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1.0.0 | problem:aim-6ece8953664f1897b245a92213025ed6 | problem | aim-6ece8953664f1897b245a92213025ed6 | Problems in High Forcing · Question 35 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Can we obtain the super tree property at $\aleph_{\omega+1}$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a92213025ed6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | 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"
] | Laura Fontanella | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.867Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c278708b-b6b9-49ea-b05a-423ad9121b4a","format_issues":null,"number":7268} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221302be39 | problem | aim-6ece8953664f1897b245a9221302be39 | Problems in High Forcing · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it possible to obtain the super tree property at a successor of a singular cardinal? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221302be39",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | 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"
] | Laura Fontanella | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
}
] | {
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"published_at": "2026-09-08T03:33:08.875Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ea65fcc9-1349-4588-b746-1eb160aae3f7","format_issues":null,"number":7269} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221302cefe | problem | aim-6ece8953664f1897b245a9221302cefe | Problems in High Forcing · Question 45 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\forall n<\omega$, $kappa_n$ has the super tree property property. If $\lambda = \sup_{n<\omega}$, does $\lambda^+$ have the tree property? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221302cefe",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | 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"
] | Laura Fontanella | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/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": "2026-09-08T03:33:08.880Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"451bb237-dc6f-427a-b848-17b184187178","format_issues":null,"number":7270} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221302dfec | problem | aim-6ece8953664f1897b245a9221302dfec | Problems in High Forcing · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\kappa$ has the strong tree property. Does SCH hold above $\kappa$? (If yes, then the strong tree property at $\aleph_2$ implies SCH.) | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221302dfec",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | 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"
] | Laura Fontanella | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a9221302dfec",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.884Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bcb8036e-0960-4ff6-adef-1fb2a747a967","format_issues":null,"number":7271} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221302f842 | problem | aim-6ece8953664f1897b245a9221302f842 | Problems in High Forcing · Question 55 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent to obtain $TP_{\aleph_2}$ together with the existence of a saturated ideal on $\aleph_2$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221302f842",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | 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"
] | Monroe Eskiw | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/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": "2026-09-08T03:33:08.889Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ead7cb3e-53e7-45a1-a219-433268e3fc01","format_issues":null,"number":7272} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213033617 | problem | aim-6ece8953664f1897b245a92213033617 | Problems in the Overlap of High and Low Forcing · Question 6 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\aleph_\omega$ is a strong limit. Is there a poset ${\mathbb P}$ of size $<\aleph_\omega$, which adds a club guessing sequence for $S^{\omega_2}_{\omega_1}$, preserving $\omega_1$, $\omega_2$, and $\omega_3$. | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a92213033617",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
If yes than by PCF theory, in ZFC it would be provable that $2^{\aleph_\omega}<\aleph_{\omega_3}$ when $\aleph_\omega$ is a strong limit. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | David Aspero | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/3/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5a810a85-da56-499e-8ccb-2fab0f96e7e3","format_issues":null,"number":7278} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221303bc0a | problem | aim-6ece8953664f1897b245a9221303bc0a | Problems in Low Forcing · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent to have $\lim^p \mathbb{A} = 0$ for all $p$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221303bc0a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
$\mathbb A = \langle A_f : f \in \omega^\omega \rangle$ is the following inverse system of abelian groups:
$$ A_f = \bigop... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
