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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34dcbc | problem | aim-0df1011a6fa8a3c46e2c977b7e34dcbc | Balmer spectrum/TTG · Question 3.3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
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}
] | Denote the 'particular subalgebra of Ext' from above question as $C^*$. For pointed Hopf algebras $H$ (set $\mathcal{C} = \text{Rep}(H)$) with abelian grouplikes in characteristic $0$, is it true that $C^* = H^*(\mathcal{C})$ modulo nilpotents? In other words, is $\text{Proj}(H^*(\mathcal{C})) = \text{Proj}(C^*)$? | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Julia Pevtsova | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e34eb8c | problem | aim-0df1011a6fa8a3c46e2c977b7e34eb8c | Balmer spectrum/TTG · Question 3.4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Take $\mathbf{K}$ to be a tensor triangular category with finite Krull-Schmidt dimension. Then, is the Balmer spectrum is Noetherian? (See the work of Negron and Stevenson.) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
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"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e34eb8c",
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Pablo Ocal | null | null | null | [
{
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{
"kind": "website",
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"cda6eac2-d8ba-4ec8-be33-1be0d39326cc","format_issues":null,"number":10626} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e350174 | problem | aim-0df1011a6fa8a3c46e2c977b7e350174 | FGC for tensor categories · Question 2.3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Does a braided finite tensor category have the tensor product property, that is, $V(A \otimes B) = V(A) \cap V(B)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/2/#0df1011a6fa8a3c46e2c977b7e350174",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Categorical questions related to FGC conjecture for Hopf algebras. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
See https://arxiv.org/abs/2306.16082 by Bergh-Plavnik-Witherspoon for recent progress. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"460f4a2f-00ba-4d6e-ba11-83641f1ac0dc","format_issues":null,"number":10621} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e350c97 | problem | aim-0df1011a6fa8a3c46e2c977b7e350c97 | Miscellaneous · Question 5.2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $\mathcal{C}$ be a symmetric tensor category. Develop duality theory for polynomial functors. Can this be applied to representations of symmetric groups? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/5/#0df1011a6fa8a3c46e2c977b7e350c97",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Guillermo Sanmarco | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/5/#0df1011a6fa8a3c46e2c977b7e350c97",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"cd4a3df2-2401-4198-914d-7870cbc36abc","format_issues":null,"number":10633} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e35103f | problem | aim-0df1011a6fa8a3c46e2c977b7e35103f | Specific cases · Question 4.3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Compute the cohomology of Deligne interpolation categories $GL_t$ for $t \in \mathbf{Z}$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/4/#0df1011a6fa8a3c46e2c977b7e35103f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Hector Pena Pollastri | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/4/#0df1011a6fa8a3c46e2c977b7e35103f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2b7b08b0-d330-4e99-8e85-5218d394d456","format_issues":null,"number":10629} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e35176d | problem | aim-0df1011a6fa8a3c46e2c977b7e35176d | Specific cases · Question 4.1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Take the Verlinde category $Ver_p$ and consider $GL(X)$ for $X \in Ver_p$. Compute the cohomology of this group scheme or other finite group schemes in $Ver_p$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/4/#0df1011a6fa8a3c46e2c977b7e35176d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Vera Serganova | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/4/#0df1011a6fa8a3c46e2c977b7e35176d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e35176d",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"9cc870f4-b456-4005-a204-26834412949f","format_issues":null,"number":10630} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3522fe | problem | aim-0df1011a6fa8a3c46e2c977b7e3522fe | FGC for tensor categories · Question 2.4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Construct examples that precisely delineate the boundaries of FGC. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/2/#0df1011a6fa8a3c46e2c977b7e3522fe",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Categorical questions related to FGC conjecture for Hopf algebras. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Paul Balmer | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
"url": "http://aimpl.org/finitetensor/2/#0df1011a6fa8a3c46e2c977b7e3522fe",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3522fe",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"df30b3a9-2b54-4d03-a629-2e24ba657feb","format_issues":null,"number":10622} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e352d0f | problem | aim-0df1011a6fa8a3c46e2c977b7e352d0f | Specific cases · Question 4.2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $\mathbf{k}$ be a Noetherian ring and $G$ a reductive group scheme over $\mathbf{k}$. Suppose that $G$ acts on a finitely generated $\mathbf{k}$-algebra $A$. Is $H^*(G, A)$ finitely generated?
- $\mathbf{Z}$ is a good ring to start with.
- This is known if $\mathbf{k}$ is a field, and als... | unassessed | {
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"url": "http://aimpl.org/finitetensor/4/#0df1011a6fa8a3c46e2c977b7e352d0f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Antoine Touze | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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"current-status-unassessed",
"source-full-text-not-present"
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.706Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5eb7525b-bd1c-4b55-ae5b-755600bf3375","format_issues":null,"number":10631} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3532a1 | problem | aim-0df1011a6fa8a3c46e2c977b7e3532a1 | FGC for Hopf algebras · Question 1.5 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $H$ be a finite-dimensional Hopf algebra over a field $\mathbf{k}$. Suppose $H$ acts on a finitely generated algebra $A$ over $\mathbf{k}$. When is $H^0(H, A)$ (i.e.~the invariants) finitely generated? | unassessed | {
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Questions related to FGC conjecture for Hopf algebras | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Antoine Touze | null | null | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"453c2ed9-5045-4a75-816d-9b8656a35632","format_issues":null,"number":10617} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e353b1e | problem | aim-0df1011a6fa8a3c46e2c977b7e353b1e | Balmer spectrum/TTG · Question 3.5 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Let $\mathcal{C}$ be an FTC. Is $\text{Spc}(\text{Stmod}(\mathcal{C}))$ independent of the monoidal structure? (e.g.~is it true for the quasi-Hopf modifications of small quantum groups $u_q^{\phi}(\mathcal{g})$?) | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e353b1e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Julia Pevtsova | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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{
"kind": "website",
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... | {
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"published_at": "2026-09-09T22:24:04.685Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0cb1947d-a1a4-4ec3-9331-22cf87ca9d3d","format_issues":null,"number":10627} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3546a3 | problem | aim-0df1011a6fa8a3c46e2c977b7e3546a3 | Balmer spectrum/TTG · Question 3.6 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | What are the relationships between finite generation, Noetherianity, and topological Noetherianity? (Does this imply the tensor triangular property?) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
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"url": "http://aimpl.org/finitetensor/3/#0df1011a6fa8a3c46e2c977b7e3546a3",
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"doi": null,
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"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to tensor triangular geometry or the Balmer spectrum. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Antoine Touze | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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"note": null,
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{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"a76626c5-3d05-474c-baee-81ed531d8325","format_issues":null,"number":10628} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e354f63 | problem | aim-0df1011a6fa8a3c46e2c977b7e354f63 | FGC for Hopf algebras · Question 1.6 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | There is a list of a few finite-dimensional Nichols algebras $B(X)$ for $X$ an irreducible Yetter-Drinfeld module over a finite non-abelian group $G$. For these, determine when the FGC conjecture holds. | unassessed | {
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"url": "http://aimpl.org/finitetensor/1/#0df1011a6fa8a3c46e2c977b7e354f63",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | ## Section context
Questions related to FGC conjecture for Hopf algebras | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nicolas Andruskiewitsch | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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"note": null,
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{
"kind": "website",
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"01f82258-7d5d-49df-9376-e35ec45f46a4","format_issues":null,"number":10618} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e355169 | problem | aim-0df1011a6fa8a3c46e2c977b7e355169 | Miscellaneous · Question 5.4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "18",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Finite tensor categories: their cohomology and geometry. http://aimpl.org/finitetensor/ Not an author-supplied MSC code."
