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"main": "math",
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"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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}
] | In the formulation of the arithmetic fundamental lemma, arithmetic intersection numbers are only formulated for regular semi-simple orbits because of proper intersections of cycles. Is it possible to define arithmetic intersection numbers in case of improper intersections of cycles (and formulate a similar analytic sid... | unassessed | {
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | S. Leslie, Z. Yun | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1a6c63 | problem | aim-0df1011a6fa8a3c46e2c977b7e1a6c63 | Special cycles, modularity and arithmetic intersection · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | In any arithmetic transfer conjectures, could we find perfect test transfer functions for (derived) orbital integrals to match arithmetic intersection numbers with no correction factors? | unassessed | {
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"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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. Rapoport, Q. Li | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1a763d | problem | aim-0df1011a6fa8a3c46e2c977b7e1a763d | Special cycles, modularity and arithmetic intersection · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | In the recent work of Li--Rapoport--Zhang on arithmetic fundamental lemma conjecture for spherical Hecke algebras, there is a conjecture on commutativity of certain Hecke operators on Grothendieck groups of coherent sheaves on unitary Rapoport--Zink spaces. How to prove this conjecture? | unassessed | {
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"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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. Rapoport | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1a80df | problem | aim-0df1011a6fa8a3c46e2c977b7e1a80df | Arithmetic intersection theory beyond classical unitary Shimura varieties · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | Similar to Kudla program, we could also define a generating series of (derived) complex multiplication cycles on Shimura varieties and conjecture its modularity. Is it possible to compute arithmetic intersection of the generating series with special divisors / Hodge bundle and prove its numerical modularity when the Sh... | unassessed | {
"key": "aimpl",
"name": "AIM · Arithmetic intersection theory on Shimura varieties",
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"citation": null,
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"license": "Editorially moderated; per-list terms",
"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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"
] | A. Mihatsch | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1a8bd3 | problem | aim-0df1011a6fa8a3c46e2c977b7e1a8bd3 | Arithmetic intersection theory beyond classical unitary Shimura varieties · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | Could we formulate and prove arithmetic Siegel--Weil formulas of special cycles on unitary Shimura varieties for U(a,b) (a, b>1) where there are no special divisors? | unassessed | {
"key": "aimpl",
"name": "AIM · Arithmetic intersection theory on Shimura varieties",
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"url": "http://aimpl.org/intersectshimura/2/#0df1011a6fa8a3c46e2c977b7e1a8bd3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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. Madapusi Pera | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/intersectshimura/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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} | 2026-10-10T16:07:49.246Z | {"database_id":"74302378-bc71-4e6d-91e2-9fa71e5dae81","format_issues":null,"number":8334} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1a8da7 | problem | aim-0df1011a6fa8a3c46e2c977b7e1a8da7 | Arithmetic intersection theory beyond classical unitary Shimura varieties · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | Could we formulate and prove arithmetic (resp. higher) Siegel--Weil formulas on Shimura varieties (resp. moduli of Shtukas) for exceptional groups? | unassessed | {
"key": "aimpl",
"name": "AIM · Arithmetic intersection theory on Shimura varieties",
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"url": "http://aimpl.org/intersectshimura/2/#0df1011a6fa8a3c46e2c977b7e1a8da7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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. Leslie | null | null | null | [
{
"kind": "website",
"citation": "Arithmetic intersection theory on Shimura varieties",
"url": "http://aimpl.org/intersectshimura/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",
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"published_at": "2026-09-08T03:33:13.790Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e8a33186-1ec1-485e-9a4d-eddf070d48ad","format_issues":null,"number":8335} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1aa19e | problem | aim-0df1011a6fa8a3c46e2c977b7e1aa19e | Arithmetic intersection theory beyond classical unitary Shimura varieties · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | Could we describe the reduced locus of Rapoport--Zink spaces (integral local Shimura varieties) for inner forms of general linear groups? It will be useful for studying arithmetic transfer conjectures in the context of linear arithmetic fundamental lemmas. | unassessed | {
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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 | [] | [] | Arithmetic intersection theory on Shimura varieties · 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"
] | A. Mihatsch | null | null | null | [
{
"kind": "website",
"citation": "Arithmetic intersection theory on Shimura varieties",
"url": "http://aimpl.org/intersectshimura/2/",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1ab536 | problem | aim-0df1011a6fa8a3c46e2c977b7e1ab536 | Arithmetic intersection theory beyond classical unitary Shimura varieties · 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/intersectshimura/ Not an author-supplied MSC code."
}
] | Study non-algebraic locally symmetric spaces for $O(4,4)$ and natural special cycles on them. What kind of structures do we expect? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/intersectshimura/2/#0df1011a6fa8a3c46e2c977b7e1ab536",
"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"... | null | null | null | not-recorded | not-recorded | null | [] | [] | Arithmetic intersection theory on Shimura varieties · 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. Kudla | null | null | null | [
{
"kind": "website",
"citation": "Arithmetic intersection theory on Shimura varieties",
"url": "http://aimpl.org/intersectshimura/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 | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1ad50f | problem | aim-0df1011a6fa8a3c46e2c977b7e1ad50f | Central derivative of Rankin--Selberg $L$-functions for weight-$2$ modular forms and congruent forms | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $f$ be a modular form of weight $2$ and let $\chi$ be a character of the class group of an imaginary quadratic number field $K$. Formulate a direct connection
$$
L'(f \otimes \theta_\chi, \frac{1}{2}) \longleftrightarrow L(g \otimes \theta_\chi, \frac{1}{2}),
$$
for a modular form $g$ on a definite quaternion... | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/1/#0df1011a6fa8a3c46e2c977b7e1ad50f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
These are the stable problems on which workshop groups worked.
## Question context
The hope is to show the non-vanishing o... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Cf. Nicolas Templier's thesis. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Philippe Michel | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/aagaautomorphic/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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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:10.326Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"259a7b1b-f3d1-4d34-9342-7ca3ca4705a7","format_issues":null,"number":7582} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1ae8ac | problem | aim-0df1011a6fa8a3c46e2c977b7e1ae8ac | Non-vanishing of the central $L$-derivative for $\mathrm{U}(n) \times \mathrm{U}(n-1)$ | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Given an automorphic representation $\pi$ of $\mathrm{U}(n)$, show that there exists an automorphic representation $\sigma$ of $\mathrm{U}(n-1)$ such that
$$
L'(\pi \otimes \sigma, \frac{1}{2}) \neq 0.
$$ | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/1/#0df1011a6fa8a3c46e2c977b7e1ae8ac",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
These are the stable problems on which workshop groups worked. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Easier version: show that there is **some** pair $(\pi, \sigma)$ such that
$$
L'(\pi \otimes \sigma, \frac{1}{2}) \neq 0.
$$ | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Wei Zhang | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1ae8ac",
"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": "2026-09-08T03:33:10.331Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4afd5aeb-4ce4-432c-b038-a5f4f813a539","format_issues":null,"number":7583} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1b6526 | problem | aim-0df1011a6fa8a3c46e2c977b7e1b6526 | Joint equidistribution of CM points | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Determine the joint equidistribution of CM points over $K$ of products of modular curves over $F$ as $\mathrm{disc}(K) \rightarrow \infty$. | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/4/#0df1011a6fa8a3c46e2c977b7e1b6526",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | 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"
] | Chris Skinner | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1b6526",
"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": "2026-09-08T03:33:10.358Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"acd8f1f4-f8c0-498d-b1f8-da8d8dc9addd","format_issues":null,"number":7589} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1c0778 | problem | aim-0df1011a6fa8a3c46e2c977b7e1c0778 | Relative conductor of $p$-adic 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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $H \leq G$ be groups over $\mathbb{Q}_p$, $\pi$ be an admissible representation of $G$, and $K_G$ be a maximal compact of $G$. Define
$$
K_H(p^n) := \{g \in K_G \mid (g \mod p^n) \in H\}.
$$
Does $\pi$ have a non-zero vector fixed by $K_H(p^n)$ for some $n$?