If strong homology is consistent for locally compact metric spaces, then the answer to this question is positive. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Justin Moore | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/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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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:08.834Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e13227a2-3a79-415d-944c-a5bbc2f14461","format_issues":null,"number":7261} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130454fd | problem | aim-6ece8953664f1897b245a922130454fd | Koml\'{o}s conjecture | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | There is a universal constant $c>0$ s.t. for every $v_1,v_2,...,v_n \in \mathbb{B_2}^d$, there exist signs $\epsilon_1,...,\epsilon_n\in \{-1,1\}$ s.t. $|| \sum_{i=1}^n \epsilon_i v_i||_{\infty} \le c$ | unassessed | {
"key": "aimpl",
"name": "AIM · Hereditary discrepancy and factorization norms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a922130454fd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | /-
Copyright 2026 The Formal Conjectures Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in ... | null | null | not-recorded | not-recorded | null | [
{
"language": "Lean 4",
"code": "/-\nCopyright 2026 The Formal Conjectures Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n https://www.apache.org/licenses/LICENSE-2... | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
$c=O(\sqrt{\log min\{d,n\}})$ was given by [Banaszczyk'98] and [Naor'05] | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"citation": "Formal Conjectures — Komlós conjecture",
"url": "https://github.com/google-deepmi... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"88faf47a-a6e4-4cfd-a648-97b1a99265c6","format_issues":null,"number":7368} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213045a2c | problem | aim-6ece8953664f1897b245a92213045a2c | Constructive Koml\'{o}s | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Find a polynomial time algorithm to find the signs above. | unassessed | {
"key": "aimpl",
"name": "AIM · Hereditary discrepancy and factorization norms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a92213045a2c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
$O(\log min\{d,n\})$ [Bansal'10, Lovett-Meka'14, Rothvoss'15] | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"published_at": "2026-09-08T03:33:09.320Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ea14ca4f-b4b1-4e39-985d-980f5d249e03","format_issues":null,"number":7369} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213046826 | problem | aim-6ece8953664f1897b245a92213046826 | Beck-Fiala conjecture and making it constructive | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Given a set system $(V,\mathcal{S})$ with $V=[n]$, $\mathcal{S}=S_1,...,S_m$. Each $i\in V$ occurs in at most $t$ sets from $\mathcal{S}$. Then there is a coloring to the elements of $V$ achieving a discrepancy of $O(\sqrt{t})$. Koml\'{o}s conjecture implies this by treating the incidence vector of each $i\in V$ as a v... | unassessed | {
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"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a92213046826",
"citation": null,
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"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A $2t-1$ guarantee which is also algorithmic was given by Beck-Fiala. Recently, [Bukh] gave a guarantee of $2t-\log^*t$. Banaszczyk's result implies a bound of $O(\sqrt{t\log m})$ but is non-cons... | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6ece8953664f1897b245a92213048e9d | problem | aim-6ece8953664f1897b245a92213048e9d | Beck-Fiala for random set system | {
"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/hereddiscrep/ Not an author-supplied MSC code."
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] | Each element $i\in [n]$ lies in $t$ randomly selected sets from $\mathcal{S}$. | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a92213048e9d",
"citation": null,
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"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
They show that when $m\ge n$, hereditary discrepancy of the set system is $O(\sqrt{t\log t})$ whp. When $n\ge m^t$, hereditary discrepancy is $O(1)$. An open question is to explore this setting f... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Esther Ezra, Shachar Lovett | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221304aa07 | problem | aim-6ece8953664f1897b245a9221304aa07 | Hypercube set system | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Given a set system where the elements are the vertices of the hypercube $\{0,1\}^n$. Corresponding to each vertex $v$, there is a set $S_v$ which is generated by picking a random subset of the neighbours of $v$ in the hypercube. What is the discrepancy of this set system? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221304aa07",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
If instead of picking a random subset of the neighbours, $S_v$ was the full set of neighbours of $v$, then there is an easy solution giving discrepancy 1. Color each vertex depending on the parit... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Shachar Lovett | null | null | 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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"published_at": "2026-09-08T03:33:09.333Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"869046be-552f-429e-bfeb-1b5bd467bb00","format_issues":null,"number":7372} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221304bbc6 | problem | aim-6ece8953664f1897b245a9221304bbc6 | Discrepancy of permutations | {
"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/hereddiscrep/ Not an author-supplied MSC code."