}
] | Does a rank variety theory exist for quantum complete intersections (e.g.~Nichols algebras under certain conditions)? What plays the role of $\mathbf{Z}/p$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Finite tensor categories: their cohomology and geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/finitetensor/5/#0df1011a6fa8a3c46e2c977b7e355169",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Finite tensor categories: their cohomology and geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Julia Pevtsova | null | null | null | [
{
"kind": "website",
"citation": "Finite tensor categories: their cohomology and geometry · Original question",
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"note": null,
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{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3720c6 | problem | aim-0df1011a6fa8a3c46e2c977b7e3720c6 | Crossing number and edge addition | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is there a constant $c < 1$ such that any graph $G$ with $m$ edges and any two non-adjacent vertices $u,v$ in $G$ satisfy $\text{cr}(G + uv) \leq \text{cr}(G) + c \cdot m$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/1/#0df1011a6fa8a3c46e2c977b7e3720c6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: 1. The same statement for $c = 1$ is known to be true. 2. The statement cannot be proven for $c < 1/8$ by considering $K_{3,... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jacob Fox | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3735df | problem | aim-0df1011a6fa8a3c46e2c977b7e3735df | Crossing number and edge deletion | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | In any graph $G$, can we always find an edge $e$ such that $\text{cr}(G - e) \geq \text{cr}(G) - o\left(\text{cr}(G)\right)$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/2/#0df1011a6fa8a3c46e2c977b7e3735df",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: It’s known there is always an edge $e$ such that $\text{cr}(G - e) \geq \frac{1}{2}\text{cr}(G)$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jacob Fox | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d7c5b70d-f606-4977-8204-fecfc2b4ff5b","format_issues":null,"number":10114} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e374050 | problem | aim-0df1011a6fa8a3c46e2c977b7e374050 | Planar-critical graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is there a constant $k$ such that every $1$-planar-critical graph is $k$-planar? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/11/#0df1011a6fa8a3c46e2c977b7e374050",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
A graph is said to be $k$-plan... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: If this statement is true, then for any $m \geq 1$, there is a constant $k$ such that every $m$-planar-critical graph is $k$... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Geza Toth | null | null | null | [
{
"kind": "website",
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"note": null,
"sort_order": 0
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"url": "http:... | {
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"updated_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c79012eb-27b9-4cc7-a1cb-a6b60b49b7a8","format_issues":null,"number":10123} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e374b27 | problem | aim-0df1011a6fa8a3c46e2c977b7e374b27 | Collinear triples and self-intersection paths | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | What is the minimal number of collinear triples in any set $P$ of $n$ points in order to guarantee a self-intersection $3$-path in $G_P$, i.e. a path $abcd$ with $ab$ and $cd$ crossing? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/14/#0df1011a6fa8a3c46e2c977b7e374b27",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
For a set $P$ in the plane wit... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Joszef Solymosi | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"df5aad10-6eae-4808-a10c-16d48b65d8d8","format_issues":null,"number":10126} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3751c9 | problem | aim-0df1011a6fa8a3c46e2c977b7e3751c9 | Distinct distances under local condition | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is it true that $f(n,5,9) \leq o(n^2)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/18/#0df1011a6fa8a3c46e2c977b7e3751c9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $f(n,p,q)$ denote the smal... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: Recently, Tao proved that $f(n,4,5) \leq O\left( n^2 / \sqrt{\log(n)}\right)$.
Reference: T. Tao. Planar point sets with fo... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | David Conlon | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/18/#0df1011a6fa8a3c46e2c977b7e3751c9",
"note": null,
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"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4f692463-b3a2-4ada-8da5-392da6cb4900","format_issues":null,"number":10130} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e376a5c | problem | aim-0df1011a6fa8a3c46e2c977b7e376a5c | Crossing number and edge partition | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is there a constant $c < 3/8$ such that any graph $G$ can be decomposed as a union of two subgraphs $G = G_1 \cup G_2$ with $\text{cr}(G_1) + \text{cr}(G_2) \leq c\cdot\text{cr}(G)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/3/#0df1011a6fa8a3c46e2c977b7e376a5c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
There is a known result: any g... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: $c = \frac{7}{24}$ is sufficient when $G$ is the complete graph.
Reference: A. Owens. On the biplanar crossing number. **IE... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Laszlo Szekely | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/3/#0df1011a6fa8a3c46e2c977b7e376a5c",
"note": null,
"sort_order": 0
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"kind": "website",
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"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:23:55.982Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c3b03907-2d30-4392-94ef-52aa525e427b","format_issues":null,"number":10115} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e377a52 | problem | aim-0df1011a6fa8a3c46e2c977b7e377a52 | Chromatic number of generalized Kneser graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is it true that for $n > sk$, the chromatic number $\chi(KG_s(n,k)) = n - sk +s$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/8/#0df1011a6fa8a3c46e2c977b7e377a52",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
We define generalized Kneser g... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: 1. Lovasz proved $\chi(KG_1(n,k)) = n - 2k +2$ for $n > 2k$. 2. Schrijver proved $\chi(KG_2(n,k)) = n - 2k +2$ for $n > 2k$.... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Shira Zerbib | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/8/#0df1011a6fa8a3c46e2c977b7e377a52",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e377a52",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:23:56.273Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c9ad7ace-b359-4cc2-a9fb-5a69a3da5e67","format_issues":null,"number":10120} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e37b251 | problem | aim-0df1011a6fa8a3c46e2c977b7e37b251 | Unavoidable crossing quaduples | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is it true that $f(n) \leq 2^{O(n)}$ | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/15/#0df1011a6fa8a3c46e2c977b7e37b251",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $f(n)$ be the smallest num... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Cosmin Pohoata | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/15/#0df1011a6fa8a3c46e2c977b7e37b251",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e37b251",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:23:56.680Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3504cf14-9524-4ae2-8885-5b626e852eb9","format_issues":null,"number":10127} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e37d1a9 | problem | aim-0df1011a6fa8a3c46e2c977b7e37d1a9 | Plane paths in simple topological graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is there a constant $c > 0$ such that $f(n) \geq \Omega(n^c)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/16/#0df1011a6fa8a3c46e2c977b7e37d1a9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
A drawing (i.e. topological gr... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: 1. It is not disproved that every complete simple topological graph (at least three vertices) contains a non-crossing Hamilt... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Andrew Suk | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/16/#0df1011a6fa8a3c46e2c977b7e37d1a9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e37d1a9",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:23:56.742Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d876abea-0004-4a9b-91de-a0a8911298a1","format_issues":null,"number":10128} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e37e2d6 | problem | aim-0df1011a6fa8a3c46e2c977b7e37e2d6 | Small hexagons in simple topological graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Prove that $h(n) \leq O(\frac{1}{n})$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/17/#0df1011a6fa8a3c46e2c977b7e37e2d6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $h(n)$ be the smallest are... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: 1. The desired statement holds for $4$-cycles. 2. There exist drawings where all odd (plane) cycles enclose regions with are... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ji Zeng | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/17/#0df1011a6fa8a3c46e2c977b7e37e2d6",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e37e2d6",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:23:56.778Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b979af96-6b02-4a36-8a5b-cfed1c5ecca7","format_issues":null,"number":10129} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e37f858 | problem | aim-0df1011a6fa8a3c46e2c977b7e37f858 | Crossing number of cones | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Compute $\phi(k)$ for $k \geq 8$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/7/#0df1011a6fa8a3c46e2c977b7e37f858",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $\phi(k) = \text{min}\{\te... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: 1. It is known that $\sqrt{k/2} \leq \phi(k) \leq O(k^{3/4})$ where the upper bound is by considering complete graphs. 2. Th... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Carlos A. Alfaro | null | null | null | [
{
"kind": "website",
"citation": "Albertson conjecture and related problems · Original question",
"url": "http://aimpl.org/albertson/7/#0df1011a6fa8a3c46e2c977b7e37f858",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e37f858",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:23:56.209Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f9766354-e7d8-49e9-9aee-49fbb2feb551","format_issues":null,"number":10119} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e380814 | problem | aim-0df1011a6fa8a3c46e2c977b7e380814 | Coloring distance on planar graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Fix a planar graph $G$ and $k=8$, is it true that the distance between any two proper $k$-colorings of $G$ is at most $O(n)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/albertson/9/#0df1011a6fa8a3c46e2c977b7e380814",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Fix a graph $G$ and an integer... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: This statement is true for $k=10$.
