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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,316 | OWR-14299289-007 | The Numerical Unramified Plancherel Conjecture | Let $G$ be a split connected reductive group over a nonarchimedean local field and let $X$ be a spherical $G$-variety with hyperspherical cotangent bundle. Is the unramified spherical Hecke module $C_c^\infty(X(F))^{G(\mathcal O)}$, with its $L^2$ inner product and basic vector, isometrically identified with functions ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | partially_solved | null | 2,025 | 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-14299289-007",
"literature-status:partially-solved",
"owr-year:2025"
] | The numerical unramified Plancherel statement is a conjecture in the general hyperspherical setting, while the report gives matching computations in several examples and Sakellaridis proves classical spherical cases. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/0905.4244",
"label": "Sakellaridis, Spherical functions on spherical varieties"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi,... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Let $G$ be a split connected reductive group over a nonarchimedean local field and let $X$ be a spherical $G$-variety with hyperspherical cotangent bundle. Is the unramified spherical Hecke module $C_c^\infty(X(F))^{G(\mathcal O)}$, with its $L^2$ inner product and basic vector, isometrically identified with functions ... | 2. Numerical unramified Plancherel conjecture Let G be a split connected reductive group over F , with dual group G∨ defined over k = Qℓ ≃ C, ℓ 6= p, and X a spherical G-variety satisfying that its cotangent bundle T ∗ X is hyperspherical. We make some normalization: • The G(F )-eigenmeasure on X(F ) satisfies that |X(... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,317 | OWR-14299289-008 | The Local Geometric Langlands Conjecture | For a Hamiltonian $G$-space $M$, can one construct a dual Hamiltonian $G^\vee$-space $M^\vee$ so that local geometric Langlands duality matches the boundary conditions associated with $M$ and $M^\vee$? In the unramified cotangent case $M=T^*X$, can this be realized by an equivalence involving $G(\mathcal D)$-equivarian... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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-14299289-008",
"literature-status:open",
"owr-year:2025"
] | The local geometric conjecture is presented with technical foundations not yet available in the extracted report; later work proves special rank-one or group cases, not the stated general equivalence. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi, Sakellaridis, and Venkatesh, Relative Langlands Duality"
},
{
"url": "https://sanathdevalapurkar.github.io/files/PGL2-... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | For a Hamiltonian $G$-space $M$, can one construct a dual Hamiltonian $G^\vee$-space $M^\vee$ so that local geometric Langlands duality matches the boundary conditions associated with $M$ and $M^\vee$? In the unramified cotangent case $M=T^*X$, can this be realized by an equivalence involving $G(\mathcal D)$-equivarian... | 2.2. The Local Geometric Conjecture. Now, the philosophy of ‘relative Lang- lands duality’ states that, to many Hamiltonian G-spaces M , one can construct boundary conditions associated to M in both AG and BG and, moreover, there should exist some Hamiltonian G∨ -space M ∨ such that the equivalence AG ≃ BG∨ should matc... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,318 | OWR-14299289-009 | Local Geometric Langlands for Hyperspherical Varieties | For a hyperspherical $G$-variety $X$, is the category of $G(\mathcal D)$-equivariant sheaves on $X(\mathring{\mathcal D})$ equivalent to the relative tensor product of the corresponding automorphic and spherical sheaf categories? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-009",
"literature-status:open",
"owr-year:2025"
] | The record contains only the label Conjecture 7.5.1, whose surrounding source identifies the local geometric Langlands equivalence; no general proof of that conjecture was located. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi, Sakellaridis, and Venkatesh, Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | For a hyperspherical $G$-variety $X$, is the category of $G(\mathcal D)$-equivariant sheaves on $X(\mathring{\mathcal D})$ equivalent to the relative tensor product of the corresponding automorphic and spherical sheaf categories? | Conjecture 7.5.1]: hAG (D), AG99KM (D)i ≃ Shv(G(D)\G(D̊))⊗Shv(G(D̊)) Shv(X(D̊)) ≃ ShvG(D)) (X(D̊)). | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,319 | OWR-14299289-010 | Dual Hamiltonian Geometry of Equivariant Sheaf Categories | For a hyperspherical pair with dual Hamiltonian space $M^\vee$, is there an equivalence $\operatorname{Shv}_{G(\mathcal D)}(X(\mathring{\mathcal D}))\simeq\operatorname{QCoh}(M^\vee)^{G^\vee}$ that is linear over the spherical Hecke category? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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-14299289-011"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-010",
"literature-status:open",
"owr-year:2025"
] | The extracted equivalence of equivariant sheaves with coherent sheaves on the dual Hamiltonian space is the stated general local conjecture; only special cases are known, so it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi, Sakellaridis, and Venkatesh, Relative Langlands Duality"
},
{
"url": "https://sanathdevalpurkar.github.io/files/PGL2-c... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | For a hyperspherical pair with dual Hamiltonian space $M^\vee$, is there an equivalence $\operatorname{Shv}_{G(\mathcal D)}(X(\mathring{\mathcal D}))\simeq\operatorname{QCoh}(M^\vee)^{G^\vee}$ that is linear over the spherical Hecke category? | Conjecture: There is an equivalence of categories ShvG(D)) (X(D̊)) ≃ ∨ ∨ QCoh(M ∨ )G ,ր that is equivariant with respect to the HG \sim = QCoh(ǧ∗ )G ,ր - module structure also subject to some conditions discussed in [3, Conjecture 7.5.1]. Remark: Recall that we have defined a vector space VX and a dual group G∨ G∨ ∨ ∨... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,320 | OWR-14299289-011 | Duplicate Local Geometric Duality Formulation | so this naturally gives an equivalent formulation of the above conjecture. Conjecture: There is an equivalence of categories ShvG(D)) (X(D̊)) ≃ ∨ ∨ QCoh(M ∨ )G ,ր that is equivariant with respect to the HG \sim = QCoh(ǧ∗ )G ,ր - module structure also subject to some conditions discussed in [3, Conjecture 7.5.1]. Remar... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the local geometric-duality equivalence represented canonically by OWR-14299289-01) | [
"OWR-14299289-010"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-011",
"literature-status:open",
"owr-year:2025"
] | This is an extracted restatement of the preceding local geometric conjecture rather than an independent theorem; the general categorical equivalence remains unproved, with only special cases established. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "Oberwolfach report"
},
{
"url": "https://www.math.ias.edu/~akshay/research/BZSVpaperV1.pdf",
"label": "Ben-Zvi, Sakellaridis, and Venkatesh, Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | so this naturally gives an equivalent formulation of the above conjecture. Conjecture: There is an equivalence of categories ShvG(D)) (X(D̊)) ≃ ∨ ∨ QCoh(M ∨ )G ,ր that is equivariant with respect to the HG \sim = QCoh(ǧ∗ )G ,ր - module structure also subject to some conditions discussed in [3, Conjecture 7.5.1]. Remar... | unrecoverable | The official report confirms that this extraction repeats the local geometric-duality equivalence represented canonically by OWR-14299289-010 and then begins its explanatory remark. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,321 | OWR-14299289-012 | Derived Geometric Satake for the Basic Object | Under derived geometric Satake, is the basic object $\delta_X$ sent to the sheared structure sheaf $\mathcal O(M^\vee)$, so that the endomorphism algebra of $\delta_X$ identifies with the sheared invariant function algebra $\mathcal O(M^\vee)^{G^\vee}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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-14299289-012",
"literature-status:open",
"owr-year:2025"
] | The extracted statement is the derived geometric Satake conjecture for the basic object. The BZSV paper and the 2025 report present it as a conjecture and give examples, but no general proof is reported. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Under derived geometric Satake, is the basic object $\delta_X$ sent to the sheared structure sheaf $\mathcal O(M^\vee)$, so that the endomorphism algebra of $\delta_X$ identifies with the sheared invariant function algebra $\mathcal O(M^\vee)^{G^\vee}$? | conjecture. Taking endomorphisms, we see that ∨ EndQCoh(M ∨ )G∨ (O(M ∨ )) = O(M ∨ )G should match with EndShvGO (XF ) (\deltaX ) = EndShvGO (XO ) (\omegaX ) = ‘equivariant Borel-Moore homology of XO ′ after shearing, which in practice means ‘treating cohomological degree like it’s a grading.’ Let’s check this explicitl... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,322 | OWR-14299289-013 | Removing Dual-Group Invariants from Plancherel Geometry | Does local geometric duality admit an equivariant upgrade that removes the $G^\vee$-invariance from the Borel–Moore-homology description and recovers the full function algebra $\mathcal O(M^\vee)$ as an algebra object over $\operatorname{QCoh}(\mathfrak g^{\vee *})^{G^\vee}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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-14299289-013",
"literature-status:open",
"owr-year:2025"
] | The proposed upgrade removing dual-group invariants is the Plancherel-algebra conjecture. The primary paper and the 2025 report still formulate it conjecturally, with no general resolution located. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Does local geometric duality admit an equivariant upgrade that removes the $G^\vee$-invariance from the Borel–Moore-homology description and recovers the full function algebra $\mathcal O(M^\vee)$ as an algebra object over $\operatorname{QCoh}(\mathfrak g^{\vee *})^{G^\vee}$? | Remark: In fact, there is an expected upgrade to the above Borel-Moore iso- morphism given in [3, Conjecture 8.1.8] which, informally speaking, removes the G∨ -invariance of the functions on O(M ∨ ). To state it precisely, recall to any affine µ Hamiltonian G∨ -space M ∨ , the moment map M ∨ − \to ǧ∗ gives rise to adj... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,323 | OWR-14299289-014 | Plancherel Algebras of Dual Hyperspherical Varieties | Under derived geometric Satake, is the internal endomorphism object of the basic sheaf on a hyperspherical variety—the Plancherel algebra—sent to the function algebra $\mathcal O(M^\vee)$ of the dual Hamiltonian variety? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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-14299289-014",
"literature-status:open",
"owr-year:2025"
] | The claim identifying the Plancherel algebra with functions on the dual hyperspherical variety is explicitly Conjecture 8.1.8. Examples and formal reductions do not constitute a proof in the general spherical setting. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Under derived geometric Satake, is the internal endomorphism object of the basic sheaf on a hyperspherical variety—the Plancherel algebra—sent to the function algebra $\mathcal O(M^\vee)$ of the dual Hamiltonian variety? | where \deltaX is the basic object, act(F ) := F ⋆ \deltaX , and actR \deltaX is its right adjoint. The object actR (\delta \deltaX X ) is sometimes called the internal endomorphisms of \delta, the Plancherel algebra (in the notation of [3, Definition 8.1.4], or the relative Coulomb branch algebra. [3, Conjecture 8.1.8]... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,324 | OWR-14299289-015 | Spectral Exchange of Period and L-Sheaves | Under geometric Langlands duality, are the spectral projection of the period sheaf and the $L$-sheaf exchanged? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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",
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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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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open 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-14299289-016"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-015",
"literature-status:open",
"owr-year:2025"
] | This fragment introduces the global geometric duality conjecture. The spectral exchange of the projected period sheaf and the L-sheaf remains conjectural beyond special cases. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Under geometric Langlands duality, are the spectral projection of the period sheaf and the $L$-sheaf exchanged? | The goal of this talk was to understand the following conjecture. Conjecture 1 (Global Geometric Duality, [BZSV24] Conjecture 12.1.1). The spectral projection of the period sheaf and the L-sheaf are exchanged under the geometric Langlands correspondence: \sim / QC ! (LocG∨ ) AUT(BunG ) o spec o / LX ∨ ,Ψ∨ (PX,Ψ ) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,325 | OWR-14299289-016 | Duplicate Global Geometric Duality Conjecture | Conjecture 1 (Global Geometric Duality, [BZSV24] Conjecture 12.1.1). The spectral projection of the period sheaf and the L-sheaf are exchanged under the geometric Langlands correspondence: \sim / QC ! (LocG∨ ) AUT(BunG ) o spec o / LX ∨ ,Ψ∨ (PX,Ψ ) The goal of this talk was to understand the following conjecture. Arbei... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
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"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction repeats the global geometric-duality conjecture represented canonically by OWR-14299289-01) | [
"OWR-14299289-015"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-016",
"literature-status:open",
"owr-year:2025"
] | This is the same Global Geometric Duality Conjecture 12.1.1 stated in full. The 2025 discussion and the BZSV primary source do not report a proof of the general equivalence. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | Conjecture 1 (Global Geometric Duality, [BZSV24] Conjecture 12.1.1). The spectral projection of the period sheaf and the L-sheaf are exchanged under the geometric Langlands correspondence: \sim / QC ! (LocG∨ ) AUT(BunG ) o spec o / LX ∨ ,Ψ∨ (PX,Ψ ) The goal of this talk was to understand the following conjecture. Arbei... | unrecoverable | The official report confirms that this extraction repeats the global geometric-duality conjecture represented canonically by OWR-14299289-015. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,326 | OWR-14299289-017 | Whittaker Special Cases of Global Geometric Duality | Establish the Whittaker case of global geometric duality by identifying the Whittaker period sheaf with the corresponding spectral object under geometric Langlands. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"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-14299289-017",
"literature-status:open",
"owr-year:2025"
] | The fragment only identifies the Whittaker special case and its proposed dual object; it does not state a standalone theorem. Since the encompassing global duality claim remains unresolved, the unclear extracted claim is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | Establish the Whittaker case of global geometric duality by identifying the Whittaker period sheaf with the corresponding spectral object under geometric Langlands. | 2. Special cases of the conjecture 2.1. The Whittaker Case. Let X = G/U and Ψ \to X the Ga -bundle associated to a generic additive character \psi : U \to Ga . The associated period sheaf W := PG/U,Ψ is called the Whittaker sheaf. This can be thought of as the geometric avatar of a period integral. Now suppose that F =... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,327 | OWR-14299289-018 | Geometric Numerical Conjecture Lead-In | 1. Overview We have discussed how hyperspherical dual pairs induce boundary theories (at dimension 2) by defining period and L-sheaves. Now we discuss numerical conjec- tures coming out of the framework, which bears the shape: “M -period of F\phi /f\phi = L-function \delta\phi /\phi on M̌ ” where F\phi and \delta\phi a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 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"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this extraction is an expository overview and setup; the actual geometric numerical conjecture is represen) | [
"OWR-14299289-019"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-018",
"literature-status:open",
"owr-year:2025"
] | This is explicitly the Geometric Numerical Conjecture. Whittaker and Tate examples are checked, but the stated formula for general hyperspherical pairs and cuspidal eigensheaves remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | null | 1. Overview We have discussed how hyperspherical dual pairs induce boundary theories (at dimension 2) by defining period and L-sheaves. Now we discuss numerical conjec- tures coming out of the framework, which bears the shape: “M -period of F\phi /f\phi = L-function \delta\phi /\phi on M̌ ” where F\phi and \delta\phi a... | unrecoverable | The official report confirms that this extraction is an expository overview and setup; the actual geometric numerical conjecture is represented canonically by OWR-14299289-019. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,328 | OWR-14299289-019 | Arithmetic Identities from Geometric Trace Formulas | For a cuspidal Hecke eigensheaf with trace function $f_\phi$, does the geometric trace formula give the predicted arithmetic identity equating the normalized global period of $f_\phi$ with the normalized sheared $L$-value attached to the dual parameter $\phi$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-14299289-018"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-019",