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] | a) discrepancy of k-permutations
For $k=3$, $[NNN'12]$ showed a lower bound of $\Omega(\log n)$ where $n$ is the number of elements in the ground set. For general $k$, we know that the answer lies in $[\sqrt{k}+\log n,\sqrt{k}\log n]$. An open question is to clsoe this gap.
b) discrepancy of k-random permutations
... | unassessed | {
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"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · 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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] | null | null | null | 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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} | 2026-10-10T16:07:49.246Z | {"database_id":"4e7512c6-cef7-41ec-bc24-7ae81ef4d29d","format_issues":null,"number":7373} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221304e404 | problem | aim-6ece8953664f1897b245a9221304e404 | Matrix Spencer | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Given matrices $A_1,...,A_n \in\mathbb{R}^{n\times n}$ satisfying $||A_i||_{op} \le 1$ where $||.||_{op}$ is the operator norm of matrices. Do there exists signs $\epsilon_1,...,\epsilon_n\in\{-1,1\}$ s.t. $||\sum_{i=1}^n\epsilon_i A_i || =O(\sqrt{n})$. | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221304e404",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
We can assume that the matrices are symmetric. Matrix chernoff gives a bound of $O(\sqrt{n\log n})$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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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":"2f272ca3-a1b3-46a8-a747-b82e42898345","format_issues":null,"number":7374} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221304fd53 | problem | aim-6ece8953664f1897b245a9221304fd53 | Steinitz conjecture | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Given vectors $v_1,...,v_n\in\mathbb{R}^d$ and a norm $X$ satisfying $\sum_{i=1}^n v_i=0$ and $||v_i||_X\le 1$ for all $i$. Define $S_n(X,d)=min_{\pi\in S^n}max_{k=1,...,n}|| \sum_{i=1}^k v_{\pi(i)}||_X$ where $S^n$ is the set of all permutations of $[n]$. Let $S(X,d)=sup_n S_n(X,d)$. Then, $S(X,d) =O(\sqrt{d})$. | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221304fd53",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
i) Sevastiyanov showed $S(X,d) \le d$. For $X$ a symmetric norm, Banaszczyk improved this to $d-\frac{1}{d}$
ii) If $X=l_p$ for $1< p < 2$, $S(X,d) =\Omega(d)$
iii) For $X=l_2$, Banaszczyk'13... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | 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 | [
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:09.347Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"adf22730-9b63-4744-816f-d33f8c98c2a3","format_issues":null,"number":7375} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130574a6 | problem | aim-6ece8953664f1897b245a922130574a6 | Vector Balancing | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Is this lower bound also an upper bound for $\alpha(X,Y,d)$ upto $\log d$ factors? | unassessed | {
"key": "aimpl",
"name": "AIM · Hereditary discrepancy and factorization norms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a922130574a6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | ## Question context
Let $X,Y$ be norms on $\mathbb{R}^d$. Given vectors $v_1,...,v_n\in \mathbb{R}^d$ satisfying $||v_i||_X\le 1$ for all $i$. We want to find signs $\epsilon_i \in \{-1,1\}$ to minimize $|| \sum_{i=1}^n\epsilon_iv_i ||_Y$. Call this the discrepancy of the vectors. Define $\alpha_n(X,Y,d)$ as the maxim... | 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": "Hereditary discrepancy and factorization norms",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"published_at": "2026-09-08T03:33:09.352Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"df0e2feb-873a-4961-9043-16913b7f958d","format_issues":null,"number":7376} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221305b1cc | problem | aim-6ece8953664f1897b245a9221305b1cc | Tusnady's problem | {
"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/hereddiscrep/ Not an author-supplied MSC code."
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] | Let $d_n$ be the discrepancy of $n$ points in $\mathbb{R}^2$ wrt all alix-aligned rectangles i.e. the set system comprises of all axis-aligned rectangles in $\mathbb{R}^2$ as sets, maximised over all choices of $n$ points. Tusnady's problem then asks for the exact value of $d_n$.
We can also ask for the same question ... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221305b1cc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
In $\mathbb{R^2}$, we know a lower bound of $O(\log n)$ on $d_n$ and an upper bound of $O(\log^{2.5}n)$. In $\mathbb{R}^d$, we know that $d_n\in[\log^{d-1}n,log^{d+1/2}n]$ | null | published | incremental | hard | [
"aim",
"historical-workshop"
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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": "2026-09-08T03:33:09.356Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b903143b-edf8-4396-a8fe-c75ca756af8c","format_issues":null,"number":7377} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221305c842 | problem | aim-6ece8953664f1897b245a9221305c842 | Beating LLL | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Consider a matrix where both columns are rows are t-sparse. LLL gives a discrepancy bound of $O(\sqrt{t\log t})$ here.
