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1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5802ed5c | problem | aim-5a5c75a582375f6beb4bc89e5802ed5c | Specific functions · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Do the coefficients of $h_m$ have enumerative significance? Can we find $h_m$ for $m \geq 9$? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/4/#5a5c75a582375f6beb4bc89e5802ed5c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
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] | {
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1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5802f9a2 | problem | aim-5a5c75a582375f6beb4bc89e5802f9a2 | Specific functions · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Does $F= \sum f_g(\tau)\lambda^{2g-2}$ have transformation properties with respect to $\lambda$? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/4/#5a5c75a582375f6beb4bc89e5802f9a2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/4/",
"note": null,
"sort_order": 0
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d9c1c83e-0194-4e87-bae8-36fc298b5804","format_issues":null,"number":7844} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58030899 | problem | aim-5a5c75a582375f6beb4bc89e58030899 | Specific functions · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Is $\sum \frac{(5n)!}{(n!)^5}z^n$ related to (non-holomorphic) forms? Is it related to automorphic objects?
Do other solutions to the Picard-Fuchs equation have modular properties? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/4/#5a5c75a582375f6beb4bc89e58030899",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/4/",
"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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.533Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dbf3a041-d83a-4b62-8c1c-97b25730b5eb","format_issues":null,"number":7845} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58032cf6 | problem | aim-5a5c75a582375f6beb4bc89e58032cf6 | Other problems · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Do the L-series of mixed mock modular forms have interesting properties? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/5/#5a5c75a582375f6beb4bc89e58032cf6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/5/",
"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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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"240f6649-6a78-4b81-bddc-3800d0b8fdf0","format_issues":null,"number":7846} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803321d | problem | aim-5a5c75a582375f6beb4bc89e5803321d | Other problems · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Do mixed mock modular forms satisfy differential equations with respect to a modular function? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/5/#5a5c75a582375f6beb4bc89e5803321d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/5/",
"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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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.545Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f396e24f-7b7c-4f34-8c26-f0a8e19ea1b3","format_issues":null,"number":7847} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58033560 | problem | aim-5a5c75a582375f6beb4bc89e58033560 | Other problems · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Determine the connection between Mock modular forms and geometric invariants like Gromov-Witten, Donaldson, and OSV conjecture. | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/5/#5a5c75a582375f6beb4bc89e58033560",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "5a5c75a582375f6beb4bc89e58033560",
"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": "2026-09-08T03:33:11.551Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f634d0c9-5866-4fa4-b3fa-eae6e9d0b76d","format_issues":null,"number":7848} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580358c9 | problem | aim-5a5c75a582375f6beb4bc89e580358c9 | Holomorphic anomaly equation · Question 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/gromwitnumthry/ Not an author-supplied MSC code."
}
] | Does the holomorphic anomaly equation "integrate" over elliptic fibrations? | unassessed | {
"key": "aimpl",
"name": "AIM · Gromov-Witten invariants and number theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gromwitnumthry/1/#5a5c75a582375f6beb4bc89e580358c9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pr... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gromov-Witten invariants and number theory · Historical workshop question | ## Workshop introduction
Since the early 90's Gromov-Witten theory on Calabi-Yau threefolds has
grown into a subject with impact on many branches of mathematics
and physics. Spurred by its relevance, the mathematical foundation
on Gromov-Witten invariants has been fully developed; the genus
zero Gromov-Witten invarian... | 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": "Gromov-Witten invariants and number theory",
"url": "http://aimpl.org/gromwitnumthry/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "5a5c75a582375f6beb4bc89e580358c9",
"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": "2026-09-08T03:33:11.466Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d5c5dffc-87d4-4afe-b1ed-79b33d749d90","format_issues":null,"number":7834} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803c44f | problem | aim-5a5c75a582375f6beb4bc89e5803c44f | Iwahori-Matsumoto presentation | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | What is the ``Iwahori-Matsumoto Presentation'' of Iwahori-Hecke algebra for $\widetilde{G}_F$ for split $G_F$? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/1/#5a5c75a582375f6beb4bc89e5803c44f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | M. Weissman | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "5a5c75a582375f6beb4bc89e5803c44f",
"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": "2026-09-08T03:33:11.627Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fd22522e-c7dc-47d5-a45a-33f153f72497","format_issues":null,"number":7863} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803d0b7 | problem | aim-5a5c75a582375f6beb4bc89e5803d0b7 | Representations · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Construct supercuspidal representations of $\widetilde{G}_{F}$. | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/1/#5a5c75a582375f6beb4bc89e5803d0b7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | W. Gan | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/1/",
"note": null,
"sort_order": 0
}
] | {
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1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803d0f6 | problem | aim-5a5c75a582375f6beb4bc89e5803d0f6 | Representations · Question 3 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/autoformcovergp/ Not an author-supplied MSC code."
}
] | What is the category of depth-zero unipotent representations for $\widetilde{G}_{F}$ for a $p$-adic field $F$? | unassessed | {
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"url": "http://aimpl.org/autoformcovergp/1/#5a5c75a582375f6beb4bc89e5803d0f6",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | K. Choiy | null | null | null | [
{
"kind": "website",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b2f2905f-f988-4692-8954-1586ae6e1489","format_issues":null,"number":7865} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803d9c8 | problem | aim-5a5c75a582375f6beb4bc89e5803d9c8 | Steinberg representation | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Define Steinberg representation of $\widetilde{G}_{F}$. What is the formal degree of Steinberg representation of $\widetilde{G}_{F}$ when $G$ is split over $F$?
