring in which each homothetic copy of $D$ containing at least $m$ points contains two points of different colors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no)**. D. Pálvölgyi (joint with B. Keszegh; OWR 19/2017, pp. 1172–1173) conjectures that every finite point set can be 3-coloured with no monochromatic member containing at least m points: for homothets of any plane convex D and some m (Conjecture 1; open for disk... | [
"owr",
"oberwolfach-reports",
"OWR-15427-008",
"literature-status:open",
"owr-year:2017"
] | The disk case of the proper three-coloring question remains open; the primary paper proves the analogous statement for convex polygons but not for disks. | [
{
"url": "https://arxiv.org/abs/1612.02158",
"label": "Keszegh and Pálvölgyi on proper coloring"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | For every plane convex body $D$, does there exist an integer $m$ such that every finite point set admits a three-coloring in which each homothetic copy of $D$ containing at least $m$ points contains two points of different colors? | For every plane convex set D, there exists m such that every finite point set admits a 3-coloring in which every homothetic copy of D containing at least m points contains two points of different colors. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,467 | OWR-15427-009 | Proper Three-Colorings for Pseudo-Disk Arrangements | Does every finite point set admit a three-coloring such that each member of every pseudo-disk family containing at least four points contains two points of different colors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (no)**. D. Pálvölgyi (joint with B. Keszegh; OWR 19/2017, pp. 1172–1173) conjectures that every finite point set can be 3-coloured with no monochromatic member containing at least m points: for homothets of any plane convex D and some m (Conjecture 1; open for disk... | [
"owr",
"oberwolfach-reports",
"OWR-15427-009",
"literature-status:open",
"owr-year:2017"
] | The stronger pseudo-disk three-coloring conjecture is unresolved; the literature records partial results for convex polygons and leaves a universal pseudo-disk threshold as an open problem. | [
{
"url": "https://arxiv.org/abs/1612.02158",
"label": "Keszegh and Pálvölgyi on proper coloring"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Does every finite point set admit a three-coloring such that each member of every pseudo-disk family containing at least four points contains two points of different colors? | For every pseudo-disk arrangement, every finite point set admits a 3-coloring such that every pseudo-disk containing at least 4 points contains two points of different colors. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,468 | OWR-15427-010 | Minimum Faces in Complexes Not Embeddable in Manifolds | Given a $k$-dimensional simplicial complex and a $2k$-dimensional manifold $M$, determine the minimum number of $k$-faces in a simplicial complex that does not embed in $M$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-010",
"literature-status:open",
"owr-year:2017"
] | The extremal number of k-faces in a complex non-embeddable into a specified manifold is not known in the stated generality; existing work gives methods and special cases rather than a general minimum. | [
{
"url": "https://ems.press/content/serial-article-files/46683",
"label": "Paták and Tancer on embeddings"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Given a $k$-dimensional simplicial complex and a $2k$-dimensional manifold $M$, determine the minimum number of $k$-faces in a simplicial complex that does not embed in $M$. | Given a k-dimensional complex and a 2k-dimensional manifold M, what is the minimum number of k-faces in a complex that does not embed in M? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,469 | OWR-15427-011 | Maximum Diameters of Lattice Polytopes in Cubes | For positive integers $d$ and $k$, let $\delta(d,k)$ be the largest diameter of a lattice polytope contained in $[0,k]^d$. Is this maximum, up to translation, attained by a Minkowski sum of lattice vectors? In particular, when $k<2d$, is $$\delta(d,k)=\left\lfloor\frac{(k+1)d}{2}\right\rfloor$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-011",
"literature-status:partially-solved",
"owr-year:2017"
] | The conjectured exact formula for lattice polytope diameter is unresolved, but strong upper bounds and computer-assisted exact values are known for several small parameter pairs. | [
{
"url": "https://arxiv.org/abs/1610.00341",
"label": "Deza and Pournin on diameter bounds"
},
{
"url": "https://doi.org/10.1016/j.dam.2019.10.026",
"label": "Chadder and Deza on exact small cases"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | For positive integers $d$ and $k$, let $\delta(d,k)$ be the largest diameter of a lattice polytope contained in $[0,k]^d$. Is this maximum, up to translation, attained by a Minkowski sum of lattice vectors? In particular, when $k<2d$, is $$\delta(d,k)=\left\lfloor\frac{(k+1)d}{2}\right\rfloor$$? | For any positive integers d and k, the maximum diameter delta(d,k) of a lattice polytope in [0,k]^d is, up to translation, attained by a Minkowski sum of lattice vectors; in particular, when k<2d, delta(d,k)=floor((k+1)d/2). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,470 | OWR-15427-012 | Covering Balls by Translated Slabs | For $d>2$, does there exist a constant $C(d)$ such that, whenever $n_i\in S^{d-1}$ are unit directions and $\varepsilon_i>0$ satisfy $\sum_i\varepsilon_i>C(d)$, suitable translates of the slabs $$\{x\in\mathbb R^d:a_i\leq\langle x,n_i\rangle\leq a_i+\varepsilon_i\}$$ cover the unit ball? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-012",
"literature-status:open",
"owr-year:2017"
] | The finite slab-translate covering question remains unresolved; Kupavskii and Pach prove a weaker infinite covering criterion and settle a related polynomial approximation problem. | [
{
"url": "https://arxiv.org/abs/1511.08111",
"label": "Kupavskii and Pach on plank covering"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | For $d>2$, does there exist a constant $C(d)$ such that, whenever $n_i\in S^{d-1}$ are unit directions and $\varepsilon_i>0$ satisfy $\sum_i\varepsilon_i>C(d)$, suitable translates of the slabs $$\{x\in\mathbb R^d:a_i\leq\langle x,n_i\rangle\leq a_i+\varepsilon_i\}$$ cover the unit ball? | For d>2, does there exist C(d) such that for any unit directions n_i in S^{d-1} and positive widths epsilon_i with sum epsilon_i>C(d), suitable translates of the slabs {x: a_i\leq<x,n_i>\leq a_i+epsilon_i} cover the unit ball in R^d? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,471 | OWR-15427-013 | Dihedral Angle Comparison for Combinatorially Equivalent Polytopes | Let $P_1,P_2\subset\mathbb R^3$ be combinatorially equivalent convex polytopes. Must there be corresponding edges $e_1\subset P_1$ and $e_2\subset P_2$ such that the dihedral angle at $e_1$ is no greater than the angle at $e_2$, unless all corresponding dihedral angles are equal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-013",
"literature-status:open",
"owr-year:2017"
] | The assertion is Conjecture 5.1 of Akopyan and Karasev; simplex cases and related angle inequalities are known, but no general proof or counterexample for combinatorially equivalent three-dimensional convex polytopes was found. | [
{
"url": "https://arxiv.org/abs/1505.05263",
"label": "Akopyan and Karasev on polytope angles"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $P_1,P_2\subset\mathbb R^3$ be combinatorially equivalent convex polytopes. Must there be corresponding edges $e_1\subset P_1$ and $e_2\subset P_2$ such that the dihedral angle at $e_1$ is no greater than the angle at $e_2$, unless all corresponding dihedral angles are equal? | If P_1 and P_2 are combinatorially equivalent convex polytopes in R^3, do there exist corresponding edges t_1 and t_2 such that the dihedral angle at t_1 is no greater than that at t_2, or all corresponding dihedral angles are equal? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,472 | OWR-15427-014 | Exponential Probability Gaps Between Random Order Types | For every probability measure $\mu$ on the plane that assigns measure zero to every line, do there exist order types $\omega_1(\mu)$ and $\omega_2(\mu)$ on $n$ points and an absolute constant $c>1$ such that a random independent $n$-point sample $X$ satisfies $$\Pr[X\text{ realizes }\omega_1(\mu)]>c^n\Pr[X\text{ realiz... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-014",
"literature-status:open",
"owr-year:2017"
] | The order-type literature proves a fixed-size bias with a ratio exceeding 1.8 for six points, but does not establish the requested exponential-in-n comparison for every measure and size. | [
{
"url": "https://arxiv.org/abs/1811.02236",
"label": "Goaoc and collaborators on limits of order types"
},
{
"url": "https://doi.org/10.4230/LIPIcs.SOCG.2015.300",