If we assume the stronger property that every pair of rows intersect in at most one element, can we get a $O(\sqrt{t})$? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221305c842",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · 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": "Hereditary discrepancy and factorization norms",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:09.360Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a9d51168-5599-4e59-b720-31915917c0fb","format_issues":null,"number":7378} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221305d698 | problem | aim-6ece8953664f1897b245a9221305d698 | Hardness of Komlos | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Can we prove some hardness statement about finding a coloring achieving Komlos guarantee or the Banaszczyk discrepancy guarantee? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221305d698",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · 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": "Hereditary discrepancy and factorization norms",
"url": "http://aimpl.org/hereddiscrep/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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"published_at": "2026-09-08T03:33:09.367Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3fc11e8f-e882-4561-8dbc-6bec5206f897","format_issues":null,"number":7379} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221305dc64 | problem | aim-6ece8953664f1897b245a9221305dc64 | Reverse Banaszczyk-type problems | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Say that a convex body $K$ has property B if for any set of vectors of length no more than $c$ (some small constant), there exists a signing of them s.t. this signed sum lies inside $K$.
What is the convex body with the smallest gaussian volume which has property $B$? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221305dc64",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · 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": "Hereditary discrepancy and factorization norms",
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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-6ece8953664f1897b245a9221305f70e | problem | aim-6ece8953664f1897b245a9221305f70e | Polysize list of colorings | {
"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/hereddiscrep/ Not an author-supplied MSC code."
}
] | Is there a list of colorings of polynomial size such that for any subset of the columns, one of these colorings gives it a discrepancy of O(h), where $h$ is the hereditary discrepancy? | unassessed | {
"key": "aimpl",
"name": "AIM · Hereditary discrepancy and factorization norms",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hereddiscrep/1/#6ece8953664f1897b245a9221305f70e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "... | null | null | null | not-recorded | not-recorded | null | [] | [] | Hereditary discrepancy and factorization norms · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This was answered in the negative. Counterexample is a simple set system comprising of $\sqrt{n}$ disjoint rows of size $\sqrt{n}$ each. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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"citation": "Hereditary discrepancy and factorization norms",
"url": "http://aimpl.org/hereddiscrep/1/",
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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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"source-full-text-not-present"
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1.0.0 | problem:aim-6ece8953664f1897b245a922130663ff | problem | aim-6ece8953664f1897b245a922130663ff | Arkhipov--Bezrukavnikov--Ginzburg · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - Is there a version of the derived equivalences of Arkhipov--Bezrukavnikov--Ginzburg that applies when $\ell$ (the order of the root of unity) is less than or equal to $h$ (the Coxeter number)?
- Same question for singular blocks rather than the principal block. | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/8/#6ece8953664f1897b245a922130663ff",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nakano | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/8/",
"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":"e491f858-6e7c-473a-9133-ad14921b7944","format_issues":null,"number":7772} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213069bf5 | problem | aim-6ece8953664f1897b245a92213069bf5 | Rational Representations: Induction, Cohomology Vanishing · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What does the induction theorem of Achar--Riche/Hodge--Karuppuchamy--Scott imply about the relationship between representations of $G(\mathbb{F}_q)$ and $B(\mathbb{F}_q)$ in defining characteristic? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/1/#6ece8953664f1897b245a92213069bf5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/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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"source-full-text-not-present"
] | [] | {