If so, what's the smallest such $n$? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/1/#0df1011a6fa8a3c46e2c977b7e1c0778",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
These are the stable problems on which workshop groups worked. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Special case: consider the case $G=\mathrm{GL}(a + b)$ and $H = \mathrm{GL}(a) \times \mathrm{GL}(b)$ (this is Jacquet--Piatetski-Shapiro--Shalika when $a = n-1, b = 1$). When can this happen? Re... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mladen Dimitrov | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1c0778",
"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": "2026-09-08T03:33:10.335Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5e59928b-96be-4f25-b6af-4bcf26bf875b","format_issues":null,"number":7584} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1c645f | problem | aim-0df1011a6fa8a3c46e2c977b7e1c645f | $p$-indivisibility of $L(\chi, 0)$ | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Fix a prime $p$. Let $q$ be a prime and let $\chi$ be an odd character of $(\mathbb{Z}/q\mathbb{Z})^\times$.
How often is $L(\chi, 0)$ indivisible by $p$? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/1/#0df1011a6fa8a3c46e2c977b7e1c645f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
These are the stable problems on which workshop groups worked. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Follow-up: This is the simplest scenario and we know $q^{\frac{1}{2} - \epsilon}$, but can this be improved? Expectation: positive proportion. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ashay Burungale | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1c645f",
"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": "2026-09-08T03:33:10.340Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"432d8746-13b5-4fcb-a022-2fc1f0564c35","format_issues":null,"number":7585} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1c710a | problem | aim-0df1011a6fa8a3c46e2c977b7e1c710a | Arithmetic applications of horizontal equidistribution results | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $K$ be an imaginary quadratic number fields. There are equidistribution results for CM points with square-free order of conductor $C$ as $C \rightarrow \infty$.
Is there an interesting arithmetic application for this? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/4/#0df1011a6fa8a3c46e2c977b7e1c710a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Note: we can ask the same question for similar results in broader contexts. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Philippe Michel | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/4/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1c710a",
"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": "2026-09-08T03:33:10.362Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"40035a0a-feee-409d-ac27-192f25329c98","format_issues":null,"number":7590} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1ccc1b | problem | aim-0df1011a6fa8a3c46e2c977b7e1ccc1b | Applications of the Hecke orbit 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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Are there applications of the recent progress on the Hecke orbit conjecture to vertical mod-$p$ non-vanishing (as in Iwasawa theory)? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/6/#0df1011a6fa8a3c46e2c977b7e1ccc1b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | 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"
] | Ashay Burungale | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1ccc1b",
"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": "2026-09-08T03:33:10.376Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"93035f8b-e8b1-41ba-b5ba-50fbbf78e408","format_issues":null,"number":7593} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1cdd0e | problem | aim-0df1011a6fa8a3c46e2c977b7e1cdd0e | Normalization of Bianchi modular forms | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Consider a Bianchi modular form, is there a correct way to normalize its coefficients in its Whittaker expansion (in $H^2$)? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/6/#0df1011a6fa8a3c46e2c977b7e1cdd0e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | 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"
] | Mladen Dimitrov | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1cdd0e",
"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": "2026-09-08T03:33:10.380Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ea3b3ce3-5295-402b-ac02-50919bd41fad","format_issues":null,"number":7594} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1cf067 | problem | aim-0df1011a6fa8a3c46e2c977b7e1cf067 | Computing Fourier coefficients from $L$-values | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $d$ be a positive integer and let $F$ be a Siegel modular form with Fourier coefficients $a(F)$. In many cases, we know the (generalized) B\"{o}cherer conjecture:
$$
\left \lvert \sum_{S \in \mathrm{Cl}_d} a(F, S) \Lambda(S) \right \rvert^2 = L\big(\pi_F \times \theta_\Lambda, \frac{1}{2}\big) = L\big(\mathrm{B... | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/5/#0df1011a6fa8a3c46e2c977b7e1cf067",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Interesting case: paramodular forms and symmetric cube $L$-functions, where the first relation is "semi-known". | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Manami Roy | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/5/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1cf067",
"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": "2026-09-08T03:33:10.366Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"460fb0f8-5f57-459b-8446-a26f0d575399","format_issues":null,"number":7591} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1d2813 | problem | aim-0df1011a6fa8a3c46e2c977b7e1d2813 | Construction of abelian surfaces for paramodular newforms | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Given a paramodular newform $F$ of weight $2$ with rational coefficients, find a construction of the abelian surface to which it corresponds. | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/3/#0df1011a6fa8a3c46e2c977b7e1d2813",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Cf. Brumer--Pacetti--Poor--Tornaria--Voight--Yuen.
Follow-up: in the setting of Problem 1.4 (Relative conductor of p-adic groups): when is the space of $K_H(p^n)$-fixed vectors one-dimensional? ... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jennifer Johnson-Leung | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/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 | [
"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": "2026-09-08T03:33:10.349Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c4d88611-eaad-47c2-ab23-4fd0d84fd5f5","format_issues":null,"number":7587} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1d635b | problem | aim-0df1011a6fa8a3c46e2c977b7e1d635b | Fixed vectors for $\mathrm{GSp}_{2n}$ | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $\pi$ be a irreducible admissible infinite-dimensional representation of $\mathrm{GSp}_{2n}(\mathbb{Q}_p)$. Consider the subgroup
$$
R(n) := \{g \equiv (\text{matrix with $1$ on the diagonal for first $n$ entries, $a$ on the diagonal for the last $n$ entries}) \pmod{p^n} \text{ for some } a \in \mathbb{Z}_p^\ti... | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/3/#0df1011a6fa8a3c46e2c977b7e1d635b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Note: If $\pi$ is generic, this might be easier because of the paramodular newform theory. Cf. "On ratios of Petersson norms of Yoshida lifts" Saha 2015. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Abhishek Saha | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/3/",
"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": "2026-09-08T03:33:10.353Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b4c4c597-2977-496e-a028-38b12c6307be","format_issues":null,"number":7588} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1daaaa | problem | aim-0df1011a6fa8a3c46e2c977b7e1daaaa | $p$-adic differential operators for higher-rank 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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | For a higher-rank group (e.g. $\mathrm{GSp}_4$), there are some standard $p$-adic differential operators. Do the images of these differential operators contain special automorphic forms coming from lower-rank groups (e.g. Yoshida lifts, Saito--Kurokawa lifts)? | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/6/#0df1011a6fa8a3c46e2c977b7e1daaaa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | 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"
] | Chi-Yun Hsu | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/6/",
"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": "2026-09-08T03:33:10.384Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1388923d-8037-4576-ac5e-75929f1b994d","format_issues":null,"number":7595} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1dad02 | problem | aim-0df1011a6fa8a3c46e2c977b7e1dad02 | Beilinson conjecture for Hecke characters of quartic CM fields | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Prove the Beilinson conjecture for Hecke characters of quartic CM fields. | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/1/#0df1011a6fa8a3c46e2c977b7e1dad02",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
These are the stable problems on which workshop groups worked. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Subproblem: how to generalize the Eisenstein symbol? | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jennifer Johnson-Leung | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1dad02",
"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": "2026-09-08T03:33:10.344Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"47ebad06-32a0-4f37-9852-22fb92f50057","format_issues":null,"number":7586} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1dc61b | problem | aim-0df1011a6fa8a3c46e2c977b7e1dc61b | Local-global description of Stark units | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $f$ be a weight-$1$ modular form with associated Galois representation $\rho_f$. The Harris--Venkatesh conjecture gives a description of Stark units for $\mathrm{Ad}^0(\rho_f)$ modulo $p$ for almost all $p$. In explicit exotic cases, can this be used to describe the Stark units for $\mathrm{Ad}^0(\rho_f)$ themselve... | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/6/#0df1011a6fa8a3c46e2c977b7e1dc61b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | 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": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/6/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e1dc61b",
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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": "2026-09-08T03:33:10.389Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a68485a3-82a8-43c5-b628-72427f956052","format_issues":null,"number":7596} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e1dd887 | problem | aim-0df1011a6fa8a3c46e2c977b7e1dd887 | Siegel modular forms | {
"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/aagaautomorphic/ Not an author-supplied MSC code."