"literature-status:open",
"owr-year:2025"
] | The extracted equation is the Geometric Numerical Conjecture after the trace-of-Hom reduction. The reduction is formal, whereas the resulting arithmetic identity is not proved in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | For a cuspidal Hecke eigensheaf with trace function $f_\phi$, does the geometric trace formula give the predicted arithmetic identity equating the normalized global period of $f_\phi$ with the normalized sheared $L$-value attached to the dual parameter $\phi$? | By lemma [2, Lem 2.6.1], which computes the trace of a hom complex, we have Conjecture 1. [2, 14.31] Geometric Numerical Conjecture. Under the above notations, for a cuspidal Hecke eigensheaf F\phi with trace f\phi : X ∗,norm X f\phi (x)PX (x) = q −bG /2 Lnorm (1, \phid , (T ∨ )( ) | \{z \} x\inBunG (Fq ) constant x\in... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,329 | OWR-14299289-020 | The Tempered Numerical Period Conjecture | For an everywhere-unramified tempered automorphic representation $\pi$ and a hyperspherical dual pair, does the normalized automorphic period of $\pi$ equal the normalized $L$-value prescribed by the extended Langlands parameter? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882](https://doi.org/10.4171/owr/2025/18)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299289-020",
"literature-status:open",
"owr-year:2025"
] | The fragment states the input to the Tempered Numerical Conjecture. The report gives examples and extensions, but the general period equals L-value formula remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/18",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2409.04677",
"label": "Relative Langlands Duality"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/18 | null | null | null | For an everywhere-unramified tempered automorphic representation $\pi$ and a hyperspherical dual pair, does the normalized automorphic period of $\pi$ equal the normalized $L$-value prescribed by the extended Langlands parameter? | 3. Tempered Numerical Conjecture We choose k ≃ C to make statements of automorphic forms. We encourage readers to omit the “norm” decoration in first reading. Conjecture 2. [2, 14.2.1] Our input: • an everywhere unramified tempered automorphic representation \pi, with corresponding extended L-parameter of [2, Ch. 2.6] ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Arbeitsgemeinschaft: Relative Langlands Duality (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/18, pp. 811--882 |
30,006,330 | OWR-14299290-001 | Discrete Symmetries in Geometric Set Minimization | How does imposing a discrete symmetry group change a geometric set-minimization problem? Does the analogous conclusion hold when the competitors are planar polygons? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities in Discrete Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/23, pp. 1163--1214](https://doi.org/10.4171/owr/2025/23)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"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-14299290-001",
"literature-status:open",
"owr-year:2025"
] | The fragment asks for the effect of discrete symmetries on set minimization and polygonal minimizers. Existing work proves only restricted small-mass and symmetry cases, so the general question remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/23",
"label": "OWR report"
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{
"url": "https://arxiv.org/abs/2004.03628",
"label": "Minimality of Polytopes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/23 | null | null | null | How does imposing a discrete symmetry group change a geometric set-minimization problem? Does the analogous conclusion hold when the competitors are planar polygons? | What is the effect of taking a discrete group of symmetries in a minimization problem over sets? Is the same true even if we restrict our attention to polygons in two dimensions? Discreteness makes you think Riccardo Cristoferi (joint work with Marco Bonacini, Ihsan Topaloglu) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Singularities in Discrete Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/23, pp. 1163--1214 |
30,006,331 | OWR-14299290-002 | Critical Points of Symmetric Geometric Energies | How do the symmetry-based minimization methods extend from minimizers to critical points and from the original polygon class to polygons with more sides? What is the appropriate notion of a maximally symmetric competitor, and is its Wulff shape the minimizer for sufficiently small masses? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities in Discrete Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/23, pp. 1163--1214](https://doi.org/10.4171/owr/2025/23)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
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"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-14299290-002",
"literature-status:partially-solved",
"owr-year:2025"
] | For critical points, arbitrary numbers of sides, and the proposed Wulff-shape conclusion, the primary work establishes restricted symmetric polygon and small-mass cases but not a general classification or minimizer theorem. | [
{
"url": "https://doi.org/10.4171/owr/2025/23",
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},
{
"url": "https://doi.org/10.1016/j.na.2020.112223",
"label": "Minimality of Polytopes"
},
{
"url": "https://arxiv.org/abs/2103.06657",
"label": "Riesz-type inequalities for polygons"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/23 | null | null | null | How do the symmetry-based minimization methods extend from minimizers to critical points and from the original polygon class to polygons with more sides? What is the appropriate notion of a maximally symmetric competitor, and is its Wulff shape the minimizer for sufficiently small masses? | What happens when we investigate the critical points? How to generalize those techniques for a larger number of sides? What is the correct notion of ‘most symmetric object’ in such a case? Is it then true that the Wulff shape is the minimizer for small masses? The report passage is retained verbatim as the relevant con... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Singularities in Discrete Systems (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/23, pp. 1163--1214 |
30,006,332 | OWR-14299291-001 | Corrupted Non-Archimedean-Geometry Contents Fragment | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525 Lucas Gerth Moduli spaces of analytic p-divisible groups . . . . . . . . . . . . . . . . . . . . . . . . . 1528 Hélène Esnault (joint with Mark Kisin and Alexander Petrov, in progress) On the vanishing in cohomology of the res... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged contents listing, not a mathematical problem. No separate clean statement is ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299291-001",
"literature-status:open",
"owr-year:2025"
] | The extracted statement is a table-of-contents fragment followed by meeting prose and does not identify a mathematical claim. Under the unresolved-claim rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | null | Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525 Lucas Gerth Moduli spaces of analytic p-divisible groups . . . . . . . . . . . . . . . . . . . . . . . . . 1528 Hélène Esnault (joint with Mark Kisin and Alexander Petrov, in progress) On the vanishing in cohomology of the res... | unrecoverable | The official report confirms that this extraction is a damaged contents listing, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,333 | OWR-14299291-002 | Essential Images in p-Adic Simpson Theory | Does every semistable Higgs bundle of degree zero on $X$ lie in $\mathcal{H}_{X,\mathrm{Exp}}$, equivalently in the essential image of the p-adic Simpson correspondence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 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-14299291-002",
"literature-status:open",
"owr-year:2025"
] | The question whether every semistable degree-zero Higgs bundle lies in the p-adic Simpson essential image is stated as widely open, including for zero Higgs field. Rank-one and restricted rank-two nilpotent cases do not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2201.06697",
"label": "Parallel transport for Higgs bundles"
},
{
"url": "https://arxiv.org/abs/2402.01365",
"label": "p-adic non-abelian Hodge theory for curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Does every semistable Higgs bundle of degree zero on $X$ lie in $\mathcal{H}_{X,\mathrm{Exp}}$, equivalently in the essential image of the p-adic Simpson correspondence? | Does every semi-stable Higgs bundle of degree zero lie in HX ,Exp? The above functors can be fitted into the following diagram: HX ,Exp ν −1 (L) ⊗C OX VB(Xv ) / HB(X) (E, 0) O O ❦❦❦❦❦5 O O ❦❦❦❦❦ ❦❦ ❦❦❦❦ HX ,Exp L RepC (\pi1 (X)) o DW VBDW (X) E V 3. Case of nilpotent Higgs bundles of rank two (joint with Xinwen Zhu) By ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,334 | OWR-14299291-003 | The Nekovář–Scholl Plectic Cohomology Conjecture | Does $R\Gamma(\operatorname{Sh}_\infty,L_\xi)\in D^b(\Gamma_E,\mathbb{Q}_\ell)$ lift canonically, via $[\mu]$, to an object of $D^b(\Gamma_{F/\mathbb{Q}},\mathbb{Q}_\ell)$ compatibly with the Hecke actions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 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-14299291-003",
"literature-status:open",
"owr-year:2025"
] | The Nekovar-Scholl plectic cohomology conjecture is described as widely open, with results for CM points and partial cases but no general canonical lift compatible with Hecke actions. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2208.09962",
"label": "The plectic conjecture over local fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Does $R\Gamma(\operatorname{Sh}_\infty,L_\xi)\in D^b(\Gamma_E,\mathbb{Q}_\ell)$ lift canonically, via $[\mu]$, to an object of $D^b(\Gamma_{F/\mathbb{Q}},\mathbb{Q}_\ell)$ compatibly with the Hecke actions? | This conjecture is partly motivated by its application to semi-simplicity of the cohomology of Shimura varieties as Galois representations, see [4], [5]. Conjecture 1 (Nekovář-Scholl). The complex RΓ(Sh\infty , Lξ ) in Db (ΓE , Qℓ ) lifts [µ] canonically to an object in Db (ΓF/Q , Qℓ ), compatibly with the Hecke acti... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,335 | OWR-14299291-004 | Torsion of Strongly p-Divisible Cohomology Classes | Let $U$ be a smooth rigid analytic (or dagger/affoid) variety over a $p$-adic field, and let $H^i(\widehat{U})$ denote the completed de Rham / pro-étale cohomology of the completion $\widehat{U}$. In the $p$-adic Green--Griffiths--Hawking--Scholze ($p$-GGHS) setting, are all strongly $p$-divisible elements of $H^i(\wid... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 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-14299291-004",
"literature-status:open",
"owr-year:2025"
] | The p-GGHS problem asks whether strongly p-divisible classes in the completed de Rham cohomology are torsion. The report states it as an open problem and records non-torsion strongly p-divisible classes in a related uncompleted cohomology group. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Let $U$ be a smooth rigid analytic (or dagger/affoid) variety over a $p$-adic field, and let $H^i(\widehat{U})$ denote the completed de Rham / pro-étale cohomology of the completion $\widehat{U}$. In the $p$-adic Green--Griffiths--Hawking--Scholze ($p$-GGHS) setting, are all strongly $p$-divisible elements of $H^i(\wid... | Are the strongly p-divisible elements in H i (Û ) all torsion? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,336 | OWR-14299291-005 | Prismatic Extension of Generic-Point Vanishing | Does generic-point vanishing for de Rham and étale cohomology extend to prismatic cohomology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 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-14299291-005",
"literature-status:open",
"owr-year:2025"
] | The fragment reports an unchecked expectation that the proof extends to prismatic cohomology rather than a completed theorem. The requested extension is therefore unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/1905.08229",
"label": "Prisms and prismatic cohomology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Does generic-point vanishing for de Rham and étale cohomology extend to prismatic cohomology? | Scholze explained to us that our proof of Theorem 2 generalizes well to prismatic cohomology. We haven’t yet checked the details. Acknowledgements: We thank all the mathematicians participating in the work- shop for their interest and questions, also Marco D’Addezio and Atsushi Shiho for earlier discussions. Most parti... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,337 | OWR-14299291-006 | q-Hodge Filtrations and Habiro Descent | Does the Hodge filtration on de Rham cohomology admit a $q$-deformation? Can $q$-de Rham cohomology be descended from $\mathbb{Z}[[q-1]]$ to the Habiro ring $\mathcal H=\varprojlim_{m\in\mathbb N}\mathbb{Z}[q]^{\wedge}_{(q^m-1)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,025 | 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-14299291-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The general q-deformation of the Hodge filtration fails in some cases, while canonical q-Hodge filtrations exist after inverting finitely many small primes; Habiro descent is proved whenever such a filtration exists. The unrestricted questions are not fully settled. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2410.23115",
"label": "Derived q-Hodge complexes and refined TC"
},
{
"url": "https://arxiv.org/abs/1905.08229",
"label": "Prisms and prismatic cohomology"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Does the Hodge filtration on de Rham cohomology admit a $q$-deformation? Can $q$-de Rham cohomology be descended from $\mathbb{Z}[[q-1]]$ to the Habiro ring $\mathcal H=\varprojlim_{m\in\mathbb N}\mathbb{Z}[q]^{\wedge}_{(q^m-1)}$? | Does the Hodge filtration on de Rham cohomology admit a q- deformation as well? Can q-de Rham cohomology be descended from Z[[q − 1]] to the Habiro ring def H = lim Z[q]∧ (qm −1) ? m\inN q-Hodge filtrations. Surprisingly, the answer to Question A turns out to be no in general. However, canonical “q-Hodge filtrations” alw... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,338 | OWR-14299291-008 | Mixed-Chromatic Cohomology Beyond the Extreme Case | In chromatic homotopy theory, let $L_{K(n)} S$ be the $K(n)$-local sphere spectrum at height $n$ and prime $p$. Extend the mixed-chromatic / prismatic cohomology comparison isomorphism for the rationalization of the $K(n)$-local sphere from chromatic level $t = n - 1$ to arbitrary $t$, and remove the completed-perfecti... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | partially_solved | null | 2,025 | 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-14299291-008",
"literature-status:partially-solved",
"owr-year:2025"
] | The stated t=n-1 cohomology isomorphism is proved in the report, but completed perfection remains on the left and the general t case is explicitly not proved. Thus the broader conjecture is only partially solved. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2402.00960",
"label": "On the rationalization of the K(n)-local sphere"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | In chromatic homotopy theory, let $L_{K(n)} S$ be the $K(n)$-local sphere spectrum at height $n$ and prime $p$. Extend the mixed-chromatic / prismatic cohomology comparison isomorphism for the rationalization of the $K(n)$-local sphere from chromatic level $t = n - 1$ to arbitrary $t$, and remove the completed-perfecti... | n − 1; it is the open subspace of Pn−1 obtained by removing all Qp -rational hyper- planes. The maps in the above diagram are torsors under the respective groups. Hence altogether we obtain a canonical isomorphism of v-stacks LTn,0 /Gn = Hn−1 / GLn (Zp ). The cohomologies of these two v-stacks correspond to the two sid... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,339 | OWR-14299291-009 | Surjectivity of the p-Adic Hitchin Morphism | Is the p-adic Hitchin morphism $\widetilde{H}_n:\operatorname{Rep}_{n,X}\to A_{n,X}$ surjective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578](https://doi.org/10.4171/owr/2025/29)
## Literature review (checked 2026-08-2... | 3 | open | null | 2,025 | 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-14299291-009",
"literature-status:open",
"owr-year:2025"
] | The p-adic Hitchin morphism is proved open and equivariant, but surjectivity is explicitly only conjectural. No later primary source located by the cutoff resolves surjectivity in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/29",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2402.01365",
"label": "p-adic non-abelian Hodge theory for curves"
},
{
"url": "https://arxiv.org/abs/2207.13819",
"label": "Moduli spaces in p-adic non-abelian Hodge theory"
}
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/29 | null | null | null | Is the p-adic Hitchin morphism $\widetilde{H}_n:\operatorname{Rep}_{n,X}\to A_{n,X}$ surjective? | e is a twist of the map with its natural Tate-twisted semi-linear GK -action. Since H that sends a Higgs bundle to the characteristic polynomial of its Higgs field, we think of elements of An as polynomials f (T ) = T n + an−1 T n−1 + \cdot \cdot \cdot + a0 with coefficients an−i \in H 0 (X, Ω⊗i (−i)) ⊗C A1 . Proposition ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Non-Archimedean Geometry and Applications (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/29, pp. 1517--1578 |
