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1.0.0 | problem:aim-30af364e265727bf114bfe5bea12f8b3 | problem | aim-30af364e265727bf114bfe5bea12f8b3 | Tensor products · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | What is the ideal structure of $\mathcal{B}\left( H\right) \otimes
_{\min }\mathcal{Q}\left( H\right) $? Does it depend on the model of set
theory? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/3/#30af364e265727bf114bfe5bea12f8b3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/3/",
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.412Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5e50f3c4-c447-4965-b46e-fac8df7808b2","format_issues":null,"number":7167} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea130391 | problem | aim-30af364e265727bf114bfe5bea130391 | Calkin algebra · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is it consistent that, for a nonseparable Hilbert space $\mathcal{H}$,
$\mathcal{B}\left( \mathcal{H}\right) \left/ \mathcal{K}\left( \mathcal{H}%
\right) \right. $ has an outer automorphism? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/2/#30af364e265727bf114bfe5bea130391",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/2/",
"note": null,
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] | {
"source_record": "30af364e265727bf114bfe5bea130391",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
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1.0.0 | problem:aim-30af364e265727bf114bfe5bea1311b2 | problem | aim-30af364e265727bf114bfe5bea1311b2 | Nonseparable C-algebras · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is the following relatively consistent with ZFC?
Every C*-algebra $A$ that has a unique irreducible representation up to the
unitary equivalence is isomorphic to the algebra of compact operators on some
Hilbert space. | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/6/#30af364e265727bf114bfe5bea1311b2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The statement is true for separable C*-algebras. The negation of the statement is relatively consistent with ZFC, since it follows from Jensen's diamond principle. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Naimark | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/6/",
"note": null,
"sort_order": 0
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"source-full-text-not-present"
] | [] | {
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"published_at": "2026-09-08T03:33:08.450Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e63a48b0-1035-493e-8e6f-3a77494d6547","format_issues":null,"number":7176} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13373d | problem | aim-30af364e265727bf114bfe5bea13373d | Borel complexity · Question 05 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is conjugacy by automorphism of masas of the hyperfinite II$_{1}$
factor classifiable by countable structures? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea13373d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13373d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.472Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d2583a06-f501-4783-9de0-ea7daa3bc75c","format_issues":null,"number":7181} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13436a | problem | aim-30af364e265727bf114bfe5bea13436a | Borel complexity · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | What is the right set-theoretic framework to deal with functorial
classification? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea13436a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13436a",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.476Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a46fa229-b37e-4b40-bdd9-640f1b27f1d4","format_issues":null,"number":7182} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea134f5a | problem | aim-30af364e265727bf114bfe5bea134f5a | Borel complexity · Question 15 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is there a constructive Borel proof of the $\mathcal{O}_{2}$ embedding theorem? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea134f5a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.481Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8044b628-a447-49ea-ad06-cb6d8a7d2b69","format_issues":null,"number":7183} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea135623 | problem | aim-30af364e265727bf114bfe5bea135623 | Borel complexity · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is the isomorphism relation in the following classes of separable
C*-algebras:
- all
- nuclear
- exact
- simple
- simple exact
- nuclear $\mathcal{Z}$-stable
- simple nuclear
complete analytic? below a group actions? above all group actions? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea135623",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea135623",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.484Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3ec93ec0-a463-407e-b8b0-8864deb015f9","format_issues":null,"number":7184} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea136296 | problem | aim-30af364e265727bf114bfe5bea136296 | Borel complexity · Question 25 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | What is the complexity of isometric isomorphism of direct limits of
not necessarily self-adjoint subalgebras of finite dimensional C*-algebras?
How does it compare to the complexity of isomorphism of AF algebras? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea136296",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.488Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"af203fce-d5cb-4808-9867-4045e59e91cb","format_issues":null,"number":7185} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea136d56 | problem | aim-30af364e265727bf114bfe5bea136d56 | Borel complexity · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is there a Borel inverse of the classification functor? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea136d56",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
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] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.493Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2eae382f-cd6d-4372-96b8-54e302089c15","format_issues":null,"number":7186} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea136ef1 | problem | aim-30af364e265727bf114bfe5bea136ef1 | Borel complexity · Question 35 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | For a separable C*-algebra $A$, what is the complexity of orbit
equivalence relations associated to the action $\mathrm{Aut}\left( A\right) $
on itself by conjugacy and to the action of $\mathrm{Inn}\left( A\right) $
on $\mathrm{\mathrm{Au}t}\left( A\right) $ by left translation? Are these
action turbulent? How are the... | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea136ef1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-30af364e265727bf114bfe5bea1375ce | problem | aim-30af364e265727bf114bfe5bea1375ce | Tensor products · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Does $\otimes _{\min }$ or $\otimes _{\max }$ commute with forcing? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/settheorycstar/3/#30af364e265727bf114bfe5bea1375ce",
"citation": null,
"doi": null,
"arxiv_id": null,
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Set theory and C-algebras",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-30af364e265727bf114bfe5bea137a17 | problem | aim-30af364e265727bf114bfe5bea137a17 | Nuclearity · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is every stably finite nuclear separable C*-algebra locally
approximable by type I C*-algebras? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/4/#30af364e265727bf114bfe5bea137a17",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/4/",
"note": null,
"sort_order": 0
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] | {
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.420Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b57e6374-2908-4e82-8a89-6e0c01477474","format_issues":null,"number":7169} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13846a | problem | aim-30af364e265727bf114bfe5bea13846a | Nuclearity · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Does every nuclear C*-algebra belong to the
bootstrap class? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/4/#30af364e265727bf114bfe5bea13846a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | ## Question context
All presently known nuclear C*-algebras are obtained from $\mathbb C$ by
taking closure under simple operations such as tensoring with
finite-dimensional matrix algebras and taking inductive limits. They
belong to the so-called bootstrap class. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/4/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.425Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"40390c8c-76ac-40ea-b0ff-65ce567805c8","format_issues":null,"number":7170} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea138be7 | problem | aim-30af364e265727bf114bfe5bea138be7 | Nuclearity · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Do all nuclear C*-algebras satisfy the UCT (Universal Coefficient
Theorem)? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/4/#30af364e265727bf114bfe5bea138be7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/4/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.429Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f604fbf4-0e88-4137-a7fc-c7e896326e5a","format_issues":null,"number":7171} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea1399a5 | problem | aim-30af364e265727bf114bfe5bea1399a5 | Borel complexity · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is the Mackey Borel
structure on the spectrum of a simple separable C*-algebra always the same when
it is not standard? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea1399a5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Diximier | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea1399a5",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.504Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b563f4b8-70fb-4257-ad51-7692998ed28a","format_issues":null,"number":7188} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13a8e6 | problem | aim-30af364e265727bf114bfe5bea13a8e6 | Borel complexity · Question 45 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Does the complexity of the Mackey Borel structure of a simple separable
C*-algebra increase as one goes from nuclear C*-algebras to exact ones to ones
that are not even exact? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea13a8e6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13a8e6",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.508Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1676843d-30c3-44aa-a89e-3080b844908a","format_issues":null,"number":7189} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13b55d | problem | aim-30af364e265727bf114bfe5bea13b55d | Borel complexity · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Assume $A$ and $B$ are C*-algebras and $E_A$ is Borel-reducible to $E_B$. What does this fact imply about the