"label": "SoCG primary paper"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | For every probability measure $\mu$ on the plane that assigns measure zero to every line, do there exist order types $\omega_1(\mu)$ and $\omega_2(\mu)$ on $n$ points and an absolute constant $c>1$ such that a random independent $n$-point sample $X$ satisfies $$\Pr[X\text{ realizes }\omega_1(\mu)]>c^n\Pr[X\text{ realiz... | For every probability measure mu charging no lines, do there exist order types omega_1(mu) and omega_2(mu), both on n points, and a constant c>0 such that for a random n-point sample X, P[X realizes omega_1(mu)]>c^n P[X realizes omega_2(mu)]? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,473 | OWR-15427-015 | Lower Bounds for Convex Decompositions of Crossing Curves | Let $M(d)$ be the least integer such that every $(d+1)$-crossing curve in $\mathbb R^d$ can be decomposed into $M(d)$ convex curves. Establish nontrivial lower bounds for $M(d)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-015",
"literature-status:partially-solved",
"owr-year:2017"
] | The decomposition theorem gives M of d at most 4d, with M of 2 equal to 4 and M of 3 at most 22, but general lower bounds and sharp values remain unresolved. | [
{
"url": "https://arxiv.org/abs/1309.1147",
"label": "Bárány Matoušek and Pór on crossing curves"
},
{
"url": "https://doi.org/10.1007/s00208-015-1232-x",
"label": "related geometric Ramsey construction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $M(d)$ be the least integer such that every $(d+1)$-crossing curve in $\mathbb R^d$ can be decomposed into $M(d)$ convex curves. Establish nontrivial lower bounds for $M(d)$. | If M(d) is such that every (d+1)-crossing curve in R^d can be split into M(d) convex curves, give lower bounds for M(d). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,474 | OWR-15427-016 | Linear Crossing Families in Dense Point Sets | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$. Must $P$ contain a crossing family of size $\Omega(n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-016",
"literature-status:partially-solved",
"owr-year:2017"
] | The linear crossing-family conjecture for dense point sets is not settled; the bound has improved from n to the n to the one minus epsilon scale and general point sets now have an n to the one minus little o of one bound. | [
{
"url": "https://doi.org/10.1016/j.aim.2021.107779",
"label": "Pach Rubin and Tardos on crossing segments"
},
{
"url": "https://archive.dimacs.rutgers.edu/TechnicalReports/TechReports/1994/94-55.html",
"label": "Valtr on dense sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$. Must $P$ contain a crossing family of size $\Omega(n)$? | Let P be a set of n points in R^2 with minimum pairwise distance 1 and diameter O(sqrt(n)). Must P contain a crossing family of size Omega(n)? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,475 | OWR-15427-017 | Quadratically Many Essentially Different Lines in Dense Point Sets | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$. Must $P$ determine $\Omega(n^2)$ pairwise essentially different lines, where two lines are essentially different if their directions differ by at least $1/n$ or their $1/\sqrt n$-neighborhoods do not intersect ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-017",
"literature-status:partially-solved",
"owr-year:2017"
] | The three density conjectures remain open in their stated sharp forms, while n to the two minus epsilon line bounds and n to the one minus epsilon crossing bounds provide substantial partial progress. | [
{
"url": "https://doi.org/10.1016/j.aim.2021.107779",
"label": "Pach Rubin and Tardos on crossing segments"
},
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$. Must $P$ determine $\Omega(n^2)$ pairwise essentially different lines, where two lines are essentially different if their directions differ by at least $1/n$ or their $1/\sqrt n$-neighborhoods do not intersect ... | Let P be as above. Must P determine Omega(n^2) pairwise essentially different lines, where two lines are essentially different if their directions differ by at least 1/n or their 1/sqrt(n)-neighborhoods do not meet inside conv(P)? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,476 | OWR-15427-018 | Incidence Lower Bounds for Dense Points and Lines | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$, and let $L$ be a family of $n$ pairwise essentially different lines, where essential difference is measured by angular separation $1/n$ or disjoint $1/\sqrt n$-neighborhoods inside $\operatorname{conv}(P)$. Mus... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** open
**... | 3 | open | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15427-018",
"literature-status:open",
"owr-year:2017"
] | The nerve question is proved only for covers with four members in the cited source; no general proof or counterexample for arbitrary m was located. | [
{
"url": "https://doi.org/10.4171/owr/2017/19",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | Let $P\subset\mathbb R^2$ consist of $n$ points with minimum pairwise distance $1$ and diameter $O(\sqrt n)$, and let $L$ be a family of $n$ pairwise essentially different lines, where essential difference is measured by angular separation $1/n$ or disjoint $1/\sqrt n$-neighborhoods inside $\operatorname{conv}(P)$. Mus... | Let P be as above and let L be a set of n pairwise essentially different lines. Must the number of pairs (p,ell) in P times L with dist(p,ell)\leq1/sqrt(n) be at least Omega(n^{4/3})? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,477 | OWR-15427-019 | Collinear Grid Triples and Rigid Bipartite Unit Distance Graphs | What is the minimum possible number of collinear triples in a subset $S\subseteq\{1,\ldots,n\}^3$ of cardinality $|S|=n^{3-s}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205](https://doi.org/10.4171/owr/2017/19)
## Literature review (checked 2026-08-21)
**Status:** partiall... | 3 | partially_solved | null | 2,017 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 update, 2026-10-09] **Preprint:** *Log-Free Supersaturation of Collinear Triples in Three-Dimensional Grids*, Alper Ferudun (Mercury Software GmbH). | [
"owr",
"oberwolfach-reports",
"OWR-15427-019",
"literature-status:partially-solved",
"owr-year:2017"
] | The grid collinear-triple problem has matching-scale constructions up to logarithmic factors and an unresolved sharp lower-bound issue, while the separate rigid bipartite unit-distance question has affirmative rigid-framework constructions. | [
{
"url": "https://arxiv.org/abs/1704.05089",
"label": "Balogh and Solymosi on collinear triples"
},
{
"url": "https://arxiv.org/abs/2607.25742",
"label": "Roche-Newton on grid constructions"
},
{
"url": "https://arxiv.org/abs/1808.04005",
"label": "Kaszanitzky and collaborators on ri... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/19 | null | null | null | What is the minimum possible number of collinear triples in a subset $S\subseteq\{1,\ldots,n\}^3$ of cardinality $|S|=n^{3-s}$? | What is the minimum number of collinear triples in a subset S of the n\times n\times n integer grid when |S|=n^{3-s}? Find a rigid bipartite unit-distance graph. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Discrete Geometry (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/19, pp. 1135--1205 |
30,003,478 | OWR-15428-001 | Asymptotic Distribution of Maximum Agreement Subtrees | What is the asymptotic distribution of $\operatorname{MAST}(T_1,T_2)$ as $|X|\to\infty$ when $T_1$ and $T_2$ are random binary trees on the leaf set $X$, for distributions such as the uniform and Yule–Harding models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-001",
"literature-status:partially-solved",
"owr-year:2017"
] | For uniform and Yule--Harding random trees, polynomial expectation bounds and improved lower exponents are known, but the asymptotic distribution and tight order remain unresolved. | [
{
"url": "https://doi.org/10.1137/140997750",
"label": "Bernstein and collaborators on MAST bounds"
},
{
"url": "https://arxiv.org/abs/2006.10545",
"label": "Aldous on the largest common subtree"
},
{
"url": "https://arxiv.org/abs/2208.05148",
"label": "improved random-tree lower bou... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | What is the asymptotic distribution of $\operatorname{MAST}(T_1,T_2)$ as $|X|\to\infty$ when $T_1$ and $T_2$ are random binary trees on the leaf set $X$, for distributions such as the uniform and Yule–Harding models? | What is the asymptotic distribution of MAST(T_1,T_2) as |X| tends to infinity for common probability distributions on random binary X-trees, such as the uniform or Yule-Harding distributions? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,479 | OWR-15428-002 | Secant Varieties of Gaussian Moment Varieties | For all $k,n,d\geq1$, determine the dimensions, degrees, and defining equations of the secant varieties $\operatorname{Sec}_k(G_{n,d})$ of Gaussian moment varieties. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-002",