Reference: V. Bartier, N. Bousquet, C. Feghali, M. Heinrich, B. Moore, T. Pierron. Recol... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Cranston | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e381ec3 | problem | aim-0df1011a6fa8a3c46e2c977b7e381ec3 | Far-away crossing pairs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Determine $f(n)$ asymptotically. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
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"url": "http://aimpl.org/albertson/13/#0df1011a6fa8a3c46e2c977b7e381ec3",
"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $f(n)$ be the maximum numb... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: Under the condition that the edges are drawn as straight-line segments (i.e. geometric graphs), we have $\Omega(n \cdot \log... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Gabor Tardos | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3829ae | problem | aim-0df1011a6fa8a3c46e2c977b7e3829ae | Crossing number within a circle | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Study $\text{cr}_\circ(G)$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
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"url": "http://aimpl.org/albertson/6/#0df1011a6fa8a3c46e2c977b7e3829ae",
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"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $\text{cr}_{\circ}(G)$ be ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: Several participants pointed out that $\text{cr}_\circ(G)$ is known as the convex crossing number. Shahrokhi et al. studied ... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jacob Fox | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3831ac | problem | aim-0df1011a6fa8a3c46e2c977b7e3831ac | Crossing number on surfaces | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Study $\text{cr}_g(K_n)$ and obtain better bounds. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
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"url": "http://aimpl.org/albertson/5/#0df1011a6fa8a3c46e2c977b7e3831ac",
"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $\text{cr}_g(G)$ be the mi... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Reference: F. Shahrokhi, L. A. Szekely, O. Sykora, I. Vrto. Drawings of Graphs on Surfaces with Few Crossings. **Algorithmica** **... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Laszlo Szekeley | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"dc9ee1ae-ffc5-4efd-90c0-3dbec27bb757","format_issues":null,"number":10117} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e385680 | problem | aim-0df1011a6fa8a3c46e2c977b7e385680 | Quasi-planar graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Is it true that for every fixed $k$ the genus $g(G)$ (Euler or orientable) of all $k$-quasi-planar graphs $G$ is in $O(n)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Albertson conjecture and related problems",
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"url": "http://aimpl.org/albertson/12/#0df1011a6fa8a3c46e2c977b7e385680",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
A graph is said to be $k$-quas... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Reference: B. Mohar, C. Thomassen. **Graphs on Surfaces**. Johns Hopkins University Press, 2001.
J. Pach, F. Shahrokhi, M. Szeged... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Radoslav Fulek | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e386c05 | problem | aim-0df1011a6fa8a3c46e2c977b7e386c05 | Crossing number (and its variations) in random graphs | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | Let $G \sim G(n,m)$ with $m \geq \omega(n)$, is it true with high probability that the crossing number $\text{cr}(G) \geq \Omega(m^2)$? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/albertson/4/#0df1011a6fa8a3c46e2c977b7e386c05",
"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
Let $G(n,m)$ denote a random g... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: The same problem can be asked for pair-crossing number $\text{pair-cr}(G)$ and odd-crossing number $\text{odd-cr}(G)$.
Refe... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Janos Pach | null | null | null | [
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"69cf84ac-73f4-433b-85fb-3dee584a188a","format_issues":null,"number":10116} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e388e8c | problem | aim-0df1011a6fa8a3c46e2c977b7e388e8c | Coloring distance and matching number | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/albertson/ Not an author-supplied MSC code."
}
] | For a fixed graph $G$ with $n$ vertices and $k = \Delta(G) + 2$, is it true that the distance between any two proper $k$-colorings of $G$ is at most $n + \mu(G)$? | unassessed | {
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"url": "http://aimpl.org/albertson/10/#0df1011a6fa8a3c46e2c977b7e388e8c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Albertson conjecture and related problems · AIMPL workshop record | ## Workshop introduction
The problems recorded here are those discussed during the open problem session but may not include all problems mentioned during the workshop. The people listed here suggested these problems but may not necessarily be their original authors.
## Question context
The definition of coloring dis... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Note: The statement is known to be true for $n + 2\mu(G)$.
Reference: S. Cambie, W.C. van Batenburg, D.W. Cranston. Optimally Rec... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Cranston | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"72e60fdc-d686-4ece-a0d6-66e854311d4a","format_issues":null,"number":10122} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3c4509 | problem | aim-0df1011a6fa8a3c46e2c977b7e3c4509 | Topology of dual complexes · Question 1.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | What are the possible fundamental groups $\pi_1(\mathcal{D}(X,B))$ for a log Calabi--Yau 4-fold $(X,B)$ of coregularity zero? Does $\mathbb{Z}/7\mathbb{Z}$ appear as such a group? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3c4509",
"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3c4509",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b9077be5-00bb-418b-8e75-ee70cefb5c41","format_issues":null,"number":10947} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3c53c6 | problem | aim-0df1011a6fa8a3c46e2c977b7e3c53c6 | Topology of dual complexes · Question 1.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Does the Poincare homology $\mathbb{S}^3$ arise as the dual complex of a log Calabi--Yau pair? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3c53c6",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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] | Let $\mathcal{X}\longrightarrow\Delta$ be a dlt degeneration of Hyperkähler varieties with $K_{\mathcal{X}/\Delta}\simeq\mathcal{O_X}$. Is
$$
\Gamma(\mathcal{X}_0) =
\begin{cases}
\text{point} & \text{if in type I} \\
\sigma_d & \text{if in type II}\\
\mathbb{CP}^d& \text{if in type III ?}
\end{cases}
$$
Given $... | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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] | Can $\text{K3}^{[5]}$ and $\text{OG}_{10}$ be distinguished via combinatorics of $\Gamma(\mathcal{X}_0)$ for degeneration $\mathcal{X}\longrightarrow\Delta$?