relation between $A$ and $B$? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/7/#30af364e265727bf114bfe5bea13b55d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | ## Question context
If A is a C*-algebra, denote by $E_A$ the relation of unitary equivalence of pure states of A. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13b55d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.512Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3bdd72c3-c9ac-49b8-95f3-2ad392e6e40b","format_issues":null,"number":7190} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13bbfa | problem | aim-30af364e265727bf114bfe5bea13bbfa | Pure states · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Does every pure state of the atomic masa in $\mathcal{B}\left( H\right) $ extend uniquely to a pure
state of $\mathcal{B}\left( H\right) $? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/5/#30af364e265727bf114bfe5bea13bbfa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Kadison-Singer | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13bbfa",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.433Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5b144560-e63c-4734-9d44-a514c6ad8b46","format_issues":null,"number":7172} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13ca8e | problem | aim-30af364e265727bf114bfe5bea13ca8e | Pure states · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Consider the following statement: for every pure state $\phi$ of $\mathcal{B}\left( H\right) $ there is a masa $\mathcal{A}$ such that
$\phi\restriction \mathcal{A}$ is multiplicative (i.e., pure). Is it consistent with ZFC? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/5/#30af364e265727bf114bfe5bea13ca8e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Its negation is known to follow from the Continuum Hypothesis (Akemann-Weaver). | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13ca8e",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.437Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1e7a47ed-ed03-412b-8780-930613c251af","format_issues":null,"number":7173} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13d640 | problem | aim-30af364e265727bf114bfe5bea13d640 | Pure states · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Consider the following statement: every pure state on $\mathcal{B}\left( H\right) $ is diagonalizable. Is it consistent with with ZFC? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/5/#30af364e265727bf114bfe5bea13d640",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Its negation is known to follow from the Continuum Hypothesis (Akemann-Weaver) or even from Martin's Axiom (Farah-Weaver). | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/settheorycstar/5/",
"note": null,
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-30af364e265727bf114bfe5bea13f2bd | problem | aim-30af364e265727bf114bfe5bea13f2bd | Ultrapowers · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Assume $A$ is separable and $A$ embeds into
$\prod_{\mathcal U}\mathcal O_2$. Is there a $\leq$-maximal embedding $\phi$ of $A$ into
$\prod_{\mathcal U}\mathcal O_2$? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/1/#30af364e265727bf114bfe5bea13f2bd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | ## Question context
If $\phi_j\colon A\to \prod_{\mathcal U} \mathcal O_2$ are *-homomorphisms, write $\phi_1\leq
\phi_2$ if there is a partial isometry $u$ in $A$ such that $u^*\phi_2
u=\phi_1$. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Kirchberg | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/1/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5d8236fa-2fa4-4b36-9197-2be767db5a42","format_issues":null,"number":7159} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea13fd0a | problem | aim-30af364e265727bf114bfe5bea13fd0a | Ultrapowers · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Can one prove in ZFC that for some free ultrafilter $\mathcal U$ on $\mathbb N$ we have $\mathcal{B}\left( H\right) '\cap \prod_{\mathcal U}\mathcal{B}\left( H\right) =
\mathbb C I$? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/1/#30af364e265727bf114bfe5bea13fd0a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Selective ultrafilters have this property. The Continuum Hypothesis implies the existence of selective ultrafilters. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea13fd0a",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.382Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"19935881-33ce-4da7-a483-387aabb02a47","format_issues":null,"number":7160} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea140e12 | problem | aim-30af364e265727bf114bfe5bea140e12 | Ultrapowers · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is a nonprincipal ultrafilter such that $\mathcal{B}\left( H\right) '\cap \mathcal{B}\left( H\right) ^{\mathcal U}\neq \mathbb C I$ flat? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/1/#30af364e265727bf114bfe5bea140e12",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | ## Question context
An ultrafilter $\mathcal U$ on $\mathbb N$ is **flat** if there are $h_n\colon
\mathbb N\searrow [0,1]$ such that
- $h_n(0)=1$,
- $\lim_j h_n(j)=0$,
- $(\forall f\colon \mathbb N\nearrow \mathbb N)\lim_{n\to \mathcal U}
\sup_{j\in \mathbb N} |h_n(j)-h_n(f(j))|=0$. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The reverse implication is true. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/1/",
"note": null,
"sort_order": 0
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.386Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bf95350e-4b48-4dbe-b077-04cc2588a1e0","format_issues":null,"number":7161} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea141962 | problem | aim-30af364e265727bf114bfe5bea141962 | Nonseparable C-algebras · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Assume $A$ is a tensor product of algebras of the form $\mathbb{M}_n(\mathbb C)$, for $n\in \mathbb N$,
$\kappa<\kappa'$ are cardinals
and $\bigotimes_{\kappa'}\mathbb{M}_2(\mathbb C)$ unitally embeds into
$A\otimes \bigotimes_{\kappa}\mathbb{M}_2(\mathbb C)$. Can we conclude that there is a unital
embedding of $\big... | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/6/#30af364e265727bf114bfe5bea141962",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Such $A$ would have to be nonseparable, and the simplest open case is whether
$\bigotimes_{\aleph_1} \mathbb{M}_2(\mathbb C)$ unitally embeds into
$\bigotimes_{\aleph_0}\mathbb{M}_2(\mathbb C)\ot... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Farah-Katsura | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/6/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.454Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"372ed48e-265f-4537-a600-228e58dadb47","format_issues":null,"number":7177} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea141ed6 | problem | aim-30af364e265727bf114bfe5bea141ed6 | Nonseparable C-algebras · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is every exact C*-algebra a subalgebra of a nuclear C*-algebra? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/6/#30af364e265727bf114bfe5bea141ed6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The answer is positive for separable algebras since
every separable exact C*-algebra is a subalgebra of $\mathcal O_2$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea141ed6",
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.458Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cfd026d8-3cc6-4bb3-88c5-4fecfe2536be","format_issues":null,"number":7178} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea14225d | problem | aim-30af364e265727bf114bfe5bea14225d | Nonseparable C-algebras · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Is there a universal nuclear C*-algebra of character density $\aleph_1$?
More generally, for which cardinals $\kappa$ is there a universal
nuclear C*-algebra of character density $\kappa$? Similar question can be asked for exact algebras. | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/6/#30af364e265727bf114bfe5bea14225d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea14225d",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.463Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1f2ab953-0633-4f84-bc72-f32430ce866d","format_issues":null,"number":7179} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea1431ba | problem | aim-30af364e265727bf114bfe5bea1431ba | Nonseparable C-algebras · Question 6 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Suppose a C*-algebra
has an approximate identity consisting of projections. Does it have an
increasing approximate identity (on some index set, possibly different)
consisting of projections? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/6/#30af364e265727bf114bfe5bea1431ba",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The answer is positive in the separable case. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Phillips | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea1431ba",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.467Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9165bd7c-079d-487e-bf8d-6975dc822fcc","format_issues":null,"number":7180} |
1.0.0 | problem:aim-30af364e265727bf114bfe5bea14597a | problem | aim-30af364e265727bf114bfe5bea14597a | Calkin algebra · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "46",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Functional analysis. http://aimpl.org/settheorycstar/ Not an author-supplied MSC code."
}
] | Does every masa in the Calkin algebra that is generated by its projections lift to a masa in $\mathcal{B}\left( H\right) $? | unassessed | {
"key": "aimpl",
"name": "AIM · Set theory and C-algebras",
"type": "workshop-problem-list",
"url": "http://aimpl.org/settheorycstar/2/#30af364e265727bf114bfe5bea14597a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Set theory and C-algebras · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Anderson | null | null | null | [
{
"kind": "website",
"citation": "Set theory and C-algebras",
"url": "http://aimpl.org/settheorycstar/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "30af364e265727bf114bfe5bea14597a",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.403Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6233db62-fbc2-40d5-8527-e3b4456182f7","format_issues":null,"number":7165} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd002508 | problem | aim-38756a1f9b537f4591526253cd002508 | Positive elements that aren't sums of squares in group algebra · Question 1.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Find a positive element of $\mathbb{C}[\mathbb{F}_n\times \mathbb{F}_n]$ -- the group algebra of the product of the free group with itself --
that is not a sum of squares.