"literature-status:partially-solved",
"owr-year:2017"
] | Many Gaussian moment and secant varieties are computed in low-dimensional cases and identifiability is known in several regimes, but a uniform description for all k, n, and d is not available. | [
{
"url": "https://arxiv.org/abs/1510.04654",
"label": "Améndola Faugère Ranestad and Sturmfels"
},
{
"url": "https://doi.org/10.1007/s10208-020-09469-6",
"label": "homoscedastic Gaussian identifiability"
},
{
"url": "https://arxiv.org/abs/2312.12335",
"label": "nondefectivity of inva... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For all $k,n,d\geq1$, determine the dimensions, degrees, and defining equations of the secant varieties $\operatorname{Sec}_k(G_{n,d})$ of Gaussian moment varieties. | Study the secant varieties Sec_k(G_{n,d}) of Gaussian moment varieties for all k,n,d\geq1, including their dimensions, degrees, and defining equations. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,480 | OWR-15428-003 | Single Polynomial Description of Binary Tensor Gram Loci | For real binary tensors of fixed format, can the Gram locus be described semialgebraically by the nonnegativity of a single polynomial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 unrefereed claim, 2026-10-02] I have released an unrefereed preprint, **Seigal's Conjecture on Gram Determinants of Real Binary Tensors Fails for n ≥ 4** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23111048) | [
"owr",
"oberwolfach-reports",
"OWR-15428-003",
"literature-status:partially-solved",
"owr-year:2017"
] | The Gram locus is characterized for three binary factors and its convex hull is known in general, but the proposed single-polynomial description for n at least 4 remains conjectural. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6051437/",
"label": "Seigal on Gram determinants"
},
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For real binary tensors of fixed format, can the Gram locus be described semialgebraically by the nonnegativity of a single polynomial? | Conjecturally, the Gram locus of real binary tensors of fixed size has a general semialgebraic characterization expressed by the nonnegativity of a single polynomial. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,481 | OWR-15428-004 | Mode Counts of Gaussian Mixtures | For mixtures of $k$ Gaussian distributions in dimension $d$, determine the distribution and maximum possible number of modes. In fixed dimension, is the maximum for isotropic mixtures bounded linearly in $k$? Give verifiable conditions ensuring at most $k$ modes, and formulate a Gaussian analogue of strong modes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-004",
"literature-status:partially-solved",
"owr-year:2017"
] | Mode-count bounds and constructions have advanced, but the full distribution and sharp maximum remain open; the binomial maximum conjecture is demonstrably false already for three bivariate heteroscedastic components. | [
{
"url": "https://arxiv.org/abs/2608.01776",
"label": "Kabata Matsumoto and Okuno counterexample"
},
{
"url": "https://arxiv.org/abs/2605.15531",
"label": "Nguyen on mode-count bounds"
},
{
"url": "https://arxiv.org/abs/1702.05066",
"label": "Améndola Engström and Haase"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For mixtures of $k$ Gaussian distributions in dimension $d$, determine the distribution and maximum possible number of modes. In fixed dimension, is the maximum for isotropic mixtures bounded linearly in $k$? Give verifiable conditions ensuring at most $k$ modes, and formulate a Gaussian analogue of strong modes. | For mixtures of k Gaussians in dimension d, what is the distribution of the number of modes? Is the number of modes of isotropic mixtures in fixed dimension bounded linearly in k? Are there verifiable conditions guaranteeing at most k modes, and is there a Gaussian analogue of strong modes? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,482 | OWR-15428-005 | Stabilization of Hidden Alphabet Distribution Models | Let $C_d$ be nested classes of observable distributions, with $C_d\subseteq C_{d'}$ for $d\leq d'$, obtained by increasing a hidden alphabet. Does some finite $d$ satisfy $C_d=C_{d'}$ for every $d'\geq d$? Does stabilization hold under cyclic symmetry or full permutation symmetry of three observed variables without inc... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-005",
"literature-status:open",
"owr-year:2017"
] | The stabilization, closure, and symmetry questions for the nested hidden-alphabet model classes remain unresolved in the stated generality; the report presents them as open problems without a later general theorem. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | Let $C_d$ be nested classes of observable distributions, with $C_d\subseteq C_{d'}$ for $d\leq d'$, obtained by increasing a hidden alphabet. Does some finite $d$ satisfy $C_d=C_{d'}$ for every $d'\geq d$? Does stabilization hold under cyclic symmetry or full permutation symmetry of three observed variables without inc... | For the nested observable-distribution models C_d with C_d subset C_{d'}, does there exist a finite d such that C_d=C_{d'} for every d'\geq d? Does the question simplify for distributions invariant under cyclic or all permutations of three variables, in particular without increasing the hidden alphabet size? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,483 | OWR-15428-006 | Three-Component Tropical Approximation of Ultrametric Data | Given ultrametrics $d_i\in U_m$, choose $D^{(1)},D^{(2)},D^{(3)}\in U_m$ to minimize $$\sum_i d_{\mathrm{tr}}(d_i,d_i'),$$ where $d_i'$ is the tropical convex combination of the three $D^{(j)}$ with coefficients $\lambda_{ij}=\min(d_i-D^{(j)})$, and $$d_{\mathrm{tr}}(v,w)=\max_{k<\ell}|v_k-w_k-v_\ell+w_\ell|.$$ Charact... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The extracted optimization problem is reduced to a linear program in the report, but a general closed-form solution or complete structural analysis of its optimizers is not established. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | Given ultrametrics $d_i\in U_m$, choose $D^{(1)},D^{(2)},D^{(3)}\in U_m$ to minimize $$\sum_i d_{\mathrm{tr}}(d_i,d_i'),$$ where $d_i'$ is the tropical convex combination of the three $D^{(j)}$ with coefficients $\lambda_{ij}=\min(d_i-D^{(j)})$, and $$d_{\mathrm{tr}}(v,w)=\max_{k<\ell}|v_k-w_k-v_\ell+w_\ell|.$$ Charact... | Given data points d_i in the ultrametric space U_m, find D^{(1)},D^{(2)},D^{(3)} in U_m minimizing sum_i d_tr(d_i,d'_i), where d'_i is the tropical convex combination of the three D^{(j)} with coefficients lambda_{ij}=min(d_i-D^{(j)}), and d_tr(v,w)=max_{k<l}|v_k-w_k-v_l+w_l|. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,484 | OWR-15428-007 | Proper Intersections of Phylogenetic Network Varieties | For two distinct phylogenetic networks $N_1$ and $N_2$, let $V_N$ denote the Zariski closure of the model variety associated with $N$. Characterize when $V_{N_1}\cap V_{N_2}$ is a proper subvariety of both $V_{N_1}$ and $V_{N_2}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-007",
"literature-status:partially-solved",
"owr-year:2017"
] | Generic distinguishability is proved for important large-cycle and level-one network classes, but conditions for proper intersections of arbitrary network varieties are not fully characterized. | [
{
"url": "https://doi.org/10.1137/17M1134238",
"label": "Gross and Long on distinguishing networks"
},
{
"url": "https://arxiv.org/abs/2607.12919",
"label": "Brits and collaborators on full level-one identifiability"
},
{
"url": "https://doi.org/10.1016/j.jsc.2020.04.012",
"label": "... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For two distinct phylogenetic networks $N_1$ and $N_2$, let $V_N$ denote the Zariski closure of the model variety associated with $N$. Characterize when $V_{N_1}\cap V_{N_2}$ is a proper subvariety of both $V_{N_1}$ and $V_{N_2}$. | Given two distinct n-leaf networks N_1 and N_2, with V_N the Zariski closure of the model variety of N, determine conditions under which V_{N_1} \cap V_{N_2} is a proper subvariety of both V_{N_1} and V_{N_2}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,485 | OWR-15428-008 | Distinguishability of Cycle and Level-One Phylogenetic Networks | For fixed $n$, classify the pairs of $k$-cycle phylogenetic networks that are distinguishable under the CFN, K2P, and K3P group-based models, and extend the classification from $k$-cycle networks to level-one networks. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-008",
"literature-status:partially-solved",
"owr-year:2017"
] | Four-leaf CFN cases and generic K2P and K3P large-cycle identifiability are known, but the requested classification for every k-cycle pair and every listed model is not complete. | [
{
"url": "https://doi.org/10.1137/17M1134238",
"label": "Gross and Long on cycle networks"
},
{