What is analogue of the trivial representation? | unassessed | {
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"url": "http://aimpl.org/autoformcovergp/1/#5a5c75a582375f6beb4bc89e5803d9c8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | G. Savin | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
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"note": null,
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"published_at": "2026-09-08T03:33:11.639Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1a04eada-791d-4f27-a4bb-a92dc2b43367","format_issues":null,"number":7866} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803f163 | problem | aim-5a5c75a582375f6beb4bc89e5803f163 | Fundamental properties · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Determine notion of stable conjugacy when stable conjugacy classes in $\widetilde{G}_F$ and $\widetilde{H}_L$ naturally are related. | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e5803f163",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | W. Gan | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/2/",
"note": null,
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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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"published_at": "2026-09-08T03:33:11.648Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f698fab-a239-42b3-8cdf-d263a55f80df","format_issues":null,"number":7868} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5803f66f | problem | aim-5a5c75a582375f6beb4bc89e5803f66f | Fundamental properties · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | In the real case, given a cover of $G_{\mathbb{R}}$, describe Brylinski-Deligne data. | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e5803f66f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | J. Adams | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/2/",
"note": null,
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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": "2026-09-08T03:33:11.652Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"64f6088e-6c92-4307-90d0-761c41a35c68","format_issues":null,"number":7869} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58040068 | problem | aim-5a5c75a582375f6beb4bc89e58040068 | ABV for covering groups | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | There is a canonical isomorphism as $K$-groups
$$
KRep \widetilde{G}_{\mathbb R} \cong \Big( KPer_{H} (X) \Big)^*,
$$
where $X$ is a $\mathbb C$-algebraic variety and $H$ is a $\mathbb C$-algebraic group (for the trivial cover, $H={^{\vee}}G$). | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e58040068",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | P. Trapa | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/2/",
"note": null,
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] | {
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"published_at": "2026-09-08T03:33:11.656Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7dcfc9cf-0d83-4ee7-a6bc-ee552f9d6503","format_issues":null,"number":7870} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580409f5 | problem | aim-5a5c75a582375f6beb4bc89e580409f5 | Lurie Conjecture | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Twisted Whittaker models by D. Gaitsgory | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e580409f5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | S. Lysenko | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/2/",
"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": "2026-09-08T03:33:11.665Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d1602533-5d3c-4517-a103-e95934e135cc","format_issues":null,"number":7871} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58042406 | problem | aim-5a5c75a582375f6beb4bc89e58042406 | Base change | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Given a genuine irreducible representation $\widetilde{\pi}$ of $\widetilde{G}_F,$ describe $Lift_{L/F}(\widetilde{\pi})$ the base change lift of $\widetilde{\pi}.$ Note that $Lift_{L/F}(\widetilde{\pi})$ is supposed to be the virtual representation of $\widetilde{G}_L.$\label{basechange} | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/3/#5a5c75a582375f6beb4bc89e58042406",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · Historical workshop question | ## Question context
- $F$ : a $p$-adic field of characteristic $0.$
- $G_F$ : an unramified linear group (quasi-split over $F$ and split over a finite unramified extension $L$ of $F.$)
- $\widetilde{G}_F$ : a covering group of degree coprime to $p.$ | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Part of the problem:
- (a) Define $\widetilde{G}_L.$
- (b) List axioms to characterize $Lift_{L/F}(\widetilde{\pi}),$ including explicit description of norm map. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | M. Weissman | null | null | null | [
{
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"url": "http://aimpl.org/autoformcovergp/3/",
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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": "2026-09-08T03:33:11.679Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f203ef3e-3ab9-4054-b97f-ba03d3b1a0d7","format_issues":null,"number":7874} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580436aa | problem | aim-5a5c75a582375f6beb4bc89e580436aa | Lifts · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Does $Gal(L/F)$ act on $\widetilde{G}_L$? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/3/#5a5c75a582375f6beb4bc89e580436aa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · Historical workshop question | ## Question context
This is a preliminary problem to Problem \ref{basechange} | 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": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/3/",
"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": "2026-09-08T03:33:11.683Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c8c63aea-d6e9-4f9d-a6d7-16a0eb8163eb","format_issues":null,"number":7875} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58044d93 | problem | aim-5a5c75a582375f6beb4bc89e58044d93 | Lifts · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Make sense of transferring representation from $\widetilde{G}_F$ to $\widetilde{G'}_F,$
where two linear groups $G_F$ and $G'_F$ are inner forms each other. | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/3/#5a5c75a582375f6beb4bc89e58044d93",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Possible trouble: centres of $\widetilde{G}_F$ and $\widetilde{G'_F}$ can be different. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | E. Lapid | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/3/",
"note": null,
"sort_order": 0
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] | {
"source_record": "5a5c75a582375f6beb4bc89e58044d93",
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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": "2026-09-08T03:33:11.688Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ffcbe9e6-dc9f-4d34-946f-24bea8e3f33c","format_issues":null,"number":7876} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58045e64 | problem | aim-5a5c75a582375f6beb4bc89e58045e64 | Lifts · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Is there a natural lifting from representations of $G_F$ to $\widetilde{G'}_F$? | unassessed | {
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58046d34 | problem | aim-5a5c75a582375f6beb4bc89e58046d34 | Covering group of tori | {
"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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Let $T$ be a (not necessary split) torus over a $p$--adic field. Construct $\widetilde{T}$
$$
1 \longrightarrow \mu_F \longrightarrow \widetilde{T}
\longrightarrow T \longrightarrow 1
$$
explicitly within Brylinski-Deligne framework. | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e58046d34",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Nice subcases: when $T$ is anisotropic or unramified. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | M. Weissman and S. Lysenko | null | null | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2692500f-bf26-4679-940b-51175117aff2","format_issues":null,"number":7872} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580484eb | problem | aim-5a5c75a582375f6beb4bc89e580484eb | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | What global covering groups have arithmetic applications? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/4/#5a5c75a582375f6beb4bc89e580484eb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | E. Lapid | null | null | null | [
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"url": "http://aimpl.org/autoformcovergp/4/",
"note": null,
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} | 2026-10-10T16:07:49.246Z | {"database_id":"967567e4-b421-45cb-bbb4-cb358b016395","format_issues":null,"number":7879} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5804915d | problem | aim-5a5c75a582375f6beb4bc89e5804915d | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Are there instances of Rankin-Selberg methods for higher covers? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/4/#5a5c75a582375f6beb4bc89e5804915d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | E. Lapid | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/4/",
"note": null,
"sort_order": 0
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] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"456ed976-2a83-4bf1-ab54-49e6fd9a8582","format_issues":null,"number":7880} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580495ce | problem | aim-5a5c75a582375f6beb4bc89e580495ce | Fundamental properties · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | What is special about $2$-fold covers? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/2/#5a5c75a582375f6beb4bc89e580495ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Maybe, $\pm \in \mathbb Q$? | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | J. Adams | null | null | null | [
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"published_at": "2026-09-08T03:33:11.675Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fa0466e6-75a8-4de3-b6d0-3e5debfa3518","format_issues":null,"number":7873} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e58049a6e | problem | aim-5a5c75a582375f6beb4bc89e58049a6e | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Are there applications of the invariant trace formula for $\widetilde{G}_{F}$? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/4/#5a5c75a582375f6beb4bc89e58049a6e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | W. Gan | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/4/",
"note": null,
"sort_order": 0
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"published_at": "2026-09-08T03:33:11.710Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"bfa77dfa-7709-4c7b-a5ab-9e338432bc89","format_issues":null,"number":7881} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5804a691 | problem | aim-5a5c75a582375f6beb4bc89e5804a691 | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Interpret formal degrees of representations of $\widetilde{G}_{F}$ on level of Hecke algebra.