"Combinatorics": integral affine structure? Lagrangian Chern class? | unassessed | {
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}
] | Do 1-parameter Hyperk\"ahler degenerations admit K-trivial, SNC models, after a finite base change?
Note: minimal dlt exist, due to Fujino, Lai. This is true in Type I (KLSV). | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3c8dd0 | problem | aim-0df1011a6fa8a3c46e2c977b7e3c8dd0 | Symplectic and log symplectic pairs · Question 4.4 | {
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"original_discipline": "mathematics"
} | [] | [
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}
] | If $(X,D)$ is log sympletic dlt (or plt) pair and $X\backslash
X^{\text{SNC}}$ has codimension $\ge3$ in $X$, are the singularities rigid (in the sense of definitions of log sympletic dlt pairs)? | unassessed | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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] | Are Type III log sympletic pairs rational, log rational, or cluster type? | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3ca620 | problem | aim-0df1011a6fa8a3c46e2c977b7e3ca620 | Symplectic and log symplectic pairs · Question 4.6 | {
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} | [] | [
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] | Local deformation theory of dlt log sympletic singularities? | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3cb43d | problem | aim-0df1011a6fa8a3c46e2c977b7e3cb43d | Symplectic and log symplectic pairs · Question 4.7 | {
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"original_discipline": "mathematics"
} | [] | [
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] | Examples of dual complexes which are not $\text{Hilb}^n$ or $\text{Kum}^n$ of a K3 degeneration?
degeneration of cubic 4-fold $X\rightsquigarrow
V(x_0x_1x_2)$.
$V(x_0x_1x_2+\epsilon f_3)\longrightarrow\Delta_{\epsilon}\rightsquigarrow
$ degeneration of FX?
$V(x_0,x_1,x_2,f_3)$ smooth? nodal? | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3cc264 | problem | aim-0df1011a6fa8a3c46e2c977b7e3cc264 | Boundedness and moduli theory · Question 5.3 | {
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] | If we degenerate a log CY pair $(X,D)$ coming from a Fano to the normal cone $\text{Cone}_N(D)$, does the deformation theory of the normal cone recover the moduli space? More precisely, do we get an isomorphism:
$$
\mathbb{C}^*\curvearrowright\text{Def}(\text{Cone}(D))^-\simeq \text{Cone}_{\text{CM}}(\mathcal{M}_{(X... | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3cc63b | problem | aim-0df1011a6fa8a3c46e2c977b7e3cc63b | Boundedness and moduli theory · Question 5.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $(X,D)$ be a log Calabi--Yau 3-fold. Is the period map
\begin{align*}
(X, D) & \mapsto \text{MHS}(H^3(X \backslash D, \mathbb{Z})) \\
\mathcal{M}_{(X, D)} & \mapsto \mathbb{D} / \text{Monodromy}
\end{align*}
injective? | unassessed | {
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"url": "http://aimpl.org/higherdimlogcy/5/#0df1011a6fa8a3c46e2c977b7e3cc63b",
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3cc9a8 | problem | aim-0df1011a6fa8a3c46e2c977b7e3cc9a8 | Boundedness and moduli theory · Question 5.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $\mathcal{M}$ be a moduli space of smooth Calabi--Yau varieties. Does there exist a compactification $\mathcal{M}\hookrightarrow \mathcal{M}^*=\mathcal{M}\sqcup\coprod_i\mathcal{M}_i$ such that for every $\mathcal{M}\hookrightarrow\overline{\mathcal{M}}$ SNC, we have $\text{Proj}\oplus_{n\ge0}H^0(\overline{\mathcal... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/5/#0df1011a6fa8a3c46e2c977b7e3cc9a8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/5/#0df1011a6fa8a3c46e2c977b7e3cc9a8",
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},
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3ccf57 | problem | aim-0df1011a6fa8a3c46e2c977b7e3ccf57 | Boundedness and moduli theory · Question 5.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Near a cusp of $\mathcal{M}^*$ prove that there is a mirror $X^{\text{mir}}$ of the general fibres $\mathcal{X}\longrightarrow\mathcal{M}$ such that
$$
\text{Nef}(X^{\text{mir}})/\Gamma= \sigma
$$
where $\sigma$ is the fan modeling the neighborhood of the cusp. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/5/#0df1011a6fa8a3c46e2c977b7e3ccf57",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
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},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"6dd4a2e2-95d8-433d-9df9-4ab75e91d8c7","format_issues":null,"number":10971} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3cde9b | problem | aim-0df1011a6fa8a3c46e2c977b7e3cde9b | Boundedness and moduli theory · Question 5.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Consider $(X,L)\in F_{2d}$, the universal family $\mathcal{X}\overset{\pi}{\longrightarrow}F_{2d}$, and $\mathbb{P}(\pi_*nL)\simeq\mathbb{P}^g$-bundle over $F_{2d}$ with a section $R$.