30,006,340 | OWR-14299292-001 | Computational Group Theory Workshop Narrative | conjecture: it was shown that every transitive solvable sub- group of Sn has polynomial diameter. Tommy Hofmann spoke on Wall’s D2 prob- lem, describing a new family of presentations of quaternion groups and explaining how computer algebra software can be used to investigate these presentations with respect to homotopy... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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 | Unrecoverable OWR statement (The official report confirms that this extraction is workshop-summary prose ending at a dangling occurrence of “conjecture”, not a standalon) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299292-001",
"literature-status:open",
"owr-year:2025"
] | The extracted statement is a table-of-contents fragment followed by general workshop prose and does not identify a precise mathematical claim. Under the unresolved-claim rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/27",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | null | conjecture: it was shown that every transitive solvable sub- group of Sn has polynomial diameter. Tommy Hofmann spoke on Wall’s D2 prob- lem, describing a new family of presentations of quaternion groups and explaining how computer algebra software can be used to investigate these presentations with respect to homotopy... | unrecoverable | The official report confirms that this extraction is workshop-summary prose ending at a dangling occurrence of “conjecture”, not a standalone mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,341 | OWR-14299292-002 | Unnamed Candidate Monster-Subgroup Extensions | Conjugacy class information resulted in two candidate groups, both of which we conjecture have minimal permutation degree about 1.2\cdot107, and which thus cannot be handled easily in such a representation. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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 | Unrecoverable OWR statement (The official report says only that conjugacy-class information produced two candidate groups for the prospective Monster maximal subgroup of) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299292-002",
"literature-status:open",
"owr-year:2025"
] | The two candidate Monster-subgroup groups were constructed and their character tables computed, but the stated minimal-permutation-degree estimate is still presented as a conjecture rather than a proved value. | [
{
"url": "https://doi.org/10.4171/owr/2025/27",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | null | Conjugacy class information resulted in two candidate groups, both of which we conjecture have minimal permutation degree about 1.2\cdot107, and which thus cannot be handled easily in such a representation. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report says only that conjugacy-class information produced two candidate groups for the prospective Monster maximal subgroup of shape $2^{10+16}.O_{10}^+(2)$; it neither names the two candidates nor gives presentations or extension data that distinguish them. Their individual minimal-permutation-degree con... | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,342 | OWR-14299292-003 | Common-Neighbor Conjecture for Generalized Saxl Graphs | Let $G$ be a finite primitive permutation group on $\Omega$ with base size $b(G)\geq2$. Form the generalized Saxl graph $\Sigma(G)$ on $\Omega$ by joining two vertices when they lie in a base of size $b(G)$. Must every two vertices of $\Sigma(G)$ have a common neighbor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | partially_solved | null | 2,025 | 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 | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (no; preprint)**; the dataset currently labels it partially solved. S. D. Freedman (with H. Y. Huang, M. Lee, K. Rekvényi), OWR 27/2025, p. 1406, Conjecture 1: for a primitive group G with base size b(G) ≥ 2, do any two vertices of the generalised Saxl graph have a... | [
"owr",
"oberwolfach-reports",
"OWR-14299292-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The Common Neighbour Conjecture for Saxl and generalized Saxl graphs remains open in general, while the primary work proves it for several families including many sporadic almost simple groups. | [
{
"url": "https://doi.org/10.4171/owr/2025/27",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2410.22613",
"label": "On generalized Saxl graphs"
},
{
"url": "https://doi.org/10.5802/alco.493",
"label": "Published generalized Saxl graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Let $G$ be a finite primitive permutation group on $\Omega$ with base size $b(G)\geq2$. Form the generalized Saxl graph $\Sigma(G)$ on $\Omega$ by joining two vertices when they lie in a base of size $b(G)$. Must every two vertices of $\Sigma(G)$ have a common neighbor? | While this conjecture is open in general, they proved it in certain cases, including many where G is a sporadic almost simple group. Bases for primitive sporadic almost simple permutation groups Saul D. Freedman (joint work with Hong Yi Huang, Melissa Lee, Kamilla Rekvényi) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,343 | OWR-14299292-004 | Class-Breadth Inequalities for Odd-Prime Groups | For a finite $p$-group $G$, write $p^{\operatorname{br}(g)}=|g^G|$ and $\operatorname{br}(G)=\max_{g\in G}\operatorname{br}(g)$. If $p$ is odd, must the nilpotency class satisfy $\operatorname{cl}(G)\leq\operatorname{br}(G)+1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-004",
"literature-status:open",
"owr-year:2025"
] | The class-breadth inequality has counterexamples for p=2, but the odd-prime case remains open in current primary literature. The extracted statement therefore is not disproved for odd primes. | [
{
"url": "https://doi.org/10.4171/owr/2025/27",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1112/jlms/s2-24.1.113",
"label": "Counterexamples to the class-breadth conjecture"
},
{
"url": "https://arxiv.org/abs/2606.13423",
"label": "On the class-breadth conjecture for p gre... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | For a finite $p$-group $G$, write $p^{\operatorname{br}(g)}=|g^G|$ and $\operatorname{br}(G)=\max_{g\in G}\operatorname{br}(g)$. If $p$ is odd, must the nilpotency class satisfy $\operatorname{cl}(G)\leq\operatorname{br}(G)+1$? | In 1987, Felsch, Neubüser, and Plesken [3] found a family of 2-groups that break the conjecture, but it remains open for odd primes. Computing the breadths of algebras and T -groups Óscar Fernández Ayala (joint work with Bettina Eick) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,344 | OWR-14299292-006 | Geometric Realizability of Algebraic Two-Complexes over Group Rings | Let $G$ be a finitely presented group. Characterize which algebraic two-complexes of $\mathbb{Z}[G]$-modules are geometrically realizable as the cellular chain complexes of finite two-dimensional CW-complexes with fundamental group $G$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-006",
"literature-status:open",
"owr-year:2025"
] | Wall's algebraic 2-complex realization problem remains open in this generality; the literature gives reductions and special finite-group cases, not a universal realization theorem. | [
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
},
{
"url": "https://ems.press/journals/cmh/articles/380",
"label": "Stable modules and Wall's D(2)-problem"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Let $G$ be a finitely presented group. Characterize which algebraic two-complexes of $\mathbb{Z}[G]$-modules are geometrically realizable as the cellular chain complexes of finite two-dimensional CW-complexes with fundamental group $G$. | For a finitely presented group G, the question is whether certain algebraic 2-complexes of Z[G]-modules are geometrically realiz- able. Finding exotic presentations of quaternion groups Tommy Hofmann (joint work with John Nicholson) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,345 | OWR-14299292-007 | Modular Isomorphism for Class-Two Exponent-p Groups | Let $G$ and $H$ be finite $p$-groups of exponent $p$ and nilpotency class two over a field $k$ of characteristic $p$. If the group algebras $kG$ and $kH$ are isomorphic, must $G$ and $H$ be isomorphic? Resolve the modular isomorphism problem for this group class over arbitrary fields. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-007",
"literature-status:open",
"owr-year:2025"
] | The modular isomorphism problem has counterexamples in general and many solved subclasses, but the exponent-p, class-2 question over arbitrary characteristic-p fields remains unresolved; recent work extends selected positive cases only. | [
{
"url": "https://arxiv.org/abs/2505.05902",
"label": "Margolis--Sakurai, Modular Isomorphism Problem over all fields"
},
{
"url": "https://doi.org/10.1365/s13291-022-00249-5",
"label": "Modular Isomorphism Problem survey"
},
{
"url": "https://ems.press/content/serial-article-files/51860... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Let $G$ and $H$ be finite $p$-groups of exponent $p$ and nilpotency class two over a field $k$ of characteristic $p$. If the group algebras $kG$ and $kH$ are isomorphic, must $G$ and $H$ be isomorphic? Resolve the modular isomorphism problem for this group class over arbitrary fields. | From the positive results we would like to highlight that though for the class of p-groups of exponent p and nilpotency class 2, featuring prominently in other talks of this wokrshop, the problem found a positive solution over the prime field already in the 1970’s [7] it remains open over general fields. Several open q... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,346 | OWR-14299292-008 | Reported Tensor Null-Pattern Algorithm | More precisely, we ask whether the existence of certain null patterns can be detected within the given array Γ and revealed by the array ΓX . Detecting structure in tensors using algebraic invariants Peter Brooksbank (joint work with Martin Kassabov, James Wilson) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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 | null | Unrecoverable OWR statement (The official report presents an algorithm that either finds a change of basis revealing the prescribed parameterized null pattern or determi) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299292-008",
"literature-status:open",
"owr-year:2025"
] | The tensor null-pattern detection problem is explicitly posed as unresolved for higher-valence tensors; matrix normal forms do not extend to a general effective invariant-based solution. | [
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Brooksbank--Kassabov--Wilson report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | null | More precisely, we ask whether the existence of certain null patterns can be detected within the given array Γ and revealed by the array ΓX . Detecting structure in tensors using algebraic invariants Peter Brooksbank (joint work with Martin Kassabov, James Wilson) | unrecoverable | The official report presents an algorithm that either finds a change of basis revealing the prescribed parameterized null pattern or determines that none exists; the extraction is therefore a reported result, not an open problem. No separate clean statement is promoted; the original record remains publicly visible and ... | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,347 | OWR-14299292-010 | Constructive Product Criteria for Alternating-Group Conjugacy Classes | Given three conjugacy classes $C_1,C_2,C_3$ in $A_n$, decide constructively whether $C_1C_2\supseteq C_3$. Prove effective large-class criteria, such as the proposed bounds in terms of $|C_i|=|A_n|^{\eta_i}$, or give explicit counterexample families. Also determine whether, for every normal subset $S\subseteq A_n$ and ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-010",
"literature-status:open",
"owr-year:2025"
] | The large-class three-factor theorem and its constructive proof are available, but the extracted passage also asks for arbitrary-class product criteria and the broader Kourovka normal-subset question; those stronger goals remain open. | [
{
"url": "https://arxiv.org/abs/2505.06012",
"label": "Dona, Products of three conjugacy classes in the alternating group"
},
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Given three conjugacy classes $C_1,C_2,C_3$ in $A_n$, decide constructively whether $C_1C_2\supseteq C_3$. Prove effective large-class criteria, such as the proposed bounds in terms of $|C_i|=|A_n|^{\eta_i}$, or give explicit counterexample families. Also determine whether, for every normal subset $S\subseteq A_n$ and ... | problem. The proof of Theorem 3 is simply a much more laborious version of the straight- forward strategy above. In particular, it produces an explicit algorithm solving the problem of finding triples of \alphai of given cycle structure satisfying \alpha1 \alpha2 = \alpha3 . Then, using also results of Dvir [3], there ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,348 | OWR-14299292-011 | Fixed-Point-Free Representations of Alternating Groups | Let $p$ and $r$ be primes. Does the alternating group $A_p$ admit a faithful irreducible representation over a field of characteristic $r>0$ in which every element of order $p$ and every element of order $p-2$ acts without nonzero fixed vectors? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-011",
"literature-status:open",
"owr-year:2025"
] | The representation question for A_p with simultaneous fixed-point-freeness on elements of orders p and p-2 is still posed as open; only the characteristic r>p obstruction is recorded. | [
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Let $p$ and $r$ be primes. Does the alternating group $A_p$ admit a faithful irreducible representation over a field of characteristic $r>0$ in which every element of order $p$ and every element of order $p-2$ acts without nonzero fixed vectors? | Does there exist a faithful irreducible representation of Ap over a field in any characteristic r > 0 such that all elements of orders p and p − 2 act fixed-point-freely? Problem 2. Prove that if G \leq Sym(Ω) has exactly two orbits of size 12 |Ω| > 1, then G has a derangement (i.e., a fixed-point-free element). This w... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,349 | OWR-14299292-013 | Simple Invariant Distinguishing Two Class-Two Exponent-$p$ Groups | Let $p$ be an odd prime and let $\omega$ generate $\mathbb{F}_p^\times$. Among groups of exponent $p$ and nilpotency class two, define $G_1=\langle a,b,c,d,e\mid[c,b]=[d,b]=[e,c]=[e,d]=1,\ [d,c]=[b,a],\ [e,b]=[c,a],\ [e,a]=[d,a]^\omega\rangle$ and $G_2=\langle a,b,c,d,e\mid[d,a]=[e,a]=[c,b]=[d,b]=[e,c]=1,\ [d,c]=[b,a],... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://zenodo.org/records/23376497",
"checked_at": "2026-10-14",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-14] I have released an unrefereed preprint, **On a Question of Stanojkovski: Abelian Subgroups of Breadth Two Distinguish Vaughan-Lee's Groups 8.5.14 and 8.5.15** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23376497) | [
"owr",
"oberwolfach-reports",
"OWR-14299292-013",
"literature-status:open",
"owr-year:2025"
] | For the two specified class-two exponent-p groups, automorphism-group size already separates them, but no simpler invariant answering the extracted question has been established. | [
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
},
{
"url": "https://arxiv.org/abs/1501.00678",
"label": "Vaughan-Lee, Automorphisms of class-two groups of prime exponent"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Let $p$ be an odd prime and let $\omega$ generate $\mathbb{F}_p^\times$. Among groups of exponent $p$ and nilpotency class two, define $G_1=\langle a,b,c,d,e\mid[c,b]=[d,b]=[e,c]=[e,d]=1,\ [d,c]=[b,a],\ [e,b]=[c,a],\ [e,a]=[d,a]^\omega\rangle$ and $G_2=\langle a,b,c,d,e\mid[d,a]=[e,a]=[c,b]=[d,b]=[e,c]=1,\ [d,c]=[b,a],... | Is there a “simpler invariant” for non-isomorphism testing of these groups? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,350 | OWR-14299292-015 | Immediate Descendants of Elliptic-Curve p-Groups | For which pairs $(E,P)$ does the associated class-two group $G_{E,P}(\mathbb{F}_p)$ admit a central extension $1\to\mathbb{Z}/p\mathbb{Z}\to G\to G_{E,P}(\mathbb{F}_p)\to1$ with $|G|=p^{10}$ and nilpotency class three? Determine whether the total number of immediate descendants, summed over the relevant isomorphism cla... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-015",
"literature-status:open",
"owr-year:2025"
] | The elliptic-curve group construction has a known exceptional family with non-PORC descendant counts, but a classification of pairs (E,P) admitting the requested central extension is not known. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869312001901",
"label": "du Sautoy--Vaughan-Lee, Non-PORC descendant p-groups"
},
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | For which pairs $(E,P)$ does the associated class-two group $G_{E,P}(\mathbb{F}_p)$ admit a central extension $1\to\mathbb{Z}/p\mathbb{Z}\to G\to G_{E,P}(\mathbb{F}_p)\to1$ with $|G|=p^{10}$ and nilpotency class three? Determine whether the total number of immediate descendants, summed over the relevant isomorphism cla... | It would be of further interest to know which pairs (E, P ) yield an immediate descendant, namely, for which pairs (E, P ) does there exist the following central extension 1 −\to Z/pZ −\to G −\to GE,P (Fp ) −\to 1? Here, G is a group with nilpotency class 3 and cardinality p10 . In [1], du Sautoy and Vaughan-Lee show t... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,351 | OWR-14299292-016 | Freeness of Two-Generator Integral Matrix Groups | Given two integral matrices $A,B\in\mathrm{GL}_n(\mathbb{Z})$, decide whether the subgroup $\langle A,B\rangle$ is freely generated by $A$ and $B$. Is this decision problem solvable uniformly in $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450](https://doi.org/10.4171/owr/2025/27)