"url": "https://doi.org/10.1016/j.jsc.2020.04.012",
"label": "Hollering and Sullivant on algebraic matroids"
},
{
"url": "https://arxiv.org/abs/2607.12919",
"label": "recent level-one iden... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For fixed $n$, classify the pairs of $k$-cycle phylogenetic networks that are distinguishable under the CFN, K2P, and K3P group-based models, and extend the classification from $k$-cycle networks to level-one networks. | For fixed n, determine which pairs of k-cycle networks are distinguishable under the CFN, K2P, and K3P group-based models, and extend the analysis from k-cycle networks to level-1 networks. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,486 | OWR-15428-010 | Defining Equations for Group-Based Phylogenetic Network Models | For each of the CFN, Jukes–Cantor, K2P, and K3P models and every phylogenetic network $N$, determine defining polynomials for the variety $V_N$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-010",
"literature-status:partially-solved",
"owr-year:2017"
] | Defining ideals are known for several small and structured network classes, including CFN level-one cases, but no general formula for the variety of an arbitrary network under all four models is known. | [
{
"url": "https://arxiv.org/abs/2312.07450",
"label": "Pfaffian structure for CFN networks"
},
{
"url": "https://doi.org/10.1137/17M1134238",
"label": "Gross and Long on network ideals"
},
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For each of the CFN, Jukes–Cantor, K2P, and K3P models and every phylogenetic network $N$, determine defining polynomials for the variety $V_N$. | For each of the CFN, Jukes--Cantor, K2P, and K3P models and each network N, determine the defining polynomials of the variety V_N. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,487 | OWR-15428-011 | Membership Testing in Likelihood Correspondences | Given the algebraic statistical model X, data u, and a candidate point p, determine whether z=(p,u) belongs to the likelihood correspondence L_X. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** open
... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents the trace test and witness-set construction as the method for deciding this membership question; the extraction) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-011",
"literature-status:open",
"owr-year:2017"
] | The general witness-set theorem gives a membership test for likelihood correspondences, but the extracted record supplies no numerical coordinates for p and u, so this particular yes-or-no membership claim is not decidable from the record. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s10208-026-09755-9",
"label": "recent likelihood correspondence theory"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | null | Given the algebraic statistical model X, data u, and a candidate point p, determine whether z=(p,u) belongs to the likelihood correspondence L_X. | unrecoverable | The official report presents the trace test and witness-set construction as the method for deciding this membership question; the extraction is an expository worked task rather than an unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,488 | OWR-15428-013 | Branch Length and Root Identifiability from Split Probabilities | For a species tree $\sigma$ under the multispecies coalescent model, are its branch lengths identifiable from split probabilities? Can an improved NJst algorithm estimate the root, and do higher-degree phylogenetic invariants exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15428-013",
"literature-status:partially-solved",
"owr-year:2017"
] | Topology identifiability from split probabilities is proved in the multispecies coalescent setting, but branch-length recovery is established only in restricted or local cases; the broader branch-length, root, and invariant questions in the record remain open. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC5766424/",
"label": "Split probabilities and species tree inference"
},
{
"url": "https://doi.org/10.1016/j.jtbi.2015.03.024",
"label": "Chor and ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | For a species tree $\sigma$ under the multispecies coalescent model, are its branch lengths identifiable from split probabilities? Can an improved NJst algorithm estimate the root, and do higher-degree phylogenetic invariants exist? | For a species tree \sigma under the multispecies coalescent model, determine whether branch lengths are identifiable from split probabilities, whether an improved NJst algorithm can estimate the root, and whether higher-degree invariants exist. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,489 | OWR-15428-014 | Degree of the Algebraic Boundary in Partial Tensor Completion | In the partial-tensor completion problem for joint distributions of independent random variables, determine the degree of the hypersurface forming the algebraic boundary of the completable set. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 unrefereed claim, 2026-09-30] I have released an unrefereed preprint, **Partial Results on the Degree of the Algebraic Boundary in Rank-One Tensor Completion** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23049796) | [
"owr",
"oberwolfach-reports",
"OWR-15428-014",
"literature-status:partially-solved",
"owr-year:2017"
] | The algebraic boundary and several diagonal or low-dimensional cases are known, but the general degree question and the universal convexity question remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://doi.org/10.1137/16M1074102",
"label": "Kahle et al., rank-one tensor completion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | In the partial-tensor completion problem for joint distributions of independent random variables, determine the degree of the hypersurface forming the algebraic boundary of the completable set. | In the partial-tensor completion problem for joint distributions of independent random variables, determine the degree of the algebraic-boundary hypersurface H and whether the set of nonnegative partial tensors that are not completable to such a distribution is always convex. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,490 | OWR-15428-015 | Convexity of Noncompletable Nonnegative Partial Tensors | Is the set of nonnegative partial tensors that cannot be completed to a joint distribution of independent random variables always convex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279](https://doi.org/10.4171/owr/2017/20)
## Literature review (checked 2026-08-21)
**Status:** parti... | 3 | partially_solved | null | 2,017 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 unrefereed claim, 2026-09-29] I have released an unrefereed preprint, **When Is the Set of Non-Completable Partial Probability Tensors Convex?** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23041938) | [
"owr",
"oberwolfach-reports",
"OWR-15428-015",
"literature-status:partially-solved",
"owr-year:2017"
] | The proposed convexity holds in computed examples and in the diagonal case, but no proof or counterexample is known for the general partial-tensor set described in the record. | [
{
"url": "https://doi.org/10.4171/owr/2017/20",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://doi.org/10.1137/16M1074102",
"label": "Kahle et al., rank-one tensor completion"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/20 | null | null | null | Is the set of nonnegative partial tensors that cannot be completed to a joint distribution of independent random variables always convex? | Is the set of nonnegative partial tensors that cannot be completed to a joint distribution of independent random variables always convex? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Algebraic Statistics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/20, pp. 1207--1279 |
30,003,491 | OWR-15429-002 | Higher Extensions Between Additive and Multiplicative Algebraic Groups | In the proposed analogue of the Milnor conjecture, describe $\operatorname{Ext}^2_{\mathcal C}(G_a,G_m)$ by generators and relations. Does $\operatorname{Ext}^i_{\mathcal C}(G_a,G_m)=0$ for all sufficiently large $i$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15429-002",
"literature-status:open",
"owr-year:2017"
] | The higher-Ext question for the full category of commutative algebraic groups remains open; later work establishes hereditary behavior only for related isogeny categories. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://doi.org/10.4171/DM/576",
"label": "Brion, isogeny categories"
},
{
"url": "https://arxiv.org/abs/1709.00175",