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"published_at": "2026-09-08T03:33:11.136Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"397da813-dda3-433a-a19d-1bcaa34cb582","format_issues":null,"number":7762} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221306ed84 | problem | aim-6ece8953664f1897b245a9221306ed84 | Rational Representations: Induction, Cohomology Vanishing · Question 2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What representations of $G(\mathbb{F}_q)$ arise by restricting a tilting module of $G$? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/1/#6ece8953664f1897b245a9221306ed84",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/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": "2026-09-08T03:33:11.140Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9330a4cd-274f-4a22-a0ac-bb2689f79317","format_issues":null,"number":7763} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221306fd73 | problem | aim-6ece8953664f1897b245a9221306fd73 | Rational Representations: Induction, Cohomology Vanishing · Question 3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What rational representations of $B$ arise by restricting a tilting module of $G$? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/1/#6ece8953664f1897b245a9221306fd73",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Scott | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/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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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.145Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6bdbc4a7-c60f-462e-9fce-688a20cf3680","format_issues":null,"number":7764} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213070122 | problem | aim-6ece8953664f1897b245a92213070122 | Rational Representations: Induction, Cohomology Vanishing · Question 4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What objects of the derived category of representations of $B$ correspond to tilting modules of $G$? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/1/#6ece8953664f1897b245a92213070122",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Achar | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/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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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.149Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c85d447d-f28f-4ad6-aa61-ca648a44f91b","format_issues":null,"number":7765} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213071bbf | problem | aim-6ece8953664f1897b245a92213071bbf | Geometric Extension Algebra · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Given an algebraic group $G$ acting on a variety $X$ with finitely many orbits and a $G$-equivariant morphism $\pi\colon \widetilde{X} \to X$ where $\widetilde{X}$ is nonsingular (not necessarily connected), consider $A = \operatorname{End}^\bullet_{D^\mathrm{b}_G(X)}(\pi_* \underline{k}_{\widetilde{X}})$, an algebra o... | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/10/#6ece8953664f1897b245a92213071bbf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Peter McNamara | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/10/",
"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": "2026-09-08T03:33:11.158Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"93ae4cfb-ce7a-417e-93d6-2578c1a73aff","format_issues":null,"number":7767} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130742fe | problem | aim-6ece8953664f1897b245a922130742fe | Highest Weight Structure on Categories of Perverse Sheaves · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a geometric proof (i.e.~avoiding Geometric Satake) that $\operatorname{Perv}_{\mathrm{sph}}(Gr, k)$ is highest-weight? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/9/#6ece8953664f1897b245a922130742fe",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mautner | null | null | null | [
{
"kind": "website",
"citation": "Sheaves and modular representations of reductive groups",
"url": "http://aimpl.org/sheavemodular/9/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:11.162Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"781ce3c6-4f16-4b00-b589-689204bcf6df","format_issues":null,"number":7768} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213077712 | problem | aim-6ece8953664f1897b245a92213077712 | Highest Weight Structure on Categories of Perverse Sheaves · Question 3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Given a symplectic resolution $\pi\colon Y \to X$, with $G = \operatorname{Aut}(X, \omega)$, consider the subcategory of $\operatorname{Perv}_G(X, k)$ generated by subquotients of $\pi_*\underline{k}_Y$. When is this highest-weight? | unassessed | {
"key": "aimpl",
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1.0.0 | problem:aim-6ece8953664f1897b245a92213079812 | problem | aim-6ece8953664f1897b245a92213079812 | Center of $\mathrm{Rep}_0G$ · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a geometric description of the center of $\mathrm{Rep}_0G$? Possibly related to affine Springer fibers? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/6/#6ece8953664f1897b245a92213079812",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Shan | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a92213079f7d | problem | aim-6ece8953664f1897b245a92213079f7d | Center of $\mathrm{Rep}_0G$ · Question 2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Does this help to describe the center of $\operatorname{Dist}(G)$? | unassessed | {
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"url": "http://aimpl.org/sheavemodular/6/#6ece8953664f1897b245a92213079f7d",
"citation": null,
"doi": null,