Here, positive means positive in all Hilbert space representations.
The problem is known for $n=2$ so the general case is $n\geq 3$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/1/#38756a1f9b537f4591526253cd002508",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | William Slofstra | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/1/#38756a1f9b537f4591526253cd002508",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/... | {
"source_record": "38756a1f9b537f4591526253cd002508",
"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": "2026-09-09T22:24:08.885Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"34c6f50c-7b27-4086-b25f-b5f3ce61f11a","format_issues":null,"number":11336} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd004fa3 | problem | aim-38756a1f9b537f4591526253cd004fa3 | Pure trace polynomials as sums of squares of rationals · Question 2.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Can a noncommutative polynomial $p$ such that $\mathrm{tr}(p(X)) \geq 0$ for all matrix evaluations be written as a sum of squares of
noncommutative rational function plus commutators of noncommutative rationals? | unassessed | {
"key": "aimpl",
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jurij Volčič | null | null | null | [
{
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd0066c0 | problem | aim-38756a1f9b537f4591526253cd0066c0 | Degree bounds for NSS/PSS · Question 3.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Find degree bounds/computability for noncommutative Nullstellens\"atze and Positivstellens\"atze. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/3/#38756a1f9b537f4591526253cd0066c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Rafael Oliveira | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/3/#38756a1f9b537f4591526253cd0066c0",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0ad0ea0c-3e93-4367-bc4d-8a1c568d5d8a","format_issues":null,"number":11338} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0079b4 | problem | aim-38756a1f9b537f4591526253cd0079b4 | Algebraic Circuits and rational identitiy testing · Question 4.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Find efficient algorithms for rational identity testing in terms of the size of algebraic circuits that represent a noncommutative rational
expression rather than using the linearization. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/4/#38756a1f9b537f4591526253cd0079b4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Rafael Oliveira | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/4/#38756a1f9b537f4591526253cd0079b4",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e4cc59d5-68e0-4135-bded-81f60be26484","format_issues":null,"number":11339} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0083f8 | problem | aim-38756a1f9b537f4591526253cd0083f8 | Matrix convexity of trace positivity set of a polynomial · Question 5.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Characterize the restrictions on a noncommutative polynomial $p$ such that $\mathcal{C}$ is matrix convex, where $\mathcal{C}$ is the set of
all matrix tuples $X$ such that $\mathrm{tr}(p(X))\geq 0$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/5/#38756a1f9b537f4591526253cd0083f8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Eric Evert | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/5/#38756a1f9b537f4591526253cd0083f8",
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{
"kind": "website",
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"url": "http://aimpl.org/... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ee9e1b9d-15d6-43d9-9524-2f2b6e0683af","format_issues":null,"number":11340} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd00a0e4 | problem | aim-38756a1f9b537f4591526253cd00a0e4 | Hyperbolic eigenvalues in Gaussian random direction · Question 6.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | What is the distribution of the hyperbolic eigenvalues in a Gaussian random direction for a hyperbolic polynomial? How does the geometry play a part? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/6/#38756a1f9b537f4591526253cd00a0e4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Nikhil Srivastava | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/6/#38756a1f9b537f4591526253cd00a0e4",
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{
"kind": "website",
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"url": "http://aimpl.org/... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f8bd320d-b321-4b8d-a962-ded876dd5ecf","format_issues":null,"number":11341} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd00ae36 | problem | aim-38756a1f9b537f4591526253cd00ae36 | Noncommutative hypoerbolic polynomials · Question 7.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Is there a noncommutative analog of hyperbolic polynomials? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/7/#38756a1f9b537f4591526253cd00ae36",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Bill Helton | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/7/#38756a1f9b537f4591526253cd00ae36",
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{
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"url": "http://aimpl.org/... | {
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd00bd39 | problem | aim-38756a1f9b537f4591526253cd00bd39 | Quantum games and sums of squares · Question 8.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | How do unique solutions for quantum games relate to their sum of squares representations? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/8/#38756a1f9b537f4591526253cd00bd39",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Bill Helton | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/8/#38756a1f9b537f4591526253cd00bd39",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/... | {
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd00cf51 | problem | aim-38756a1f9b537f4591526253cd00cf51 | Algebra of 2XOR game · Question 9.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Is it true that the algebra of a 2XOR game is finite dimensional if and only if the game is uniquely solvable? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/9/#38756a1f9b537f4591526253cd00cf51",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | William Slofstra | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/9/#38756a1f9b537f4591526253cd00cf51",
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"url": "http://aimpl.org/... | {
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd00e3a9 | problem | aim-38756a1f9b537f4591526253cd00e3a9 | Testing membership in a subalgebra of the free algebra · Question 10.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | If $\mathcal{P}$ is a finite collection of noncommutative polynomials and $q$ is a noncommutative polynomial, then is $q$ in the unital
subalgebra generated by $\mathcal{P}$ if and only if $q(X) = q(Y)$ for all matrices $X$ and $Y$ such that $p(X) = p(Y)$ for all $p\in
\mathcal{P}$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/10/#38756a1f9b537f4591526253cd00e3a9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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 answer is no. The the coordinates of $P = (x, xy, yx, y + yxy)$ do not generate the free algebra, yet $P$ is injective on matr... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd011d88 | problem | aim-38756a1f9b537f4591526253cd011d88 | Finding rational simple eigenvalues of a noncommutative rational · Question 11.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Suppose $r$ is a noncommutative rational function. Can we find $\Xi$, a tuple of matrices over the field of univariate rational functions,
such that $r(\Xi)$ is a matrix of rational functions with a simple rational eigenvalue? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/11/#38756a1f9b537f4591526253cd011d88",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Jurij Volčič | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/11/#38756a1f9b537f4591526253cd011d88",
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"url": "http://aimpl.org... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"6c4aafe5-078f-4100-920c-d4ff2f77d3a8","format_issues":null,"number":11346} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd013961 | problem | aim-38756a1f9b537f4591526253cd013961 | Convexity of a specific class of trace functions · Question 12.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Characterize the convexity of $\mathrm{Tr}\left[(K^*A^{q/2}B^pA^{q/2}K)^s\right]$ (taken over all $K$ and positive-definite $A$ and $B$). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/12/#38756a1f9b537f4591526253cd013961",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Anna Vershynina | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/12/#38756a1f9b537f4591526253cd013961",
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{
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"published_at": "2026-09-09T22:24:08.947Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8305f5f4-4830-424f-8308-2e0ee48409b6","format_issues":null,"number":11347} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd013acd | problem | aim-38756a1f9b537f4591526253cd013acd | Rational Free Bertini · Question 13.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Suppose $r$ is a noncommutative rational function and for any $\lambda\in \mathbb{C}$ and positive integer $n$, let
$\mathcal{L}_{n,\lambda}(r)$ be the set of all tuples of $n\times n$ matrices such that $\det(r(X) - \lambda I_n) = 0$.