}
] | Let $F$ be a Siegel cusp form of full level and weight $k$ that is a Hecke eigenform. Assume any standard conjecture on $L$-values (e.g. GRH) and all conjectural period formulae.
Prove that for some $\delta > 0$,
$$
\lvert a(F, S) \rvert \ll_{F} \det(S)^{\frac{K}{2}-\frac{1}{2}-\delta}.
$$ | unassessed | {
"key": "aimpl",
"name": "AIM · Analytic, arithmetic, and geometric aspects of automorphic forms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/aagaautomorphic/5/#0df1011a6fa8a3c46e2c977b7e1dd887",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analytic, arithmetic, and geometric aspects of automorphic forms · Historical workshop question | ## Workshop introduction
Section 1 contains the stable working group problems. The remaining sections contain the other proposed problems from the first day of the workshop.
## Section context
Problems from the afternoon session of January 29, 2024 | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Known: assuming GRH, proved with $\delta = 0$ using the weighted average expression of Problem 5.1. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Abhishek Saha | null | null | null | [
{
"kind": "website",
"citation": "Analytic, arithmetic, and geometric aspects of automorphic forms",
"url": "http://aimpl.org/aagaautomorphic/5/",
"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": "2026-09-08T03:33:10.371Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a023f951-a4e5-4c40-83a5-ce4e1e37fc78","format_issues":null,"number":7592} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e20434a | problem | aim-0df1011a6fa8a3c46e2c977b7e20434a | Toeplitz Determinants and Toeplitz Operators · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | The Borodin-Okounkov-Case-Geronimo identity is given by
$$
\text{det}(T_N(e^f))=(e^{N\hat{f}(0)+\sum k\hat{f}(k)\hat{f}(-k)})\text{det}(1-k)
$$
Find a useful adjustment to the right-hand side so that an identity holds in the Fisher-Hartwig case. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/1/#0df1011a6fa8a3c46e2c977b7e20434a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Maurice Duits | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e20434a",
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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": "2026-09-08T03:33:12.487Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"171fa95d-762e-4f4d-80e5-e6b1d98356bd","format_issues":null,"number":8051} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e205c24 | problem | aim-0df1011a6fa8a3c46e2c977b7e205c24 | Toeplitz Determinants and Toeplitz Operators · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Investigate the connection between the $\tau$ function from Painlev\`{e} equations and block Toeplitz determinants. Seek explicit examples in which $\tau$ function asymptotics is known. Find the block Toeplitz determinant. What is it and what do we learn? Use Riemann-Hilbert to connect this to Fuchsian Riemann-Hilbert ... | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/1/#0df1011a6fa8a3c46e2c977b7e205c24",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Maksim Kosmakov | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e205c24",
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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": "2026-09-08T03:33:12.492Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5587c6df-a170-4ba5-91d5-4eb0bb83727c","format_issues":null,"number":8052} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e207a87 | problem | aim-0df1011a6fa8a3c46e2c977b7e207a87 | Riemann-Hilbert Problems · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Given $Q$, produce $Q(z^d)$ with multiple disjoint support sets for the droplet. Study the soft Riemann-Hilbert problem for orthogonal polynomials. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e207a87",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Tamara Grava | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e207a87",
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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": "2026-09-08T03:33:12.510Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bc827316-251e-4241-8726-629d16493103","format_issues":null,"number":8056} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e209c0b | problem | aim-0df1011a6fa8a3c46e2c977b7e209c0b | Riemann-Hilbert Problems · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Study potential theory for $k \times k$ Riemann-Hilbert problems for $k>2$ when multiple orthogonal polynomials are involved. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e209c0b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Pavel Blaher | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e20a8a3 | problem | aim-0df1011a6fa8a3c46e2c977b7e20a8a3 | Riemann-Hilbert Problems · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | In general, can you pose matrix Riemann Hilbert problems for KdV? | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e20a8a3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Manuela Girotti | null | null | null | [
{
"kind": "website",
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"note": null,
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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] | [] | {
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"solved_at": null
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e20bde5 | problem | aim-0df1011a6fa8a3c46e2c977b7e20bde5 | Toeplitz Determinants and Toeplitz Operators · Question 3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Study merging singularities or double scaling limits for Toeplitz determinants with two symbols. Compare $\text{det}(T_n(a_{\lambda}b_{\lambda}))$ and $\text{det}T_n(a_{\lambda})T_n(b_{\lambda})$. Under what conditions does the ratio converge? | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/1/#0df1011a6fa8a3c46e2c977b7e20bde5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Torsten Ehrhardt | null | null | null | [
{
"kind": "website",
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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",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e20d81c | problem | aim-0df1011a6fa8a3c46e2c977b7e20d81c | Riemann-Hilbert Problems · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | For planar orthogonal polynomials, we know that
$$
\overline{\partial} Y=\overline{Y} \begin{bmatrix}
0 & w \\
0 & 0 \\
\end{bmatrix}
$$
and
$$
\int p_j\overline{p_k}wdA=h_j\delta_{j,k}.
$$
Is there an analogue of small norm theory of such $\overline{\partial}$-problems (i.e. $\overline{\partial} A=\overline{A} W +... | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e20d81c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Aron Wennman | null | null | null | [
{
"kind": "website",
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:12.522Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"150f24e4-ea1e-4c4c-88c5-fe7e5d47f568","format_issues":null,"number":8059} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e211fb2 | problem | aim-0df1011a6fa8a3c46e2c977b7e211fb2 | Riemann-Hilbert Problems · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Analyze the condition given by
$$
\overline{\partial}\phi=\overline{H_n}e^{-NQ},
$$
where $Q=|z|^2+2t\text{Re}(z^2)$ and where $\overline{H_n}$ is Hermite. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e211fb2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ken McLaughlin | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/2/",
"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": "2026-09-08T03:33:12.527Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3abffd07-70fe-4e4e-bc9f-5d64371e0be6","format_issues":null,"number":8060} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2152e5 | problem | aim-0df1011a6fa8a3c46e2c977b7e2152e5 | Random Matrix Theory · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Study the expansion of partition functions of normal matrix models for
$$
v(z,\overline{z})=(z \overline{z})^d-t(z^d+\overline{z}^d)
$$
and
$$
z_N=C(d,N)\prod_{\mathscr{l}=0}^{d-1} \mathbb{E}_{\text{Gin}}\Big\{\Big|\text{det}(M_{\text{Gin}}-z)\Big|^{\gamma_{\mathscr{l}}}\Big\},
$$
where $z=t\sqrt{d}$. Study the "m... | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/4/#0df1011a6fa8a3c46e2c977b7e2152e5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | ## Question context
Please see Alfredo Dea\~{n}o and Nick Simm's article "Characteristic polynomials of complex random matrices and Painlev\`{e} transcendents" for background on this problem. | 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"
] | Tamara Grava | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/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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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8906e5ed-40b0-4ade-b8aa-9ac4f6b4b729","format_issues":null,"number":8067} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e21643f | problem | aim-0df1011a6fa8a3c46e2c977b7e21643f | Spectrum of Hilbert Matrices · Question 1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | The $\mathscr{l}^2$-spectrum for the Hilbert matrix $H_{m n}=\frac{1}{m+n+1}$ is known. Find the spectrum on spaces of the form $\mathscr{l}_2(\alpha)=\{\sum |a_n|^2(n+1)^{\alpha}<\infty\}$. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/3/#0df1011a6fa8a3c46e2c977b7e21643f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alfonso Montes Rodriguez | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/3/",
"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": "2026-09-08T03:33:12.554Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"75378bf7-2fec-48f2-8610-37282d947bb8","format_issues":null,"number":8065} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e21721d | problem | aim-0df1011a6fa8a3c46e2c977b7e21721d | Riemann-Hilbert Problems · Question 6 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Consider
$$
\prod_{i=1}^N \begin{bmatrix}
1 & a_iz \\
b_i & 1 \\
\end{bmatrix},
$$
for constants $a_i, b_i$. Suppose Wiener-Hopf factorization has no partial indices. Study the behavior as $N \rightarrow \infty$. The asymptotics are known if the $a_i$'s and $b_i$'s are periodic. What happens in the more general case? | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e21721d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Tomas Berggren | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/2/",
"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": "2026-09-08T03:33:12.531Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4852d2c0-7680-4260-80c1-e3a665a6a1bf","format_issues":null,"number":8061} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e218088 | problem | aim-0df1011a6fa8a3c46e2c977b7e218088 | Riemann-Hilbert Problems · Question 7 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Consider
$$
Z_N=\int_{\Gamma} \cdots \int_{\Gamma} \prod_{i \leq j < k \leq N} |z_k-z_j|^{2\beta} \prod_{j=1}^N\Big(\frac{1}{1+|z_j|^2}\Big)^{(N-1)\beta+1} d|z_1| \cdots d|z_N|.