Can we find a semi-toric compactification $F_{2d} \hookrightarrow \overline{F}^{\mathcal{F}}_{2d}$ and $\overline{\mathcal{X}}$ its uni... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/5/#0df1011a6fa8a3c46e2c977b7e3cde9b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d0f043c8-8802-44f6-b090-cad2dd7528ca","format_issues":null,"number":10972} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3d590c | problem | aim-0df1011a6fa8a3c46e2c977b7e3d590c | Topology of dual complexes · Question 1.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Does the Wu manifold appear as the dual complex of a log Calabi-Yau pair? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3d590c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3d590c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url": "htt... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"51be0477-9b86-45f3-9be6-3f5c4992d989","format_issues":null,"number":10949} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3d6909 | problem | aim-0df1011a6fa8a3c46e2c977b7e3d6909 | Topology of dual complexes · Question 1.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Does there exist a log smooth simple normal crossing Calabi--Yau variety $X$ for which $\mathcal{D}(X)$ is homotopy equivalent to the Wu manifold? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/1/#0df1011a6fa8a3c46e2c977b7e3d6909",
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"81c70b12-46e7-4f64-93b1-fb74b1966812","format_issues":null,"number":10950} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3edac3 | problem | aim-0df1011a6fa8a3c46e2c977b7e3edac3 | Properties of K\"ahler differentials · Question 1.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What characterizes a variety Z with $\Omega_Z^k$ reflexive for all (some) k? Does $\Omega_Z^k$ being reflexive for all (some) k implies X is smooth or lci? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/1/#0df1011a6fa8a3c46e2c977b7e3edac3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ben Tighe | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/1/#0df1011a6fa8a3c46e2c977b7e3edac3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
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] | [] | {
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.393Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8403bb39-3d28-42d6-be3e-8ca68ffc3fc3","format_issues":null,"number":10921} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3eebab | problem | aim-0df1011a6fa8a3c46e2c977b7e3eebab | Properties of K\"ahler differentials · Question 1.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What characterizes a variety $\Omega_Z^k/torsion$ being reflexive or $S_2$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/1/#0df1011a6fa8a3c46e2c977b7e3eebab",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sándor Kovács | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/1/#0df1011a6fa8a3c46e2c977b7e3eebab",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2181525a-b5df-44b7-9f18-81396b83c070","format_issues":null,"number":10922} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3f0b75 | problem | aim-0df1011a6fa8a3c46e2c977b7e3f0b75 | Positive/mixed characteristic · Question 2.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Does there exist a map $X \to \mathbb{Z}_p$ such that $(X,X_p)$ is log canonical (where $X_p$ is the closed fiber) and $X_p$ is irreducible but not $S_2$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3f0b75",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
It was noted that there is no such map for $p=2$, so the question should be posed for $p>2$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Iacopo Brivio | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3f0b75",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3f0b75",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.404Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a39955b0-e68a-493d-9ff5-29fad3336b53","format_issues":null,"number":10923} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3f16ce | problem | aim-0df1011a6fa8a3c46e2c977b7e3f16ce | Positive/mixed characteristic · Question 2.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there an analogue of $\underline{\Omega}_X^\bullet$ in positive characteristic which makes the Hodge-to-de Rham spectral sequence degenerate at $E_1$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3f16ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Wanchun Shen | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3f16ce",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3f16ce",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.410Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"822587d7-864b-4dd2-8afd-6d957a62be69","format_issues":null,"number":10924} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3f93d8 | problem | aim-0df1011a6fa8a3c46e2c977b7e3f93d8 | Properties of higher singularities and minimal exponents · Question 3.05 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Let X be a variety, and H a Cartier divisor on X. Suppose H is m-Du Bois. Is X m-Du Bois around H? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3f93d8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mihnea Popa | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3f93d8",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3f93d8",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.437Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c768d55e-9fbc-4e24-bec8-a5c86d79eda2","format_issues":null,"number":10929} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3fb3a4 | problem | aim-0df1011a6fa8a3c46e2c977b7e3fb3a4 | Positive/mixed characteristic · Question 2.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there an analog of the minimal exponent in positive characteristics? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3fb3a4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e3fb3a4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3fb3a4",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.415Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a8227cb2-09d3-44a0-a136-23805112e5ab","format_issues":null,"number":10925} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3fc2ce | problem | aim-0df1011a6fa8a3c46e2c977b7e3fc2ce | Definitions of higher singularities and related invariants · Question 4.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there an analytic characterization of the minimal exponent in the lci case? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e3fc2ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Shend Zhjeqi | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e3fc2ce",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3fc2ce",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.512Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b869be41-e869-499e-9f82-dd9872ccc060","format_issues":null,"number":10942} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3fd1bc | problem | aim-0df1011a6fa8a3c46e2c977b7e3fd1bc | Properties of higher singularities and minimal exponents · Question 3.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What can we say about higher singularities for pure morphisms (e.g. direct summands, linearly reductive group quotients)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3fd1bc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Zhengze Xin | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3fd1bc",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3fd1bc",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.442Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7a3d4c0e-503e-498d-8631-d7c34311e0cd","format_issues":null,"number":10930} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3fde38 | problem | aim-0df1011a6fa8a3c46e2c977b7e3fde38 | Definitions of higher singularities and related invariants · Question 4.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What is the correct notion of higher DB singularities in the symplectic case? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e3fde38",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alexandra Viktorova | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e3fde38",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3fde38",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.517Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a1987e37-5317-4d62-9e6d-0672b35d1f8e","format_issues":null,"number":10943} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3feb38 | problem | aim-0df1011a6fa8a3c46e2c977b7e3feb38 | Properties of higher singularities and minimal exponents · Question 3.15 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What is the relation between non-smoothability and 1-Du Bois singularities? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3feb38",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Wanchun Shen | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e3feb38",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e3feb38",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.451Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"08cbc4dd-3891-4964-b9c8-702e63fa79fe","format_issues":null,"number":10931} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e3ffa8c | problem | aim-0df1011a6fa8a3c46e2c977b7e3ffa8c | Definitions of higher singularities and related invariants · Question 4.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What is the a definition of m-Du Bois singularities satisfying:
- 0-Du Bois = Du Bois;
- m-Du Bois $\Rightarrow$ (m-1)-Du Bois;
- $R^i f_* \Omega_{X/S}^m$ is locally free, and compatible with base change for any flat family $f: X \rightarrow S$ with pre-m-Du Bois fibers. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e3ffa8c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Radu Laza and Sándor Kovács | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4016bb | problem | aim-0df1011a6fa8a3c46e2c977b7e4016bb | Properties of higher singularities and minimal exponents · Question 3.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Let X be a normal variety of dimension n. X is pre-$\lceil \frac{n}{2} \rceil$-Du Bois. Then is X pre-n-Du Bois? X is pre-$\lfloor \frac{n}{2} \rfloor$-rational. Then is X pre-n-rational? | unassessed | {
"key": "aimpl",
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"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sridhar Venkatesh | null | null | null | [
{
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e402042 | problem | aim-0df1011a6fa8a3c46e2c977b7e402042 | Positive/mixed characteristic · Question 2.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there a notion of pseudo p-rationality? That is, $H^d_m(R) \rightarrow H^d_m(\mathbb{R} \pi_*\mathcal{O}_Y)$ is injective, where $\pi: Y \rightarrow X$ is a proper birational map and $d = \dim X$. (This definition assumes X is Cohen-Macaulay) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
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"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e402042",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Rahul Ajit | null | null | null | [
{
"kind": "website",
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"sort_order": 0
},
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e402ece | problem | aim-0df1011a6fa8a3c46e2c977b7e402ece | Properties of higher singularities and minimal exponents · Question 3.25 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Are there universal bounds on the multiplicity of a p-DB and p-rational singularities?
For p=0, dim X = n, embedding dimension of x=e, then $mult_x \le \binom{e}{n}$ when X is Du Bois, and $\binom{e-1}{n-1}$ when X is rational? | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sung Gi Park | null | null | null | [
{
"kind": "website",
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"note": null,
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},
{
"kind": "website",
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"url... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4033ee | problem | aim-0df1011a6fa8a3c46e2c977b7e4033ee | Positive/mixed characteristic · Question 2.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | If X is rational, this means something like $\mathcal{O}_X \rightarrow B$ where B is Cohen-Macaulay algebra, then $H^i_x(\mathcal{O}_X) \rightarrow H^i_x(B)$ is injective.
- Is there an analog of this for Du Bois singularities? (where B is almost CM?)
- Is there a m-rational version of this?
- Is there a cha... | unassessed | {
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"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Karl Schwede | null | null | null | [
{
"kind": "website",
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4045f6 | problem | aim-0df1011a6fa8a3c46e2c977b7e4045f6 | Properties of higher singularities and minimal exponents · Question 3.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Let H = Z(f), $p\in H$. Is the minimal exponent $\tilde{\alpha}_p(H) \le lct(\mathfrak{m}_p \cdot Jac(f))$?
This is related to Tessier's conjecture and also to the work of Dano Kim who proved that this is true if $\tilde{\alpha}_p(H) = lct(H)$. Mircea also commented that it is easy to reduce to the case of isolated si... | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e4045f6",
"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mircea Mustaţă | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e4045f6",
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{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e405839 | problem | aim-0df1011a6fa8a3c46e2c977b7e405839 | Properties of higher singularities and minimal exponents · Question 3.35 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Consider a family of hypersurfaces with non-isolated singularities. Is there a condition for the minimal exponent to be constant in the family?