Is it true that $\mathcal{L}_{n,\lambda}(r)$ is irreducible for all but finitely ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Noncommutative inequalities",
"type": "workshop-problem-list",
"url": "http://aimpl.org/noncommineqV/13/#38756a1f9b537f4591526253cd013acd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Noncommutative inequalities · 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"
] | Jurij Volčič | null | null | null | [
{
"kind": "website",
"citation": "Noncommutative inequalities · Original question",
"url": "http://aimpl.org/noncommineqV/13/#38756a1f9b537f4591526253cd013acd",
"note": null,
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},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d1c8b813-8da4-4f54-9d31-21f1656de48f","format_issues":null,"number":11348} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd018070 | problem | aim-38756a1f9b537f4591526253cd018070 | Automorphism Loci · Question 1.1 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Given a subgroup $G$ of ${\rm{PGL}}_{N+1}$, we define $\mathcal{M}_d^N[G]$ to be the Zariski closed subset defined by maps whose automorphism group contains an isomorphic copy of $G$. Investigate these loci. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd018070",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | L. DeMarco and J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd018070",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd018070",
"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 | [
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.341Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"561eccc8-6525-4474-9c76-8b9ecb284223","format_issues":null,"number":11252} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01a061 | problem | aim-38756a1f9b537f4591526253cd01a061 | Automorphism Loci · Question 1.2 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What is the class determined by $\mathcal{M}_d^N[G]$ in the homology? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01a061",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01a061",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01a061",
"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",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:24:08.347Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"21e09672-9b7b-42e8-b038-8fc26bdb7ba4","format_issues":null,"number":11253} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01ae31 | problem | aim-38756a1f9b537f4591526253cd01ae31 | Automorphism Loci · Question 1.3 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What are possible automorphism groups for maps at the boundary of $(\mathcal{M}_d^N)^{\rm{ss}}$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01ae31",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | M. Weinreich | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01ae31",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01ae31",
"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": "2026-09-09T22:24:08.353Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d040f529-d729-4f8f-9591-a8ec101f8f55","format_issues":null,"number":11254} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01ba4c | problem | aim-38756a1f9b537f4591526253cd01ba4c | Automorphism Loci · Question 1.4 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What is the essential dimension of $\mathcal{M}_d^N[G]$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01ba4c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | D. Bejleri | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01ba4c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01ba4c",
"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": "2026-09-09T22:24:08.358Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d31326a2-7801-437b-91b3-a9c69bd4945a","format_issues":null,"number":11255} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01c08c | problem | aim-38756a1f9b537f4591526253cd01c08c | Automorphism Loci · Question 1.5 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Relate the singular locus of $\mathcal{M}_d^N$ to the automorphism locus
$$\{\langle f\rangle\in \mathcal{M}_d^N\mid {\rm{Aut}}(f) \text{ is non-trivial}\}$$
which is where the conjugation action fails to be free. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01c08c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | K. Filom | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/1/#38756a1f9b537f4591526253cd01c08c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01c08c",
"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": "2026-09-09T22:24:08.364Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"14f353e3-3eaf-4d7b-8702-24ee73e63627","format_issues":null,"number":11256} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01d4e2 | problem | aim-38756a1f9b537f4591526253cd01d4e2 | Arithmetic Questions · Question 2.05 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Do ``rigid'' -- analogues of maps that are not flexible Lattès -- PCF maps form a subset of bounded height in $\mathcal{M}_d^N(\overline{\Bbb{Q}})$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd01d4e2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | P. Ingram, H. Krieger | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd01d4e2",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01d4e2",
"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": "2026-09-09T22:24:08.369Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8b026610-05c5-4352-bdb5-172e566adef8","format_issues":null,"number":11257} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd01e3f3 | problem | aim-38756a1f9b537f4591526253cd01e3f3 | Arithmetic Questions · Question 2.1 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is there a countable Zariski dense (Galois invariant) subset of ``dynamically interesting'' maps in
$\mathcal{M}_d^N(\overline{\Bbb{Q}})$ (with bounded height)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd01e3f3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | L. DeMarco and J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd01e3f3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd01e3f3",
"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": "2026-09-09T22:24:08.374Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a8392c77-6325-4ae0-a012-d4600895fcf7","format_issues":null,"number":11258} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd025381 | problem | aim-38756a1f9b537f4591526253cd025381 | Arithmetic Questions · Question 2.15 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
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] | What is the locus in $\mathcal{M}_d^N$ of maps with ``small'' arboreal image? More precisely, what can be said about the locus in $\mathcal{M}_d^N\times\Bbb{P}^N$ formed by $(f,P)$ such that the image of the associated arboreal representation is of infinite index? Do such points lie on any ``dynamically special'' subva... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | H. Krieger | null | null | null | [
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd0266dd | problem | aim-38756a1f9b537f4591526253cd0266dd | Arithmetic Questions · Question 2.2 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | For a map $f$ defined over a field $K$, let $K^{\rm{pre}}_f$ be the extension of $K$ generated by all preperiodic points of $f$.
What can be said about $[K^{\rm{pre}}_f:K]$?
What $K^{\rm{pre}}_f=K^{\rm{pre}}_g$ implies about maps $f$ and $g$?
What if $K^{\rm{pre}}$ is replaced with $K^{\rm{preper}}$ or $K^{\rm{mult}}$... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd0266dd",
"citation": null,
"doi": null,
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"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd026e77 | problem | aim-38756a1f9b537f4591526253cd026e77 | Arithmetic Questions · Question 2.25 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | The Shafarevich dimension of $\mathcal{M}_d^N$ is defined as
$$
\sup_{(K,S)}\dim \overline{\left\{\text{elements of } \mathcal{M}_d^N(K) \text{ that have good reduction outside } S\right\}}.
$$
What is this dimension? Is it equal to $2d-2$ when $N=1$? | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | H. Krieger, J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
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"note": null,
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{
"kind": "website",
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"url": "ht... | {
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd028007 | problem | aim-38756a1f9b537f4591526253cd028007 | PCF Maps in Higher Dimensions · Question 3.1 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | In the definition of PCF maps in higher dimensions, is the ``all the way down'' condition needed? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/modalgdyn/3/#38756a1f9b537f4591526253cd028007",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/3/#38756a1f9b537f4591526253cd028007",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd028007",
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd028a02 | problem | aim-38756a1f9b537f4591526253cd028a02 | PCF Maps in Higher Dimensions · Question 3.2 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is the set of PCF maps in $\mathcal{M}_d^N$ Zariski dense for $N\geq 2$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
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"url": "http://aimpl.org/modalgdyn/3/#38756a1f9b537f4591526253cd028a02",
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"doi": null,
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"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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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"sort_order": 0
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{
"kind": "website",
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"url": "ht... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"df3815a9-1cd6-4e05-bb3a-0be3b445ae10","format_issues":null,"number":11270} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd02905d | problem | aim-38756a1f9b537f4591526253cd02905d | PCF Maps in Higher Dimensions · Question 38756a1f | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | For which $(N+1)\times (N+1)$ matrices $A$ the map
$\mathbf{X}\in\Bbb{P}^N\mapsto A\mathbf{X}^d\in\Bbb{P}^N$ is PCF for some $d\geq 2$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/3/#38756a1f9b537f4591526253cd02905d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | P. Ingram | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/3/#38756a1f9b537f4591526253cd02905d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd02905d",
"imported_at": "2026-09-10",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c6b9ef10-c9fb-4763-b2fa-e89257554cb7","format_issues":null,"number":11271} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd02c99b | problem | aim-38756a1f9b537f4591526253cd02c99b | Generalization of Complex Dynamical Results to Higher Dimensions · Question 5.1 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What is the bifurcation measure $\mu_{\rm{bif}}$ in $\mathcal{M}_d^N$ (over a field $\Bbb{C}_\nu$)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/5/#38756a1f9b537f4591526253cd02c99b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | H. Krieger, C. Petsche | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/5/#38756a1f9b537f4591526253cd02c99b",
"note": null,
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{
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"url": "ht... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e27f37db-43fe-444b-90eb-9cb6fb423b84","format_issues":null,"number":11283} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd02e68b | problem | aim-38756a1f9b537f4591526253cd02e68b | Generalization of Complex Dynamical Results to Higher Dimensions · Question 5.2 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is a dynamically stable algebraic family of degree $d$ maps $\Bbb{CP}^N\rightarrow\Bbb{CP}^N$ (i.e. a subvariety of ${\rm{End}}^N_d$) which is not Lattès or isotrivial necessarily PCF? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/5/#38756a1f9b537f4591526253cd02e68b",
"citation": null,
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"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | L. DeMarco | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/5/#38756a1f9b537f4591526253cd02e68b",
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{
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"url": "ht... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"fbd8b9d6-12d7-4f12-80d8-c0d4fb029205","format_issues":null,"number":11284} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd02ffee | problem | aim-38756a1f9b537f4591526253cd02ffee | Generalization of Complex Dynamical Results to Higher Dimensions · Question 5.3 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Self-similarity of $p$-adic bifurcation loci in $1$-parameter families when $p<\text{ the degree}$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/5/#38756a1f9b537f4591526253cd02ffee",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