$$
Study $Z_N$ as $N \rightarrow \infty$, where $\Gamma$ is a smooth loop on the Riemann sphere. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e218088",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Haakan Hedemaim | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/2/",
"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": "2026-09-08T03:33:12.538Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"27fd27dc-e6c5-4328-a3dc-29246f07be69","format_issues":null,"number":8062} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e219057 | problem | aim-0df1011a6fa8a3c46e2c977b7e219057 | Toeplitz Determinants and Toeplitz Operators · Question 4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | (Berger-Coburr 1994): On the Fock/Bergman space, define the projection $\prod:L^2(\mathbb{C},e^{-|z|^2}dA) \rightarrow \mathscr{F}_{\mathbb{C}}$. Take $p: \mathbb{C} \rightarrow \mathbb{C}$ and define $T_p(f)=\prod(p(z)f(z))$. $T_p$ is bounded on the Fock space iff for all $(x,y) \in \mathbb{R}^2$, $u_t=\Delta u,$ $u\B... | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/1/#0df1011a6fa8a3c46e2c977b7e219057",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | ## Question context
Please see C.A. Berger and L.A. Coburn's 1994 article "Heat Flow and Berlin-Toeplitz Estimates" for background on this conjecture. | 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"
] | Michael Hitrik | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/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 | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:12.501Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"162f2f15-bb31-4b9a-92bf-bccac167eca3","format_issues":null,"number":8054} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2196f5 | problem | aim-0df1011a6fa8a3c46e2c977b7e2196f5 | Toeplitz Determinants and Toeplitz Operators · Question 5 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | The determinant of Toeplitz $+$ Handle is expressible in terms of the $4 \times 4$ Riemann-Hilbert problem for Szego type symbols. The obstacle to asymptotic analysis is the existence of a solution to model problems. If $d \tilde{d}=1$ on $\{|z|=1\}$, where $d=\frac{\phi(z)}{w(z)}$ and $\tilde{d}=\frac{\phi(1/z)}{w(1/z... | unassessed | {
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"url": "http://aimpl.org/riemhilberttoeplitz/1/#0df1011a6fa8a3c46e2c977b7e2196f5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Roozbeh Gharakhloo | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e21c3a9 | problem | aim-0df1011a6fa8a3c46e2c977b7e21c3a9 | Riemann-Hilbert Problems · Question 8 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | The discrete Bessel process is connected to Poissonized Plancherel measure. Consider the distance of the largest particle: $\mathbb{P}[Q_{\text{max}}\leq x]=q(x)$, where $q$ solves the cylindrical Toda equation. Take the limit to get cylindrical KdV. Is there a connection to Riemann-Hilbert Problems? | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e21c3a9",
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"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Maksim Kosmakov | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e21cb3a | problem | aim-0df1011a6fa8a3c46e2c977b7e21cb3a | Random Matrix Theory · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Study the topological phase transition in the asymptotics of planar orthogonal polynomials with normal Random Matrix Theory. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/4/#0df1011a6fa8a3c46e2c977b7e21cb3a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Maurice Duits | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/4/",
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}
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e21db36 | problem | aim-0df1011a6fa8a3c46e2c977b7e21db36 | Riemann-Hilbert Problems · Question 9 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Formulate and then analyze general finite matrix symbol with the analog of zeros and jumps. | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/2/#0df1011a6fa8a3c46e2c977b7e21db36",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Estelle Basor | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/2/",
"note": null,
"sort_order": 0
}
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e220c2c | problem | aim-0df1011a6fa8a3c46e2c977b7e220c2c | Spectrum of Hilbert Matrices · Question 2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [] | Define
$$
u_{\xi, \alpha(z)}=e^{-\alpha\Big(\frac{\xi+z}{\xi-z}\Big)},
$$
for $\alpha >0$ and $|\xi|=1$. Given $\xi_1, \xi_2, \xi_3$ and $\alpha_1, \alpha_2, \alpha_3$, can we approximate
$$
\sum_{m=0}^{\infty} c_m^{(1)}u_1^m+c_m^{(2)}u_2^m+c_m^{(3)}u_3^m?
$$ | unassessed | {
"key": "aimpl",
"name": "AIM · Riemann-Hilbert problems, Toeplitz matrices, and applications",
"type": "workshop-problem-list",
"url": "http://aimpl.org/riemhilberttoeplitz/3/#0df1011a6fa8a3c46e2c977b7e220c2c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Riemann-Hilbert problems, Toeplitz matrices, and applications · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alfonso Montes Rodriguez | null | null | null | [
{
"kind": "website",
"citation": "Riemann-Hilbert problems, Toeplitz matrices, and applications",
"url": "http://aimpl.org/riemhilberttoeplitz/3/",
"note": null,
"sort_order": 0
}
] | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0a4853e1-554a-4365-8f8b-bcc5110df51b","format_issues":null,"number":8066} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e22588c | problem | aim-0df1011a6fa8a3c46e2c977b7e22588c | Initial Problem Session · Question 02 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | There were several questions proposed around this, including
* What should the predicted values of $a,b,c$ be?
* What is the "shape" of the set $U$ that one should take? In the usual Manin conjecture, one expects that $U$ can be taken to be the complement of a thin set.
* Can one compute asymptotics for $N_{X,\maths... | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e22588c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
The goal is to formulate a Manin-type conjecture for degree $d$ points on Fano varieties. Let $X/k$ be a Fano variety defined over a number field $k$. For a subset $U\subset X$, an integer $d$, a real number $B>0$, and a line bundle $\mathscr L$ on $X$, define
$$N_{X,\mathscr L}(U,B;d) := \#\left\{... | 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"
] | Caleb Ji | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2ca530c8-6264-440a-8e81-7521c6901718","format_issues":null,"number":7903} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e22ac34 | problem | aim-0df1011a6fa8a3c46e2c977b7e22ac34 | Initial Problem Session · Question 04 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Is there a $\mathbb Q$-irrational del Pezzo surface $X$ which is $\mathbb Q$-unirational for which $\operatorname{Sym}^dX$ is $\mathbb Q$-rational for some $d>1$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e22ac34",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Adam Logan | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/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 | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f8b7d19c-20aa-435c-87fa-858160d2c405","format_issues":null,"number":7904} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e22f8f5 | problem | aim-0df1011a6fa8a3c46e2c977b7e22f8f5 | Initial Problem Session · Question 06 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Can we give a method to construct a Zariski dense set of degree $d$ points on a variety different from the one just mentioned?