"label": "Brion, homological dimension"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | In the proposed analogue of the Milnor conjecture, describe $\operatorname{Ext}^2_{\mathcal C}(G_a,G_m)$ by generators and relations. Does $\operatorname{Ext}^i_{\mathcal C}(G_a,G_m)=0$ for all sufficiently large $i$? | Can Ext^2_C(G_a,G_m) be described by generators and relations in the proposed Milnor-conjecture analogue, and is Ext^i_C(G_a,G_m)=0 for all sufficiently large i? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,492 | OWR-15429-006 | Tamagawa Formula for Connected Linear Algebraic Groups | For every connected linear algebraic group $G$ over a global field $k$, is the Tamagawa-number identity $$\tau(G)=\frac{\#\operatorname{Ext}^1(G,G_m)}{\#X(G)}$$ valid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,017 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15429-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The Tamagawa formula is proved for connected commutative groups and for all pseudoreductive groups in characteristic greater than three, but the remaining small-characteristic exotic cases prevent a general solution. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://msp.org/ant/2021/15-8/ant-v15-n8-p01-p.pdf",
"label": "Rosengarten, Tamagawa numbers of pseudoreductive groups"
},
{
"url": "https://arxiv.org/abs/1907.06225",
"label": "Rosengart... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | For every connected linear algebraic group $G$ over a global field $k$, is the Tamagawa-number identity $$\tau(G)=\frac{\#\operatorname{Ext}^1(G,G_m)}{\#X(G)}$$ valid? | For every connected linear algebraic group G over a global field k, is the Tamagawa formula \tau(G)=\#Ext^1(G,G_m)/\#X(G) valid? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,493 | OWR-15429-008 | Cluster Duality and Classical Canonical Bases | What is the relationship between the canonical basis $B_{\mathrm{can}}$ constructed by cluster duality and the classical canonical basis $B$ of $\mathbb C[G/U]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15429-008",
"literature-status:open",
"owr-year:2017"
] | Later work relates potential functions to crystal and Lusztig parametrizations, including type-specific results, but it does not establish the exact equality or general relation between the two bases asked about here. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1711.07176",
"label": "Genz et al., canonical bases and cluster duality"
},
{
"url": "https://arxiv.org/abs/1611.03465",
"label": "Genz et al., type A canonical base... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | What is the relationship between the canonical basis $B_{\mathrm{can}}$ constructed by cluster duality and the classical canonical basis $B$ of $\mathbb C[G/U]$? | What is the relationship between the canonical basis B_{can} constructed by cluster duality and the classical canonical basis B of C[G/U]? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,494 | OWR-15429-009 | QQ Systems for Spectral Determinants and Integrable Models | What structural mechanism produces the QQ-tilde system for spectral determinants of affine opers, and is there an analogous system on the integrable-model side? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** partially... | 3 | partially_solved | null | 2,017 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15429-009",
"literature-status:partially-solved",
"owr-year:2017"
] | The q-Oper and QQ-System theory proves substantial special cases and links polynomial solutions to Bethe ansatz, but the broad explanatory and integrable-model question in the record remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
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{
"url": "https://arxiv.org/abs/2002.07344",
"label": "Frenkel et al., q-Opers and QQ-Systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | What structural mechanism produces the QQ-tilde system for spectral determinants of affine opers, and is there an analogous system on the integrable-model side? | What explains the QQ-tilde system for spectral determinants of affine opers, and does an analogous system hold on the integrable-model side? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,495 | OWR-15429-010 | Transfer Matrix Eigenvalue Polynomials for Quantum Affine Algebras | For the joint eigenvalues of transfer matrices acting on a common generalized eigenspace $W$ in a tensor product of finite-dimensional quantum-affine-algebra modules, characterize the Baxter polynomials $Q_{i,k}(z)$ that occur in the eigenvalue formulas. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
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"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15429-010",
"literature-status:open",
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] | Later papers construct many polynomial QQ-System solutions and Wronskian recurrences, but the extracted question does not define the family Q sub i comma k precisely and no general answer can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
"label": "Oberwolfach Reports 2018"
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{
"url": "https://arxiv.org/abs/2002.07344",
"label": "Frenkel et al., q-Opers and QQ-Systems"
},
{
"url": "https://arxiv.org/abs/2208.08018",
"label": "On Wronskians and QQ-Systems"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | For the joint eigenvalues of transfer matrices acting on a common generalized eigenspace $W$ in a tensor product of finite-dimensional quantum-affine-algebra modules, characterize the Baxter polynomials $Q_{i,k}(z)$ that occur in the eigenvalue formulas. | What are the polynomials Q_{i,k} appearing in the eigenvalue formulas for transfer matrices of quantum affine algebras? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,496 | OWR-15429-011 | Polynomial Identities and Symbolic Calculus for Noncommutative Algebras | For a noncommutative algebra $A$, particularly a matrix algebra, characterize its polynomial identities and construct the symbolic calculus determined by those identities. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347](https://doi.org/10.4171/owr/2017/21)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,017 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-15429-011",
"literature-status:open",
"owr-year:2017"
] | The extracted record is an underspecified fragment about a symbolic calculus for a noncommutative algebra, so it does not identify a definite claim whose truth has been settled. | [
{
"url": "https://doi.org/10.4171/owr/2017/21",
"label": "Oberwolfach Reports 2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/21 | null | null | null | For a noncommutative algebra $A$, particularly a matrix algebra, characterize its polynomial identities and construct the symbolic calculus determined by those identities. | Which polynomial identities are satisfied by a given noncommutative algebra, in particular a matrix algebra, and what symbolic calculus results from those identities? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Algebraic Groups (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/21, pp. 1281--1347 |
30,003,497 | OWR-15430-002 | Model-Theoretic Advantages of Logarithmic-Derivative Transforms | For an expansion of the real field by a real entire function $F$, what technical and model-theoretic advantages arise from studying
$$G(z)=\left(z\frac{F'(z)}{F(z)}\right)'$$
instead of $F$ itself? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | open | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-002",
"literature-status:open",
"owr-year:2017"
] | The question fragment refers to functions F and G without defining the relevant construction or claim, so no definite resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | For an expansion of the real field by a real entire function $F$, what technical and model-theoretic advantages arise from studying
$$G(z)=\left(z\frac{F'(z)}{F(z)}\right)'$$
instead of $F$ itself? | For expansions of the real field by a real entire function F, why is it technically and mathematically useful to study G=(zF'/F)' instead of F? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,498 | OWR-15430-003 | Definability of Canonical Products with Sparse Zero Sets | For $0<s<1$, does the real field define the canonical Weierstrass product with zero sequence $(n^s)$ on $(0,\infty)$? More generally, for $\alpha>1$, what definable sets arise in the expansion of the real field by the canonical product associated with the geometric sequence $a_n=\alpha^n$, beyond the definable set $\al... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | open | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-003",
"literature-status:open",
"owr-year:2017"
] | Canonical-product expansions have been analyzed for important parameter ranges, but the stated definability question for every parameter between zero and one and the requested expansion remain open. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1812.05547",
"label": "Miller and Speissegger, canonical products"
},
{
"url": "https://doi.org/10.4153/S0008439519000572",