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"url": "ht... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"cb814831-4839-4196-9d8a-90f97191da18","format_issues":null,"number":11285} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd031c1c | problem | aim-38756a1f9b537f4591526253cd031c1c | Geometry and Topology of Moduli Spaces · Question 4.05 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is the moduli space $\mathcal{M}_d^N:={\rm{End}}^N_d/{\rm{PGL}}_{N+1}$ rational? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd031c1c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd031c1c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
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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": "2026-09-09T22:24:08.451Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d5112ed8-e262-4a18-ad0d-d82ac687aae6","format_issues":null,"number":11272} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd033a81 | problem | aim-38756a1f9b537f4591526253cd033a81 | Geometry and Topology of Moduli Spaces · Question 4.1 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is $\mathcal{M}_d^N[n]$ (the moduli space of maps with marked points of period $n$) a variety of general type for
$n\geq C(d,N)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd033a81",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd033a81",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd033a81",
"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": "2026-09-09T22:24:08.457Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1df1e38f-cad2-4213-a4cc-db79e7557f79","format_issues":null,"number":11273} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0351dd | problem | aim-38756a1f9b537f4591526253cd0351dd | Geometry and Topology of Moduli Spaces · Question 4.15 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Does the gonality of $\mathcal{M}_d^N[n]$ tend to infinity as $n\to\infty$? How about the moduli spaces $\mathcal{M}_d^N[\mathcal{P}]$ where $\mathcal{P}$ is a portrait? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0351dd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | M. Manes and J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0351dd",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd0351dd",
"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": "2026-09-09T22:24:08.462Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"27844658-2c2e-4547-bc12-ec192d92f822","format_issues":null,"number":11274} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03724f | problem | aim-38756a1f9b537f4591526253cd03724f | Arithmetic Questions · Question 2.3 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Generalizations of dynamical local/global\\ PCF (post-critically finite) $\Leftrightarrow$ PCB (post-critically bounded)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03724f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | C. Petsche, B. Thompson | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03724f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03724f",
"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": "2026-09-09T22:24:08.396Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"48886920-e185-4947-855d-7fc9c617e32f","format_issues":null,"number":11262} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd038233 | problem | aim-38756a1f9b537f4591526253cd038233 | Arithmetic Questions · Question 2.35 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Find an appropriate critical/canonical height on $\mathcal{M}_d^N$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd038233",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | N. Looper | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd038233",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd038233",
"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": "2026-09-09T22:24:08.401Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2561f87d-10aa-4e1d-b885-0d8c33723e89","format_issues":null,"number":11263} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd038d5e | problem | aim-38756a1f9b537f4591526253cd038d5e | Arithmetic Questions · Question 2.4 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Find/prove dynamical analogues of the Szpiro conjecture. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd038d5e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | N. Looper | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd038d5e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd038d5e",
"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": "2026-09-09T22:24:08.407Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d0b602fc-e67a-478e-afaa-551abefa0069","format_issues":null,"number":11264} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd039f2e | problem | aim-38756a1f9b537f4591526253cd039f2e | Arithmetic Questions · Question 2.45 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | For $\alpha\in\bar{\Bbb{Q}}$, investigate
$\max\{\hat{\lambda}_{\nu,f}(\sigma\alpha)\mid \sigma\in{\rm{Gal}}(\bar{\Bbb{Q}}/\Bbb{Q})\}$ ($\hat{\lambda}_{\nu,f}$ the local height associated with a map $f$ and a valuation $\nu$). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd039f2e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | H. Krieger | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd039f2e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd039f2e",
"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": "2026-09-09T22:24:08.412Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5cdba3ef-5f57-4040-815b-0773420047d9","format_issues":null,"number":11265} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03a183 | problem | aim-38756a1f9b537f4591526253cd03a183 | Arithmetic Questions · Question 2.5 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Lift ${\rm{End}}^N_d(\overline{\Bbb{F}_p})$ to PCF elements of ${\rm{End}}^N_d(\overline{\Bbb{Q}_p})$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03a183",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | A. Shankar | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03a183",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03a183",
"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": "2026-09-09T22:24:08.419Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5e7c81bf-f7c7-436c-aa6f-10acc8308eab","format_issues":null,"number":11266} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03a6fd | problem | aim-38756a1f9b537f4591526253cd03a6fd | Arithmetic Questions · Question 2.55 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is there a bound for $[K_{\rm{def}}:K_{\rm{moduli}}]$ depending on $N$ but not on $d$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03a6fd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03a6fd",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03a6fd",
"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": "2026-09-09T22:24:08.424Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"24b1c1d5-283e-454f-b812-9591c3e307b2","format_issues":null,"number":11267} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03ca9c | problem | aim-38756a1f9b537f4591526253cd03ca9c | Arithmetic Questions · Question 2.6 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Study dynamical systems $\Bbb{P}^N\rightarrow\Bbb{P}^N$ whose field of moduli is contained in $\Bbb{R}$. When can they be defined over the reals? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03ca9c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/2/#38756a1f9b537f4591526253cd03ca9c",
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},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03ca9c",
"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",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.429Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7cab7b95-8260-4464-8bdf-59b202144bf5","format_issues":null,"number":11268} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03e2fb | problem | aim-38756a1f9b537f4591526253cd03e2fb | Geometry and Topology of Moduli Spaces · Question 4.2 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Is the class of $\mathcal{M}_d^1$ the same as that of $\Bbb{A}^{2d-2}$ in the Grothendieck ring of varieties? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd03e2fb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | K. Filom | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd03e2fb",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03e2fb",
"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": "2026-09-09T22:24:08.467Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"77cf4305-815d-4cc5-96ce-df1c0907efe8","format_issues":null,"number":11275} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd03f595 | problem | aim-38756a1f9b537f4591526253cd03f595 | Geometry and Topology of Moduli Spaces · Question 4.25 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Compute Betti numbers and the fundamental group of $\mathcal{M}_d^N(\Bbb{C})$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd03f595",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | K. Filom | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd03f595",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd03f595",
"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": "2026-09-09T22:24:08.473Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1bf773cf-015e-41cf-bc34-9a9efaa1b732","format_issues":null,"number":11276} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0407d6 | problem | aim-38756a1f9b537f4591526253cd0407d6 | Geometry and Topology of Moduli Spaces · Question 4.3 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Understand ``dynamically significant'' ``fibrations'' $\mathcal{M}_d^N\rightarrow\Bbb{A}^{m}$ (singular fibers allowed), e.g. those defined by multipliers. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0407d6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | H. Krieger | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0407d6",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd0407d6",
"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": "2026-09-09T22:24:08.481Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0d0d7c2b-8898-401f-82a0-28809d8b94fe","format_issues":null,"number":11277} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd040b46 | problem | aim-38756a1f9b537f4591526253cd040b46 | Geometry and Topology of Moduli Spaces · Question 4.35 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Obtain an dynamical understanding of $(\mathcal{M}_d^N)^{\rm{ss}}-\mathcal{M}_d^N$ and $(\mathcal{M}_d^N)^{\rm{unstable}}:=\Bbb{P}^M-(\mathcal{M}_d^N)^{\rm{ss}}\quad (M=\binom{N+d}{d}(N+1)-1)$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd040b46",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Silverman, M. Weinreich | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd040b46",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd040b46",
"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": "2026-09-09T22:24:08.541Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e1f9001e-3cca-4550-9692-97bc763fa622","format_issues":null,"number":11278} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0419e1 | problem | aim-38756a1f9b537f4591526253cd0419e1 | Geometry and Topology of Moduli Spaces · Question 4.4 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What is the equivariant cohomology of the semi-stable locus $(\mathcal{M}_d^N)^{\rm{ss}}$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0419e1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | D. Bejleri | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0419e1",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd0419e1",
"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": "2026-09-09T22:24:08.547Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f25fb50b-79f0-4340-8be1-10e1c35b8c06","format_issues":null,"number":11279} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd041c08 | problem | aim-38756a1f9b537f4591526253cd041c08 | Geometry and Topology of Moduli Spaces · Question 4.45 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | What are some non-GIT compactifications of $\mathcal{M}_d^N$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd041c08",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | D. Bejleri | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd041c08",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd041c08",
"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": "2026-09-09T22:24:08.552Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"45708b6d-24e2-43ec-8cb0-efaae46bfffb","format_issues":null,"number":11280} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0426d7 | problem | aim-38756a1f9b537f4591526253cd0426d7 | Geometry and Topology of Moduli Spaces · Question 4.5 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Understand different GIT quotients for $\mathcal{M}_d^N[n]$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0426d7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | H. Moon | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd0426d7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd0426d7",
"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": "2026-09-09T22:24:08.557Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"991f98af-da0d-4534-bc47-e1e8ae20c9a5","format_issues":null,"number":11281} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd042d32 | problem | aim-38756a1f9b537f4591526253cd042d32 | Geometry and Topology of Moduli Spaces · Question 4.55 | {
"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/modalgdyn/ Not an author-supplied MSC code."