## Literature review (checked 2026-08-22)
**Status:**... | 3 | open | null | 2,025 | 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-14299292-016",
"literature-status:open",
"owr-year:2025"
] | Freeness of a subgroup generated by two integral matrices is decidable in low-dimensional special cases, but the uniform GL(n,Z) question in the extracted record remains open. | [
{
"url": "https://ems.press/content/serial-article-files/51860",
"label": "Oberwolfach Report 27/2025"
},
{
"url": "https://mathoverflow.net/questions/328165/do-two-integral-matrices-generate-a-free-group",
"label": "Current discussion of integral-matrix freeness"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/27 | null | null | null | Given two integral matrices $A,B\in\mathrm{GL}_n(\mathbb{Z})$, decide whether the subgroup $\langle A,B\rangle$ is freely generated by $A$ and $B$. Is this decision problem solvable uniformly in $n$? | Is it decidable if hA, Bi is free on \{A, B\}? Tommy Hofmann. For n \geq 3, there exists a polynomial time algorithm that given q and n determines a presentation of SLn (Fq ). This follows from a simplified version of the Steinberg presentation due to Chiaselotti. Question: Does there exists a polynomial time algorithm... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Computational Group Theory (2025), Oberwolfach Reports, DOI 10.4171/owr/2025/27, pp. 1389--1450 |
30,006,352 | OWR-14299511-001 | Reflection-Positive Two-Dimensional Quantum Field Theories with Boundary | Identify the generalized $O(2)$-action on algebras whose fixed points are von Neumann algebras. Classify reflection-positive, remote-detectable, flat-space Lorentz-invariant two-dimensional quantum field theories with boundary: are von Neumann algebras the complete list, or do other examples exist? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-001",
"literature-status:open",
"owr-year:2025"
] | The proposed noninvertible O(2)-action and the classification of reflection-positive remote-detectable two-dimensional theories are explicitly left as open puzzles, with no general solution located. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Identify the generalized $O(2)$-action on algebras whose fixed points are von Neumann algebras. Classify reflection-positive, remote-detectable, flat-space Lorentz-invariant two-dimensional quantum field theories with boundary: are von Neumann algebras the complete list, or do other examples exist? | What is the “O(2)-action” on algebras that von Neumann algebras are the fixed points of? Are there other reflection-positive remote-detectable flat-space Lorentz-invariant 2D QFTs with boundary, or are von Neumann algebras the exact classification? The report passage is retained verbatim as the relevant context for this ex... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,353 | OWR-14299511-002 | Superselection Sectors of Braided Fusion Spin Systems | Let $\mathcal{B}$ be a unitary braided fusion category with strong tensor generator $X$, and let its braided fusion spin system be the associated two-dimensional net with local algebras $\operatorname{End}_{\mathcal{B}}(X^{\otimes I})$. Prove that the superselection-sector category of this net is equivalent to the $W^*... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-002",
"literature-status:open",
"owr-year:2025"
] | The claimed equivalence between the net's superselection sectors and the W*-completion of the braided category is stated as a conjecture for the braided fusion spin system, not as a proved general theorem. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
},
{
"url": "https://link.springer.com/article/10.1007/s00220-025-05315-4",
"label": "Superselection sectors for posets of von Neumann algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Let $\mathcal{B}$ be a unitary braided fusion category with strong tensor generator $X$, and let its braided fusion spin system be the associated two-dimensional net with local algebras $\operatorname{End}_{\mathcal{B}}(X^{\otimes I})$. Prove that the superselection-sector category of this net is equivalent to the $W^*... | Conjecture 1. The superselection sectors for this net is equivalent to the com- pletion of B as a W∗ braided tensor category. and inclusion is given by tensoring with copies of idX as appropriate. One the recovers the bulk topological order by looking at C. Jones’ DHR bimodules for this 1D fusion spin system [Jon24]. F... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,354 | OWR-14299511-003 | SU(3) Braided Fusion Spin Systems and Haah Nets | Prove that the braided fusion spin system associated with $\mathrm{SU}(3)_1$, or with its reverse braiding, is bounded-spread isomorphic to Haah's proposed two-dimensional net of algebras with the specified local clock-and-shift generators. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-003",
"literature-status:open",
"owr-year:2025"
] | The proposed bounded-spread isomorphism between the SU(3)_1 braided fusion spin system and Haah's net remains a conjectural identification; no proof or counterexample was found. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
},
{
"url": "https://arxiv.org/abs/2305.10180",
"label": "Gui--Zhang, Analytic conformal blocks I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Prove that the braided fusion spin system associated with $\mathrm{SU}(3)_1$, or with its reverse braiding, is bounded-spread isomorphic to Haah's proposed two-dimensional net of algebras with the specified local clock-and-shift generators. | Conjecture 2. The braided fusion spin system for SU (3)1 (or possibly its reverse) is bounded-spread isomorphic to a net of algebras from [Haa23, Fig. 1] discussed by Jeongwan Haah in his Oberwolfach talk given just prior to this talk, i.e., the net of algebras with local generators Conjecture 1. The superselection sec... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,355 | OWR-14299511-004 | Modular S-Transform Equivalence for Strongly Finite Vertex Algebras | For a strongly finite $C_2$-cofinite vertex operator algebra, prove that the categorical $S$-transformation defined by Hopf links agrees with the modular $S$-transformation induced by $\tau\mapsto-1/\tau$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,025 | 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"
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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-14299511-004",
"literature-status:partially-solved",
"owr-year:2025"
] | Gui and Zhang solved the sewing-factorization problem and essentially identified the Lyubashenko coend interpretation, and proved the Gainutdinov--Runkel conjecture; the strongly-finite equivalence of categorical and modular S-transforms remains open. | [
{
"url": "https://arxiv.org/abs/2503.23995",
"label": "Gui--Zhang, Sewing-Factorization Theorems"
},
{
"url": "https://arxiv.org/abs/2508.04532",
"label": "Gui--Zhang, Pseudo-q-traces and coends"
},
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfac... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | For a strongly finite $C_2$-cofinite vertex operator algebra, prove that the categorical $S$-transformation defined by Hopf links agrees with the modular $S$-transformation induced by $\tau\mapsto-1/\tau$. | How can one prove the Gainutdinov-Runkel conjecture? (3) In TQFT, torus conformal blocks are studied via the Lyubashenko coend L [Lyu96]. How can this isomorphism be proved? How can this coend version of the sewing-factorization theo- rem be proved in the setting of C2 -cofinite VOAs? (5) In the strongly-rational case, ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,356 | OWR-14299511-005 | Quadrilaterals of Subfactors with Two Intermediate Factors | Develop the planar-algebra theory of finite-index subfactor quadrilaterals $N\subset P,Q\subset M$ with two intermediate subfactors, accounting for the relative position of $P$ and $Q$ beyond the known commuting-square and restricted cocommuting cases. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-005",
"literature-status:open",
"owr-year:2025"
] | The general configuration with two intermediate subfactors N subset P,Q subset M remains an open quadrilateral problem, despite substantial results for restricted irreducible and structured cases. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
},
{
"url": "https://arxiv.org/abs/0704.1121",
"label": "Classification of noncommuting quadrilaterals of factors"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Develop the planar-algebra theory of finite-index subfactor quadrilaterals $N\subset P,Q\subset M$ with two intermediate subfactors, accounting for the relative position of $P$ and $Q$ beyond the known commuting-square and restricted cocommuting cases. | However, the situation for a subfactor with two intermediate subfactors N \subset P, Q \subset M , re- mains an open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,357 | OWR-14299511-006 | A-Infinity Realization of Finite-Depth Subfactor Indices | Prove that every index realized by a finite-depth irreducible hyperfinite subfactor is also realized by an $A_\infty$ subfactor. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | partially_solved | null | 2,025 | 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-14299511-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The A-infinity index conjecture is verified for several exceptional indices, including the listed values, but the universal assertion for every finite-depth irreducible hyperfinite subfactor index remains unproved. | [
{
"url": "https://arxiv.org/abs/2509.00227",
"label": "Bisch--Caceres, New hyperfinite subfactors with infinite depth"
},
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Prove that every index realized by a finite-depth irreducible hyperfinite subfactor is also realized by an $A_\infty$ subfactor. | Conjecture 1. Every index of a finite depth irreducible hyperfinite subfactor is also the index of an A\infty -subfactor. \sqrt{ } \sqrt{ } \sqrt{ } \sqrt{ } We have shown the conjecture holds for 5+2 13 , \approx 4.3772, 5+2 17 , 3+ 3, 5+2 21 , \sqrt{ } 5 and 3 + 5. The novel idea in our work is to combine a classical c... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,358 | OWR-14299511-007 | Vertex Operator Algebras with Haagerup Symmetry | Construct a vertex operator algebra arising in conformal field theory whose representation category contains the Haagerup fusion category or its symmetry data, or prove that no such vertex operator algebra exists. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-007",
"literature-status:open",
"owr-year:2025"
] | Constructive computational methods and lattice models with Haagerup symmetry exist, but realizing that symmetry inside the representation category of a VOA remains an open problem. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
},
{
"url": "https://arxiv.org/abs/2102.05664",
"label": "Topological field theory with Haagerup symmetry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Construct a vertex operator algebra arising in conformal field theory whose representation category contains the Haagerup fusion category or its symmetry data, or prove that no such vertex operator algebra exists. | We propose a new program to construct subfactors and planar algebras by classical and quantum computers. It remains an open question that whether their is a Vertex operator algebra in conformal field theory whose representation category contains the Haagerup symmetry. Construct Subfactors by Classical and Quantum Comput... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,359 | OWR-14299511-008 | Irreducible Forest Decomposition of Consistency-Equation Varieties | Prove that the forest decomposition of the algebraic variety defined by the fusion consistency equations is its irreducible decomposition. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-008",
"literature-status:open",
"owr-year:2025"
] | The claim that the forest decomposition equals the irreducible decomposition of the consistency-equation variety is presented as a conjecture, and no proof or counterexample was located. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Prove that the forest decomposition of the algebraic variety defined by the fusion consistency equations is its irreducible decomposition. | We conjecture that the forest de- composition of the algebraic variety of the consistency equations is the irreducible decomposition. • The variables akl kl ij , bij are \pm1 or 0 determined by Γ• ; • Nijk is sum of the variables dℓ with integer coefficients determined by Γ• . • All consistency equations reduces to linea... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,360 | OWR-14299511-009 | Reported Quantum Search for Binary Fusion Data | How to efficiently find Γkij \in \{0, 1\} with solutions? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report asks how to find binary fusion data efficiently and immediately presents the authors’ quantum algorithm as a solution; i) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299511-009",
"literature-status:open",
"owr-year:2025"
] | The efficient general construction of binary solutions Gamma is posed as an unresolved computational problem; available work gives structural and special-case methods rather than a general efficient algorithm. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | null | How to efficiently find Γkij \in \{0, 1\} with solutions? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report asks how to find binary fusion data efficiently and immediately presents the authors’ quantum algorithm as a solution; it notes that the algorithm produces examples rather than a mathematical classification. No separate clean statement is promoted; the original record remains publicly visible and re... | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,361 | OWR-14299511-010 | AQFT Locality of Unitary Vertex Operator Algebras | Prove that every unitary vertex operator algebra is local in the sense required to construct its associated algebraic quantum field theory conformal net. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-010",
"literature-status:open",
"owr-year:2025"
] | The AQFT-locality conjecture for every unitary VOA remains open; the cited construction results do not establish locality in full generality. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
},
{
"url": "https://arxiv.org/abs/2305.10180",
"label": "Gui--Zhang, Analytic conformal blocks I"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Prove that every unitary vertex operator algebra is local in the sense required to construct its associated algebraic quantum field theory conformal net. | Following [CKLW18], we conjecture that every unitary VOA is AQFT-local, but this problem remains open, and new ideas will be required. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,362 | OWR-14299511-011 | Goldman-Type Theorem for Sharply Transitive Permutation Groups | Let $G$ be a sharply $k$-transitive finite permutation group with point stabilizer $H$, and let $\Gamma_{G>H}$ be the principal graph of the group-subgroup subfactor $R\rtimes G\supset R\rtimes H$. Prove that every subfactor $P\supset Q$ with principal graph $\Gamma_{G>H}$ is itself of the form $R\rtimes_\alpha G\supse... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886](https://doi.org/10.4171/owr/2025/34)
## Literature review (checked 2026-08-22)
**Status:*... | 3 | open | null | 2,025 | 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-14299511-011",
"literature-status:open",
"owr-year:2025"
] | The record only establishes the conjecture for k=2,3,4; the general k statement is not resolved, so the extracted claim remains open. | [
{
"url": "https://ems.press/content/serial-article-files/52239",
"label": "Oberwolfach Report 34/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/34 | null | null | null | Let $G$ be a sharply $k$-transitive finite permutation group with point stabilizer $H$, and let $\Gamma_{G>H}$ be the principal graph of the group-subgroup subfactor $R\rtimes G\supset R\rtimes H$. Prove that every subfactor $P\supset Q$ with principal graph $\Gamma_{G>H}$ is itself of the form $R\rtimes_\alpha G\supse... | The above conjecture is true for k = 2, 3, 4. For example, the group S(32 ) is isomorphic Z23 ⋊ Q8 . There are exactly two families of sharply 3-transitive permutation groups L(q) and M (q), and they are transitive extensions of H(q) and S(q) respectively (see [4, Chapter XI, Section 2]). To describe their actions, it ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Subfactors and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/34, pp. 1823--1886 |
30,006,363 | OWR-14299512-001 | Topological Invariance of Helicity | Is helicity invariant under topological conjugacy of exact volume-preserving vector fields? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299512-001",
"literature-status:partially-solved",
"owr-year:2025"
] | Topological conjugacy preserves helicity for nowhere-vanishing exact volume-preserving flows, with a topological extension in that setting; the full question allowing fixed points remains unresolved. | [
{
"url": "https://arxiv.org/abs/2508.10609",
"label": "Edtmair--Seyfaddini, Universal extension of helicity"
},
{
"url": "https://ems.press/content/serial-article-files/52240",
"label": "Oberwolfach Report 31/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Is helicity invariant under topological conjugacy of exact volume-preserving vector fields? | Is helicity preserved under topological conjugacy, i.e. if X1 and X2 are two exact volume-preserving vector fields which are topologically conjugate, is it true that H(X1 ) = H(X2 )? On the topological invariance of helicity Oliver Edtmair (joint work with Sobhan Seyfaddini) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,364 | OWR-14299512-002 | Area-Spectral Rigidity of Convex Planar Domains | If two convex planar domains $\Omega$ and $\Omega'$ have equal area and the same billiard length spectrum, must they differ by a unitary affine transformation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299512-002",