* Maybe one can replace $\mathbb P^n$ with another sort of variety?
* Maybe one can do something totally different and give a construction not coming from a correspondence. | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e22f8f5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
Let $X$ be a variety. Suppose one has a diagram $X\dashleftarrow Y\dashrightarrow\mathbb P^n$, where $Y\dashrightarrow\mathbb P^n$ is finite of degree $d$. Then, as a consequence of Hilbert irreducibility, $X$ will have a Zariski dense set of degree $d$ points. | 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"
] | Isabel Vogt + Olivier Martin | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0c0e0ac4-9e92-43e7-9427-233b16dab466","format_issues":null,"number":7905} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2315de | problem | aim-0df1011a6fa8a3c46e2c977b7e2315de | Initial Problem Session · Question 08 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | With some hypotheses on $X$ and $X\to\operatorname{Alb}(X)$, study the image of $\operatorname{Sym}^d(X)\to\operatorname{Alb}(X)$ for some small $d$.
What are examples of $X$ for which the fibers of $\operatorname{Sym}^dX\to\operatorname{Alb}(X)$ are "well-understood"? For example, when are they finite or rational? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e2315de",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Morena Porzio + Isabel Vogt | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
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"published_at": "2026-09-08T03:33:11.825Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a8c7094a-fe16-4e6f-b00f-64adf3f07d10","format_issues":null,"number":7906} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e232f4d | problem | aim-0df1011a6fa8a3c46e2c977b7e232f4d | Initial Problem Session · 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/degreedsurface/ Not an author-supplied MSC code."
}
] | Let $X/k$ be a nice variety, and let $\delta(X/k)=\{d:$ degree $d$ points on $X$ are Zariski dense in $X\}$ be its density degree set. How different can $\min\delta(X/k)$ be from $\operatorname{uni.irr}(X),\operatorname{cov.gon}(X)$, and/or $\operatorname{conn.cov.gon}(X)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
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"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e232f4d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
Let $X/k$ be a nice variety. We define a few measures of irrationality.
* Its covering gonality $\operatorname{cov.gon}(X)$ is the minimal $d$ such that there exists a diagram $B\leftarrow\mathcal C\dashrightarrow X$, where $\mathcal C\dashrightarrow X$ is a dominant rational map and $\mathcal C\t... | 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"
] | Olivier Martin | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"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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"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"400cbaeb-2b97-46d0-8207-5d8239da3ede","format_issues":null,"number":7907} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2343d6 | problem | aim-0df1011a6fa8a3c46e2c977b7e2343d6 | Initial Problem Session · Question 12 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Skorobogatov constructed a bielliptic surface $X/\mathbb Q$ such that $X(\mathbb A_{\mathbb Q})^{\operatorname{Br}}\neq\emptyset$, but $X(\mathbb Q)=\emptyset$. It is known that $\min\delta(X/\mathbb Q)\le3$. Where do these Zariski-dense degree 3 points come from? Can one compute $\mathcal D(X/\mathbb Q),\delta(X/\math... | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e2343d6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
Let $X/k$ be a nice variety. In addition to its density degree set $\delta(X/\mathbb Q)$, define
$$\mathcal D(X/\mathbb Q):=\{d:X\text{ has a point of degree }d\},$$
and
$$\mathcal P(X/\mathbb Q)=\bigcup_{[k':k]<\infty}\delta(X/k').$$ | 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"
] | Valia Gazaki + Bianca Viray | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2343d6",
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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": "2026-09-08T03:33:11.834Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4799ad77-042a-43cb-a9aa-72568744926c","format_issues":null,"number":7908} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2364a3 | problem | aim-0df1011a6fa8a3c46e2c977b7e2364a3 | Initial Problem Session · Question 14 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Let $C,D$ be hyperelliptic curves of genus $\ge2$ over a number field $k$. Must $2\in\delta(C\times D/k)$? Must it be in $\mathcal P(C\times D/k)$?
More generally, let $Z\subset C\times D$ be the closure of the degree $d$ points. When is there a component of $Z$ which dominates both $C$ and $D$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e2364a3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Nathan Chen + Olivier Martin | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2364a3",
"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": "2026-09-08T03:33:11.839Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d26a604b-ffda-423c-ac9e-7900e6404f36","format_issues":null,"number":7909} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e237aca | problem | aim-0df1011a6fa8a3c46e2c977b7e237aca | Initial Problem Session · Question 16 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Let $C$ be a curve of genus $\ge2$ over a number field. Must $2\in\delta(\operatorname{Sym}^2_C/k)$ or in $\mathcal P(\operatorname{Sym}^2_C/k)$? What do these sets look like? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e237aca",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | James Rawson | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e237aca",
"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": "2026-09-08T03:33:11.843Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"51cfd630-5001-45ff-8079-66b65aae2440","format_issues":null,"number":7910} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e23831e | problem | aim-0df1011a6fa8a3c46e2c977b7e23831e | Initial Problem Session · Question 18 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Given a finite map $f:X\to Y$ (over a number field), how are $\delta(X/k)$ and $\delta(Y/k)$ related? Are there examples showing that the obvious relations are sharp? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e23831e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Adam Logan + Bianca Viray | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e23831e",
"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": "2026-09-08T03:33:11.848Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6c9519fc-0770-4936-ad4c-504abef2f394","format_issues":null,"number":7911} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2397eb | problem | aim-0df1011a6fa8a3c46e2c977b7e2397eb | Initial Problem Session · 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/degreedsurface/ Not an author-supplied MSC code."
}
] | Is $\operatorname{Hilb}^2(C\times D)(k)$ Zariski dense in $\operatorname{Hilb}^2(C\times D)$, where $C,D/k$ are hyperelliptic curves over a number field. More generally, for which varieties $X$ over a number field is there a $d$ such that $\operatorname{Hilb}^d(X)(k)$ is Zariski dense? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e2397eb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Morena Porzio + Isabel Vogt | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2397eb",
"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": "2026-09-08T03:33:11.852Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8e951eff-1ed3-4e83-b5d8-7e969ffb4910","format_issues":null,"number":7912} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e23cbe9 | problem | aim-0df1011a6fa8a3c46e2c977b7e23cbe9 | Initial Problem Session · Question 22 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Given some specific geometric construction showing that $d\in\delta(X/k)$, can one use it to construct a dominant rational map $X\dashrightarrow\mathbb P^2$ of degree $nd$, for some small $n$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e23cbe9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Shamil Asgarli + Bianca Viray | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e23cbe9",
"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": "2026-09-08T03:33:11.856Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"65b81866-8a1f-4eb4-9e57-8875dce57dba","format_issues":null,"number":7913} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e23cf60 | problem | aim-0df1011a6fa8a3c46e2c977b7e23cf60 | Initial Problem Session · Question 24 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Given a covering family $T\leftarrow\mathcal C\dashrightarrow X$ of curves, where $T(k)$ is Zariski dense, how does $\operatorname{gon}(C)$ (for $C$ a generic member of the family) compare to $\min\delta(X/k)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e23cf60",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Nathan Chen | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e23cf60",
"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": "2026-09-08T03:33:11.862Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9598fff4-a707-469b-b113-1a40540fc5f6","format_issues":null,"number":7914} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e23d8a2 | problem | aim-0df1011a6fa8a3c46e2c977b7e23d8a2 | Initial Problem Session · Question 26 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Compute $\operatorname{irr}(X/F)$ for a del Pezzo surface $X$ over a general field $F$. | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e23d8a2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
For a variety $X/F$, define its degree of irrationality $\operatorname{irr}(X)$ to be the minimum degree of a rational map $X\dashrightarrow\mathbb P^2$ (defined over $F$). | 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"
] | Nathan Chen | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e23d8a2",
"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": "2026-09-08T03:33:11.866Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fac5e93b-e138-4952-9b59-12620cd0a3b4","format_issues":null,"number":7915} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e23e6ab | problem | aim-0df1011a6fa8a3c46e2c977b7e23e6ab | Initial Problem Session · Question 28 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | How do all of these invariants (e.g. $\min\delta(X/k),\operatorname{irr}(X/k),\operatorname{cov.gon}(X/k)$, etc.) behave under specialization/deformation in a smooth family? This includes the arithmetic case, where the base is something like $\operatorname{Spec}\mathscr O_{k,S}$. | unassessed | {
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"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e23e6ab",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nathan Chen + Lena Ji | null | null | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"3ccdbb9e-e7a1-4bcb-985d-bb367695ff06","format_issues":null,"number":7916} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e240bd0 | problem | aim-0df1011a6fa8a3c46e2c977b7e240bd0 | Initial Problem Session · 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/degreedsurface/ Not an author-supplied MSC code."