}
] | Are distinguished curves in $\mathcal{M}_d^N$ or $\mathcal{M}_d^N[n]$ (e.g. dynatomic curves) irreducible or smooth? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moduli spaces for algebraic dynamical systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd042d32",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moduli spaces for algebraic dynamical systems · 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"
] | J. Doyle | null | null | null | [
{
"kind": "website",
"citation": "Moduli spaces for algebraic dynamical systems · Original question",
"url": "http://aimpl.org/modalgdyn/4/#38756a1f9b537f4591526253cd042d32",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "ht... | {
"source_record": "38756a1f9b537f4591526253cd042d32",
"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": "2026-09-09T22:24:08.563Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0d0867d1-5379-4a8a-9830-a10d048812d0","format_issues":null,"number":11282} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd04b9fd | problem | aim-38756a1f9b537f4591526253cd04b9fd | Second Eigenvalue Multiplicity | {
"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/spectralhypergraph/ Not an author-supplied MSC code."
}
] | Let $G$ be a graph with maximum degree bounded by $\Delta$. For the following choices of Hermitian matrix $M_G$ associated with $G$, what is the maximum multiplicity of the second largest eigenvalue of $M_G$?
For the following choices of Hermitian matrix $M_G$ associated with $G$, what is the maximum multiplicity of t... | unassessed | {
"key": "aimpl",
"name": "AIM · Spectral graph and hypergraph theory: connections and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/spectralhypergraph/1/#38756a1f9b537f4591526253cd04b9fd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per... | null | null | null | not-recorded | not-recorded | null | [] | [] | Spectral graph and hypergraph theory: connections and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Spectral graph and hypergraph theory: connections and applications",
"url": "http://aimpl.org/spectralhypergraph/1/",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.164Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"03e2c562-67c1-463b-9c86-df8087488658","format_issues":null,"number":8534} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd057e98 | problem | aim-38756a1f9b537f4591526253cd057e98 | Problems · Question 2 | {
"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/spectralhypergraph/ Not an author-supplied MSC code."
}
] | For a fixed choice of parameters $\rho$ and $\Delta$, what is the largest possible multiplicity of the second eigenvalue of the adjacency matrix $A_G$ with the constraint that $\lambda_2(A_G) = \rho$. | unassessed | {
"key": "aimpl",
"name": "AIM · Spectral graph and hypergraph theory: connections and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/spectralhypergraph/1/#38756a1f9b537f4591526253cd057e98",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per... | null | null | null | not-recorded | not-recorded | null | [] | [] | Spectral graph and hypergraph theory: connections and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Spectral graph and hypergraph theory: connections and applications",
"url": "http://aimpl.org/spectralhypergraph/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "38756a1f9b537f4591526253cd057e98",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.169Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df5a882b-270a-4ef2-80e6-2e9c6087f806","format_issues":null,"number":8535} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0594bf | problem | aim-38756a1f9b537f4591526253cd0594bf | Nonbacktracking Matrix | {
"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/spectralhypergraph/ Not an author-supplied MSC code."
}
] | Let $G$ be any graph on $n$ vertices and $m$ edges, and let $B_G$ denote the **nonbacktracking matrix** of $G$, which is a $2m\times 2m$ matrix whose rows and columns are indexed by directed edges of $G$, defined as follows:
$$
B_G[uv, xy] =
\begin{cases}
1 & \text{if $v = x$, $u\ne y$} \\
0 &... | unassessed | {
"key": "aimpl",
"name": "AIM · Spectral graph and hypergraph theory: connections and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/spectralhypergraph/1/#38756a1f9b537f4591526253cd0594bf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per... | null | null | null | not-recorded | not-recorded | null | [] | [] | Spectral graph and hypergraph theory: connections and applications · Historical workshop question | ## Question context
Basic questions about the eigenvalues and eigenvectors of the nonbacktracking matrix of irregular graphs remain open. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Spectral graph and hypergraph theory: connections and applications",
"url": "http://aimpl.org/spectralhypergraph/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "38756a1f9b537f4591526253cd0594bf",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.173Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0676037b-dd8b-4a29-9e71-918fd80d137e","format_issues":null,"number":8536} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd05ca25 | problem | aim-38756a1f9b537f4591526253cd05ca25 | Positive and negative $\ell_2$-mass on spectrum | {
"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/spectralhypergraph/ Not an author-supplied MSC code."
}
] | Let $G$ be a connected graph and let $\lambda_1\ge\dots\ge\lambda_s\ge 0>\lambda_{s+1}\ge\dots\ge\lambda_n$ be the eigenvalues of the adjacency matrix of $G$. Defining:
\begin{align*}
S^+(G) &:=\sum_{i=1}^s \lambda_i^2\\
S^-(G) &:= \sum_{i=s+1}^n \lambda_i^2.