"label": "Miller and Speissegger, publish... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | For $0<s<1$, does the real field define the canonical Weierstrass product with zero sequence $(n^s)$ on $(0,\infty)$? More generally, for $\alpha>1$, what definable sets arise in the expansion of the real field by the canonical product associated with the geometric sequence $a_n=\alpha^n$, beyond the definable set $\al... | For 0<s<1, does the real field define the canonical Weierstrass product with zero sequence (n^s) on (0,\infty)? More generally, for \alpha>1, what definable sets arise in the expansion of the real field by the canonical product associated with the geometric sequence a_n=\alpha^n, beyond the definable set \alpha^{\mathb... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,499 | OWR-15430-005 | Arc-Smooth and Whitney-Smooth Functions on Closed Sets | For functions defined on non-open subsets $X\subseteq\mathbb R^d$, when do the arc-generated smoothness classes $A^\infty(X)$ and $A^M(X)$ coincide with the corresponding Whitney-type classes $C^\infty(X)$ and $C^M(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | partially_solved | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-005",
"literature-status:partially-solved",
"owr-year:2017"
] | Results cover important non-open domains, including closed fat sets and subanalytic settings, but the question for arbitrary non-open subsets and the full ultradifferentiable framework remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1801.08335",
"label": "Rainer, arc-smooth functions on closed sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | For functions defined on non-open subsets $X\subseteq\mathbb R^d$, when do the arc-generated smoothness classes $A^\infty(X)$ and $A^M(X)$ coincide with the corresponding Whitney-type classes $C^\infty(X)$ and $C^M(X)$? | For functions defined on non-open subsets X\subseteq\mathbb R^d, when do the arc-generated smoothness classes A^\infty(X) and A^M(X) coincide with the corresponding Whitney-type classes C^\infty(X) and C^M(X)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,500 | OWR-15430-006 | Arc-Smoothness on Closed Fat Sets | For a closed fat set $X\subseteq\mathbb R^d$, when do $A^\infty(X)=C^\infty(X)$ and $A^M(X)=C^M(X)$ hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | partially_solved | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-006",
"literature-status:partially-solved",
"owr-year:2017"
] | The equivalence of the smooth and ultradifferentiable classes is proved under uniform cusp or cone hypotheses and in several subanalytic cases, while the general compact-set question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1801.08335",
"label": "Rainer, arc-smooth functions on closed sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | For a closed fat set $X\subseteq\mathbb R^d$, when do $A^\infty(X)=C^\infty(X)$ and $A^M(X)=C^M(X)$ hold? | For a closed fat set X\subseteq\mathbb R^d, when do A^\infty(X)=C^\infty(X) and A^M(X)=C^M(X) hold? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,501 | OWR-15430-007 | Sobolev Sheaves on Subanalytic Sites | Does there exist a Sobolev sheaf complex $H^s$ on the subanalytic Grothendieck topology of a manifold $M$ such that, on every relatively compact Lipschitz open set $U$, $H^s(U)$ is concentrated in degree zero and equals the Sobolev space $H^s(U)$, particularly for $s\geq1/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | partially_solved | null | 2,017 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-007",
"literature-status:partially-solved",
"owr-year:2017"
] | Sobolev-sheaf constructions and positive-regularity results are available in dimension two and related settings, but existence for all regularities at least one half remains open in general. | [
{
"url": "https://doi.org/10.24033/ast.1006",
"label": "Lebeau, Sobolev spaces and Sobolev sheaves"
},
{
"url": "https://arxiv.org/abs/2308.08077",
"label": "Oudrane, Sobolev sheaves on the plane"
},
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | Does there exist a Sobolev sheaf complex $H^s$ on the subanalytic Grothendieck topology of a manifold $M$ such that, on every relatively compact Lipschitz open set $U$, $H^s(U)$ is concentrated in degree zero and equals the Sobolev space $H^s(U)$, particularly for $s\geq1/2$? | Does there exist a Sobolev sheaf complex H^s on the subanalytic Grothendieck topology of a manifold M such that, on every relatively compact Lipschitz open set U, H^s(U) is concentrated in degree zero and equals the Sobolev space H^s(U), particularly for s\geq 1/2? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,502 | OWR-15430-009 | Optimal Complexity of Definable Cylindrical Decompositions | Can the quantitative bounds for semi-cylindrical or cylindrical decompositions of definable, even semialgebraic, sets be improved to optimal bounds in higher dimensions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | open | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-009",
"literature-status:open",
"owr-year:2017"
] | The report explicitly identifies the nonoptimal higher-dimensional quantitative bounds as a major open problem, and no later general optimal bound was located. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | Can the quantitative bounds for semi-cylindrical or cylindrical decompositions of definable, even semialgebraic, sets be improved to optimal bounds in higher dimensions? | Can the quantitative bounds for semi-cylindrical or cylindrical decompositions of definable, even semialgebraic, sets be improved to optimal bounds in higher dimensions? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,503 | OWR-15430-010 | Trajectory Geometry Near Analytic Vector-Field Singularities | Let $X$ be a real analytic vector field with a singular point at $0\in\mathbb R^n$. What qualitative dynamics near $0$ can be described from geometric properties of trajectories converging to $0$, including their finiteness properties with respect to analytic sets and their behavior relative to neighboring trajectories... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | partially_solved | null | 2,017 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-010",
"literature-status:partially-solved",
"owr-year:2017"
] | Special cases such as interlaced three-dimensional analytic vector fields and several asymptotic classes are understood, but the general qualitative dynamics and finiteness questions around the singularity remain open. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1310.2225",
"label": "Le Gal et al., interlaced analytic vector fields"
},
{
"url": "https://arxiv.org/abs/2311.06821",
"label": "Le Gal and Sanz, trajectories near ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | Let $X$ be a real analytic vector field with a singular point at $0\in\mathbb R^n$. What qualitative dynamics near $0$ can be described from geometric properties of trajectories converging to $0$, including their finiteness properties with respect to analytic sets and their behavior relative to neighboring trajectories... | Let X be a real analytic vector field with a singular point at 0\in\mathbb R^n. What qualitative dynamics near 0 can be described from geometric properties of trajectories converging to 0, including their finiteness properties with respect to analytic sets and their behavior relative to neighboring trajectories? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,504 | OWR-15430-011 | Monotone Cylindrical Decompositions of Compact Sets | For a compact set $K\subset\mathbb R^n$ and a function $f:K\to\mathbb R$, does there exist a partition of $K$ into monotone cylindrical cells, possibly using different coordinate orders, such that $f$ restricted to every cell is monotone? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | open | null | 2,017 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-011",
"literature-status:open",
"owr-year:2017"
] | The monotone-cell partition conjecture is proved for compact sets of dimension at most two, but the arbitrary-dimensional statement, including the three-dimensional case highlighted in the report, remains open. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "Oberwolfach Reports 2018"
},
{
"url": "https://arxiv.org/abs/1402.0460",
"label": "Basu et al., triangulations of monotone families"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | For a compact set $K\subset\mathbb R^n$ and a function $f:K\to\mathbb R$, does there exist a partition of $K$ into monotone cylindrical cells, possibly using different coordinate orders, such that $f$ restricted to every cell is monotone? | For a compact set K\subset\mathbb R^n and a function f:K\to\mathbb R, does there exist a partition of K into monotone cylindrical cells, possibly using different coordinate orders, such that f restricted to every cell is monotone? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,505 | OWR-15430-014 | Finiteness of Optimal Points in Shimura Subvarieties | Let $S$ be a Shimura variety and $V\subseteq S$ a subvariety. Call a subvariety $W\subseteq V$ optimal in $V$ if every subvariety $Y$ with $W\subsetneq Y\subseteq V$ has larger defect $\delta(Y)=\dim\langle Y\rangle-\dim Y$, where $\langle Y\rangle$ is the smallest special subvariety containing $Y$. Does $V$ contain on... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420](https://doi.org/10.4171/owr/2017/22)