(\`a la Opdam, Reeder, et al) | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/4/#5a5c75a582375f6beb4bc89e5804a691",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | P. Trapa | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/4/",
"note": null,
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.713Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cc3521ab-beea-422b-863c-8097447b744c","format_issues":null,"number":7882} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580637a3 | problem | aim-5a5c75a582375f6beb4bc89e580637a3 | Representations · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | What is theta correspondence for $\widetilde{G}$?
e.g.) $SL_2 \times \widetilde{SL}^{(3)}_2 \hookrightarrow \widetilde{G_2}^{(3)}$ (G-R-S)
$SL_3 \times \widetilde{SL}^{(2)}_3 \hookrightarrow \widetilde{F_4}^{(2)}$
$\widetilde{Spin}^{(2)}_{2a+1} \times \widetilde{Spin}^{(2)}_{2b} \hookrightarrow \widetilde{Spin}^{(2)... | unassessed | {
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"url": "http://aimpl.org/autoformcovergp/1/#5a5c75a582375f6beb4bc89e580637a3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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"
] | W. Gan | null | null | null | [
{
"kind": "website",
"citation": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/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":"20b977c6-0ed6-4310-b3be-bde63cb9a436","format_issues":null,"number":7867} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580668f2 | problem | aim-5a5c75a582375f6beb4bc89e580668f2 | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Are there global applications of the trace formula, automorphic forms, Whittaker models, the Langlands-Shahidi method for $\widetilde{G}$ ?
-- Classify automorphic representations of covers of split tori. | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/4/#5a5c75a582375f6beb4bc89e580668f2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/4/",
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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"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.717Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dea3defa-a6dd-4bb3-bd3b-8ef1f3647273","format_issues":null,"number":7883} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e580692b2 | problem | aim-5a5c75a582375f6beb4bc89e580692b2 | Applications · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | Study the residual spectrum for $\widetilde{GL}(n)$.
-- Can the lifting of Levi subgroups be done over $p$-adic? If so, is it one of the Brylinski-Deligne extensions?
-- Describe covers of $GL(n)$ not arising from Kazhdan-Petterson. | unassessed | {
"key": "aimpl",
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/4/",
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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",
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.722Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"52da1a39-802e-46c6-b564-ab5f8c305c9b","format_issues":null,"number":7884} |
1.0.0 | problem:aim-5a5c75a582375f6beb4bc89e5807081f | problem | aim-5a5c75a582375f6beb4bc89e5807081f | Lifts · Question 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/autoformcovergp/ Not an author-supplied MSC code."
}
] | What is the local character identity for $Mp(2n)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Automorphic forms and harmonic analysis on covering groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/autoformcovergp/3/#5a5c75a582375f6beb4bc89e5807081f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Automorphic forms and harmonic analysis on covering groups · 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": "Automorphic forms and harmonic analysis on covering groups",
"url": "http://aimpl.org/autoformcovergp/3/",
"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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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.697Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"925cce27-ddb3-48c4-8494-530a694a8b3a","format_issues":null,"number":7878} |
1.0.0 | problem:aim-66ebf8b863d4cad898b035507318f906 | problem | aim-66ebf8b863d4cad898b035507318f906 | Miscellaneous Problems · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | \label{nonzero_approx}
Let be $K\subset\mathbb{C}$ be compact, let $\mathbb{C}\setminus K$ be connected, and let $f$ be a continuous function on $K$ which is holomorphic and non-zero on the interior of $K$. Is there a sequence of polynomials $\{p_n\}_{n=1}^\infty$ with no zeros in $K$ such that $p_n\to f$? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/9/#66ebf8b863d4cad898b035507318f906",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | P.~Gauthier | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b035507318f906",
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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": "2026-09-08T03:33:16.283Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"94f90551-c18b-4c47-9c5b-9d8fd1f210d2","format_issues":null,"number":8779} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731915eb | problem | aim-66ebf8b863d4cad898b03550731915eb | Miscellaneous Problems · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | \label{conj_universal}
Let be $K\subset\mathbb{C}$ be compact, $\mathbb{C}\setminus K$ connected, and $f$ be a continuous function on $K$ which is holomorphic and non-zero on the interior of $K$.
Suppose $K\subseteq\{z:\frac{1}{2}<{\rm Re} z < 1\}$, then
$$
\overline{d}\left( \left\{t\in\mathbb{R}: ||\zeta(\cdot + it... | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/9/#66ebf8b863d4cad898b03550731915eb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | J.~Andersson, D.~Farmer | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731915eb",
"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": "2026-09-08T03:33:16.287Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"44c60e46-65ce-4a3b-a274-46c2b873c7bf","format_issues":null,"number":8780} |
1.0.0 | problem:aim-66ebf8b863d4cad898b0355073192ebc | problem | aim-66ebf8b863d4cad898b0355073192ebc | Miscellaneous Problems · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\mu$ be a probability measure on $\{0,1\}^n$. Consider
$$
f(\vec{z}\,) = \int {\vec{z}}^{\;\vec{\alpha}} d\mu(\vec{\alpha}\,)
$$
and
$$
g(\vec{\lambda}\,) = \int e^{\;\vec{\lambda}\cdot\vec{\alpha}} d\mu(\vec{\alpha}\,).
$$
What property of $g$ is equivalent to the stability of $f$? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/9/#66ebf8b863d4cad898b0355073192ebc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | R.~Pemantle | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b0355073192ebc",
"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": "2026-09-08T03:33:16.292Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d2985d82-4586-46b7-ad31-a7d698f06c86","format_issues":null,"number":8781} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731948d6 | problem | aim-66ebf8b863d4cad898b03550731948d6 | Combinatorics and Graph Theory · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | - Is it true that
$$
\alpha:=\liminf_n \frac{\log\mu_{2n}}{2n}>-\infty \text{ ?}
$$
- Estimate $\mu_{2n}$. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/4/#66ebf8b863d4cad898b03550731948d6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | S.~Friedland | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731948d6",
"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": "2026-09-08T03:33:16.212Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3320f73f-086f-46ab-a976-d60c3ea844e5","format_issues":null,"number":8764} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731961cc | problem | aim-66ebf8b863d4cad898b03550731961cc | Zeros of derivatives · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $p\in\mathbb{R}[x]$, $\deg(p)=n>2$. There are at least $n-1$ points of extreme curvature $\kappa(p)$ ( more generally where $\kappa'(p)=0$ ) \cite{MR2104693}. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/5/#66ebf8b863d4cad898b03550731961cc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | S.~Edwards | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731961cc",
"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": "2026-09-08T03:33:16.230Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1d5aa252-8eb3-49b0-9cef-fea670d75a1e","format_issues":null,"number":8768} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731972bc | problem | aim-66ebf8b863d4cad898b03550731972bc | Matrix Theory · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Given $p\in\mathbb{C}[x]$, $\deg(p) = n$, find an $n\times n$ Hermitian matrix whose inertia $(n_+, n_{-}, n_0)$ counts the zeros of $p$ in $H_+, H_{-}, H_0=\mathbb{R}$. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/2/#66ebf8b863d4cad898b03550731972bc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | A.~Sokal | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731972bc",
"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": "2026-09-08T03:33:16.176Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f7f76d72-e868-40ba-9958-9e122d043a33","format_issues":null,"number":8756} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731983c1 | problem | aim-66ebf8b863d4cad898b03550731983c1 | Orthogonal polynomials · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | There are no common zeros between $L_m^\alpha$ and $L_n^\alpha$, $|m-n|>1$, for $\alpha$ rational. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/6/#66ebf8b863d4cad898b03550731983c1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | K.~Driver | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731983c1",
"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": "2026-09-08T03:33:16.239Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2748b3ed-ab66-4815-8282-2e461dae14a8","format_issues":null,"number":8770} |
1.0.0 | problem:aim-66ebf8b863d4cad898b035507319a333 | problem | aim-66ebf8b863d4cad898b035507319a333 | Orthogonal polynomials · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Consider a subspace $S$ of $\mathbb{C}[x]$ of codimension $k$ (defined by $k$ linear constraints, explicitly given). Given a scalar product on $\mathbb{C}[x]$, find an orthogonal basis of $S$ (ordered by degree); some degrees will be missing.