\end{align*}
Some conjectures and questions of inte... | unassessed | {
"key": "aimpl",
"name": "AIM · Spectral graph and hypergraph theory: connections and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/spectralhypergraph/1/#38756a1f9b537f4591526253cd05ca25",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per... | null | null | null | not-recorded | not-recorded | null | [] | [] | Spectral graph and hypergraph theory: connections and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Spectral graph and hypergraph theory: connections and applications",
"url": "http://aimpl.org/spectralhypergraph/1/",
"note": null,
"sort_order": 0
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] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.178Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a401a907-6b2e-4646-9616-1996b7ede451","format_issues":null,"number":8537} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd07e2bb | problem | aim-38756a1f9b537f4591526253cd07e2bb | Stability of the Liouville property | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | For any group $G$ and two measures $\mu_1$, $\mu_2$ which are symmetric and finitely supported, the Poisson boundary for $(G, \mu_1)$ is trivial if and only if the Poisson boundary for $(G, \mu_2)$ is trivial. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/1/#38756a1f9b537f4591526253cd07e2bb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
Relations between Poisson boundaries, Martin boundaries, Gromov Boundaries, Sublinearly Morse boundaries, etc. | 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"
] | Vadim Kaimanovich | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/1/#38756a1f9b537f4591526253cd07e2bb",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "38756a1f9b537f4591526253cd07e2bb",
"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",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:09.761Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0e5c4a13-43e2-49be-82c9-a399b4861d09","format_issues":null,"number":11486} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd081774 | problem | aim-38756a1f9b537f4591526253cd081774 | Poisson boundary for random walks on free (semi)-groups with infinite moment | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | For any random walk on the free group or free semigroup, the Gromov boundary with the hitting measure is a topological model for the Poisson boundary. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/1/#38756a1f9b537f4591526253cd081774",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
Relations between Poisson boundaries, Martin boundaries, Gromov Boundaries, Sublinearly Morse boundaries, etc. | 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"
] | Vadim Kaimanovich | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/1/#38756a1f9b537f4591526253cd081774",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "38756a1f9b537f4591526253cd081774",
"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": "2026-09-09T22:24:09.766Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd9f3e13-151b-4028-9ca1-681508aff718","format_issues":null,"number":11487} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd083661 | problem | aim-38756a1f9b537f4591526253cd083661 | Singularity of the Harmonic Measure | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | Let $\Gamma$ be a Fuchsian group, and let $\mu$ be a finitely supported measure on $\Gamma$. Is the harmonic measure singular with respect to the Lebesgue measure on the circle? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd083661",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
For a random walk on the fundamental group of a manifold of constant negative curvature, one has almost sure convergence to the boundary of hyperbolic space. This lets one define the hitting measure, by pushing forward the shift-space measure to the boundary S^n. How do properties of this measure re... | 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"
] | Vadim Kaimanovich | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd083661",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "38756a1f9b537f4591526253cd083661",
"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": "2026-09-09T22:24:09.778Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e4ed06b2-9757-4573-8c61-ad0d52fbc338","format_issues":null,"number":11489} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0841a8 | problem | aim-38756a1f9b537f4591526253cd0841a8 | Dimension of Harmonic Measure over Moduli Space | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | Fix some measure $\mu$ on $\pi_1(M)$, where $M$ is a manifold of curvature -1. Construct the random walk on hyperbolic $n$-space by picking a representation $\rho: \pi_1(M) \to \text{Aut}(\mathbb{H}^n)$. How does the dimension of the harmonic measure $\nu$ change as a function of $\rho$? Is the function $\rho \to -\log... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd0841a8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
For a random walk on the fundamental group of a manifold of constant negative curvature, one has almost sure convergence to the boundary of hyperbolic space. This lets one define the hitting measure, by pushing forward the shift-space measure to the boundary S^n. How do properties of this measure re... | 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 Lessa | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd0841a8",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "38756a1f9b537f4591526253cd0841a8",
"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": "2026-09-09T22:24:09.786Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9506161f-f49a-4e55-a109-9bd59c36dc7d","format_issues":null,"number":11490} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0850e0 | problem | aim-38756a1f9b537f4591526253cd0850e0 | Witnessing a Conformal Measure | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | Let $G$ be a $\delta$-hyperbolic group. Let $\nu$ be a conformal measure on the Gromov Boundary $\partial_{\text{Gromov}} G$. does there exist some probability measure $\mu$ on $G$ such that $\nu$ and the hitting measure for $\mu$ lie in the same measure class? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd0850e0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
For a random walk on the fundamental group of a manifold of constant negative curvature, one has almost sure convergence to the boundary of hyperbolic space. This lets one define the hitting measure, by pushing forward the shift-space measure to the boundary S^n. How do properties of this measure re... | 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"
] | Francois Ledrappier | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/2/#38756a1f9b537f4591526253cd0850e0",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http:/... | {
"source_record": "38756a1f9b537f4591526253cd0850e0",
"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": "2026-09-09T22:24:09.792Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2cd16588-5b6c-47d6-9e9a-e8d207360871","format_issues":null,"number":11491} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd087735 | problem | aim-38756a1f9b537f4591526253cd087735 | The Sublinearly Morse boundary and the Martin boundary | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | If $G$ is a Hierarchically Hyperbolic Space, and $\mu$ is a symmetric non-degenerate probability measure on $G$ with finite support, then the Sublinearly Morse Boundary of $G$ embeds into the Martin boundary of $(G, \mu)$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/1/#38756a1f9b537f4591526253cd087735",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic groups · AIMPL workshop record | ## Section context
Relations between Poisson boundaries, Martin boundaries, Gromov Boundaries, Sublinearly Morse boundaries, etc.
## Question context
The Sublinearly Morse boundary of a geodesic metric space encodes the set of 'nearly-hyperbolic directions'. The Martin boundary for a measured group $(G, \mu)$ is the... | 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"
] | Ilya Gekhtman | null | null | null | [
{
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd088fad | problem | aim-38756a1f9b537f4591526253cd088fad | Exponential Genericity of Pseudo-Anosovs | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [
{
"code": "20F",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/randwalkgroup/ Not an author-supplied MSC code."
}
] | Let $S$ be a generating set for the mapping class group. Does the number of non-pseudo-Anosov elements in the R-ball with respect to S converge exponentially to 0 as $R$ goes to infinity? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Random walks beyond hyperbolic groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/randwalkgroup/3/#38756a1f9b537f4591526253cd088fad",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Random walks beyond hyperbolic 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"
] | Inhyeok Choi | null | null | null | [
{
"kind": "website",
"citation": "Random walks beyond hyperbolic groups · Original question",
"url": "http://aimpl.org/randwalkgroup/3/#38756a1f9b537f4591526253cd088fad",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f2cddd74-bebd-400a-a7a2-b1792108ee50","format_issues":null,"number":11492} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08a19e | problem | aim-38756a1f9b537f4591526253cd08a19e | Finite-dimensional interpretation of Bridgeland stability | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Find or describe a finite-dimensional analogue of the dHYM equation and its relation to stability, similar to how finite-dimensional geometric invariant theory is formally similar to traditional Hermitian Yang--Mills and slope stability, which may be seen as an infinite-dimensional Kempf--Ness theorem.
Furthermore, ... | unassessed | {
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"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08a19e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08a19e",
"note": null,
"sort_order": 0
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{
"kind": "website",
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"url": "http://aimpl.org/s... | {
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"evidence_label": "Workshop record · status unassessed",
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"published_at": "2026-09-09T22:24:10.542Z",
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd08b1c0 | problem | aim-38756a1f9b537f4591526253cd08b1c0 | Dimensional reduction of deformed Hermitian Yang--Mills | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Understand the solvability of the dHYM equation on higher rank bundles in any examples. In particular:
- On complex surfaces with (special) Lagrangian torus fibrations and semi-flat metrics, such as elliptically fibered K3 surfaces.