## Literature rev... | 3 | open | null | 2,017 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15430-014",
"literature-status:open",
"owr-year:2017"
] | The general finiteness statement for optimal points is the point-counting form of Zilber-Pink and remains unproved; published work gives reductions and conditional or special-case results, not an unconditional theorem for arbitrary Shimura subvarieties. | [
{
"url": "https://doi.org/10.4171/owr/2017/22",
"label": "original OWR report"
},
{
"url": "https://www.cambridge.org/core/journals/compositio-mathematica/article/abs/applications-of-the-hyperbolic-ax-schanuel-conjecture/8EE3CB331B39E5E9D9D4A002D3727A5F44",
"label": "Daw and Ren, Applications of... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/22 | null | null | null | Let $S$ be a Shimura variety and $V\subseteq S$ a subvariety. Call a subvariety $W\subseteq V$ optimal in $V$ if every subvariety $Y$ with $W\subsetneq Y\subseteq V$ has larger defect $\delta(Y)=\dim\langle Y\rangle-\dim Y$, where $\langle Y\rangle$ is the smallest special subvariety containing $Y$. Does $V$ contain on... | Conjecture 2: For a subvariety V of S, V contains only finitely many points that are optimal in V. | corrected_verified | The official report was checked. The reconstruction identifies the Shimura-variety setting and restores the source definition of optimality and defect. | null | null | null | null | null | O-Minimality and its Applications to Number Theory and Analysis (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/22, pp. 1349--1420 |
30,003,506 | OWR-15431-001 | Stochastic Regularization of Two-Dimensional Euler Flows | For the two-dimensional incompressible Euler equations on the torus, can transport-type stochastic noise restore uniqueness, prevent singular behavior, or otherwise improve well-posedness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/23, pp. 1421--1462](https://doi.org/10.4171/owr/2017/23)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,017 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15431-001",
"literature-status:partially-solved",
"owr-year:2017"
] | Transport and Kraichnan noise yield rigorous existence, uniqueness, and stronger regularity in several vorticity classes, but a general regularization theorem for two-dimensional Euler remains unresolved. | [
{
"url": "https://doi.org/10.1007/s00205-015-0957-8",
"label": "Brzezniak, Flandoli, and Maurelli"
},
{
"url": "https://doi.org/10.1088/1361-6544/ae621b",
"label": "Coghi and Maurelli, Kraichnan noise"
},
{
"url": "https://doi.org/10.4171/owr/2017/23",
"label": "original OWR report"
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/23 | null | null | null | For the two-dimensional incompressible Euler equations on the torus, can transport-type stochastic noise restore uniqueness, prevent singular behavior, or otherwise improve well-posedness? | For the two-dimensional incompressible Euler equations on the torus, can suitable transport-type stochastic noise improve well-posedness by restoring uniqueness or preventing singularities? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geophysical Fluid Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/23, pp. 1421--1462 |
30,003,507 | OWR-15431-002 | Well-Posedness Beyond Known Noisy Euler Regimes | For the stochastic two-dimensional Euler vorticity equation on the torus, can existence be extended below the treated $L^p$ classes, uniqueness from $L^\infty$ to finite $L^p$, and noncollapse of the stochastic flow be proved? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geophysical Fluid Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/23, pp. 1421--1462](https://doi.org/10.4171/owr/2017/23)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,017 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15431-002",
"literature-status:open",
"owr-year:2017"
] | The extracted question is an unspecified request for results beyond the report's partial stochastic Euler theorems; it states no precise claim that has been settled. | [
{
"url": "https://doi.org/10.4171/owr/2017/23",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/23 | null | null | null | For the stochastic two-dimensional Euler vorticity equation on the torus, can existence be extended below the treated $L^p$ classes, uniqueness from $L^\infty$ to finite $L^p$, and noncollapse of the stochastic flow be proved? | For the noisy 2D Euler vorticity equation on the torus, can one prove further existence, uniqueness, non-collapse, or regularization results beyond the known L^p existence and L^\infty uniqueness? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Geophysical Fluid Dynamics (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/23, pp. 1421--1462 |
30,003,508 | OWR-15432-001 | Convergence of Spectral Estimators for Diffusion Tensors | Let $(\nu_k,u_k)$ be noisy observations of eigenpairs and let $\mu$ be an invariant density satisfying $$\operatorname{div}(S\nabla u_k)=\nu_k\mu u_k$$ with Neumann boundary conditions. Prove convergence of the spectral reconstruction estimator obtained by fitting these equations to recover the matrix-valued coefficien... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Inverse Problems for Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/24, pp. 1463--1549](https://doi.org/10.4171/owr/2017/24)
## Literature r... | 3 | open | null | 2,017 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15432-001",
"literature-status:open",
"owr-year:2017"
] | The report explicitly poses convergence analysis for its spectral estimator of a matrix-valued diffusion coefficient from noisy eigenpairs as open; later convergence results found concern different inverse-problem observation models. | [
{
"url": "https://doi.org/10.4171/owr/2017/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/24 | null | null | null | Let $(\nu_k,u_k)$ be noisy observations of eigenpairs and let $\mu$ be an invariant density satisfying $$\operatorname{div}(S\nabla u_k)=\nu_k\mu u_k$$ with Neumann boundary conditions. Prove convergence of the spectral reconstruction estimator obtained by fitting these equations to recover the matrix-valued coefficien... | Given noisy observations of eigenpairs (\nu_k,u_k) and an invariant density \mu satisfying \operatorname{div}(S\nabla u_k)=\nu_k\mu u_k with Neumann boundary conditions, can convergence of the proposed estimator of the matrix-valued coefficient S be proved? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Computational Inverse Problems for Partial Differential Equations (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/24, pp. 1463--1549 |
30,003,509 | OWR-15433-004 | Property (TWN+) for Reductive Groups | Does every reductive group $G$ over a number field satisfy property (TWN+)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-004",
"literature-status:partially-solved",
"owr-year:2017"
] | The all-reductive-groups property TWN+ conjecture remains unproved; it is established for GLn and inner forms, quasi-split classical and similitude groups, G2, and groups related by derived isogeny. | [
{
"url": "https://arxiv.org/abs/1603.05475",
"label": "Finis and Lapid, analytic properties of intertwining operators"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1017/fms.2024.59",
"label": "current Eisenstein-ser... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | Does every reductive group $G$ over a number field satisfy property (TWN+)? | Conjecture: Every reductive group G over a number field satisfies property (TWN+). | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,510 | OWR-15433-005 | Bounded-Degree Property for Reductive Groups | Does every reductive group $G$ over a number field satisfy property (BD) for $S=S_{\mathrm{fin}}$, the set of all non-Archimedean places? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-005",
"literature-status:partially-solved",
"owr-year:2017"
] | The universal property BD statement for all reductive groups with the full finite-place set remains open; it holds for GLn and SLn and several classical cases, and outside a finite exceptional set of places for every reductive group. | [
{
"url": "https://doi.org/10.1007/s11856-019-1843-0",
"label": "Finis and Lapid, local degree bounds"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1017/fms.2024.59",