- Which degrees get skipped?
- Characterize these orthogonal polynomia... | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/6/#66ebf8b863d4cad898b035507319a333",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | P.~Moussa | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b035507319a333",
"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": "2026-09-08T03:33:16.244Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f321f492-1d7f-485c-8c45-f1e053f67bb0","format_issues":null,"number":8771} |
1.0.0 | problem:aim-66ebf8b863d4cad898b035507319b539 | problem | aim-66ebf8b863d4cad898b035507319b539 | Zeros of specific functions · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let
$$
p_n(z) = \sum_{k=0}^n (-1)^k(2k+1)z^{k(k+1)}
$$
where, $n=2,3,4,\ldots.$
Each $p_n$ has no real zeros for even $n$, and exactly two real zeros for odd $n$. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/8/#66ebf8b863d4cad898b035507319b539",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | A.~Vishnyakova | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/8/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b035507319b539",
"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 | [
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"published_at": "2026-09-08T03:33:16.265Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"225a0d7e-1542-4078-9b68-224f30b74c71","format_issues":null,"number":8775} |
1.0.0 | problem:aim-66ebf8b863d4cad898b035507319f17c | problem | aim-66ebf8b863d4cad898b035507319f17c | Orthogonal polynomials · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $P_n^{\;\alpha, \,\beta}$ denote the Jacobi polynomial of $\deg n$ with parameters $\alpha, \beta> -1$.
Then $P_n^{\;\alpha', \,\beta'}$ and $P_n^{\;\alpha, \,\beta}$ interlace for $\alpha\approx\alpha'$, and $\beta\approx\beta'$. Does the failure of interlacing correspond to some physical law being ``violated''... | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/6/#66ebf8b863d4cad898b035507319f17c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | K.~Driver | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/6/",
"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 | [
"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": "2026-09-08T03:33:16.248Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"87c4e241-78e5-46b1-9fc8-238f93d9e563","format_issues":null,"number":8772} |
1.0.0 | problem:aim-66ebf8b863d4cad898b035507319fedf | problem | aim-66ebf8b863d4cad898b035507319fedf | Log Concavity · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let
$$
Q_n^{(\alpha, \beta)}:=\sum_{k=0}^n\binom{n}{k}f_kf_{n-k}((x+\alpha)_k(x+\beta)_{n-k} - (x+\alpha+\beta)_k(x)_{n-k}),
$$
where $\alpha, \beta>0$, $f_k^2\ge f_{k-1}f_{k+1}$, and $(x)_k = x(x+1)\cdots(x+k-1)$. Then the Maclaurin coefficients of $Q^{(\,\alpha,\,\beta)}$ are non-negative. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/3/#66ebf8b863d4cad898b035507319fedf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | D.~Karp | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/3/",
"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": "2026-09-08T03:33:16.203Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cfbbd0b1-4f8e-4a81-8404-97c80cb76374","format_issues":null,"number":8762} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a10b8 | problem | aim-66ebf8b863d4cad898b03550731a10b8 | Combinatorics and Graph Theory · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Prove that E(x) has only real zeros. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/4/#66ebf8b863d4cad898b03550731a10b8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | F.~Brenti | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/4/",
"note": null,
"sort_order": 0
}
] | {
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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": "2026-09-08T03:33:16.217Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"aac96fd3-9e75-4ea6-9ee5-52ea35902e76","format_issues":null,"number":8765} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a1600 | problem | aim-66ebf8b863d4cad898b03550731a1600 | Combinatorics and Graph Theory · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Is there a decent multivariate extension of the Chudnovsky-Seymour Theorem that the vertex independent set polynomial of a claw-free graph has only real roots? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/4/#66ebf8b863d4cad898b03550731a1600",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | A.~Sokal | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a1600",
"imported_at": "2026-09-08",
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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": "2026-09-08T03:33:16.221Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"14f2f006-743f-45a8-8157-bd940d95d3fc","format_issues":null,"number":8766} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a286c | problem | aim-66ebf8b863d4cad898b03550731a286c | Riemann $\Xi$-function · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Investigate the zeros of $P_n$ and $Q_n.$ | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/7/#66ebf8b863d4cad898b03550731a286c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The motivation for this problem is the following. If for all $n\in\mathbb{N}$, $P_n(z,z,\ldots,z)$ vanishes only when $z=i\alpha$, with $\alpha\in\mathbb{R}$, then the Riemann hypothesis is true... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | D.~Dimitrov | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a286c",
"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": "2026-09-08T03:33:16.256Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"60626754-b69b-4113-a9da-c3bdc137a623","format_issues":null,"number":8773} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a62e6 | problem | aim-66ebf8b863d4cad898b03550731a62e6 | Zeros of specific functions · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Consider the function
$$
f(z) := \sum_{k} \frac{z^k}{(a^k+1)(a^{k-1}+1)\cdots (a+1)}, \qquad a>1.
$$
For which values of $a$ is $f$ in $\mathcal{L}\text{-}\mathcal{P}$? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/8/#66ebf8b863d4cad898b03550731a62e6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | A.~Vishnyakova | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/8/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a62e6",
"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": "2026-09-08T03:33:16.269Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"92749d84-8fa6-42a2-a989-07930c395ff8","format_issues":null,"number":8776} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a7614 | problem | aim-66ebf8b863d4cad898b03550731a7614 | Miscellaneous Problems · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $p(z)\in\mathbb{C}[z]$, $\deg(p)=n$. Suppose $p(z)\neq 0$ for all $|z|\le1$. Define $p^*(z):=z^n\overline{p\left(\frac{1}{\bar{z}}\right)}$. Then it is known that
$$
p(A)p(A)^\dagger \ge p^*(A)(p^*(A))^\dagger \;\; **for any contractive matrix ** A.