}
] | Is there a surface $X$ over a number field $k$ and a finite extension $k'/k$ such that $\delta(X/k)\not\subset\delta(X/k')$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e240bd0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Isabel Vogt | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:11.875Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"feb8ab69-93f2-4f93-bb71-f6142ac9b08f","format_issues":null,"number":7917} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e242d47 | problem | aim-0df1011a6fa8a3c46e2c977b7e242d47 | Initial Problem Session · Question 32 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Let $X_d\subset\mathbb P^3_k$ ($k$ a number field) be a smooth surface of degree $d$. Are the degree $\le d-3$ points not Zariski dense? What is $\min\delta(X_d/k)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e242d47",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
The following is asked as an analogue of a result due to Debarre and Klassen \cite{arXiv:alg-geom/9210004}. | 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"
] | Olivier Martin | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"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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} | 2026-10-10T16:07:49.246Z | {"database_id":"32c1b757-a644-4111-813b-f3dae7b3512f","format_issues":null,"number":7918} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e244f21 | problem | aim-0df1011a6fa8a3c46e2c977b7e244f21 | Initial Problem Session · Question 34 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Given a dominant map $\psi:X\dashrightarrow\mathbb P^{\dim X}$ of minimal degree $d$, is the gonality of the pullback of a general line equal to $d$? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e244f21",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Olivier Martin | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/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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"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4f23ba6b-ceae-4aba-891e-d148441be489","format_issues":null,"number":7919} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e245e18 | problem | aim-0df1011a6fa8a3c46e2c977b7e245e18 | Initial Problem Session · Question 36 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Given a general smooth degree $d$ hypersurface $X_d\subset\mathbb P^3_k$, for $d$ sufficiently large, must a general degree $d$ point arise from intersecting $X$ with a line? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e245e18",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Shamil Asgarli | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/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",
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.888Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"954f52db-fe1b-4374-9e77-ecdd655c0888","format_issues":null,"number":7920} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e246050 | problem | aim-0df1011a6fa8a3c46e2c977b7e246050 | Initial Problem Session · Question 38 | {
"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/degreedsurface/ Not an author-supplied MSC code."
}
] | Classify surfaces $X/k$ of general type with $2\in\delta(X/k)$, possibly using geometric and/or dynamical constructions. | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e246050",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · Historical workshop question | ## Question context
The following is asked in analogy with a result of Harris and Silverman showing that, for a curve $C/k$, $2\in\delta(C/k)\iff C$ is a double cover of $\mathbb P^1$ or a positive rank elliptic curve (see https://www.ams.org/journals/proc/1991-112-02/S0002-9939-1991-1055774-0/S0002-9939-1991-1055774-... | 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"
] | Nathan Chen | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/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": "2026-09-08T03:33:11.892Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"37d33b79-1bf7-4c14-bcc1-f4ebf8f84d70","format_issues":null,"number":7921} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e24806d | problem | aim-0df1011a6fa8a3c46e2c977b7e24806d | Initial Problem Session · 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/degreedsurface/ Not an author-supplied MSC code."
}
] | 1.) Find effective obstructions to the existence of solvable points on varieties (in any characteristic).
2.) Do there exist curves (over surfaces) over $\mathbb Q$ without solvable points? | unassessed | {
"key": "aimpl",
"name": "AIM · Degree d points on algebraic surfaces",
"type": "workshop-problem-list",
"url": "http://aimpl.org/degreedsurface/1/#0df1011a6fa8a3c46e2c977b7e24806d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Degree d points on algebraic surfaces · 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"
] | Jesse Wolfson | null | null | null | [
{
"kind": "website",
"citation": "Degree d points on algebraic surfaces",
"url": "http://aimpl.org/degreedsurface/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e24806d",
"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": "2026-09-08T03:33:11.897Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"52f8d6e0-8fc0-4c99-8caf-875e72de6014","format_issues":null,"number":7922} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2510d5 | problem | aim-0df1011a6fa8a3c46e2c977b7e2510d5 | $c^k$-approximations and contactomorphisms · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can hypersurfaces be $c^\infty$-approximated by Weinstein convex hypersurfaces? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/2/#0df1011a6fa8a3c46e2c977b7e2510d5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2510d5",
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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",
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.241Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d633c735-c23a-433b-8f56-14f42936da5c","format_issues":null,"number":7786} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2542f0 | problem | aim-0df1011a6fa8a3c46e2c977b7e2542f0 | $c^k$-approximations and contactomorphisms · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For what $k$ can we $c^k$-approximate the mapping tori of ergodic time-1 flows of contact vector fields by a contactomorphism whose mapping torus is convex? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/2/#0df1011a6fa8a3c46e2c977b7e2542f0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Eliashberg | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e2542f0",
"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": "2026-09-08T03:33:11.246Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bdaa10f3-c52b-448e-a81f-6ab81732c3ca","format_issues":null,"number":7787} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25510d | problem | aim-0df1011a6fa8a3c46e2c977b7e25510d | Tightness and symplectic field theory · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do there exist tight but not fillable contact structures whose fillability is not obstructed by SFT? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/5/#0df1011a6fa8a3c46e2c977b7e25510d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Zhou | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/5/",
"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": "2026-09-08T03:33:11.281Z",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25604b | problem | aim-0df1011a6fa8a3c46e2c977b7e25604b | Explicit contact handlebodies · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Give a bypass description of convex surfaces foliating the region in $(S^5,\xi_k):=\text{OBD}(T^*S^2, \tau^{2k+1})$ between two Darboux balls. | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
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"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e25604b",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Breen | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e256de5 | problem | aim-0df1011a6fa8a3c46e2c977b7e256de5 | Explicit contact handlebodies · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Find other interesting explicit bypass decompositions of contact manifolds. | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e256de5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e258bae | problem | aim-0df1011a6fa8a3c46e2c977b7e258bae | Explicit contact handlebodies · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we characterize trivial bypasses in terms of the belt sphere of $n$-handle and the attaching sphere of the $n+1$ handle? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e258bae",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Murphy | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2594c8 | problem | aim-0df1011a6fa8a3c46e2c977b7e2594c8 | Explicit contact handlebodies · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can triviality be detected via capacities on balls around the intersection point? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e2594c8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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 | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2596c9 | problem | aim-0df1011a6fa8a3c46e2c977b7e2596c9 | Liouville vs Weinstein · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Explicitly describe Weinstein convex perturbations of Liouville convex hypersurfaces. For instance, doubles of Liouville manifolds. | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/3/#0df1011a6fa8a3c46e2c977b7e2596c9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Breen | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
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"sort_order": 0