- By dimensionally reducing from 4 (real) dimensions to two dimensions using... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08b1c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08b1c0",
"note": null,
"sort_order": 0
},
{
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"url": "http://aimpl.org/s... | {
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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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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.548Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"21997127-de9b-4e68-b00f-af0f681cb7b4","format_issues":null,"number":11625} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08b47e | problem | aim-38756a1f9b537f4591526253cd08b47e | Toric mirror symmetry and asymptotically admissible Lagrangians | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Provide an algebro-geometric or categorical interpretation of the central charge-type term
$$\int_{L_\mathcal{X}^\delta} \tilde \Omega$$
appearing in the study of deformations of special Lagrangians in toric mirror symmetry for mirrors to pushforwards of $\mathcal{O}(-\delta E)$ coming from birational models $\mathca... | unassessed | {
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"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08b47e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08b47e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"url": "http://aimpl.org/s... | {
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"published_at": "2026-09-09T22:24:10.553Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"43c1d3a1-f512-4a37-829d-de489209f8a5","format_issues":null,"number":11626} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08be49 | problem | aim-38756a1f9b537f4591526253cd08be49 | Lagrangian mean curvature flow for K\"ahler--Einstein manifolds with definite first Chern class. | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | What does Lmcf look like for K\"ahler--Einstein manifolds with definite first Chern class. In particular:
- What does Lmcf look like for $c_1(X)>0$. For example Evans work on $\mathbb{CP}^2$ shows possible oscillating behaviour for Lmcf where a (non minimal) Clifford torus can flow to a Chekanov torus and back t... | unassessed | {
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"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08be49",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08be49",
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{
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"url": "http://aimpl.org/s... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"7374a974-c045-4cc9-85bd-62e5fe79376c","format_issues":null,"number":11627} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08bff8 | problem | aim-38756a1f9b537f4591526253cd08bff8 | Lagrangian mean curvature flow with dilations | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | What happens under Lmcf to Lagrangians in, for example, $\mathbb{R}^{2n} \cong T^* \mathbb{R}^n$ where one also allows dilations of the fibres (see work of Neves who shows that singularities are generic). In particular if you squish the initial Lagrangian very close to the zero section before running Lmcf are singulari... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08bff8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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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"url": "http://aimpl.org/s... | {
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd08c566 | problem | aim-38756a1f9b537f4591526253cd08c566 | Definition of dHYM in higher rank for complexes of vector bundles | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | What is the right definition of the higher rank dHYM equation for complexes of vector bundles? Such a definition would need to satisfy certain desirable properties:
- It should be mirror to the special Lagrangian condition, possibly for multisection special Lagrangians in a semi-flat SYZ model.
- Existence o... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08c566",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08c566",
"note": null,
"sort_order": 0
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{
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"url": "http://aimpl.org/s... | {
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"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 | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.573Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c4a802c3-b388-4edb-9b34-d9582c7a34a3","format_issues":null,"number":11629} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08c916 | problem | aim-38756a1f9b537f4591526253cd08c916 | Deriving higher rank dHYM from Lagrangian multisections using mirror symmetry | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | How can one derive mathematically the higher rank dHYM equation from Lagrangian multisections using mirror symmetry. For example consider the case $T\mathbb{CP}^2$ relating to a multisection with one ramification point. | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08c916",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08c916",
"note": null,
"sort_order": 0
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{
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"url": "http://aimpl.org/s... | {
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"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.578Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"77eb3d51-d5cf-4c28-a404-e33e4e6398ce","format_issues":null,"number":11630} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08cf35 | problem | aim-38756a1f9b537f4591526253cd08cf35 | Thomas--Yau--Joyce conjecture for the flat 2-torus | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Prove a version of the Thomas--Yau--Joyce conjecture for curves in the flat 2-torus, or just on $\mathbb{R}^2$. Technicalities that occur include:
- One must restrict to the immersed case, as the embedded case is already understood.
- Finite time singularities will occur, due to for example figure-eights.
... | unassessed | {
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"name": "AIMPL · Stability in mirror symmetry",
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"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08cf35",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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 | [
{
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{
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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": "2026-09-09T22:24:10.583Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b08cbb02-0b13-48b9-ab58-289f4fec42a0","format_issues":null,"number":11631} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08d3fa | problem | aim-38756a1f9b537f4591526253cd08d3fa | Geometric structures on the space of complexified Kahler classes and of stability conditions | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | What are natural Weil--Peterson-type metrics on moduli of complexified K\"ahler classes, and what can be said about the geometry of the moduli space using them. For example what are geodesics? (This requires a search of the Physics and Bridgeland stability literature beforehand, where such questions have been investiga... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08d3fa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08d3fa",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/s... | {
"source_record": "38756a1f9b537f4591526253cd08d3fa",
"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",
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"published_at": "2026-09-09T22:24:10.589Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ce3d8c88-d067-487f-ac42-ce75f7d943c2","format_issues":null,"number":11632} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08df2c | problem | aim-38756a1f9b537f4591526253cd08df2c | Examples of Joyce--Lee--Tsui translators in explicit cases | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Study whether an almost-calibrated translator arises in Lmcf, for example in the simplest case ($\mathbb{C}^2$). The grim reaper translator is not allowed as this is not strictly almost-calibrated (having phase change exactly $\pi$). The Joyce program predicts the existence of such translators in the immersed case in d... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08df2c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08df2c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/s... | {
"source_record": "38756a1f9b537f4591526253cd08df2c",
"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": "2026-09-09T22:24:10.595Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eaa422d7-4125-4179-9da4-241c354a0b2d","format_issues":null,"number":11633} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08e9f6 | problem | aim-38756a1f9b537f4591526253cd08e9f6 | Study mirror symmetry in model Calabi-Yau metrics arising out of real Monge--Ampere equations near large volume limit. | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Study the existence and flows for dHYM and special Lagrangians in semi-flat SYZ model Calabi--Yau metrics arising from real Monge--Ampere equations near the large volume limit. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08e9f6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08e9f6",
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},
{
"kind": "website",
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"url": "http://aimpl.org/s... | {
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"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 | [
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.601Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d98d64c4-e2ea-4170-aae0-14a3d8875f8d","format_issues":null,"number":11634} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08f659 | problem | aim-38756a1f9b537f4591526253cd08f659 | Finite time singularities in dHYM flows and graphical Lagrangian mean curvature flow. | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Study the possibility of finite-time singularities for dHYM flows (any which seem applicable to the problem, or new flows). Note that finite-time singularity formation does occur in Lmcf which should be mirror to dHYM flow, but that dHYM arises as mirror to the study of Lagrangian **sections** and currently it is not k... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08f659",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08f659",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/s... | {
"source_record": "38756a1f9b537f4591526253cd08f659",
"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": "2026-09-09T22:24:10.606Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c1f819eb-1302-4741-9545-6c26ee312195","format_issues":null,"number":11635} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08f6df | problem | aim-38756a1f9b537f4591526253cd08f6df | Subsolutions of higher rank dHYM and Z-critical equation | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Is a solution to the higher rank dHYM equation necessarily a subsolution in the sense of Dervan--McCarthy--Sektnan. The analogous condition for dHYM in rank 1 is an equivalence by work of Gao Chen, and it is easily seen that in higher rank not every subsolution is a solution, but the converse implication is not known. ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08f6df",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08f6df",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/s... | {
"source_record": "38756a1f9b537f4591526253cd08f6df",
"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": "2026-09-09T22:24:10.612Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f9c7310-9b3a-4755-bc28-741bae726d41","format_issues":null,"number":11636} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd08fd05 | problem | aim-38756a1f9b537f4591526253cd08fd05 | Generating Lagrangians in the Fukaya category of P^2 relative to an elliptic curve | {
"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 list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Do special Lagrangians generate the Fukaya--Seidel category $\mathrm{FS}(W)$ for a superpotential $W$ mirror to $\mathbb{CP}^2$ relative to an elliptic curve $E$, $\mathbb{CP}^2/E$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08fd05",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists prod... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability in mirror symmetry · 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": "Stability in mirror symmetry · Original question",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd08fd05",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/s... | {
"source_record": "38756a1f9b537f4591526253cd08fd05",
"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": "2026-09-09T22:24:10.617Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bdf4a8fd-5fb2-477a-997d-a44e11b9980f","format_issues":null,"number":11637} |
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