$$
($A$ is **contractive** means $\sup\limits_x \frac{||A... | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/9/#66ebf8b863d4cad898b03550731a7614",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | G.~Knese | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a7614",
"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": "2026-09-08T03:33:16.297Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"edefd66f-6119-4136-9af9-c253890c39a2","format_issues":null,"number":8782} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a82cc | problem | aim-66ebf8b863d4cad898b03550731a82cc | Matrix Theory · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Study the zeros of Bessis-Moussa-Villani polynomials $t\to\text{tr}(A+tB)^m$. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/2/#66ebf8b863d4cad898b03550731a82cc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | O.~Holtz | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a82cc",
"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": "2026-09-08T03:33:16.180Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"25809a97-a0f1-41a2-8283-38533888d35f","format_issues":null,"number":8757} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731a8f3f | problem | aim-66ebf8b863d4cad898b03550731a8f3f | Zeros of specific functions · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | For all $|w|>1$, all the zeros of $P_n(\cdot,w)$ are simple and separated in modulus (by a factor of at least $|w|^2$). \label{conj_sokal} | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/8/#66ebf8b863d4cad898b03550731a8f3f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | A.~Sokal | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/8/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731a8f3f",
"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": "2026-09-08T03:33:16.274Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"db7a849d-0ea6-46ae-92f7-ebbf733d37bf","format_issues":null,"number":8777} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731aabdd | problem | aim-66ebf8b863d4cad898b03550731aabdd | Matrix Theory · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Find a simple proof of BMV conjecture for $3\times 3$ matrices (and an explicit formula for the BMV measure for $3\times 3$ matrices; the existence of the measure is due to recent work of Stahl). | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/2/#66ebf8b863d4cad898b03550731aabdd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | P.~Moussa | null | null | null | [
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1.0.0 | problem:aim-66ebf8b863d4cad898b03550731ac166 | problem | aim-66ebf8b863d4cad898b03550731ac166 | Combinatorics and Graph Theory · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Generalize the Chudnovsky-Seymour (Heilmann-Lieb) Theorem. Extend the common interlacing property to several variables. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/4/#66ebf8b863d4cad898b03550731ac166",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | S.~Friedland | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/4/",
"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 | [
"current-status-unassessed",
"source-full-text-not-present"
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:16.225Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e2a25740-5130-4ec3-93e1-bef62ad265c6","format_issues":null,"number":8767} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731acadb | problem | aim-66ebf8b863d4cad898b03550731acadb | Matrix Theory · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Any real polynomial can be written as $\det(A-\lambda I),$ where $A$ has the (tridiagonal) form
$$
\left[\begin{array}{cccccc}
+ & + & & & & \\
- & 0 & + & & &\\
& - & 0 & + & &\\
& & \ddots & \ddots & \ddots & \\
& & & ... | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/2/#66ebf8b863d4cad898b03550731acadb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | M.~Tyaglov | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/2/",
"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 | [
"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": "2026-09-08T03:33:16.189Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"50f1aaad-bbfa-47a7-94d7-ff13ed5e066d","format_issues":null,"number":8759} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731ad7b8 | problem | aim-66ebf8b863d4cad898b03550731ad7b8 | Multiplier sequences and CZDS · Question 3.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\{c_k\}_{k=0}^n\subset\mathbb{R}$ be given. Does there exist a real rooted polynomial, $p(x)$, with zeros outside $[0,n]$ such that $c_k=p(k)$, $k=0,1,\ldots,n$? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/1/#66ebf8b863d4cad898b03550731ad7b8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Note that this implies $\{c_k\}_{k=0}^n$ is an n-CZDS. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | A.~Vishnyakova | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/1/",
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"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 | [
"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": "2026-09-08T03:33:16.167Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f932c2d-4941-478f-b1a6-a6ca825b907f","format_issues":null,"number":8754} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731ae124 | problem | aim-66ebf8b863d4cad898b03550731ae124 | Multiplier sequences and CZDS · Question 3.2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $f(z)$ be a meromorphic function. When is the sequence $\{f(k)\}_{k=0}^\infty$ a multiplier sequence? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/1/#66ebf8b863d4cad898b03550731ae124",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | G. Csordas | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/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": "2026-09-08T03:33:16.171Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c1e9c356-075c-485f-9d78-1626d3c9da2b","format_issues":null,"number":8755} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731aec34 | problem | aim-66ebf8b863d4cad898b03550731aec34 | Riemann $\Xi$-function · Question 8.2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Are there any non-real zeros of
$$
\int_{0}^\infty \Phi^\alpha(t)\cos(zt)dt \qquad \text{for}\qquad \alpha>0 ?
$$ | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/7/#66ebf8b863d4cad898b03550731aec34",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | J.~Haglund | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/7/",
"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 | [
"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": "2026-09-08T03:33:16.261Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"806081db-88ea-4736-87ac-dc0fe1098513","format_issues":null,"number":8774} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731aef25 | problem | aim-66ebf8b863d4cad898b03550731aef25 | Zeros of derivatives · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | What are the zero spacing effects of higher order differential operators on functions which belong to $\mathcal{L}\text{-}\mathcal{P}$? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/5/#66ebf8b863d4cad898b03550731aef25",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | A.~Sokal | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731aef25",
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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": "2026-09-08T03:33:16.235Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"405bd03c-f03d-45ad-939e-822639ebb004","format_issues":null,"number":8769} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731afd68 | problem | aim-66ebf8b863d4cad898b03550731afd68 | Log Concavity · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Let $\{\phi_k(x)\}_{k=0}^\infty$ and $\{f_k\}_{k=0}^\infty$ be log-concave. When is $\sum f_k\phi_k(x)$ log-concave ? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/3/#66ebf8b863d4cad898b03550731afd68",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings.