"arxiv_id": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221307c6ca | problem | aim-6ece8953664f1897b245a9221307c6ca | Geometric Interpretation of Frobenius Twist · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Under geometric Satake, what operation on perverse sheaves corresponds to Frobenius twist? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/7/#6ece8953664f1897b245a9221307c6ca",
"citation": null,
"doi": null,
"arxiv_id": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
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"url": "http://aimpl.org/sheavemodular/7/",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221307f0ea | problem | aim-6ece8953664f1897b245a9221307f0ea | $p$-Kazhdan--Lusztig polynomials · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a homological interpretation of the $p$-Kazhdan--Lusztig polynomials? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/4/#6ece8953664f1897b245a9221307f0ea",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Scott | null | null | null | [
{
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"url": "http://aimpl.org/sheavemodular/4/",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308111d | problem | aim-6ece8953664f1897b245a9221308111d | Quasi-Maps and Rational Represetations · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is $\mathrm{Rep}_0(G_1T)$ equivalent to a category of perverse sheaves on a space of quasi-maps from $\mathbb{P}^1$ to $G/B$? | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/2/#6ece8953664f1897b245a9221308111d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Lanini | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/sheavemodular/2/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-6ece8953664f1897b245a92213082ea6 | problem | aim-6ece8953664f1897b245a92213082ea6 | Quasi-Maps and Rational Represetations · Question 2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | What geometric category is equivalent to $\mathrm{Rep}_0(G_rT)$ or $\mathrm{Rep}_{\mathrm{res}}(\mathfrak{g})$? | unassessed | {
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"name": "AIM · Sheaves and modular representations of reductive groups",
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"url": "http://aimpl.org/sheavemodular/2/#6ece8953664f1897b245a92213082ea6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a92213084bc2 | problem | aim-6ece8953664f1897b245a92213084bc2 | Moduli Stack of Torsion Coherent Sheaves on $\mathbb{P}^1$ · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $X$ be the moduli stack of torsion coherent sheaves on $\mathbb{P}^1$ over $\mathbb{C}$. Is it true that $H^{\mathrm{odd}}(X, k) = 0$ for all fields $k$?
(Motivated by KLR algebras for affine $\mathfrak{sl}_2$.) | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/11/#6ece8953664f1897b245a92213084bc2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | McNamara | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308618f | problem | aim-6ece8953664f1897b245a9221308618f | Parity Sheaves and Torsion in IC Sheaves · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - For which primes $p$ is it true that all indecomposable $B$-constructible parity $\mathbb{F}_p$ sheaves on $G/B$ are perverse?
- Same question for $I$-constructible parity $\mathbb{F}_p$-sheaves on $Gr$.
(Expect this to be true for large $p$.) | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/5/#6ece8953664f1897b245a9221308618f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Achar--Williamson | null | null | null | [
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"published_at": "2026-09-08T03:33:11.216Z",
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1.0.0 | problem:aim-6ece8953664f1897b245a92213088534 | problem | aim-6ece8953664f1897b245a92213088534 | Parity Sheaves and Torsion in IC Sheaves · Question 3 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Give nontrivial sufficient conditions for indecomposable parity sheaves on $G/B$ or $Gr$ or $Fl$ to be simple perverse sheaves. | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
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"url": "http://aimpl.org/sheavemodular/5/#6ece8953664f1897b245a92213088534",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Williamson | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308ae13 | problem | aim-6ece8953664f1897b245a9221308ae13 | Parity Sheaves and Torsion in IC Sheaves · Question 4 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a faster algorithm to compute indecomposable parity sheaves on $\operatorname{Perv}_{\mathrm{sph}}(Gr, \mathbb{F}_p)$ than by computing the $p$-canonical basis?
(Motivated by A. Broer's algorithm in characteristic 0.) | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/5/#6ece8953664f1897b245a9221308ae13",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Achar | null | null | null | [
{
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"url": "http://aimpl.org/sheavemodular/5/",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308e173 | problem | aim-6ece8953664f1897b245a9221308e173 | Modular Character Sheaves · Question 1 | {
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} | [] | [] | Can one develop a theory of modular character sheaves on $G$ that relates to the representation theory of $G(\mathbb{F}_p)$ in non-defining characteristic? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308eea9 | problem | aim-6ece8953664f1897b245a9221308eea9 | Steenrod Algebra · Question 1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | - What is the representation-theoretic meaning of the Steenrod algebra action on mod-p cohomology? For example, on the cohomology of $Gr$?