(When the hypersurfaces have isolated singularities, there is a condition in terms of Milnor numbers.) | unassessed | {
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e405839",
"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alexandra Viktorova | null | null | null | [
{
"kind": "website",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f80b48a0-0654-4a5b-b1cc-b579467159e5","format_issues":null,"number":10935} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e405cc2 | problem | aim-0df1011a6fa8a3c46e2c977b7e405cc2 | Definitions of higher singularities and related invariants · Question 4.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there a notion of minimal exponent in the non-lci case related to higher singularities? This requires p-Du Bois $\Rightarrow$ (p-1)-rational.
Is there an invariant characterizing rational singularities? | unassessed | {
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"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Brad Dirks | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e407325 | problem | aim-0df1011a6fa8a3c46e2c977b7e407325 | Properties of higher singularities and minimal exponents · Question 3.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | How do we decide if a hypersurface H is m-Du Bois or m-rational in the non-isolated case? | unassessed | {
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"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Radu Laza | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"a0cecf8d-efc3-4b46-b5d8-beffff6e5a25","format_issues":null,"number":10936} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e41bd9e | problem | aim-0df1011a6fa8a3c46e2c977b7e41bd9e | Properties of higher singularities and minimal exponents · Question 3.45 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | What are the $(n+1)\times (n+1)$ tables with entries either 0 or 1, depending on whether $\mathcal(H)^q \underline{\Omega}_X^p$ is zero or not?
Most simple case: Is there a surface X with $\mathcal(H)^1 \underline{\Omega}_X^1 = 0$, but $\mathcal(H)^1 \underline{\Omega}_X^0 \neq 0$? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e41bd9e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mihnea Popa | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4374e2 | problem | aim-0df1011a6fa8a3c46e2c977b7e4374e2 | Properties of higher singularities and minimal exponents · Question 3.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Maxim-Yang prove a result characterizing $m$-Du Bois and $m$-rational hypersurface singularities in terms of characteristic classes. Can we extend this to the lci case? | unassessed | {
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"name": "AIMPL · Higher Du Bois and higher rational singularities",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e4374e2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Wanchun Shen | null | null | null | [
{
"kind": "website",
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"sort_order": 0
},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"7e8563f7-a1b0-40b1-beac-dee83479e89a","format_issues":null,"number":10938} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e438e75 | problem | aim-0df1011a6fa8a3c46e2c977b7e438e75 | Definitions of higher singularities and related invariants · Question 4.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Is there a good notion of a relative Du Bois complex? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/4/#0df1011a6fa8a3c46e2c977b7e438e75",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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},
{
"kind": "website",
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"url... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"74b43e4b-393e-42ab-a0d0-31fc8de33f2c","format_issues":null,"number":10946} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e439419 | problem | aim-0df1011a6fa8a3c46e2c977b7e439419 | Properties of higher singularities and minimal exponents · Question 3.55 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Can we prove that a variety with `enough' endomorphisms is pre-$m$-Du Bois for all $m$? This would support a conjecture which predicts that such varieties have to be toric. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e439419",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jakub Witaszek | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e439419",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"6924588f-02eb-41d5-8341-13df2af894c9","format_issues":null,"number":10939} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e43951a | problem | aim-0df1011a6fa8a3c46e2c977b7e43951a | Properties of higher singularities and minimal exponents · Question 3.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Study the global behavior of period map on $m$-Du Bois loci. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e43951a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e43951a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
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"published_at": "2026-09-09T22:24:06.501Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ce38a659-f3f6-4754-823c-f176770c0ca9","format_issues":null,"number":10940} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e43a357 | problem | aim-0df1011a6fa8a3c46e2c977b7e43a357 | Positive/mixed characteristic · Question 2.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Understand KSBA moduli spaces in char p (Hodge bundles, local freeness + commutes with base change, E_1 degeneration etc). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e43a357",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Iacopo Brivio | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/2/#0df1011a6fa8a3c46e2c977b7e43a357",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url... | {
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] | [] | {
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"published_at": "2026-09-09T22:24:06.431Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2aa32ef5-760c-4d32-8de9-0e66b5fc34de","format_issues":null,"number":10928} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e43a643 | problem | aim-0df1011a6fa8a3c46e2c977b7e43a643 | Properties of higher singularities and minimal exponents · Question 3.65 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdubois/ Not an author-supplied MSC code."
}
] | Understand the higher Du Bois singularities in the case of cubics and see what are some examples of Hodge structures in the case of cubics. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher Du Bois and higher rational singularities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e43a643",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher Du Bois and higher rational singularities · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher Du Bois and higher rational singularities · Original question",
"url": "http://aimpl.org/higherdubois/3/#0df1011a6fa8a3c46e2c977b7e43a643",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url... | {
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"published_at": "2026-09-09T22:24:06.506Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8e2f9c6b-6ea0-420c-bfba-31a633fa0c0a","format_issues":null,"number":10941} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e448950 | problem | aim-0df1011a6fa8a3c46e2c977b7e448950 | Brauer Group · Question 1.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | What is the (relative to $E_n$) Brauer group of the category of $K(n)$-local spectra? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Chromatic homotopy theory and p-adic geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/chromhomotopy/1/#0df1011a6fa8a3c46e2c977b7e448950",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
People have studied $\text{Br}^{\text{et}}(\text{TMF})$ and $\text{Br}(\text{Sp}_{K(1)})$. Related to $H^2(\mathbf{G}_n, \text{LT}... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Chromatic homotopy theory and p-adic geometry · Original question",