#... | 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"
] | D.~Karp | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731afd68",
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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": "2026-09-08T03:33:16.207Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6de6a1eb-93a7-498d-aabf-18854a2960a1","format_issues":null,"number":8763} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731b026d | problem | aim-66ebf8b863d4cad898b03550731b026d | Matrix Theory · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Investigate the signs of Hurwitz minors for P\'olya frequency sequences. | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/2/#66ebf8b863d4cad898b03550731b026d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | L.~Grabarek, M.~Tyaglov | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731b026d",
"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": "2026-09-08T03:33:16.194Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2e9fd29a-4d76-4a0c-b6aa-b410b125e5c5","format_issues":null,"number":8760} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731b088a | problem | aim-66ebf8b863d4cad898b03550731b088a | Miscellaneous Problems · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Find more examples and attempt to characterize Markov processes preserving stability. Explicitly, let $\psi:\mathbb{R}_{MA}[x,y,z]\to\mathbb{R}_{MA}[x,y,z]$ be a linear operator. When is $e^{t\psi}:\mathbb{R}[x,y,z]\to\mathbb{R}[x,y,z]$ stability preserving for all $t\ge0$ ? | unassessed | {
"key": "aimpl",
"name": "AIM · Stability, hyperbolicity, and zero localization of functions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hyperbolicpoly/9/#66ebf8b863d4cad898b03550731b088a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | 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"
] | P.~Br\"and\'en | null | null | null | [
{
"kind": "website",
"citation": "Stability, hyperbolicity, and zero localization of functions",
"url": "http://aimpl.org/hyperbolicpoly/9/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "66ebf8b863d4cad898b03550731b088a",
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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": "2026-09-08T03:33:16.301Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"800e9412-9f9c-451b-abaf-c66d532dca5b","format_issues":null,"number":8783} |
1.0.0 | problem:aim-66ebf8b863d4cad898b03550731b5ba4 | problem | aim-66ebf8b863d4cad898b03550731b5ba4 | Zeros of specific functions · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Generalize conjecture \ref{conj_sokal}
to $Q_n(z,w)=\sum_{k=0}^n a_kz^kw^{k(n-k)}$. For what class of $\{a_n\}$ does the conjecture still hold? | unassessed | {
"key": "aimpl",
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"license": "Editorially moderated; per-list term... | null | null | null | not-recorded | not-recorded | null | [] | [] | Stability, hyperbolicity, and zero localization of functions · Historical workshop question | ## Workshop introduction
A list of the problems from the workshop on stability, hyperbolicity, and zero localization of functions, held December 5-9, 2011, is presented below. The problems have been loosely categorized for convenience, although many of the problems could be listed under several different headings. | Historical workshop record. Current open/solved status has not been independently reassessed.
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924007bb9 | problem | aim-6adb9ed5d4e8053cb940175924007bb9 | Effective Jumps · Question 1.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | For which equivalence relation $E$ is $E < E^+$? (In both the computable and Borel context.)
- For which orbit equivalence relation?
- For which $\Sigma^1_1$ equivalence relation?
- Is there an $E$ for which we do not know if $E < E^+$? | unassessed | {
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"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb940175924007bb9",
"citation": null,
"doi": null,
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400830a | problem | aim-6adb9ed5d4e8053cb94017592400830a | Effective Jumps · Question 1.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Given an equivalence relation $E$ on $X$ and a countable group $G$, define an equivalence relation on $X^G$ by $\alpha E^{[G]} \beta$ iff there is some $g\in G$ such that for every $h\in G$, we have $\alpha(g^{-1} h) E \beta(h)$. For which $E$ and $G$ is $E < E^{[G]}$? What about the effective versions of this problem? | unassessed | {
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"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb94017592400830a",
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924008325 | problem | aim-6adb9ed5d4e8053cb940175924008325 | Effective Jumps · Question 1.3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | For countable groups $G$, $H$, and an equivalence relation $E$, is there a countable group $K$ such that $(E^{[G]})^{[H]}$ is bi-reducible with $E^{[K]}$ | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariant descriptive computability theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb940175924008325",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924008714 | problem | aim-6adb9ed5d4e8053cb940175924008714 | Effective Jumps · Question 1.4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | For a ``reasonable" computable group $G$ and some arithmetical $E$ is $E^{[G]}$ always universal at some $\Sigma^0_n$ level? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariant descriptive computability theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb940175924008714",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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{
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"sort_order": 0
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{
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924009248 | problem | aim-6adb9ed5d4e8053cb940175924009248 | Effective Jumps · Question 1.5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Modify the Friedman--Stanley jump by using a fixed subgroup $G \le S_\infty$. Ask the above questions. | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb940175924009248",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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{
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"kind": "website",
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924009f54 | problem | aim-6adb9ed5d4e8053cb940175924009f54 | Effective Jumps · Question 1.6 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider the Louveau jump: let $F$ be a filter on $\omega$ and $E$ an equivalence relation, define $E^F$ to be the equivalence relation on $X^\omega$ by $\alpha E^F \beta$ iff $\{n:\alpha(n) E \beta(n)\}\in F$.
On $X = \omega$, define $i E^F j$ iff $\{n \mid \varphi_i(n) E \varphi_j(n)\}\in F$. Ask the above question... | unassessed | {
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"url": "http://aimpl.org/invdesccomp/1/#6adb9ed5d4e8053cb940175924009f54",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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{
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400ac52 | problem | aim-6adb9ed5d4e8053cb94017592400ac52 | Theory of $(D,\le)$ · Question 2.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What is the complexity of the theory of the Borel equivalence relation under Borel reducibility? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Invariant descriptive computability theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/2/#6adb9ed5d4e8053cb94017592400ac52",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · 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/invdesccomp/2/#6adb9ed5d4e8053cb94017592400ac52",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "htt... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"a37088f0-4a23-4ded-8830-a0c97ed3fea1","format_issues":null,"number":11036} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400d0e9 | problem | aim-6adb9ed5d4e8053cb94017592400d0e9 | Continuous degrees of smooth equivalence relations · Question 3.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | What is the complexity of the theory of the smooth equivalence relations under continuous reducibility? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/3/#6adb9ed5d4e8053cb94017592400d0e9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400d980 | problem | aim-6adb9ed5d4e8053cb94017592400d980 | Continuous degrees of smooth equivalence relations · Question 3.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Does every $\Pi^0_1$ smooth equivalence relation on $\omega^\omega$ continuously reduce to $=^+$? Does every strictly ascending sequence has a supremum? | unassessed | {
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"name": "AIMPL · Invariant descriptive computability theory",
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"url": "http://aimpl.org/invdesccomp/3/#6adb9ed5d4e8053cb94017592400d980",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
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"url": "htt... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400f178 | problem | aim-6adb9ed5d4e8053cb94017592400f178 | Reducibility on a cone · Question 4.1 | {
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"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | For each $X\in \omega^\omega$, we have $\Phi = \Phi_X$ is an equivalence relation on $\omega$, such that whenever $x \equiv_T y$ then $\Phi(x)$ is computably equivalent to $\Phi(y)$. Given $\Phi$ and $\Psi$ as above, define $\Phi \le^\triangledown \Psi$ if there exists $ c$ such that for every $y \ge_T c$, $\Phi(y)$ is... | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592400fe72 | problem | aim-6adb9ed5d4e8053cb94017592400fe72 | Reducibility on a cone · Question 4.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Given $A$ and $B$ classes of structures, define $A\le_{\text{eff}}^\triangledown B$ if there is a $c$ such that for every $y\ge_T c$, there is a computable $\Phi$ such that for all $i,j$, if $w_i^y, w_j^y$ are structures in $A$, then $\Phi^y(i), \Phi^y(j)\in B$ and $w_i^y \equiv w_j^y$ iff $\Phi^y(i) \equiv \Phi^y(j)$.... | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924011017 | problem | aim-6adb9ed5d4e8053cb940175924011017 | Isomorphism problems in a variety · Question 5.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is every $\Sigma^0_2$ equivalence relation on $\omega$ which is a quotient of $=^{ce}$ actually $\Delta^0_2$?