"literature-status:partially-solved",
"owr-year:2025"
] | Area spectral rigidity is proved for axial or selected centrally symmetric strictly convex domains near ellipses, with a 2026 strengthening for the axial class; the unrestricted equality question remains open. | [
{
"url": "https://arxiv.org/abs/2410.12644",
"label": "Baracco--Bernardi--Nardi, Area spectral rigidity"
},
{
"url": "https://doi.org/10.3934/jmd.2026012",
"label": "Area spectral rigidity for axial symplectic billiards"
},
{
"url": "https://ems.press/content/serial-article-files/52240",... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | If two convex planar domains $\Omega$ and $\Omega'$ have equal area and the same billiard length spectrum, must they differ by a unitary affine transformation? | Then a natural question arises: is it true that if A(Ω) = A(Ω′ ), then Ω and Ω′ are necessarily equal up to a unitary affine transformation of the plane? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,365 | OWR-14299512-003 | Aperiodic Stable Transitivity Near Anosov Flows | Does there exist a stably transitive diffeomorphism with no periodic points? More specifically, can the time-one map of a geodesic flow on a negatively curved surface be stably transitive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 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-14299512-003",
"literature-status:open",
"owr-year:2025"
] | The existence of a stably transitive diffeomorphism without periodic points, and stable transitivity of the relevant non-suspension Anosov-flow time-one maps, are still posed as open questions. | [
{
"url": "https://ems.press/content/serial-article-files/52240",
"label": "Oberwolfach Report 31/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Does there exist a stably transitive diffeomorphism with no periodic points? More specifically, can the time-one map of a geodesic flow on a negatively curved surface be stably transitive? | It has been an open question about whether there can be stably transitive diffeomorphism isotopic to the identity, until the solution by Bonatti-Diaz [1] in 1995, who proved that certain perturbation of the time-1 maps of Anosov flow is C 1 -stably transitive. The following natural question remains open: Question 1. Is t... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,366 | OWR-14299512-005 | Closed-Orbit Multiplicity on Star-Shaped Hypersurfaces | Let $M$ be the smooth boundary of a star-shaped domain in $\mathbb R^{2n}$. Must its Reeb flow have at least $n$ prime closed orbits? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299512-005",
"literature-status:open",
"owr-year:2025"
] | The general multiplicity conjecture for arbitrary smooth star-shaped hypersurfaces remains open; the recent theorem proves the lower bound under dynamical convexity, not in the full stated generality. | [
{
"url": "https://arxiv.org/abs/2410.13093",
"label": "Cineli--Ginzburg--Gurel primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/31",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Let $M$ be the smooth boundary of a star-shaped domain in $\mathbb R^{2n}$. Must its Reeb flow have at least $n$ prime closed orbits? | This report is based on the work [5] dedicated to the memory of Edi Zehnder who was a long-time co-organizer of the workshop Dynamische Systeme. We consider the multiplicity question for prime closed orbits of Reeb flows on the boundary of a star-shaped domain in R2n or, equivalently, on the standard contact sphere S 2n... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,367 | OWR-14299512-006 | The N-or-Infinity Conjecture for Reeb Pseudo-Rotations | Let $M$ be the smooth boundary of a star-shaped domain in $\mathbb R^{2n}$. If its Reeb flow has only finitely many prime closed orbits, must it have exactly $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 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-14299512-006",
"literature-status:open",
"owr-year:2025"
] | The n-or-infinity dichotomy is proved for centrally symmetric, dynamically convex, non-degenerate flows and related restricted classes, but remains unresolved for the general Reeb flows stated here. | [
{
"url": "https://arxiv.org/abs/2410.13093",
"label": "Cineli--Ginzburg--Gurel primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/31",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Let $M$ be the smooth boundary of a star-shaped domain in $\mathbb R^{2n}$. If its Reeb flow has only finitely many prime closed orbits, must it have exactly $n$? | conjecture: the Reeb flow on M has exactly n prime closed orbits whenever the flow is a Reeb pseudo-rotation, i.e., the number of prime closed orbits is finite. In dimensions 2n \geq 6, the case where the novelty of [5] lies in, very little is known about either part of the conjecture in such a generality. For instance, w... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,368 | OWR-14299512-007 | Two-Point Connectivity by Fixed-Energy Magnetic Geodesics | Given two points on a closed manifold and a fixed positive energy, does there always exist a magnetic geodesic of that energy joining them, and how does the answer depend on the Mañé critical values? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 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-14299512-007",
"literature-status:open",
"owr-year:2025"
] | For finite-dimensional magnetic systems on closed manifolds, the supercritical Mañé-threshold connectivity question remains open; the extracted passage does not specify hypotheses sufficient for a stronger classification. | [
{
"url": "https://doi.org/10.1007/s00220-026-05651-z",
"label": "Albers--Maier primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/31",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Given two points on a closed manifold and a fixed positive energy, does there always exist a magnetic geodesic of that energy joining them, and how does the answer depend on the Mañé critical values? | Here, we investigate whether an analogous result holds for magnetic geodesics: given two points and a fixed positive energy, does there exist a magnetic geodesic connecting them? A central role in this question is played by the so-called Mañé critical values [14], which mark dynamical and geometric thresholds in the m... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,369 | OWR-14299512-008 | Quadratic Growth of Periodic Points for Hamiltonian Maps | Let $\phi$ be a Hamiltonian diffeomorphism with infinitely many nontrivial periodic points, and let $h(\phi)$ denote their polynomial growth exponent. Must $h(\phi)\geq2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706](https://doi.org/10.4171/owr/2025/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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-14299512-008",
"literature-status:open",
"owr-year:2025"
] | The proposed quadratic lower bound for the growth of non-trivial periodic points in this asymptotically linear Hamiltonian setting is explicitly presented as a conjecture, with no proof found. | [
{
"url": "https://arxiv.org/abs/2403.01855",
"label": "Masci primary preprint"
},
{
"url": "https://doi.org/10.4171/owr/2025/31",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/31 | null | null | null | Let $\phi$ be a Hamiltonian diffeomorphism with infinitely many nontrivial periodic points, and let $h(\phi)$ denote their polynomial growth exponent. Must $h(\phi)\geq2$? | Taking inspiration from Franks’ Poincaré-Birkhoff theorem [6, Corollary 2.4], we conjecture that if \phi has infinitely many non-trivial periodic points, then h(\phi) \geq 2, i.e. the growth is at least quadratic. It would be interesting to understand the rate of growth of these subharmonics in terms of their period, na... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Dynamische Systeme (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/31, pp. 1647--1706 |
30,006,370 | OWR-14299513-002 | Rational Points Near Submanifolds | Given a submanifold $M$, how many rational points of height at most $H$ can lie in a prescribed small neighborhood of $M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | open | null | 2,025 | 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-14299513-002",
"literature-status:open",
"owr-year:2025"
] | This is an open counting question about rational points of bounded height near a bounded immersed submanifold; the extracted record gives no assertion or hypotheses that have been proved in general. | [
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/fdbbbd0a-d4c1-475f-aaa8-2151151a7f4b/content",
"label": "primary workshop text"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | Given a submanifold $M$, how many rational points of height at most $H$ can lie in a prescribed small neighborhood of $M$? | How many rational points with denominator of bounded size (height) are contained in a “small neighborhood” of M? Counting, Curvature and Convex Duality Rajula Srivastava | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,371 | OWR-14299513-003 | Truncated Harmonic-Analysis Conjecture | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction contains only an isolated conjecture label and no independently recoverable mathematical s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299513-003",
"literature-status:open",
"owr-year:2025"
] | The extracted record contains only the word `conjecture' and no recoverable mathematical statement; under the required uncertainty rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | null | conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this extraction contains only an isolated conjecture label and no independently recoverable mathematical statement. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,372 | OWR-14299513-004 | Fractal-Time Local Smoothing | For a fractal time set $E\subset[1,2]$ and a maximal $2^{-j}$-separated subset $E_j$, establish sharp local smoothing: $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^p(\mathbb{R}^d)}^p\right)^{1/p}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | partially_solved | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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-14299513-004",
"literature-status:partially-solved",
"owr-year:2025"
] | The classical local smoothing conjecture is settled in dimension two and in substantial higher-dimensional ranges, but the extracted fractal-time extension is only known in restricted cases, including radial data. | [
{
"url": "https://arxiv.org/abs/2501.12805",
"label": "Beltran--Roos--Rutar--Seeger primary paper"
},
{
"url": "https://doi.org/10.1112/blms.70214",
"label": "published fractal local smoothing paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | For a fractal time set $E\subset[1,2]$ and a maximal $2^{-j}$-separated subset $E_j$, establish sharp local smoothing: $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^p(\mathbb{R}^d)}^p\right)^{1/p}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$. | holds for some s < sp when p > 2. The classical local smoothing conjecture [14] postulates that this holds for all s > \sigmap = max(0, sp − p1 ) when p > 2. Wolff [15] showed this for large enough p using an early decoupling inequality. The decoupling approach has been pushed to its limits by Bourgain and Demeter [4] w... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,373 | OWR-14299513-005 | Legendre–Assouad Bounds for Fractal Local Smoothing | For $p>2$, does $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^p(\mathbb{R}^d)}^p\right)^{1/p}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$ hold whenever $s>p^{-1}\nu_E^{\#}(ps_p)$, where $s_p=(d-1)(1/2-1/p)$ and $\nu_E^{\#}$ is the Legendre–Assouad function of $E$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
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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-14299513-005",
"literature-status:open",
"owr-year:2025"
] | The Legendre--Assouad exponent conjecture for arbitrary time sets is proved for radial functions and known to be sharp below the predicted exponent, but the general upper estimate remains open. | [
{
"url": "https://arxiv.org/abs/2501.12805",
"label": "Beltran--Roos--Rutar--Seeger primary paper"
},
{
"url": "https://doi.org/10.1112/blms.70214",
"label": "published fractal local smoothing paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | For $p>2$, does $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^p(\mathbb{R}^d)}^p\right)^{1/p}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$ hold whenever $s>p^{-1}\nu_E^{\#}(ps_p)$, where $s_p=(d-1)(1/2-1/p)$ and $\nu_E^{\#}$ is the Legendre–Assouad function of $E$? | We conjecture that (3) holds when the sum runs over t \in Ej and whenever p > 2 and ♯ s > p1 νE (psp ). ♯ log(sup\delta\leq|J|\leq1 |J|−a N (E \cap J, \delta)) (4) νE (\alpha) = lim\delta\to0 , log( 1\delta ) In [2] it was shown that this holds for radial functions and that it fails for s < 1 ♯ p νE (psp ). Setting E =... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,374 | OWR-14299513-006 | Fractal Local Smoothing for General Time Sets | For an arbitrary time set $E\subset[1,2]$, does fractal local smoothing hold throughout the range $p>2$ and $s>p^{-1}\nu_E^{\#}(ps_p)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
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"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299513-006",
"literature-status:open",
"owr-year:2025"
] | This continuation of the fractal local smoothing conjecture remains unresolved for general time sets; current work establishes radial and structural partial results rather than the stated general bound. | [
{
"url": "https://arxiv.org/abs/2501.12805",
"label": "Beltran--Roos--Rutar--Seeger primary paper"
},
{
"url": "https://doi.org/10.1112/blms.70214",
"label": "published fractal local smoothing paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | For an arbitrary time set $E\subset[1,2]$, does fractal local smoothing hold throughout the range $p>2$ and $s>p^{-1}\nu_E^{\#}(ps_p)$? | In [2] it was shown that this holds for radial functions and that it fails for s < 1 ♯ p νE (psp ). Setting E = [1, 2] recovers the classical local smoothing conjecture (2). The Legendre–Assouad function is closely related to the Assouad spectrum of E, which is the function \theta 7\to dimA,\theta E defined as the infimu... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,375 | OWR-14299513-007 | Fractal-Time Local Smoothing Between Lebesgue Spaces | Let $1<p\leq q<\infty$, and let $p'=p/(p-1)$ be the Hölder conjugate of $p$. If $q>p'$, does $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^q(\mathbb{R}^d)}^q\right)^{1/q}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$ hold whenever $s>\frac{d+1}{2}(\frac1p-\frac1q)+\frac1q\nu_E^{\#}(\frac{q(d-1)}2(1-\f... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752](https://doi.org/10.4171/owr/2025/32)
## Literature review (checked ... | 3 | open | null | 2,025 | 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-14299513-007",
"literature-status:open",
"owr-year:2025"
] | The stated fractal-time Lp-to-Lq conjecture is known in the easy p=2 case and has matching lower bounds, but the general range remains conjectural. | [
{
"url": "https://arxiv.org/abs/2501.12805",
"label": "Beltran--Roos--Rutar--Seeger primary paper"
},
{
"url": "https://doi.org/10.1112/blms.70214",
"label": "published fractal local smoothing paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/32",
"label": "Oberwolfach report"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/32 | null | null | null | Let $1<p\leq q<\infty$, and let $p'=p/(p-1)$ be the Hölder conjugate of $p$. If $q>p'$, does $\left(\sum_{t\in E_j}\lVert e^{it\sqrt{-\Delta}}P_jf\rVert_{L^q(\mathbb{R}^d)}^q\right)^{1/q}\leq C2^{js}\lVert f\rVert_{L^p(\mathbb{R}^d)}$ hold whenever $s>\frac{d+1}{2}(\frac1p-\frac1q)+\frac1q\nu_E^{\#}(\frac{q(d-1)}2(1-\f... | There is also an Lp \to Lq variant of this problem, where for every 1 < p \leq q < \infty, q > p′ , we conjecture that X \sqrt{ } 1q keit −∆ Pj f kqLq (Rd ) \leq C 2js kf kLp(Rd ) t\inEj holds for all j \geq 1 when 1 ♯ q(d−1) s > d+1 1 1 2 ( p − q ) + q νE 2 (1 − p1 − q1 ) . This matches lower bounds proved in [2], whe... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis, and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/32, pp. 1707--1752 |
30,006,376 | OWR-14299516-001 | Truncated Algebraic-K-Theory Abstract Fragment | conjecture. These advances and their implications will be thoroughly explored at the upcoming workshop. The event will feature several presentations on the applications of algebraic K-theory to neighboring areas of mathematics, showcasing the field’s broad impact and ongoing developments. Mathematics Subject Classificati... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction begins with the tail of a sentence from the workshop abstract and does not contain a stand) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299516-001",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a truncated occurrence of the word `conjecture' and contains no identifiable mathematical claim; it therefore cannot be verified beyond the open classification. | [
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | null | conjecture. These advances and their implications will be thoroughly explored at the upcoming workshop. The event will feature several presentations on the applications of algebraic K-theory to neighboring areas of mathematics, showcasing the field’s broad impact and ongoing developments. Mathematics Subject Classificati... | unrecoverable | The official report confirms that this extraction begins with the tail of a sentence from the workshop abstract and does not contain a standalone conjecture. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,377 | OWR-14299516-002 | Enriched Gromov–Witten Invariants of Del Pezzo Surfaces | Let $k$ be a perfect field of characteristic different from $2$ and $3$, and let $X$ be a rational del Pezzo surface of degree at least $4$ obtained by blowing up $\mathbb{P}^2_k$ along the prescribed finite étale subschemes. Prove the conjectural identity $W^{\mathrm{WD}}(A_0,A_1,\ldots,A_r)=Q_{X,D}(A_0)$ between the ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299516-002",