"url": "http://aimpl.org/chromhomotopy/1/#0df1011a6fa8a3c46e2c977b7e448950",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url":... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4008b247-3f55-4115-8407-5851895501f3","format_issues":null,"number":10274} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e44dca1 | problem | aim-0df1011a6fa8a3c46e2c977b7e44dca1 | Two Towers Isomorphism · Question 2.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | This isomorphism can be understood in terms of the respective moduli problems when evaluated on perfectoid rings. Is there a geometric description of the two tower isomorphism for more general rings? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Chromatic homotopy theory and p-adic geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/chromhomotopy/2/#0df1011a6fa8a3c46e2c977b7e44dca1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | ## Section context
The two towers isomorphism is a $\text{GL}_n(\mathbf{Q}_p) \times D_{1/n}^\times$-equivariant isomorphism of perfectoid spaces $$\text{LT}_{n,\infty} \cong \mathcal{H}^{n-1}_\infty,$$ where $\mathcal{H}^{n-1}$ is Drinfeld symmetric space in dimension $n -1$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e44e3a5 | problem | aim-0df1011a6fa8a3c46e2c977b7e44e3a5 | Two Towers Isomorphism · Question 2.2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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] | Is there a way to enhance the two tower isomorphism in terms of analytic stacks? | unassessed | {
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"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | ## Section context
The two towers isomorphism is a $\text{GL}_n(\mathbf{Q}_p) \times D_{1/n}^\times$-equivariant isomorphism of perfectoid spaces $$\text{LT}_{n,\infty} \cong \mathcal{H}^{n-1}_\infty,$$ where $\mathcal{H}^{n-1}$ is Drinfeld symmetric space in dimension $n -1$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e44fab2 | problem | aim-0df1011a6fa8a3c46e2c977b7e44fab2 | Power Operations · Question 3.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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] | Can one use the $\text{GL}_n(\mathbf{Z}_p)$ action on $\mathcal{H}^{n-1}$ to understand power operations of $L_{K(0)} E_n$? | unassessed | {
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## Status note in the source
For example, in the context of HKR character theory. The example for $BG$ for a finite group $G$ is worked out in [Source citatio... | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e451ade | problem | aim-0df1011a6fa8a3c46e2c977b7e451ade | Pro-etale cohomology of Lubin-Tate space · Question 4.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
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] | What is $H^*_\text{proet}(\text{LT}_n, \mathscr{O}^+)$ (e.g. when $n = 1,2$)? What is $H^*_\text{proet}([\text{LT}_n/\mathbf{G}_n], \mathscr{O}^+)$? Is it of finite cohomological dimension? Is it finitely generated? | unassessed | {
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## Status note in the source
This is studied in [Source citation: arxiv:2402.00960](http://aimpl.org/chromhomotopy/bib/) with bounds on the $p$-torsion. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4530ef | problem | aim-0df1011a6fa8a3c46e2c977b7e4530ef | Rational Homotopy of Invariants · Question 5.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | What is $\pi_*(E^{h\Gamma}) \otimes \mathbf{Q}$ for closed subgroups $\Gamma \subset \mathbf{G}_n$? | unassessed | {
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"url": "http://aimpl.org/chromhomotopy/5/#0df1011a6fa8a3c46e2c977b7e4530ef",
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"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
If $\Gamma$ is open this could be understood using finite covers of $\mathcal{H}^{n-1}$. If the image of $\Gamma$ under $\text{det... | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e454fb3 | problem | aim-0df1011a6fa8a3c46e2c977b7e454fb3 | Rational Homotopy of Invariants · Question 5.2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | What is the connection between a choice of maximal torus of $\mathbf{G}_n$ of dimension $n$ and there being $n$ exterior generators?
Can this be related to the identification (say $p \neq 2$) $$\text{THH}(\mathbf{Z}_p) \cong t_{\ge 0} (\text{im}(J))^{tC_p}?$$ What about $\text{THH}(\text{BP}\langle n \rangle)$. Is i... | unassessed | {
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"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e455c8c | problem | aim-0df1011a6fa8a3c46e2c977b7e455c8c | Hopkins' Chromatic Splitting Conjecture · Question 6.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | What are the iterated localizations $$L_{K(t_0)}L_{K(t_1)} \dots L_{K(t_n)} \mathbf{S}$$ where $t_0 < t_1 < \dots < t_n$? | unassessed | {
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"url": "http://aimpl.org/chromhomotopy/6/#0df1011a6fa8a3c46e2c977b7e455c8c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
The chromatic splitting predicts an answer. For example is it true that $$L_{K(n-1)} L_{K(n)} \mathbf{S} \cong L_{K(n-1)}(\mathbf{... | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e456a4d | problem | aim-0df1011a6fa8a3c46e2c977b7e456a4d | Hopkins' Chromatic Splitting Conjecture · Question 6.2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "55",
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"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
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] | Is $\pi_0(L_{K(n-1)} L_{K(n)} E_n)$ a Huber ring? (Probably not.) Is it a solid ring? | unassessed | {
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"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e45a369 | problem | aim-0df1011a6fa8a3c46e2c977b7e45a369 | Hopkins' Chromatic Splitting Conjecture · Question 6.3 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | Is it true that $$L_{K(n-1)} (E^{h\mathbf{G}_n^1}) \cong L_{K(n-1)} \mathbf{S}?$$ | unassessed | {
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"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e45b7f4 | problem | aim-0df1011a6fa8a3c46e2c977b7e45b7f4 | Hopkins' Chromatic Splitting Conjecture · Question 6.4 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | In char $p$, $$H^*(\mathbf{G}_n^1, E_{n, *}/(p, u_1, \dots, u_{n-2}))[u_{n-1}^{\pm 1}] \cong H^*(\mathbf{G}_{n-1}, k[u^{\pm 1}]).$$ | unassessed | {
"key": "aimpl",
"name": "AIMPL · Chromatic homotopy theory and p-adic geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/chromhomotopy/6/#0df1011a6fa8a3c46e2c977b7e45b7f4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e45c8c0 | problem | aim-0df1011a6fa8a3c46e2c977b7e45c8c0 | Approach to Fargues-Fontaine Curve using THH · Question 7.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | There is an identification $\text{THH}(\mathbf{Z}_p) \cong t_{\ge 0} (\text{im}(J))^{tC_p}$. Does this isomorphism yield an integral version of the Fargues-Fontaine curve? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Chromatic homotopy theory and p-adic geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/chromhomotopy/7/#0df1011a6fa8a3c46e2c977b7e45c8c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | ## Question context
Analogy coming from period rings and the modulo $p$ isomorphism $\text{THH}(\mathbf{F}_p) \cong t_{> 0} (\text{im}(J))^{tC_p}$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Chromatic homotopy theory and p-adic geometry · Original question",
"url": "http://aimpl.org/chromhomotopy/7/#0df1011a6fa8a3c46e2c977b7e45c8c0",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e45e815 | problem | aim-0df1011a6fa8a3c46e2c977b7e45e815 | Exceptional element of Pic at (2,2) · Question 8.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "55",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Chromatic homotopy theory and p-adic geometry. http://aimpl.org/chromhomotopy/ Not an author-supplied MSC code."