Fix a variety. Consider the equivalence on the c.e.\ sets by isomorphisms of the correspondingly recursively presented object in the variety. What is the complexity of this equivalence relation as a function o... | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924012c48 | problem | aim-6adb9ed5d4e8053cb940175924012c48 | Countable and finitary reducibility · Question 6.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is $E_\infty \le^{<\omega} E_0$? Is $E_{\text{set}}$ universal for $\le ^{<\omega}$ among $\Pi^0_3$ equivalence relations? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924013130 | problem | aim-6adb9ed5d4e8053cb940175924013130 | Countable and finitary reducibility · Question 6.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider the class $B$ defined by some $L_{\omega_1,\omega}$-sentence $\varphi$ (where the topology is generated by the fragments of the language). What are the possible complexities of the isomorphism relations on $B$ as a set? It is known that $\Sigma^0_1$ and $\Sigma^0_\alpha$ for limit $\alpha$ are not possible. | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592401397b | problem | aim-6adb9ed5d4e8053cb94017592401397b | Countable and finitary reducibility · Question 6.3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider versions of $\le^n$ or $\le^\omega$ obtained by playing a game for the reals. (I.e., you give the first input, the functional returns the first output, then you give the second input, etc.) What can be said about these reducibilities? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924014b31 | problem | aim-6adb9ed5d4e8053cb940175924014b31 | Model-theoretic equivalence relations · Question 7.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there an $L_{\omega_1,\omega}$-elementary class $K$ of structures which is Borel complete and there is an $X\subseteq \omega$ such that there is no $X$-computable model in $K$ of Scott rank $\omega_1^X$? | unassessed | {
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"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240157fd | problem | aim-6adb9ed5d4e8053cb9401759240157fd | Model-theoretic equivalence relations · Question 7.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider the equivalence relations on countable structures, by model theoretic bi-interpretability (in first-order logic). Is this equivalence relation $\Sigma^1_1$-complete? We may ask both the question of completeness as a set and question of completeness as an equivalence relations. | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924016165 | problem | aim-6adb9ed5d4e8053cb940175924016165 | Effectivizing hyper-finiteness · Question 8.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is some version of the hyperaperiodicity argument useful for the $\omega$-content? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/invdesccomp/8/#6adb9ed5d4e8053cb940175924016165",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Pro... | null | null | null | not-recorded | not-recorded | null | [] | [] | Invariant descriptive computability theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240175a7 | problem | aim-6adb9ed5d4e8053cb9401759240175a7 | Further questions · Question 9.1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Consider the collection $C$ of countable structures. Consider two equivalence relations on $C$:
- Medvedev equivalence: $A\equiv_s B$ if there are two Turing functionals $\Phi$ and $\Psi$ such that for every $A'\cong A$, we have $\Phi(A') \cong B$, and for every $B'\cong B$, we have $\Psi(B') \cong A$.
-... | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592401834e | problem | aim-6adb9ed5d4e8053cb94017592401834e | Further questions · Question 9.2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there a $T_2$ (or $T_1$) and second countable space such that the relation $x E y$ iff $\bigcup_n U_{X(n)} = \bigcup_n U_{Y(n)}$ has arbitrarily high Borel rank (but is Borel)? (Even for rank $\ge 2$?) | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924018a3d | problem | aim-6adb9ed5d4e8053cb940175924018a3d | Further questions · Question 9.3 | {
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"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Which equivalence relations on c.e.\ sets are induced by an action of a semi-group computable on the indices? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240193ed | problem | aim-6adb9ed5d4e8053cb9401759240193ed | Further questions · Question 9.4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Are there Borel (or continuous) non-reducibility result proved using the recursion theorem? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592401dac7 | problem | aim-6adb9ed5d4e8053cb94017592401dac7 | Knot homology theories and categorification · Question 4.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can Cristina Anghel's approach to knot polynomials (via intersections of Lagrangians in configuration spaces) be categorified in instances via Lagrangian Floer cohomology? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592401dac7",
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Question context
Cristina Anghel has several papers on interpretations of quantum invariants (Alexander, Jones, colored versions of these, WRT) in terms of intersections in covers of symmetric products of Riemann surfaces. It is natural to ask whether these constructions are shadows of certain Lagrangian Floer theo... | 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"
] | Ciprian Manolescu | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240263a7 | problem | aim-6adb9ed5d4e8053cb9401759240263a7 | Asymptotics of spectral invariants | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For a symplectic surface $(\Sigma, \omega)$ and a Hamiltonian $H \in C^{\infty}([0,1] \times \Sigma, \mathbb{R})$, investigate the subleading asymptotic of $c_d(H) \rightarrow \text{Cal}(H)$, where $c_d$ is the $d^{\text{th}}$ link spectral invariant associated to $H$ and $\text{Cal}(H)$ is the Calabi invariant. | unassessed | {
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"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb9401759240263a7",
"citation": null,
"doi": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | 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"
] | Ivan Smith | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924027aaa | problem | aim-6adb9ed5d4e8053cb940175924027aaa | Quantitative Heegaard Floer theory and ECH · Question 2.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | The same question as the previous one for periodic Floer homology (PFH) spectral invariants. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb940175924027aaa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | 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"
] | Dan Cristofaro-Gardiner | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924028aec | problem | aim-6adb9ed5d4e8053cb940175924028aec | Symplectic topology and dynamics · Question 3.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Given a closed symplectic manifold $(M, \omega)$, consider $\text{Ham}^{\text{aut}}(M, \omega) \subset \text{Ham}(M, \omega)$ the subset of autonomous Hamiltonian diffeomorphism groups. For $\phi \in \text{Ham}(M, \omega)$, can the Hofer distance from $\phi$ to $\text{Ham}^{\text{aut}}(M, \omega)$ be arbitrarily large? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924028aec",
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"doi": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · 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
Yes when $M$ is a surface other than $S^2$, unknown for $S^2$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Egor Shelukhin | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592402a282 | problem | aim-6adb9ed5d4e8053cb94017592402a282 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.05 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For a symplectic manifold $(X, \omega)$, what is the relationship between $\mathcal{F}^{S_n}(X^n)$ and $\mathcal{F}(\text{Sym}^n(X))$? Here $\mathcal{F}^{S_n}(X^n)$ is (some sort of) $S_n$-equivariant Fukaya category, while $\mathcal{F}(\text{Sym}^n(X))$ is (some kind of) orbifold Fukaya category. | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592402a282",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Peng Zhou | null | null | null | [
{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592402c268 | problem | aim-6adb9ed5d4e8053cb94017592402c268 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Continuing the previous problem, if $X$ is a Weinstein manifold of dimension at least $4$, are there (canonical) resolutions of $\text{Sym}^n(X)$ that have well-behaved Floer theory? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592402c268",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Peng Zhou | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592402ded9 | problem | aim-6adb9ed5d4e8053cb94017592402ded9 | Knot homology theories and categorification · Question 4.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is it true that $\mathfrak{gl}_{n|m}$ and $\mathfrak{gl}_{m|n}$ knot homologies are isomorphic if one switches the role of $t$ and $q$ variable? In particular, what is happening for the $\mathfrak{gl}_{1|1}$ theory (= knot Floer homology)? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592402ded9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · 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"
] | Alexei Oblomkov | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592402ded9",
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{
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... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592403113e | problem | aim-6adb9ed5d4e8053cb94017592403113e | Knot homology theories and categorification · Question 4.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Compare different approaches to $\mathfrak{gl}_{n|m}$ knot homologies. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592403113e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · 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"