"literature-status:partially-solved",
"owr-year:2025"
] | The conjectural identity for quadratically enriched Gromov--Witten invariants is proved for del Pezzo surfaces of degree greater than five and in toric cases, while the full stated degree-at-least-four assertion remains open. | [
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Wickelgren--Brugalle--Rau Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/52244?nt=1",
"label": "primary report text"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | Let $k$ be a perfect field of characteristic different from $2$ and $3$, and let $X$ be a rational del Pezzo surface of degree at least $4$ obtained by blowing up $\mathbb{P}^2_k$ along the prescribed finite étale subschemes. Prove the conjectural identity $W^{\mathrm{WD}}(A_0,A_1,\ldots,A_r)=Q_{X,D}(A_0)$ between the ... | We conjecture the following. W WD,R (Es−1 0 \times Rn0 −2s0 , . . . , Es−1 r \times Rnr −2sr ) = WelXn1 +...+nr ,s1 +...+sr (d; s0 ) Conjecture 1. Let k be a perfect field of characteristic not 2 or 3. Fix (n1 , . . . , nr ) \in Nr and (A1 , . . . , Ar ) \in Etn (k) and suppose that X is a rational del Pezzo surface of ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,378 | OWR-14299516-003 | Quadratic Curve Counts on Low-Degree Del Pezzo Surfaces | For a rational del Pezzo surface $X$ of degree at least $4$ over a perfect field of characteristic different from $2$ and $3$, prove $W^{\mathrm{WD}}(A_0,A_1,\ldots,A_r)=Q_{X,D}(A_0)$ for the incidence data specified by the blown-up finite étale subschemes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299516-003",
"literature-status:partially-solved",
"owr-year:2025"
] | The displayed Conjecture 1 is established for degree greater than five and for toric del Pezzo surfaces, but not in the full generality of perfect fields and degree at least four stated here. | [
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Wickelgren--Brugalle--Rau Oberwolfach report"
},
{
"url": "https://ems.press/content/serial-article-files/52244?nt=1",
"label": "primary report text"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | For a rational del Pezzo surface $X$ of degree at least $4$ over a perfect field of characteristic different from $2$ and $3$, prove $W^{\mathrm{WD}}(A_0,A_1,\ldots,A_r)=Q_{X,D}(A_0)$ for the incidence data specified by the blown-up finite étale subschemes. | Conjecture 1. Let k be a perfect field of characteristic not 2 or 3. Fix (n1 , . . . , nr ) \in Nr and (A1 , . . . , Ar ) \in Etn (k) and suppose that X is a rational del Pezzo surface of degree at least 4 constructed as the blow up of P2k along the zero-dimensional subschemes p1 , . . . , pr \subset P2k such that pi = ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,379 | OWR-14299516-004 | Rhetorical Condensed-Cohomology Talk Heading | Why should we replace Galois cohomology? Duality for condensed cohomology of the Weil group of a p-adic field Marco Artusa | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a rhetorical talk heading followed by its title and author, not a standalone open probl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299516-004",
"literature-status:open",
"owr-year:2025"
] | This rhetorical question is not accompanied by a precise replacement theory in the extracted record, and no uniquely identifiable resolved claim can be assigned to it. | [
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | null | Why should we replace Galois cohomology? Duality for condensed cohomology of the Weil group of a p-adic field Marco Artusa | unrecoverable | The official report confirms that this extraction is a rhetorical talk heading followed by its title and author, not a standalone open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,380 | OWR-14299516-005 | q-de Rham Cohomology over the Habiro Ring | Construct a canonical version of $q$-de Rham cohomology with coefficients in the Habiro ring $\mathcal H=\varprojlim_{m\in\mathbb N}\mathbb{Z}[q]^{\wedge}_{(q^m-1)}$, rather than only in $\mathbb{Z}[[q-1]]$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299516-005",
"literature-status:partially-solved",
"owr-year:2025"
] | Habiro cohomology has been constructed via q-Hodge filtrations and computed in broad classes, including important smooth and homotopy-theoretic cases, but a general canonical theory answering the question without extra hypotheses is not established. | [
{
"url": "https://arxiv.org/abs/2510.06057",
"label": "Wagner primary paper"
},
{
"url": "https://hdl.handle.net/20.500.11811/13819",
"label": "Wagner 2026 dissertation"
},
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | Construct a canonical version of $q$-de Rham cohomology with coefficients in the Habiro ring $\mathcal H=\varprojlim_{m\in\mathbb N}\mathbb{Z}[q]^{\wedge}_{(q^m-1)}$, rather than only in $\mathbb{Z}[[q-1]]$. | Habiro cohomology \& THH(−/ku) Ferdinand Wagner Habiro cohomology is supposed to be a (positive) answer to the following question of Peter Scholze: Question. Is there a version of q-de Rham cohomology with coefficients not in the power series ring Z[[q − 1]], but in the Habiro ring def H = lim Z[q]∧ (qm −1) ? m\inN A coh... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,381 | OWR-14299516-007 | Categorical Künneth Formula for Étale Motives | If $Y$ is smooth and proper over $k$, does exterior product induce an equivalence $\mathrm{DM}(X)^{\prime}\otimes_{\mathrm{DM}(k)}\mathrm{DM}(Y)^{\prime}\simeq\mathrm{DM}(X\times_kY)^{\prime}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,025 | 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-14299516-007",
"literature-status:partially-solved",
"owr-year:2025"
] | The categorical Kunneth equivalence is proved for adic sheaves, etale torsion under the listed hypotheses, and cohomological motives, while the full etale-motive conjecture in the extracted statement remains open. | [
{
"url": "https://arxiv.org/abs/2503.14416",
"label": "Richarz--Scholbach primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | If $Y$ is smooth and proper over $k$, does exterior product induce an equivalence $\mathrm{DM}(X)^{\prime}\otimes_{\mathrm{DM}(k)}\mathrm{DM}(Y)^{\prime}\simeq\mathrm{DM}(X\times_kY)^{\prime}$? | Conjecture 1. If Y is smooth and proper over k, the exterior product induces an equivalence (of stable \infty-categories) \sim = DM(X)′ ⊗DM(k) DM(Y )′ \to DM(X\timesk Y )′ . We call this a categorical Künneth formula. In addition to its intrinsic beauty, we study this question because of potential applications in the ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,382 | OWR-14299516-008 | Künneth Equivalence for Enlarged Motivic Subcategories | If $Y$ is smooth and proper over $k$, does exterior product induce an equivalence $\mathrm{DM}(X)^{\prime\prime}\otimes_{\mathrm{DM}(k)}\mathrm{DM}(Y)^{\prime\prime}\simeq\mathrm{DM}(X\times_kY)^{\prime\prime}$ for the enlarged motivic subcategories? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012](https://doi.org/10.4171/owr/2025/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,025 | 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-14299516-008",
"literature-status:open",
"owr-year:2025"
] | The analogous equivalence for the larger double-prime subcategories is posed as a question and is not covered by the partial Kunneth theorems currently available. | [
{
"url": "https://arxiv.org/abs/2503.14416",
"label": "Richarz--Scholbach primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/36",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/36 | null | null | null | If $Y$ is smooth and proper over $k$, does exterior product induce an equivalence $\mathrm{DM}(X)^{\prime\prime}\otimes_{\mathrm{DM}(k)}\mathrm{DM}(Y)^{\prime\prime}\simeq\mathrm{DM}(X\times_kY)^{\prime\prime}$ for the enlarged motivic subcategories? | Is there an equivalence (for Y smooth and proper) \sim = DM(X)′′ ⊗DM(k) DM(Y )′′ \to DM(X\timesk Y )′′ ? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic K-theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/36, pp. 1949--2012 |
30,006,383 | OWR-14299517-002 | Near-Linear List Decoding of AEL and Ta-Shma Codes | Can Alon–Edmonds–Luby codes be list-decoded up to capacity in linear time? Can Ta-Shma codes be list-decoded up to a radius approaching one half, or up to the Johnson bound, in near-linear time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299517-002",
"literature-status:open",
"owr-year:2025"
] | AEL and related expander-based constructions now admit near-linear-time list decoding up to capacity, but exact linear-time decoding in the stated long-standing problem remains unresolved. | [
{
"url": "https://arxiv.org/abs/2504.20333",
"label": "Srivastava--Tulsiani primary paper"
},
{
"url": "https://doi.org/10.1109/FOCS63196.2025.00077",
"label": "FOCS 2025 primary paper"
},
{
"url": "https://doi.org/10.4171/owr/2025/41",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | Can Alon–Edmonds–Luby codes be list-decoded up to capacity in linear time? Can Ta-Shma codes be list-decoded up to a radius approaching one half, or up to the Johnson bound, in near-linear time? | Therefore, these AEL based codes become natural candidates to achieve linear time list decoding up to capacity, a long-standing open problem. • Ta-Shma’s Codes: Can be list decoded up to a radius approaching 1/2 in near-linear time for binary codes in near-linear time, and even better up to Johnson bound, but with slow... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,384 | OWR-14299517-003 | Griesmer Bounds and Solomon–Stiffler Constructions in Other Metrics | Find analogues of the Griesmer bound, together with Solomon–Stiffler-type constructions attaining them, for coding spaces equipped with metrics other than Hamming distance. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-14299517-003",
"literature-status:open",
"owr-year:2025"
] | Finding Griesmer-type bounds together with attaining Solomon--Stiffler-type constructions for other metric spaces remains an explicitly stated open problem; no general resolution was found. | [
{
"url": "https://doi.org/10.4171/owr/2025/41",
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"url": "https://content.ems.press/assets/public/full-texts/serials/owr/22/3/14299517/online/10.4171-owr-2025-41.pdf",
"label": "primary report text"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | Find analogues of the Griesmer bound, together with Solomon–Stiffler-type constructions attaining them, for coding spaces equipped with metrics other than Hamming distance. | Open problem. Open problem Find Griesmer type bound bounds and attaining Solomon–Stiffler type constructions for other metric spaces. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,385 | OWR-14299517-004 | List Sizes Beyond Coordinate-Wise Constraints | For a random linear code over $\mathbb F_q$ and a ball defined by constraints more general than coordinate-wise restrictions, is the number of codewords in every such ball at most $q^{\varepsilon n}(1+o(1))$ with high probability? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299517-004",
"literature-status:open",
"owr-year:2025"
] | The Oberwolfach survey explicitly leaves this above-capacity question open: the violating list is exponential in n and beyond the current local-property framework. Later random-linear list-recovery results cover important capacity regimes but not the stated uniform bound. | [
{
"url": "https://ems.press/content/serial-article-files/52245",
"label": "Oberwolfach Report 41 2025"
},
{
"url": "https://arxiv.org/abs/2502.13877",
"label": "Near-Optimal List-Recovery of Linear Code Families"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | For a random linear code over $\mathbb F_q$ and a ball defined by constraints more general than coordinate-wise restrictions, is the number of codewords in every such ball at most $q^{\varepsilon n}(1+o(1))$ with high probability? | We conclude with several open problems: (1) Beyond coordinate-wise constraints. Is it true that, for a random linear code, with high probability every such ball contains at most q ǫn \cdot (1 + o(1)) codewords? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,386 | OWR-14299517-005 | Optimal List Decoding and Recovery of Random Code Ensembles | Which random code ensembles are optimally list-decodable and list-recoverable, and at what radii and list sizes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299517-005",
"literature-status:open",
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] | Capacity or near-optimal results are known for random linear codes and punctured Reed--Solomon codes in important regimes, but no general characterization of optimally list-decodable and list-recoverable codes is known; the broad question remains open. | [
{
"url": "https://ems.press/content/serial-article-files/52245",
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"url": "https://arxiv.org/abs/2502.13877",
"label": "Near-Optimal List-Recovery of Linear Code Families"
},
{
"url": "https://arxiv.org/abs/2406.02238",
"label": "Random Reed--... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | Which random code ensembles are optimally list-decodable and list-recoverable, and at what radii and list sizes? | A fundamental question is: what kinds of codes are optimally list-decodable and list-recoverable? List-Decoding and List-Recovery of Random Codes Ensembles Ray Li (joint work with Omar Alrabiah, Venkatesan Guruswami, and Nikhil Shagrithaya) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,387 | OWR-14299517-006 | New Quantum LDPC Codes with Good Parameters | Construct new families of quantum low-density parity-check codes with asymptotically good parameters. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"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"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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"OWR-14299517-006",
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] | Asymptotically good qLDPC families are known, but alternative constructions with genuinely good parameters remain an open direction; the 2025 homological-product result reaches close-to-linear, rather than linear, dimension and distance. | [
{
"url": "https://ems.press/content/serial-article-files/52245",
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{
"url": "https://doi.org/10.4230/LIPIcs.CCC.2025.25",
"label": "Quantum LDPC Codes of Almost Linear Distance"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | Construct new families of quantum low-density parity-check codes with asymptotically good parameters. | It remains an open question to find new constructions of qLDPC codes with good parameters. (Almost) Good Quantum Codes via Tensor Products Louis Golowich (joint work with Venkatesan Guruswami) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,388 | OWR-14299517-007 | Iterative Quantum LDPC Constructions from Weaker Seeds | Is there an iterative construction of asymptotically good quantum low-density parity-check codes that starts from a weaker seed object? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242](https://doi.org/10.4171/owr/2025/41)
## Literature review (checked 2026-0... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
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"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-14299517-007",
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] | The iterative construction still requires a strong constant-size qLTC, and its authors leave weaker starting objects and additional fundamentally different good or almost-good qLDPC constructions open. | [
{
"url": "https://doi.org/10.4230/LIPIcs.CCC.2025.25",
"label": "Quantum LDPC Codes of Almost Linear Distance"
},
{
"url": "https://ems.press/content/serial-article-files/52245",
"label": "Oberwolfach Report 41 2025"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/41 | null | null | null | Is there an iterative construction of asymptotically good quantum low-density parity-check codes that starts from a weaker seed object? | It is an interesting open question whether there exists an iterative construction with a weaker starting object. Our work also raises multiple additional open questions. It remains an open problem to find additional, fundamentally different constructions of qLDPC codes with good or almost good parameters. The report pass... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | New Mathematical Directions in Coding Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/41, pp. 2187--2242 |
30,006,389 | OWR-14299518-002 | Two Erdős Problems on Partial Block Designs | Two Erdős questions concern partial block designs. (1) For every fixed $0<c<1$, does a constant $C=C(c)$ exist such that, whenever $A_1,\ldots,A_m\subseteq[n]$ satisfy $|A_i|>c\sqrt n$ and $|A_i\cap A_j|\leq1$ for $i<j$, there is a set $B\subseteq[n]$ with $0<|B\cap A_i|\leq C$ for every $i$? (2) Call $n\geq x_1\geq\cd... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | solved | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
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} | Already answered in the original Oberwolfach workshop report (not an open problem) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-002",
"literature-status:open",
"owr-year:2025"
] | Alon’s source abstract gives a counterexample to the first question and an affirmative answer to the second (Theorems 3 and 4, pp. 2249–2250). They correspond to Erdős problems 664 and 732. A further structural-characterisation demand in the previous note was not part of either question.