}
] | Is $\text{Pic}_{2,2} \rightarrow \text{Pic}^\text{alg}_{2,2}$ surjective? This is the last remaining case not covered by [Source citation: arxiv:2407.20958](http://aimpl.org/chromhomotopy/bib/). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Chromatic homotopy theory and p-adic geometry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/chromhomotopy/8/#0df1011a6fa8a3c46e2c977b7e45e815",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes":... | null | null | null | not-recorded | not-recorded | null | [] | [] | Chromatic homotopy theory and p-adic geometry · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Chromatic homotopy theory and p-adic geometry · Original question",
"url": "http://aimpl.org/chromhomotopy/8/#0df1011a6fa8a3c46e2c977b7e45e815",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url":... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e474c1c | problem | aim-0df1011a6fa8a3c46e2c977b7e474c1c | Log rational and cluster type pairs · Question 2.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $T$ be a toric $3$-fold and $B\sim |-K_T|$ be an slc hypersurface of coregularity zero. Show that $(T,B)$ is log rational. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e474c1c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e474c1c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "htt... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e475277 | problem | aim-0df1011a6fa8a3c46e2c977b7e475277 | Log rational and cluster type pairs · Question 2.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $(X,B)$ be a log Calabi--Yau pair of dimension $n$. Let $(Y,B_Y)\rightarrow (X,B)$ be a dlt modification. Assume that every strata of $(Y,B_Y)$, inlcuding $Y$ itself, is a rational variety. Furthermore, assume that $\mathcal{D}(Y,B_Y)\simeq_{\rm PL} \mathbf{S}^{n-1}$. Prove that $(X,B)$ is a log rational pair. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e475277",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e47b7dd | problem | aim-0df1011a6fa8a3c46e2c977b7e47b7dd | Log rational and cluster type pairs · Question 2.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Classify log rational smooth Fano $3$-folds. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47b7dd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47b7dd",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "htt... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e47b7dd",
"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"770e2b42-f560-4445-ade6-cd029eb1db84","format_issues":null,"number":10953} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e47c562 | problem | aim-0df1011a6fa8a3c46e2c977b7e47c562 | Log rational and cluster type pairs · Question 2.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $(X,B)$ be a log Calabi--Yau pair of dimension $n$, index one, and Picard rank $\rho$. Assume that the number of components of $B$ equals $n+\rho-1$. Show that $(X,B)$ is of cluster type. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47c562",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47c562",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "htt... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"dac9b704-378f-43e9-9af4-7eab113a6fc0","format_issues":null,"number":10954} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e47d45e | problem | aim-0df1011a6fa8a3c46e2c977b7e47d45e | Log rational and cluster type pairs · Question 2.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Classify which smooth Fano blow-ups of $\mathbb{P}^3$ are of cluster type. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47d45e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
"url": "http://aimpl.org/higherdimlogcy/2/#0df1011a6fa8a3c46e2c977b7e47d45e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "htt... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e47d45e",
"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.595Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"9d7c098f-b8f9-453b-bf33-85815cea9f03","format_issues":null,"number":10955} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e47e66b | problem | aim-0df1011a6fa8a3c46e2c977b7e47e66b | Log rational and cluster type pairs · Question 2.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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] | Let $X$ be a cluster type variety defined over an algebraically closed field $k$ of characteristic $p>1$. Show that $X$ is liftable over $\mathbb{W}_2(k)$. | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4809fa | problem | aim-0df1011a6fa8a3c46e2c977b7e4809fa | Mukai conjecture and related problems · Question 3.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $X$ be a klt Fano variety. Write $-K_X\equiv \sum_{i=1}^k a_i M_i$ where each $a_i \in \mathbb{R}_{>0}$ and each $M_i$ is a nef Cartier divisor which is not numerically trivial. Then, we have $\sum_{i=1}^k a_i\leq \dim(X)+\rho(X)$ and the equality holds if and only if $X$ is a product of projective spaces. | unassessed | {
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"url": "http://aimpl.org/higherdimlogcy/3/#0df1011a6fa8a3c46e2c977b7e4809fa",
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4812ad | problem | aim-0df1011a6fa8a3c46e2c977b7e4812ad | Mukai conjecture and related problems · Question 3.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $X$ be a klt Fano variety of dimension $n$. Write $-K_X\equiv \sum_{i=1}^k a_i M_i$ where each $a_i\in \mathbb{R}_{>0}$ and each $M_i$ is a nef Cartier divisor which is not numerically trivial. Then, we have $\sum_{i=1}^k a_i\leq 2n$. Furthermore, the equality holds if and only if $X\simeq (\mathbb{P}^1)^n$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/3/#0df1011a6fa8a3c46e2c977b7e4812ad",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4841b3 | problem | aim-0df1011a6fa8a3c46e2c977b7e4841b3 | Mukai conjecture and related problems · Question 3.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $(X,B,\mathbf{M})$ be a generalized log Calabi--Yau pair. Let $B=\sum_{i=1}^k a_i B_i$ be its decomposition into prime components. Let $X'$ be the model where the b-nef divisor $\mathbf{M}$ descends. Assume we can write $\mathbf{M}_{X'}\equiv \sum_{i=1}^j b_i M_i$ where each $b_i\geq 0$ and each $M_i$ is a nef Cart... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/3/#0df1011a6fa8a3c46e2c977b7e4841b3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e484a90 | problem | aim-0df1011a6fa8a3c46e2c977b7e484a90 | Mukai conjecture and related problems · Question 3.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $X$ be a smooth Fano variety all whose extremal contractions are fibrations. Prove that ${\rm Nef}(X)$ is a simplicial cone. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Higher-dimensional log Calabi-Yau pairs",
"type": "workshop-problem-list",
"url": "http://aimpl.org/higherdimlogcy/3/#0df1011a6fa8a3c46e2c977b7e484a90",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional log Calabi-Yau pairs · AIMPL workshop record | ## Workshop introduction
Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional log Calabi-Yau pairs · Original question",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0ec359e7-089f-4d3b-a828-3d7db5eb2bc4","format_issues":null,"number":10960} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4873b6 | problem | aim-0df1011a6fa8a3c46e2c977b7e4873b6 | Torelli group orbits | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Classify the finite orbits of $T_{g,n}$ on the character varieties $M(\Sigma_{g,n}, r)$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e4873b6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
The Torelli group $T_{g,n}$ is the kernel of the action of the mapping class group of $\Sigma_{g,n}$ on homology $H_1(\Sigma_{g,n}, \mathbb{Z})$. Restricting the mapping class group action to this subgroup gives an action on the character variety $M(\Sigma_{g,n}, r)$ of rank $r$ semi-simple local s... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
For $r = 1$ the Torelli group acts trivially. Some possible interesting examples: representations valued in the infinite Dihedral ... | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e48c2fa | problem | aim-0df1011a6fa8a3c46e2c977b7e48c2fa | Mapping class group orbits in higher rank | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | What are some sufficient conditions for a point to have a Zariski dense orbit under the mapping class group on $M_\gamma(\Sigma_{g,n}, \mathrm{SL}_3)$? Here $\gamma$ is a fixed characteristic polynomial for monodromy around the punctures. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e48c2fa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e48c2fa",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url": "http://aimp... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"477603d4-68e8-4d27-88f8-92296dbf7c36","format_issues":null,"number":11313} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e48d486 | problem | aim-0df1011a6fa8a3c46e2c977b7e48d486 | Classification of MCG-finite localy systems of higher rank | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Can we classify the finite orbts under the mapping class group in $M(\Sigma_{0,n}, \mathrm{SL}_3)$, in particular the case $n = 4$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e48d486",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
Recent work of Lam, Landesman, Litt has led to a mostly complete understanding of the finite orbits under the mapping class group of rank $2$ local systems on $\Sigma_{0,n}$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
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"url": "http://aimp... | {
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"published_at": "2026-09-09T22:24:08.750Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8e7aa294-7583-4e24-99da-3d391cc308c8","format_issues":null,"number":11314} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e48fe9e | problem | aim-0df1011a6fa8a3c46e2c977b7e48fe9e | Fixed points of special elements of the mapping class group | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Fix $\gamma \in \mathrm{Mod}(\Sigma_g)$ can we understand the set of fixed points $M(\Sigma_g, 2)(\overline{\mathbb{Z}})^{\gamma}$ of its action on the rank $2$ character variety? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e48fe9e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
"url": "http://aimpl.org/motivesandmcg/1/#0df1011a6fa8a3c46e2c977b7e48fe9e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimp... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e48fe9e",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.755Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6fc0bc0d-a99d-4171-bc06-1d042235e81d","format_issues":null,"number":11315} |
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