"label": "current Eisenstein-series bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | Does every reductive group $G$ over a number field satisfy property (BD) for $S=S_{\mathrm{fin}}$, the set of all non-Archimedean places? | Conjecture: Every reductive group G over a number field satisfies property (BD) for S=S_{\mathrm{fin}}, the set of all non-archimedean valuations. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,511 | OWR-15433-007 | Stable Prasad Multiplicity Conjecture | In the $p$-adic Galois-pair setting, let $\phi$ be a discrete $L$-parameter with stable representation $\Pi_\phi$. Is the multiplicity given by $$m(\Pi_\phi,\chi)=|\ker^1(F;H,G)|^{-1}\sum_\psi\frac{|Z(\phi)|}{|Z(\psi)|},$$ where the sum ranges over compatible lifts $\psi$ through $H^\vee_\chi\to{}^LG$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15433-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-007",
"literature-status:partially-solved",
"owr-year:2017"
] | Beuzart-Plessis proved important transfer-invariance and Steinberg consequences, and the stable-discrete multiplicity formula is known in selected families such as GLn, U(n), and GSp4, but the general conjecture remains unproved. | [
{
"url": "https://arxiv.org/abs/1707.06495",
"label": "Beuzart-Plessis, distinction for Galois pairs"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | In the $p$-adic Galois-pair setting, let $\phi$ be a discrete $L$-parameter with stable representation $\Pi_\phi$. Is the multiplicity given by $$m(\Pi_\phi,\chi)=|\ker^1(F;H,G)|^{-1}\sum_\psi\frac{|Z(\phi)|}{|Z(\psi)|},$$ where the sum ranges over compatible lifts $\psi$ through $H^\vee_\chi\to{}^LG$? | Stable Prasad conjecture: for the p-adic Galois-pair setting and a discrete L-parameter \phi with stable representation \Pi_\phi, the multiplicity m(\Pi_\phi,\chi) equals |\ker^1(F;H,G)|^{-1}\sum_{\psi}|Z(\phi)|/|Z(\psi)|, where the sum runs over the compatible lifts \psi through H^\vee_\chi\to{}^LG. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,512 | OWR-15433-008 | Stable Prasad Multiplicity Conjecture | Stable Prasad conjecture: in the p-adic Galois-pair setting, for a discrete L-parameter \phi and its stable representation \Pi_\phi, the multiplicity is the weighted sum over compatible L-parameter lifts \psi, namely m(\Pi_\phi,\chi)=|\ker^1(F;H,G)|^{-1}\sum_{\psi}|Z(\phi)|/|Z(\psi)|. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | 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"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this record is a second extraction of the stable Prasad multiplicity conjecture retained as OWR-15433-007. No) | [
"OWR-15433-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-008",
"literature-status:partially-solved",
"owr-year:2017"
] | The geometric Arthur-packet identity is proved in important special cases including GLn and split odd special orthogonal groups and has been computed in examples, but no theorem establishes the universal statement for all pure forms and reductive groups. | [
{
"url": "https://arxiv.org/abs/1705.01885",
"label": "Cunningham et al., geometric packets"
},
{
"url": "https://arxiv.org/abs/2302.10300",
"label": "Cunningham and Ray, GLn case"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | null | Stable Prasad conjecture: in the p-adic Galois-pair setting, for a discrete L-parameter \phi and its stable representation \Pi_\phi, the multiplicity is the weighted sum over compatible L-parameter lifts \psi, namely m(\Pi_\phi,\chi)=|\ker^1(F;H,G)|^{-1}\sum_{\psi}|Z(\phi)|/|Z(\psi)|. | unrecoverable | The official report shows that this record is a second extraction of the stable Prasad multiplicity conjecture retained as OWR-15433-007. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,513 | OWR-15433-009 | Geometric Description of Pure Local Arthur Packets | For every Arthur parameter $\psi$ of $G$, is the pure local Arthur packet $$\Pi^{\mathrm{pure},\psi}(G/F)=\{[\pi,\delta]\in\Pi^{\mathrm{pure}}(G/F):\operatorname{Ev}^0_\psi(P(\pi,\delta))\neq0\},$$ with pairing $$\langle a,[\pi,\delta]\rangle_\psi=\operatorname{Trace}\!\left(\operatorname{Ev}^0_\psi(P(\pi,\delta))(a)\r... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15433-010"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-009",
"literature-status:partially-solved",
"owr-year:2017"
] | The geometric Arthur-packet identity is proved in important special cases including GLn and split odd special orthogonal groups and has been computed in examples, but no theorem establishes the universal statement for all pure forms and reductive groups. | [
{
"url": "https://arxiv.org/abs/1705.01885",
"label": "Cunningham et al., geometric packets"
},
{
"url": "https://arxiv.org/abs/2302.10300",
"label": "Cunningham and Ray, GLn case"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | For every Arthur parameter $\psi$ of $G$, is the pure local Arthur packet $$\Pi^{\mathrm{pure},\psi}(G/F)=\{[\pi,\delta]\in\Pi^{\mathrm{pure}}(G/F):\operatorname{Ev}^0_\psi(P(\pi,\delta))\neq0\},$$ with pairing $$\langle a,[\pi,\delta]\rangle_\psi=\operatorname{Trace}\!\left(\operatorname{Ev}^0_\psi(P(\pi,\delta))(a)\r... | For every Arthur parameter \psi of G, the pure local Arthur packet is \Pi^{\mathrm{pure},\psi}(G/F)=\{[\pi,\delta]\in\Pi^{\mathrm{pure}}(G/F):\operatorname{Ev}^0_\psi(P(\pi,\delta))\ne0\}; moreover, \langle a,[\pi,\delta]\rangle_\psi=\operatorname{Trace}(\operatorname{Ev}^0_\psi(P(\pi,\delta))(a)) for a\in A_\psi. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,514 | OWR-15433-010 | Geometric Description of Pure Local Arthur Packets | For every Arthur parameter \psi of G, the pure local Arthur packet is \Pi^{\mathrm{pure},\psi}(G/F)=\{[\pi,\delta]\in\Pi^{\mathrm{pure}}(G/F):\operatorname{Ev}^0_\psi(P(\pi,\delta))\ne0\}; moreover, \langle a,[\pi,\delta]\rangle_\psi=\operatorname{Trace}(\operatorname{Ev}^0_\psi(P(\pi,\delta))(a)) for a\in A_\psi. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | 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"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report shows that this record duplicates the pure local Arthur-packet conjecture retained as OWR-15433-009. No separate clean s) | [
"OWR-15433-009"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-010",
"literature-status:partially-solved",
"owr-year:2017"
] | The geometric Arthur-packet identity is proved in important special cases including GLn and split odd special orthogonal groups and has been computed in examples, but no theorem establishes the universal statement for all pure forms and reductive groups. | [
{
"url": "https://arxiv.org/abs/1705.01885",
"label": "Cunningham et al., geometric packets"
},
{
"url": "https://arxiv.org/abs/2302.10300",
"label": "Cunningham and Ray, GLn case"
},
{
"url": "https://doi.org/10.4171/owr/2017/25",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | null | For every Arthur parameter \psi of G, the pure local Arthur packet is \Pi^{\mathrm{pure},\psi}(G/F)=\{[\pi,\delta]\in\Pi^{\mathrm{pure}}(G/F):\operatorname{Ev}^0_\psi(P(\pi,\delta))\ne0\}; moreover, \langle a,[\pi,\delta]\rangle_\psi=\operatorname{Trace}(\operatorname{Ev}^0_\psi(P(\pi,\delta))(a)) for a\in A_\psi. | unrecoverable | The official report shows that this record duplicates the pure local Arthur-packet conjecture retained as OWR-15433-009. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
30,003,515 | OWR-15433-011 | Epsilon Dichotomy for Generic General Linear Representations | Let $\pi$ be a generic representation of $\operatorname{GL}_6(F)$ with central character $\chi^2$. Is $$m(\pi)=1\iff\epsilon\!\left(\frac12,(\wedge^3\pi)\otimes\chi^{-1}\right)=1,$$ and equivalently $m(\pi)=0$ precisely when this epsilon factor is $-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630](https://doi.org/10.4171/owr/2017/25)
## Literature review (checked 2026-08-21)... | 3 | partially_solved | null | 2,017 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15433-011",
"literature-status:partially-solved",
"owr-year:2017"
] | The epsilon-dichotomy identity is proved for archimedean cases and broad p-adic tempered or non-discrete classes, but exceptional p-adic discrete-series and the full generic case remain unresolved. | [
{
"url": "https://sites.rutgers.edu/chen-wan/wp-content/uploads/sites/518/2020/08/GRgeneric.pdf",
"label": "Wan, local Ginzburg--Rallis model"
},
{
"url": "https://hal.science/hal-01941350v1/document",
"label": "local trace formula for the generalized Shalika model"
},
{
"url": "https://... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2017/25 | null | null | null | Let $\pi$ be a generic representation of $\operatorname{GL}_6(F)$ with central character $\chi^2$. Is $$m(\pi)=1\iff\epsilon\!\left(\frac12,(\wedge^3\pi)\otimes\chi^{-1}\right)=1,$$ and equivalently $m(\pi)=0$ precisely when this epsilon factor is $-1$? | Epsilon-dichotomy conjecture: for a generic representation \pi of GL_6(F) with central character \chi^2, m(\pi)=1 if and only if \epsilon(1/2,(\wedge^3\pi)\otimes\chi^{-1})=1, while m(\pi)=0 if and only if that epsilon factor equals -1. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Harmonic Analysis and the Trace Formula (2018), Oberwolfach Reports, DOI 10.4171/owr/2017/25, pp. 1551--1630 |
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