- Does the Steenrod algebra act on the cohomology of any parity sheaf? (Note: examples of Goresky show that this fails for mod-p IC sheaves.) | unassessed | {
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"url": "http://aimpl.org/sheavemodular/13/#6ece8953664f1897b245a9221308eea9",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221308fd51 | problem | aim-6ece8953664f1897b245a9221308fd51 | Parity Sheaves and Torsion in IC Sheaves · Question 2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | For which primes $p$ do the IC sheaves on $\operatorname{Perv}_I(Gr, \mathbb{Z}_p)$ have torsion-free stalks?
(Related to Problem 10.1 part 2, and to Ext-vanishing between reduced standard and costandard modules.) | unassessed | {
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"url": "http://aimpl.org/sheavemodular/5/#6ece8953664f1897b245a9221308fd51",
"citation": null,
"doi": null,
"arxiv_id": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
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"aim",
"historical-workshop"
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1.0.0 | problem:aim-6ece8953664f1897b245a92213090c85 | problem | aim-6ece8953664f1897b245a92213090c85 | Rational Representations: Induction, Cohomology Vanishing · Question 5 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $P$ be a parabolic subgroup of $G$. Is it true in characteristic $p$ that $R^i\operatorname{Ind}_P^G\operatorname{Sym}(\mathfrak{n}_P^\bullet) = 0$ for all $i > 0$? (Known for $P = B$ and for certain other parabolics. Possible connection with normality of nilpotent orbit closures.) | unassessed | {
"key": "aimpl",
"name": "AIM · Sheaves and modular representations of reductive groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/1/#6ece8953664f1897b245a92213090c85",
"citation": null,
"doi": null,
"arxiv_id": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nakano | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a92213092546 | problem | aim-6ece8953664f1897b245a92213092546 | Highest Weight Structure on Categories of Perverse Sheaves · Question 2 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | More generally, when is a category of perverse sheaves constructible with respect to a fixed stratification highest-weight? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/sheavemodular/9/#6ece8953664f1897b245a92213092546",
"citation": null,
"doi": null,
"arxiv_id": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Sheaves and modular representations of reductive groups · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221309d7ec | problem | aim-6ece8953664f1897b245a9221309d7ec | Reconstruction · Question 05 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Of the ten possibilities, how many of the solutions can be real? | unassessed | {
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"url": "http://aimpl.org/algvision/1/#6ece8953664f1897b245a9221309d7ec",
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · Historical workshop question | ## Section context
A fundamental topic in algebraic vision is that of reconstructing a scene from images.
## Question context
The essential variety is a 5-dimensional variety of degree 10. A point correspondence gives a linear constraint so a five point correspondence should give 10 complex solutions. | Historical workshop record. Current open/solved status has not been independently reassessed.
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1.0.0 | problem:aim-6ece8953664f1897b245a9221309e430 | problem | aim-6ece8953664f1897b245a9221309e430 | Reconstruction · Question 1 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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] | How many linear constraints does a point correspondence in three views determine on the trifocal tensor variety ? | unassessed | {
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"license": "Editorially moderated; per-list terms",
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A fundamental topic in algebraic vision is that of reconstructing a scene from images. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Numerical results suggest that there are 4 constraints but they only intersect the trifocal tensor variety in codimension three. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221309e880 | problem | aim-6ece8953664f1897b245a9221309e880 | Reconstruction · Question 15 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | How do the 24 linear constraints lead a minimal problem? How many complex solutions are there? | unassessed | {
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A fundamental topic in algebraic vision is that of reconstructing a scene from images.