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2598c3 | problem | aim-0df1011a6fa8a3c46e2c977b7e2598c3 | Liouville vs Weinstein · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Are all Liouville manifolds with half-dimensional homotopy type Liouville homotopic to Weinstein manifolds? 1-parametric version? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/3/#0df1011a6fa8a3c46e2c977b7e2598c3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Eliashberg, Murphy | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e259fab | problem | aim-0df1011a6fa8a3c46e2c977b7e259fab | Liouville vs Weinstein · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What about in the special case where the skeleton is stratified by manifolds of dimension at most half? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/3/#0df1011a6fa8a3c46e2c977b7e259fab",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Eliashberg | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25c0bd | problem | aim-0df1011a6fa8a3c46e2c977b7e25c0bd | Tightness criteria via convex hypersurface theory · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we characterize convex hypersurfaces with tight neighbourhoods? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/4/#0df1011a6fa8a3c46e2c977b7e25c0bd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/4/",
"note": null,
"sort_order": 0
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25cb18 | problem | aim-0df1011a6fa8a3c46e2c977b7e25cb18 | Tightness criteria via convex hypersurface theory · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Must every almost contact class admit a tight structure? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/4/#0df1011a6fa8a3c46e2c977b7e25cb18",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Massot | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25cffb | problem | aim-0df1011a6fa8a3c46e2c977b7e25cffb | Tightness criteria via convex hypersurface theory · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Given the existence of one tight structure in this almost contact class, must there be infinitely many? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/4/#0df1011a6fa8a3c46e2c977b7e25cffb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Murphy | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e25d585 | problem | aim-0df1011a6fa8a3c46e2c977b7e25d585 | Symplectic fillings of contact submanifolds · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Given a Weinstein domain, can we construct a distinct Weinstein filling of its countact boundary and/or a contactomorphism of its boundary inducing the same augmentation. | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/9/#0df1011a6fa8a3c46e2c977b7e25d585",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Chaidez | null | null | null | [
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we define an appropriate notion for overtwistedness for conformally symplectic manifolds? Two potential options: the existence of an embedded model, having a contactization which is overtwisted. | unassessed | {
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"license": "Editorially moderated; per-list terms",
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The source supplies no status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e260ecf | problem | aim-0df1011a6fa8a3c46e2c977b7e260ecf | Symplectic fillings of contact submanifolds · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Classify symplectic fillings of contact submanifolds of $(S^5,\xi_{std})$ in its standard $D^6$ filling. E.g. Show that the standard $S^3\subset S^5$ has a unique filling up to Hamiltonian isotopy. | unassessed | {
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"url": "http://aimpl.org/highdimcontacttop/9/#0df1011a6fa8a3c46e2c977b7e260ecf",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e263359 | problem | aim-0df1011a6fa8a3c46e2c977b7e263359 | Donaldson's results via convex hypersurface theory · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can Donaldson's theorem be proved on a closed symplectic manifolds via CHT techniques? | unassessed | {
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"url": "http://aimpl.org/highdimcontacttop/6/#0df1011a6fa8a3c46e2c977b7e263359",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Eliashberg | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2640ce | problem | aim-0df1011a6fa8a3c46e2c977b7e2640ce | Explicit contact handlebodies · Question 5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Understand contact connected sum in high dimensions: can non-standard structures on $S^5$ connect sum to give $\xi_{std}$? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e2640ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Murphy | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/7/",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e264fc4 | problem | aim-0df1011a6fa8a3c46e2c977b7e264fc4 | Explicit contact handlebodies · Question 6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Does connected sum preserve tightness? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e264fc4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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 | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e26545e | problem | aim-0df1011a6fa8a3c46e2c977b7e26545e | Explicit contact handlebodies · Question 7 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can non-destabilizable OBDs connect sum to a destabilizable (or otherwise non-minimal) OBD? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/7/#0df1011a6fa8a3c46e2c977b7e26545e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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 | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e265587 | problem | aim-0df1011a6fa8a3c46e2c977b7e265587 | Symplectic fillings of contact submanifolds · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we restrict the topology of symplectic fillings using convex surfaces in their boundaries? (c.f. filling by holomorphic curves) | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/9/#0df1011a6fa8a3c46e2c977b7e265587",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Gironella | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e26595e | problem | aim-0df1011a6fa8a3c46e2c977b7e26595e | Contact submanifolds · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Taxonomize h-principles for contact submanifolds: Write down a full h-principle for twisted contact submanifolds for some (or any) definition of twisted. | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/1/#0df1011a6fa8a3c46e2c977b7e26595e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Casals | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
"url": "http://aimpl.org/highdimcontacttop/1/",
"note": null,
"sort_order": 0
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e266e15 | problem | aim-0df1011a6fa8a3c46e2c977b7e266e15 | Miscellaneous · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | In higher dimensions, do intersections of convex hypersurfaces admit a standard model? Can we describe edge rounding? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/10/#0df1011a6fa8a3c46e2c977b7e266e15",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Ganatra | null | null | null | [
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"kind": "website",
"citation": "Higher-dimensional contact topology",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e268aaa | problem | aim-0df1011a6fa8a3c46e2c977b7e268aaa | Donaldson's results via convex hypersurface theory · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is it true that given a Liouville domain, there is a codimension two Liouville submanifold whose complement is Weinstein? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/6/#0df1011a6fa8a3c46e2c977b7e268aaa",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Proble... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e268da8 | problem | aim-0df1011a6fa8a3c46e2c977b7e268da8 | Flexibility | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do properly embedded codimension 2 Weinstein domains satisfy an existence h-principle? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimcontacttop/10/#0df1011a6fa8a3c46e2c977b7e268da8",
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The source supplies no status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2699cb | problem | aim-0df1011a6fa8a3c46e2c977b7e2699cb | Miscellaneous · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do Liouville domains of dimension at least six satisfy an existence h-principle? | unassessed | {
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"url": "http://aimpl.org/highdimcontacttop/10/#0df1011a6fa8a3c46e2c977b7e2699cb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Lazarev | null | null | null | [
{
"kind": "website",
"citation": "Higher-dimensional contact topology",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e269a17 | problem | aim-0df1011a6fa8a3c46e2c977b7e269a17 | Miscellaneous · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What do CHT techniques tell us about the map $$\text{Cont}(M,\xi)\to \text{Diff}(M)?$$ Is $\pi_1(\text{Cont}(S^5, \xi))\to \pi_1(\text{Diff}(S^5))$ a surjection? | unassessed | {
"key": "aimpl",
"name": "AIM · Higher-dimensional contact topology",
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"url": "http://aimpl.org/highdimcontacttop/10/#0df1011a6fa8a3c46e2c977b7e269a17",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Higher-dimensional contact topology · 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"
] | Casals | null | null | null | [
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"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e26e7a4 | problem | aim-0df1011a6fa8a3c46e2c977b7e26e7a4 | Parameter determination for post-quantum hash functions | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | In the design of the hash function one has control over two parameters; the dimension of the special linear group considered, and the characteristic of the underlying field. We would like to determine appropriate choices for both via two branches of cryptanalysis: first, by analysis of the multivariate system implied b... | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/1/#0df1011a6fa8a3c46e2c977b7e26e7a4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems in the analysis of some of the schemes discussed at the workshop.