**What remains.** Both questio... | [
{
"url": "https://www.erdosproblems.com/664",
"label": "Erdős problem 664 — negative answer"
},
{
"url": "https://www.erdosproblems.com/732",
"label": "Erdős problem 732 — affirmative answer"
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{
"url": "https://doi.org/10.4171/owr/2025/42",
"label": "Combinatorics, Probability and ... | 2026-09-28T00:00:00 | Erdős problem 664 — negative answer: https://www.erdosproblems.com/664
Erdős problem 732 — affirmative answer: https://www.erdosproblems.com/732
Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322: https://doi.org/10.4171/owr/2025/42 | https://doi.org/10.4171/owr/2025/42 | null | null | null | Two Erdős questions concern partial block designs. (1) For every fixed $0<c<1$, does a constant $C=C(c)$ exist such that, whenever $A_1,\ldots,A_m\subseteq[n]$ satisfy $|A_i|>c\sqrt n$ and $|A_i\cap A_j|\leq1$ for $i<j$, there is a set $B\subseteq[n]$ with $0<|B\cap A_i|\leq C$ for every $i$? (2) Call $n\geq x_1\geq\cd... | Results We consider two related open problems of Erdős on block designs. Is it true that for every fixed positive constant c < 1 there is a finite constant C = C(c) so that the following holds. Is there an absolute constant c > 0 so that for all 1/2 large n there are at least ecn log n sequences that are block-compatibl... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,390 | OWR-14299518-003 | Transversals in Random Subsets of Projective Planes | Let $P$ be the point set of a projective plane of order $q$, and retain each point independently with probability $1/2$ to form $R$. With high probability, must every $B\subseteq R$ meeting every nonempty line section $L\cap R$ satisfy $|B|/q>f(q)$ for some $f(q)\to\infty$? Can one take $f(q)=\Omega(\log q)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-003",
"literature-status:open",
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] | The projective-plane random-subset conjecture remains open: the cited report explicitly says that related container results have substantially different parameters and do not prove the required growing lower bound for the transversal subset. | [
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"url": "https://web.math.princeton.edu/~nalon/PDFS/remark191.pdf",
"label": "Alon Blocking Partial Designs and Block-Compatible Sequences"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Let $P$ be the point set of a projective plane of order $q$, and retain each point independently with probability $1/2$ to form $R$. With high probability, must every $B\subseteq R$ meeting every nonempty line section $L\cap R$ satisfy $|B|/q>f(q)$ for some $f(q)\to\infty$? Can one take $f(q)=\Omega(\log q)$? | This remains open although we suspect that the answer here is negative as well. and xi = 2 for all n < i \leq m. Then S is block-compatible for n. Therefore, the number of sequences that are block-compatible for n is at least n+q−2 1/2 = 2(0.5+o(1))n log n . q−2 Conjecture 5. Let q be a (large) prime power, put n = q 2... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,391 | OWR-14299518-004 | Minimum Random-Projective-Plane Hitting Sets | Let $P$ be the point set of a projective plane of order $q$, and retain each point independently with probability $1/2$ to form $R$. With high probability, must the minimum size of a subset $B\subseteq R$ meeting every nonempty $L\cap R$ grow faster than $q$, perhaps as $\Omega(q\log q)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-004",
"literature-status:open",
"owr-year:2025"
] | The conjecture on the minimum hitting subset of a random half-set of a projective plane remains explicitly open; no source found a proof of either the asserted divergence or the stronger logarithmic rate. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/72e281a6-ba33-4ac7-baf7-6fadd1126345/download",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://web.math.princeton.edu/~nalon/PDFS/remark191.pdf",
"label": "Alon Blocking Partial Designs and Block-Compatible Sequences"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Let $P$ be the point set of a projective plane of order $q$, and retain each point independently with probability $1/2$ to form $R$. With high probability, must the minimum size of a subset $B\subseteq R$ meeting every nonempty $L\cap R$ grow faster than $q$, perhaps as $\Omega(q\log q)$? | Conjecture 5. Let q be a (large) prime power, put n = q 2 + q + 1, let P be the set of n points of a projective plane of order q and let L1 , L2 , . . . , Ln be the sets of points of its lines. Let R be a random subset of P obtained by picking each point of P randomly and independently to lie in R with probability 1/2.... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,392 | OWR-14299518-005 | Valid Orderings of Subsets of Finite Groups | For which finite groups $G$ does every subset $S\subseteq G\setminus\{\mathrm{id}\}$ admit an ordering whose successive partial products are all distinct? Does this hold for every finite group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 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-14299518-005",
"literature-status:open",
"owr-year:2025"
] | The general finite-group subset-ordering problem is unresolved. Work over F_2^n proves all sufficiently large subsets admit valid orderings, but this does not settle arbitrary subsets in arbitrary finite groups. | [
{
"url": "https://arxiv.org/abs/2508.18254",
"label": "On Graham's Rearrangement Conjecture over F_2^n"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870826001143",
"label": "Towards Graham's Rearrangement Conjecture via Rainbow Paths"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | For which finite groups $G$ does every subset $S\subseteq G\setminus\{\mathrm{id}\}$ admit an ordering whose successive partial products are all distinct? Does this hold for every finite group? | Here, we will be concerned not only with the case when an entire group G admits a valid ordering but with the more general question of when an arbitrary subset S of a given group G admits a valid ordering. On Graham’s rearrangement conjecture over Fn 2 Matija Bucić (joint work with Benjamin Bedert, Noah Kravitz, Richa... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,393 | OWR-14299518-006 | Graham’s Rearrangement Conjecture over Prime Fields | For every prime $p$, does every subset $S\subseteq\mathbb{F}_p\setminus\{0\}$ admit an ordering whose successive partial sums are all distinct? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,025 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-006",
"literature-status:partially-solved",
"owr-year:2025"
] | The intermediate-size regime is no longer wholly open for prime cyclic groups: Pham and Sauermann resolve the conjecture for all sufficiently large primes by combining small- and large-subset results. The broader arbitrary finite-group question remains open. | [
{
"url": "https://arxiv.org/abs/2602.15797",
"label": "On Graham's Rearrangement Conjecture"
},
{
"url": "https://arxiv.org/abs/2508.18254",
"label": "On Graham's Rearrangement Conjecture over F_2^n"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | For every prime $p$, does every subset $S\subseteq\mathbb{F}_p\setminus\{0\}$ admit an ordering whose successive partial sums are all distinct? | It seems feasible that the answer to this question is affirmative for every finite group G. In the graph-theoretic formulation of these problems, which we will describe below, Gordon’s setting corresponds to the complete graph case (in particular, a directed variant of a well-known conjecture of Andersen [2]), whereas The... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,394 | OWR-14299518-012 | Minimum Detectable Planted Trees in Sparse Random Graphs | How small can a planted tree $T$ be while remaining statistically detectable in $G(n,p)\cup T$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-012",
"literature-status:partially-solved",
"owr-year:2025"
] | For most uniformly random labelled trees, detection is proved above logarithmic size at low mean degree and impossible below square-root size at high mean degree, but the full smallest-tree threshold across the parameter range is not determined. | [
{
"url": "https://ems.press/content/serial-article-files/52246",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://arxiv.org/abs/1811.01800",
"label": "Planting Trees in Graphs and Finding Them Back"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | How small can a planted tree $T$ be while remaining statistically detectable in $G(n,p)\cup T$? | How small can such a planted tree T can be while still leaving a detectable property in G(n, p) \cup T ? Theorem 1 (Possibility of detecting most known trees). Let p = c/n. There is a constant C such that the following holds. Let T be a uniform random labelled tree on k vertices. For most trees T , the following holds. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,395 | OWR-14299518-013 | Detection-Threshold Transition for Planted Random Trees | As the mean degree $pn$ increases, how does the minimum detectable size of a typical planted tree transition from order $\log^2 n$ to order $\sqrt n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-013",
"literature-status:open",
"owr-year:2025"
] | The transition of the smallest detectable typical tree from polylogarithmic size to square-root size as the mean degree changes is explicitly left as an open problem, with only endpoint regimes established. | [
{
"url": "https://ems.press/content/serial-article-files/52246",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://proceedings.mlr.press/v291/elimelech25a.html",
"label": "Detecting Arbitrary Planted Subgraphs in Random Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | As the mean degree $pn$ increases, how does the minimum detectable size of a typical planted tree transition from order $\log^2 n$ to order $\sqrt n$? | It could also come as a surprise that the size of \sqrt{ } the smallest detectable tree transitions from the order of magnitude log2 n to n as the mean degree pn increases, and understanding this transition remains an intriguing open problem. (a) If c < 1.2 and k > C log n, then there is a test which distinguishes Gp (... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,396 | OWR-14299518-014 | Algorithmic and Structural Problems in Planted-Tree Detection | Determine the detection threshold for planted $d$-ary trees. When $pn<1.1$, can an unknown random tree of size $O(\log n)$ be detected? Can the hairy-path test be implemented in polynomial time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-014",
"literature-status:open",
"owr-year:2025"
] | The listed questions about d-ary trees, unknown random trees of logarithmic size below mean degree 1.1, and polynomial-time implementation of the hairy-path test remain open in the current report. | [
{
"url": "https://ems.press/content/serial-article-files/52246",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://arxiv.org/abs/1811.01800",
"label": "Planting Trees in Graphs and Finding Them Back"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Determine the detection threshold for planted $d$-ary trees. When $pn<1.1$, can an unknown random tree of size $O(\log n)$ be detected? Can the hairy-path test be implemented in polynomial time? | Open problems. We point out only a few of the many open problems remaining in the area. What about d-ary trees? • For pn < 1.1, is it possible to detect an unknown random tree of size O(log n)? • Can our method (the hairy-path test ) be performed in polynomial time? The report passage is retained verbatim as the releva... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,397 | OWR-14299518-016 | The Alon–Tarsi Conjecture for Latin Squares | For every even integer $n$, is the difference between the numbers of even and odd Latin squares of order $n$ nonzero? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 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-14299518-016",
"literature-status:open",
"owr-year:2025"
] | The Alon--Tarsi conjecture remains open in general for even orders; asymptotic cancellation and many special families do not establish the required nonzero signed enumeration for every even order. | [
{
"url": "https://arxiv.org/abs/1412.7574",
"label": "Square-Root Cancellation for the Signs of Latin Squares"
},
{
"url": "https://arxiv.org/abs/2509.13125",
"label": "Parities in Random Latin Squares"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | For every even integer $n$, is the difference between the numbers of even and odd Latin squares of order $n$ nonzero? | In other words, if the Alon–Tarsi conjecture is true, then it is true “just barely”. Parities in random Latin squares Matthew Kwan (joint work with Kalina Petrova, Mehtaab Sawhney) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,398 | OWR-14299518-019 | Color Patterns and the Erdős–Rogers Function | For every fixed $k\geq 3$, is the color-pattern parameter $P_r(k)$ asymptotic in order to $r\,f_{k,k+1}(r)^2$, that is, is $P_r(k)=\Theta\!\left(rf_{k,k+1}(r)^2\right)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 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-14299518-019",
"literature-status:partially-solved",
"owr-year:2025"
] | The current construction gives bounds within a logarithmic factor of the conjectured Theta(r times the squared Erdos--Rogers function), but the conjectured asymptotic order is not proved in full. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/72e281a6-ba33-4ac7-baf7-6fadd1126345/download",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://arxiv.org/abs/2510.09068",
"label": "Improved Bounds for Minimal Multicolor Ramsey Graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | For every fixed $k\geq 3$, is the color-pattern parameter $P_r(k)$ asymptotic in order to $r\,f_{k,k+1}(r)^2$, that is, is $P_r(k)=\Theta\!\left(rf_{k,k+1}(r)^2\right)$? | Conjecture 5.2] even predicted that for every fixed k \geq 3 we will have Pr (k) = Θ(r \cdot (fk,k+1 (r))2 ). Considering the recent improvements of Mubayi and Verstraete [9] on the Erdős- Rogers function, Theorem 2 comes within a log-factor of resolving this conjecture. Good constructions for the Erdős-Rogers functio... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,399 | OWR-14299518-020 | Resolved Root-Distribution Lead-In for Littlewood Polynomials | What can be said about the distribution of roots of fn ? Consider a random polynomial of the form n X fn (z) = ξj z j j=0 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses the broad root-distribution question as a lead-in to theorems proved in the reported work rather than as a separate) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-020",
"literature-status:open",
"owr-year:2025"
] | The bulk location and angular equidistribution of roots, and recently their minimum-spacing law, are known for this Littlewood ensemble, but the broad request for the full root distribution remains open rather than a single settled theorem. | [
{
"url": "https://ems.press/content/serial-article-files/52246",
"label": "Oberwolfach Report 42 2025"
},
{
"url": "https://arxiv.org/abs/2505.02723",
"label": "Limit Law for Root Separation in Random Polynomials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | null | What can be said about the distribution of roots of fn ? Consider a random polynomial of the form n X fn (z) = ξj z j j=0 | unrecoverable | The official report uses the broad root-distribution question as a lead-in to theorems proved in the reported work rather than as a separately posed open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,400 | OWR-14299518-023 | The Sharp Asymptotic for Triangle Ramsey Numbers | Is the triangle Ramsey number asymptotic to $R(3,k)=\left(\frac12+o(1)\right)\frac{k^2}{\log k}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 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-14299518-023",
"literature-status:open",
"owr-year:2025"
] | The conjectured asymptotic for R(3,k) remains unresolved: the 2025--2026 literature gives a lower bound with constant one half but no matching upper bound. | [
{
"url": "https://arxiv.org/abs/2510.19718",
"label": "Improving R(3,k) in just two bites"
},
{
"url": "https://doi.org/10.4171/owr/2025/42",
"label": "Oberwolfach Report 42/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Is the triangle Ramsey number asymptotic to $R(3,k)=\left(\frac12+o(1)\right)\frac{k^2}{\log k}$? | Perhaps somewhat boldly, we conjecture this would be optimal. Conjecture 2. 2 1 k R(3, k) = + o(1) . 2 log k In fact, we have a conjectural construction, based on the Cayley sum graph generated by the sum-free process on Fd2 , that would imply the lower bound in this conjecture along an infinite sequence. The constructi... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,401 | OWR-14299518-024 | Cayley-Sum Constructions for Triangle Ramsey Numbers | Can a Cayley-sum graph generated by the sum-free process on $\mathbb{F}_2^d$ attain $R(3,k)\geq\left(\frac12-o(1)\right)k^2/\log k$ along an infinite sequence? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 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"
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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-14299518-024",
"literature-status:open",
"owr-year:2025"
] | The conjectured asymptotic for R(3,k) remains unresolved: the 2025--2026 literature gives a lower bound with constant one half but no matching upper bound. | [
{
"url": "https://arxiv.org/abs/2510.19718",
"label": "Improving R(3,k) in just two bites"
},
{
"url": "https://doi.org/10.4171/owr/2025/42",
"label": "Oberwolfach Report 42/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Can a Cayley-sum graph generated by the sum-free process on $\mathbb{F}_2^d$ attain $R(3,k)\geq\left(\frac12-o(1)\right)k^2/\log k$ along an infinite sequence? | Conjecture 2. 2 1 k R(3, k) = + o(1) . 2 log k In fact, we have a conjectural construction, based on the Cayley sum graph generated by the sum-free process on Fd2 , that would imply the lower bound in this conjecture along an infinite sequence. The construction. Our construction is actually quite easy to describe: we fir... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,402 | OWR-14299518-026 | The Log-Rank Conjecture | Prove the log-rank conjecture: the deterministic communication complexity of a Boolean function is bounded by a polylogarithmic function of the rank of its communication matrix. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-026",
"literature-status:open",
"owr-year:2025"
] | The log-rank conjecture identified in the extract is still widely open; recent work supplies equivalent formulations and improved bounds but not a proof or disproof. | [
{
"url": "https://doi.org/10.4230/LIPIcs.CCC.2026.7",
"label": "The Log-Rank Conjecture: New Equivalent Formulations"
},
{
"url": "https://doi.org/10.1007/s00208-026-03355-2",