] | Alexei Oblomkov | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592403113e",
"note": null,
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},
{
"kind": "website",
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... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924031492 | problem | aim-6adb9ed5d4e8053cb940175924031492 | Knot homology theories and categorification · Question 4.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Compute knot homology of a `local' infinite twist in any of these cases. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb940175924031492",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · 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"
] | Alexei Oblomkov | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb940175924031492",
"note": null,
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{
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5cbc337a-a4f5-4859-80ed-6ddf02e9a022","format_issues":null,"number":10696} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924033199 | problem | aim-6adb9ed5d4e8053cb940175924033199 | Symplectic topology and dynamics · Question 3.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Develop a toolkit for producing Lagrangian links in symplectic manifolds, and study its relationship to questions such as the Lagrangian packing problem and problems from dynamics. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924033199",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · 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"
] | Ivan Smith | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924033199",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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... | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924034b53 | problem | aim-6adb9ed5d4e8053cb940175924034b53 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.15 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Study resolution of the diagonal on symmetric products (equipped with potentials) and applications to fixed point Floer cohomology models for link invariants. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924034b53",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Mina Aganagic | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"32ddafc0-ee82-4a1a-a645-e4c0731d355c","format_issues":null,"number":10669} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924034f02 | problem | aim-6adb9ed5d4e8053cb940175924034f02 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Continuing the previous problem, understand explicitly the resolution of diagonals in Landau--Ginzburg models. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924034f02",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924034f02",
"note": null,
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} | 2026-10-10T16:07:49.246Z | {"database_id":"9bc16b06-28ba-4827-8978-5ca070a24a1d","format_issues":null,"number":10670} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924036c49 | problem | aim-6adb9ed5d4e8053cb940175924036c49 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.25 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Give a mathematical construction of a link invariant using the Fukaya category associated to potentials on $\text{Hilb}^n(\mathbb{C}^* \times \mathbb{C}^*)_{hor}$ and Mak--Smith's cylindrical model [Source citation: MR4422212](http://aimpl.org/floerhilbert/bib/). | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924036c49",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Mohammed Abouzaid | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924036c49",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924037720 | problem | aim-6adb9ed5d4e8053cb940175924037720 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Barmeier--Wang [Source citation: arXiv:2211.03354](http://aimpl.org/floerhilbert/bib/) recently exhibited a nontrivial deformation of the extended arc algebra via Hochschild cohomology computations. What is the symplectic meaning of this? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924037720",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Mohammed Abouzaid | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924037720",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1db5b021-d14f-48ba-8ea1-396e657fc75b","format_issues":null,"number":10672} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924037939 | problem | aim-6adb9ed5d4e8053cb940175924037939 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.35 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is the B-model interpretation of the deformation introduced in the previous problem? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924037939",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | 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"
] | Mohammed Abouzaid | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb940175924037939",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"fbc4e5c6-6edd-459c-b248-6b95fa039a05","format_issues":null,"number":10673} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240382ce | problem | aim-6adb9ed5d4e8053cb9401759240382ce | Knot homology theories and categorification · Question 4.8 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a direct proof that $HF^*(I \ \text{brane}, E \ \text{brane})$ is a knot invariant which does not pass through resolving $E$ branes by $T$ branes? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb9401759240382ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Question context
Aganagic's proposal on defining $\mathfrak{gl}_{1|1}$ knot homology proves invariance of the relevant Lagrangian Floer homology under Markov moves and skein relations by resolving the Lagrangians using a specific choice of generators, which reduces the proofs to algebraic arguments. The following p... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Robert Lipshitz | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"7ab16f01-8e4b-45b6-9adf-2d64fdd23c29","format_issues":null,"number":10697} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924039800 | problem | aim-6adb9ed5d4e8053cb940175924039800 | Further developments of quantitative Floer theory in low dimensions | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is the relationship between the link and PFH spectral invariants? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb940175924039800",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
See the work of Guanheng Chen [Source citation: arXiv:2111.11891](http://aimpl.org/floerhilbert/bib/), [Source citation: arXiv:2... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Cristofaro-Gardiner | null | null | null | [
{
"kind": "website",
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"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.008Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"43d1d766-9a7e-4173-8f1b-2633d4f7919e","format_issues":null,"number":10680} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924039c87 | problem | aim-6adb9ed5d4e8053cb940175924039c87 | Quantitative Heegaard Floer theory and ECH · Question 2.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can quantitative Heegaard Floer invariants be used to give quantitative invariants of contact forms on $3$-manifolds related to ECH spectral invariants by analogy with the previous problem? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb940175924039c87",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | 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"
] | Dan Cristofaro-Gardiner | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb940175924039c87",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "6adb9ed5d4e8053cb940175924039c87",
"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": "2026-09-09T22:24:05.015Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4a3a3760-24ea-4337-9281-be0d60315ea7","format_issues":null,"number":10681} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592403ac75 | problem | aim-6adb9ed5d4e8053cb94017592403ac75 | Quantitative Heegaard Floer theory and ECH · Question 2.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | If one could provide a positive answer to the previous question, can it be used to better understand the subleading asymptotics of ECH spectral invariants? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb94017592403ac75",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | 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
Cf. conjectures of Hutchings [Source citation: MR4441526](http://aimpl.org/floerhilbert/bib/). | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Cristofaro-Gardiner | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb94017592403ac75",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "6adb9ed5d4e8053cb94017592403ac75",
"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": "2026-09-09T22:24:05.020Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dcdcc654-cf31-40ba-9fb7-6795a107ca8f","format_issues":null,"number":10682} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592403d6f7 | problem | aim-6adb9ed5d4e8053cb94017592403d6f7 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How can we explicitly understand the mirror symmetry equivalence between the A model and B model knot homology constructions in a way which allows one to compare (e.g., functorial) structures? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592403d6f7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ben Webster | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592403d6f7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "6adb9ed5d4e8053cb94017592403d6f7",
"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": "2026-09-09T22:24:04.971Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cf435618-bb42-4f28-9527-54190b1c5efc","format_issues":null,"number":10674} |
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