## Question context
Ramón Flores presented a Tillich-Zémor-style hash function using the Cayley graph of special linear groups in arbitrary dimension. Questions remain, however, about the optimal choice of parameters f... | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/1/",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e26f779 | problem | aim-0df1011a6fa8a3c46e2c977b7e26f779 | Cryptanalysis of SDLP | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | On the quantum side the question of quantum equivalence of SDLP and the CDH-type problem underpinning semidirect product key exchange (SCDH) remains unproven, though we have strong cause to suspect their equivalence given the quantum equivalence of the heavily related vectorisation and parallelisation problems. The dec... | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/1/#0df1011a6fa8a3c46e2c977b7e26f779",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems in the analysis of some of the schemes discussed at the workshop.
## Question context
Various problems relating to the cryptanalysis, both quantum and classical, of SDLP remain open. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e271a9a | problem | aim-0df1011a6fa8a3c46e2c977b7e271a9a | Quantum lower bounds for group-theoretic problems in the generic group model | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | We would like to solidify the credentials of group-theoretic cryptography as post-quantum by developing lower bounds for the quantum complexity of problems arising in group theory. It would be especially nice to develop such a bound for the vectorisation problem, since this underpins many hardness problems in the area. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/1/#0df1011a6fa8a3c46e2c977b7e271a9a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems in the analysis of some of the schemes discussed at the workshop. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/1/",
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"sort_order": 0
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e2739e2 | problem | aim-0df1011a6fa8a3c46e2c977b7e2739e2 | Advanced digital signature functionality from group theory | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | We would like to use generic group-action tools to build ring signatures, blind signatures, threshold signatures and more. We would also like to apply the "twist" technique present in similar isogeny schemes to improve the memory performance of group-based digital signatures. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/2/#0df1011a6fa8a3c46e2c977b7e2739e2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems relating to the design of protocols in group-theoretic cryptography.
## Question context
The connection between SDLP and group actions suggests the availability of generic group-action tools to build more efficient signatures, or signatures with more specialised properties. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/2/",
"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":"5be2dfb4-0416-4720-9d34-3480e7b34ce6","format_issues":null,"number":8152} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e275146 | problem | aim-0df1011a6fa8a3c46e2c977b7e275146 | Applications of infinite non-abelian groups to cryptography | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | Several cryptanalytic methods against group-based cryptography suggest possible use cases for infinite non-abelian groups; for example, non-Hopfian groups. We would like to develop tools to understand how these infinite objects can fit into a cryptographic context, and whether their use can be used to address some of t... | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/3/#0df1011a6fa8a3c46e2c977b7e275146",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
More general group-theoretic questions with implications in the field. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/3/",
"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":"7d5b91ff-9231-4894-921b-9752f4c9a30a","format_issues":null,"number":8156} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e277613 | problem | aim-0df1011a6fa8a3c46e2c977b7e277613 | Creation of challenge instances | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | Across the various group-based protocols there is a general lack of precision on which parameter specification. As the field matures we should make available challenge instances of each protocol. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/2/#0df1011a6fa8a3c46e2c977b7e277613",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems relating to the design of protocols in group-theoretic cryptography. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/2/",
"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",
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e27814f | problem | aim-0df1011a6fa8a3c46e2c977b7e27814f | Implementation of group-based cryptography | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | In general very little work exists on efficient implementation of group-based protocols; over time we would like to build up a software library of such implementations. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/2/#0df1011a6fa8a3c46e2c977b7e27814f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems relating to the design of protocols in group-theoretic cryptography. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/2/",
"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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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e278296 | problem | aim-0df1011a6fa8a3c46e2c977b7e278296 | Methods of key establishment from group theory | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | Generally speaking the field does not seem to offer methods of key establishment. It remains open to construct standard key exchange protocols as well as more complicated multi-party variants. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/2/#0df1011a6fa8a3c46e2c977b7e278296",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems relating to the design of protocols in group-theoretic cryptography. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/2/",
"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",
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.961Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"98474609-bf01-442b-9a82-a76e805133d6","format_issues":null,"number":8155} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e278a1c | problem | aim-0df1011a6fa8a3c46e2c977b7e278a1c | Cryptographic building blocks from problems in group theory | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | We would like to use computational problems in group theory to derive fundamental cryptographic objects including one-way functions and multilinear maps. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/3/#0df1011a6fa8a3c46e2c977b7e278a1c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
More general group-theoretic questions with implications in the field. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e278a1c",
"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": "2026-09-08T03:33:12.969Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c26f9927-0f73-42d8-8bbb-11743c5fe3d0","format_issues":null,"number":8157} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e27a537 | problem | aim-0df1011a6fa8a3c46e2c977b7e27a537 | Computational problems from graph groups | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | It is known that it is possible to establish correspondence between certain NP-hard graph problems and problems in group theory; we would like to expand our portfolio of such problems. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/3/#0df1011a6fa8a3c46e2c977b7e27a537",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
More general group-theoretic questions with implications in the field. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/3/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e27a537",
"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": "2026-09-08T03:33:12.974Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f07e41da-c6c7-4ef4-8568-6827c60e279f","format_issues":null,"number":8158} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e27aff0 | problem | aim-0df1011a6fa8a3c46e2c977b7e27aff0 | Machine learning-based cryptanalysis of group-theoretic protocols | {
"main": "computer science",
"sub": "cryptography",
"slug": "cryptography",
"name": "Cryptography",
"original_discipline": "computer-science"
} | [] | [
{
"code": "94A60",
"basis": "community-map",
"evidence": "Inferred from community field: cryptography"
}
] | There have been some results in the application of machine learning to the cryptanalysis of lattice-based schemes; whether these methods translate to the group-theoretic realm remains open. | unassessed | {
"key": "aimpl",
"name": "AIM · Post-quantum group-based cryptography",
"type": "workshop-problem-list",
"url": "http://aimpl.org/postquantgroup/1/#0df1011a6fa8a3c46e2c977b7e27aff0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | Post-quantum group-based cryptography · Historical workshop question | ## Section context
Open problems in the analysis of some of the schemes discussed at the workshop. | 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": "Post-quantum group-based cryptography",
"url": "http://aimpl.org/postquantgroup/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e27aff0",
"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": "2026-09-08T03:33:12.943Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"73c1a4bd-076c-454e-8fe1-d539b3d291f5","format_issues":null,"number":8151} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e27f1f4 | problem | aim-0df1011a6fa8a3c46e2c977b7e27f1f4 | Entropy Freiman-Ruzsa lower bounds | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/highdimdiscrete/ Not an author-supplied MSC code."
}
] | Can we give lower bounds for $d[X,U_H]$? | unassessed | {
"key": "aimpl",
"name": "AIM · High-dimensional phenomena in discrete analysis",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highdimdiscrete/1/#0df1011a6fa8a3c46e2c977b7e27f1f4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | High-dimensional phenomena in discrete analysis · Historical workshop question | ## Question context
Theorem. Let $X$ be any $\mathbb{F}_2^n$-valued random variable such that $d[X,X]\leq \log K$, where $d$ is the entropic Ruzsa distance. Then there is a subspace $H\subset \mathbb{F}_2^n$ such that $d[X,U_H]\leq 11\log K$, where $U_H$ is uniform on $H$. | 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"
] | Terence Tao | null | null | null | [
{
"kind": "website",
"citation": "High-dimensional phenomena in discrete analysis",
"url": "http://aimpl.org/highdimdiscrete/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "0df1011a6fa8a3c46e2c977b7e27f1f4",
"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": "2026-09-08T03:33:12.030Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5cbe9e2a-fe39-4913-9b9b-3b7e1b45aa66","format_issues":null,"number":7951} |
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