"label": "Factorization norms and an inverse theorem for MaxCut"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Prove the log-rank conjecture: the deterministic communication complexity of a Boolean function is bounded by a polylogarithmic function of the rank of its communication matrix. | Zarankiewicz’s problem is one of the long-standing open problems in Extremal Graph Theory asking to find the maximum number of edges in a bipartite graph G with parts of size m and n, which does not contain a complete bipartite graph with parts of size s and t. The main question in this area is the well- known log-rank ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,403 | OWR-14299518-027 | Zero Submatrices in Sparse Low-Rank Matrices | Let $M$ be an $n\times n$ real matrix of rank $r$ with at most $\varepsilon n^2$ nonzero entries, where $0<\varepsilon<1/2$. Must $M$ contain an all-zero square submatrix of size at least $n\exp\!\left(-O(\sqrt{\varepsilon r})\right)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-14299518-027",
"literature-status:open",
"owr-year:2025"
] | Lovett's sparse low-rank matrix zero-submatrix conjecture remains unresolved; current results improve related zero-rectangle bounds but do not reach the conjectured exponential scale. | [
{
"url": "https://arxiv.org/abs/2411.13510",
"label": "Disjoint pairs in set systems and combinatorics of low rank matrices"
},
{
"url": "https://doi.org/10.4171/owr/2025/42",
"label": "Oberwolfach Report 42/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Let $M$ be an $n\times n$ real matrix of rank $r$ with at most $\varepsilon n^2$ nonzero entries, where $0<\varepsilon<1/2$. Must $M$ contain an all-zero square submatrix of size at least $n\exp\!\left(-O(\sqrt{\varepsilon r})\right)$? | In the same paper [11], Lovett proposed to study the size of all-zero rectangles in low-rank sparse real matrices, stating the following conjecture. Conjecture 5 ([11]). Let M be an n \times n real matrix with rank(M ) = r such that at most \varepsilonn2 entries of M are not zero, where \varepsilon \in (0,\sqrt{ }1/2).... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,404 | OWR-14299518-028 | Maximum Sizes of Cover-Free Families | Determine the maximum possible size of an $r$-cover-free family. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322](https://doi.org/10.4171/owr/2025/42)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,025 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
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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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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299518-028",
"literature-status:open",
"owr-year:2025"
] | The exact maximum size of a general r-cover-free family remains open; recent work determines special classes such as finite vector spaces but not the general problem. | [
{
"url": "https://doi.org/10.1016/j.jcta.2025.106131",
"label": "On cover-free families of finite vector spaces"
},
{
"url": "https://doi.org/10.4171/owr/2025/42",
"label": "Oberwolfach Report 42/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/42 | null | null | null | Determine the maximum possible size of an $r$-cover-free family. | Determining the maximum size of an r-cover-free family has been a long-standing open problem, of interest both in combinatorics and in coding theory. In the same paper [11], Lovett proposed to study the size of all-zero rectangles in low-rank sparse real matrices, stating the following conjecture. Conjecture 5 ([11]). ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Combinatorics, Probability and Computing (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/42, pp. 2243--2322 |
30,006,405 | OWR-14299519-001 | Nonflat Graphical Special Lagrangian Cones in Higher Dimensions | For every $n\geq5$, do there exist nonflat graphical special Lagrangian cones in $\mathbb C^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822](https://doi.org/10.4171/owr/2025/33)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,025 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
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"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-14299519-001",
"literature-status:open",
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] | The extracted record identifies the non-flat graphical special Lagrangian cone problem and explicitly records it as open in dimensions n at least five. | [
{
"url": "https://ems.press/content/serial-article-files/52247",
"label": "Oberwolfach Report 33/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/33 | null | null | null | For every $n\geq5$, do there exist nonflat graphical special Lagrangian cones in $\mathbb C^n$? | Problem 1 remains open in dimensions n \geq 5. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822 |
30,006,406 | OWR-14299519-002 | Nonfattening and Intersection Principles for Level-Set Flows | For a level-set mean-curvature flow $(M_t)_{t\geq0}$, to what extent is nonfattening equivalent to nondiscrepancy and to the intersection principle with every smooth closed mean-curvature flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822](https://doi.org/10.4171/owr/2025/33)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299519-002",
"literature-status:open",
"owr-year:2025"
] | The general equivalence between non-fattening and the intersection principle remains unresolved; the 2025 intersection-principle work proves important finite-singularity and conditional cases. | [
{
"url": "https://arxiv.org/abs/2505.11600",
"label": "An Intersection Principle for Mean Curvature Flow"
},
{
"url": "https://arxiv.org/abs/1704.00431",
"label": "Non-fattening of Mean Curvature Flow at Singularities of Mean Convex Type"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/33 | null | null | null | For a level-set mean-curvature flow $(M_t)_{t\geq0}$, to what extent is nonfattening equivalent to nondiscrepancy and to the intersection principle with every smooth closed mean-curvature flow? | It is an open question to what extent non-fattening of level set flows is equivalent to the intersection principle. Hershkovits–White showed that this conjecture is true for flows with mean convex neighborhoods of (1) Mt is non-fattening. (2) Mt is non-discrepant. That is, the inner and outer flows coincide with Mt . (3) ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822 |
30,006,407 | OWR-14299519-004 | Boundary Branching of Area-Minimizing Currents | For an area-minimizing current with analytic boundary, what is the structure and maximal dimension of the boundary branching set? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822](https://doi.org/10.4171/owr/2025/33)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,025 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-14299519-004",
"literature-status:open",
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] | Boundary branching for area-minimizing currents with analytic boundaries remains an open regularity problem, despite substantial progress for two-dimensional and special boundary settings. | [
{
"url": "https://arxiv.org/abs/2502.15047",
"label": "An essential one-sided boundary singularity for a 3-dimensional area-minimizing current"
},
{
"url": "https://doi.org/10.4171/owr/2025/33",
"label": "Oberwolfach Report 33/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/33 | null | null | null | For an area-minimizing current with analytic boundary, what is the structure and maximal dimension of the boundary branching set? | In the framework of area-minimizing currents, the upper bound on the dimension of the branching set in the interior is known thanks to the monumental work of Almgren and the subsequent works of De Lellis and Spadaro, while the branching behavior at the boundary, for analytic boundaries, is currently an open problem. Th... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822 |
30,006,408 | OWR-14299519-006 | The Hölder Threshold for Isometric-Immersion Rigidity | Does there exist a critical exponent $\alpha_0$ such that $C^{1,\alpha}$ isometric immersions are rigid for $\alpha>\alpha_0$, while the Nash–Kuiper flexibility theorem extends to $C^{1,\alpha}$ for $\alpha<\alpha_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822](https://doi.org/10.4171/owr/2025/33)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,025 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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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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"literature-status:open",
"owr-year:2025"
] | The optimal C one alpha flexibility-rigidity threshold is not known; recent work improves flexible exponents and confirms that the optimal exponent remains unknown. | [
{
"url": "https://arxiv.org/abs/2603.08382",
"label": "Flexibility of Codimension One C one theta Isometric Immersions"
},
{
"url": "https://arxiv.org/abs/2503.13867",
"label": "A Nash-Kuiper theorem for isometric immersions beyond Borisov's exponent"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/33 | null | null | null | Does there exist a critical exponent $\alpha_0$ such that $C^{1,\alpha}$ isometric immersions are rigid for $\alpha>\alpha_0$, while the Nash–Kuiper flexibility theorem extends to $C^{1,\alpha}$ for $\alpha<\alpha_0$? | This strong contrast between flexibility in C 1 and rigidity in C 2 raises the natural question: is there a critical Hölder regularity threshold \alpha0 that separates flexibility from rigidity? That is, does there exist a threshold \alpha0 such that • if \alpha > \alpha0 , isometric immersions u \in C 1,\alpha exhibit ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/33, pp. 1753--1822 |
30,006,409 | OWR-14299520-001 | Interdisciplinary Renormalization Discussion Prompt | What can the physicist and the mathematician learn from each other in such cases? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Renormalisation and Randomness (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/44, pp. 2351--2400](https://doi.org/10.4171/owr/2025/44)
## Literature review (checked 2026-... | 3 | open | null | 2,025 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this is a broad workshop-motivation prompt about interaction between physicists and mathematicians, not a ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299520-001",
"literature-status:open",
"owr-year:2025"
] | The record is a broad interdisciplinary question about renormalisation and randomness rather than a mathematically specified claim; no determinate resolution can be assigned. | [
{
"url": "https://doi.org/10.4171/owr/2025/44",
"label": "Oberwolfach Report 44/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/44 | null | null | null | null | What can the physicist and the mathematician learn from each other in such cases? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official report confirms that this is a broad workshop-motivation prompt about interaction between physicists and mathematicians, not a standalone mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Renormalisation and Randomness (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/44, pp. 2351--2400 |
30,006,410 | OWR-14299521-001 | Corrupted Differential-Geometry Contents Fragment | Conjecture . . . . . . . 1609 Yi Lai (joint with Otis Chodosh, Kai Xu) 3-Manifolds with positive scalar curvature and bounded geometry . . . . . . 1610 Claude LeBrun Einstein Constants and Differential Topology . . . . . . . . . . . . . . . . . . . . . . . 1612 Yang Li Large mass limit of G2 and Calabi-Yau monopoles . .... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is a damaged contents-listing fragment, not a mathematical problem. No separate clean stat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14299521-001",
"literature-status:open",
"owr-year:2025"
] | The extracted record is a table-of-contents fragment ending at the word conjecture and contains no identifiable mathematical proposition to verify. | [
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | null | Conjecture . . . . . . . 1609 Yi Lai (joint with Otis Chodosh, Kai Xu) 3-Manifolds with positive scalar curvature and bounded geometry . . . . . . 1610 Claude LeBrun Einstein Constants and Differential Topology . . . . . . . . . . . . . . . . . . . . . . . 1612 Yang Li Large mass limit of G2 and Calabi-Yau monopoles . .... | unrecoverable | The official report confirms that this extraction is a damaged contents-listing fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,411 | OWR-14299521-002 | Scalar-Curvature Smoothing at Critical-Codimension Singular Sets | For $n\geq 3$, does there exist an $L^\infty$ Riemannian metric on $\mathbb{R}^n$, uniformly bilipschitz to the Euclidean metric and smooth away from a singular set of finite $(n-2)$-dimensional Minkowski content, for which nonnegative-scalar-curvature smoothing fails? Does such a counterexample exist when that Minkows... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 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-14299521-002",
"literature-status:open",
"owr-year:2025"
] | The cited smoothing theorem treats singular sets of strictly smaller effective dimension; the critical finite n minus two Minkowski-content case and possible counterexamples remain unresolved. | [
{
"url": "https://arxiv.org/abs/2406.04564",
"label": "Smoothing L infinity Riemannian metrics with nonnegative scalar curvature outside of a singular set"
},
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | For $n\geq 3$, does there exist an $L^\infty$ Riemannian metric on $\mathbb{R}^n$, uniformly bilipschitz to the Euclidean metric and smooth away from a singular set of finite $(n-2)$-dimensional Minkowski content, for which nonnegative-scalar-curvature smoothing fails? Does such a counterexample exist when that Minkows... | For n \geq 3, does there exist a L\infty metric on Rn that is uniformly bilipschitz to the Euclidean metric smooth outside of a singular set of finite (n−2)- dimensional Minkowski content, for which the conclusion of Theorem 1 fails? Does there exist such a metric for which the (n − 2)-dimensional Minkowski content of t... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,412 | OWR-14299521-004 | Angle Dependence of One-Phase Bernoulli Singularities | Can the optimal singular-set dimension for one-phase Bernoulli free boundaries depend on the contact angle? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 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-14299521-004",
"literature-status:open",
"owr-year:2025"
] | The one-phase Bernoulli critical dimension is still only known to lie in the set five, six, or seven, and current angle-dependent capillary results do not determine whether the optimum changes with angle. | [
{
"url": "https://arxiv.org/abs/2601.18794",
"label": "Area-minimizing capillary cones"
},
{
"url": "https://arxiv.org/abs/2401.08028",
"label": "Improved regularity for minimizing capillary hypersurfaces"
},
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Repor... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Can the optimal singular-set dimension for one-phase Bernoulli free boundaries depend on the contact angle? | The sharp regularity bound for one-phase Bernoulli is a hard open question, but is know to be \in \{n−5, n−6, n−7\}. Could this optimal dimension change with the angle? both understood in a distributional sense. One can think of the interface where E meets \partialΩ as a kind of non-linear free-boundary problem. Strict... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,413 | OWR-14299521-005 | Classification of Four-Dimensional Ricci-Flow $\kappa$-Solutions | Classify all $\kappa$-solutions of four-dimensional Ricci flow, up to scaling and finite quotients, as follows: the shrinkers $S^4$, $\mathbb{CP}^2$, $S^2\times S^2$, $\mathbb{R}\times S^3$, and $\mathbb{R}^2\times S^2$; the four-dimensional Bryant soliton, the three-dimensional Bryant soliton times a line, and Lai’s o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 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-14299521-005",
"literature-status:open",
"owr-year:2025"
] | The extracted record only announces a conjecture for the related four-dimensional Ricci-flow problem without stating its mathematical content; the claim is therefore unresolved and unclear. | [
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Classify all $\kappa$-solutions of four-dimensional Ricci flow, up to scaling and finite quotients, as follows: the shrinkers $S^4$, $\mathbb{CP}^2$, $S^2\times S^2$, $\mathbb{R}\times S^3$, and $\mathbb{R}^2\times S^2$; the four-dimensional Bryant soliton, the three-dimensional Bryant soliton times a line, and Lai’s o... | Finally, for the related problem for 4d Ricci flow we conjecture: Conjecture 1 ([11]). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,414 | OWR-14299521-006 | Abundance of Negatively Curved Einstein Manifolds | In a meaningful asymptotic or topological sense, how abundant are closed manifolds admitting Einstein metrics with negative sectional curvature? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,025 | 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-14299521-006",
"literature-status:partially-solved",
"owr-year:2025"
] | Jaeckel and Hamenstaedt construct infinitely many closed manifolds with negatively curved Einstein metrics in every dimension at least four, but the broader meaning of abundance in the question is not fully classified. | [
{
"url": "https://bonndoc.ulb.uni-bonn.de/xmlui/handle/20.500.11811/13264",
"label": "Stability and construction of negatively curved Einstein metrics"
},
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | In a meaningful asymptotic or topological sense, how abundant are closed manifolds admitting Einstein metrics with negative sectional curvature? | Are there, in some sense, many closed manifolds admitting an Ein- stein metric with negative sectional curvature? A Riemannian metric g on a smooth manifold M is called Einstein if for some \lambda \in R, called the Einstein constant, Ric(g) = \lambdag, that is, if (M, g) has constant Ricci curvature. The study of Eins... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
30,006,415 | OWR-14299521-007 | Coexistence of Einstein Metrics with Different Constants | Can odd-dimensional closed manifolds carry Einstein metrics with different Einstein constants? In particular, can Ricci-flat and positive-Einstein metrics coexist, and can special-holonomy methods decide this? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646](https://doi.org/10.4171/owr/2025/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,025 | 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-14299521-007",
"literature-status:open",
"owr-year:2025"
] | The no-coexistence theorem for Sasaki-Einstein and G2 metrics on compact seven-manifolds settles one special case, while the broader odd-dimensional and zero-versus-positive Einstein-constant questions remain open. | [
{
"url": "https://doi.org/10.4171/owr/2025/30",
"label": "Oberwolfach Report 30/2025"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2025/30 | null | null | null | Can odd-dimensional closed manifolds carry Einstein metrics with different Einstein constants? In particular, can Ricci-flat and positive-Einstein metrics coexist, and can special-holonomy methods decide this? | Can one construct odd-dimensional examples of coexistence? What can be proved, for example, about the coexistence of Einstein metrics with \lambda = 0 and \lambda > 0? Can any light be shed on the questions we have just raised by means of ideas related to special holonomy? Theorem 3 (L ’25). No smooth compact 7-manifol... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Differentialgeometrie im Großen (2026), Oberwolfach Reports, DOI 10.4171/owr/2025/30, pp. 1591--1646 |
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