## Question context
It is known that the trifocal tensor variety is dimension 18 with degree 297 inside of $\mathbb{P}^{28}$. It is also known that a six point correspondence in three views is a minimal problem. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Numerical methods show that each point correspondence only intersects the variety in codimension 3 and so will lead to a minimal problem. The degree is cut down at each step of imposing condition... | null | published | incremental | hard | [
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1.0.0 | problem:aim-6ece8953664f1897b245a9221309fff4 | problem | aim-6ece8953664f1897b245a9221309fff4 | Reconstruction · Question 2 | {
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"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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] | In between the calibrated and uncalibrated cases there are partially calibrated cameras, say with both focal lengths known or with the center position known. What can we say about these situations? | unassessed | {
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"license": "Editorially moderated; per-list terms",
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A fundamental topic in algebraic vision is that of reconstructing a scene from images. | 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-6ece8953664f1897b245a922130a17bf | problem | aim-6ece8953664f1897b245a922130a17bf | More Varieties · Question 1 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
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"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | For any of the standard varieties considered it might be possible to study the projective dual. What can we learn from studying these objects? | unassessed | {
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"url": "http://aimpl.org/algvision/2/#6ece8953664f1897b245a922130a17bf",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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-6ece8953664f1897b245a922130a1a8d | problem | aim-6ece8953664f1897b245a922130a1a8d | More Varieties · Question 2 | {
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] | What can we say about the convex hull of all the varieties we have considered? Can we give a good description of them? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a1e9a | problem | aim-6ece8953664f1897b245a922130a1e9a | More Varieties · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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] | What is the functor of points of multiview geometry? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a37a8 | problem | aim-6ece8953664f1897b245a922130a37a8 | Reconstruction · Question 25 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
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"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Given an algebraic curve in two views, when are they compatible? This is interesting when the cameras are fixed beforehand. | unassessed | {
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A fundamental topic in algebraic vision is that of reconstructing a scene from images. | Historical workshop record. Current open/solved status has not been independently reassessed.
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a5262 | problem | aim-6ece8953664f1897b245a922130a5262 | Reconstruction · Question 3 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
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"code": "14",
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"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | What is the Hurwitz form of the essential variety? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a5a5f | problem | aim-6ece8953664f1897b245a922130a5a5f | Reconstruction · Question 35 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Can we use conic correspondence between two images to do reconstruction? Can we use point and curve correspondences to do reconstruction? Can we use cubic spline correspondences to do reconstruction? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a6ad5 | problem | aim-6ece8953664f1897b245a922130a6ad5 | Reconstruction · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Fix two cameras and two image curves. Is there is a curve in $\mathbb{P}^3$ that projects onto these two curves? What if we put restriction on degrees or smoothness? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a7277 | problem | aim-6ece8953664f1897b245a922130a7277 | Invariants · Question 1 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | How complete are these invariants? If two curves have the same signature what can we say about them? | unassessed | {
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From a differential geometry perspective we can assign invariants to a smooth curve or surface. This allows us to assign a signature curve to each curve. | 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 | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a8142 | problem | aim-6ece8953664f1897b245a922130a8142 | Invariants · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | What can we say about the degree of a signature curve? How is it related to the automorphism group of the original curve? | unassessed | {
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From a differential geometry perspective we can assign invariants to a smooth curve or surface. This allows us to assign a signature curve to each curve. | Historical workshop record. Current open/solved status has not been independently reassessed.
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"aim",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a85c7 | problem | aim-6ece8953664f1897b245a922130a85c7 | Invariants · Question 3 | {
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"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | What is the signature curve of a general canonical curve? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a8fab | problem | aim-6ece8953664f1897b245a922130a8fab | Invariants · Question 4 | {
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"name": "Geometry and topology",
"original_discipline": "mathematics"
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"code": "14",
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"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | What can we say about the signature of the signature of a curve? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a949a | problem | aim-6ece8953664f1897b245a922130a949a | Invariants · Question 5 | {
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"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Which curves occur as signatures of another curve? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130a9941 | problem | aim-6ece8953664f1897b245a922130a9941 | Invariants · Question 6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
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"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Can we use differential (integral, other…) invariants to construct a moduli space? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130aa705 | problem | aim-6ece8953664f1897b245a922130aa705 | Invariants · Question 7 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | How can we use these signatures for object recognition? | unassessed | {
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"url": "http://aimpl.org/algvision/3/#6ece8953664f1897b245a922130aa705",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · Historical workshop question | ## Section context
From a differential geometry perspective we can assign invariants to a smooth curve or surface. This allows us to assign a signature curve to each curve. | Historical workshop record. Current open/solved status has not been independently reassessed.
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ab8f5 | problem | aim-6ece8953664f1897b245a922130ab8f5 | More Varieties · Question 4 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | What is the functor of points in the calibrated case? | unassessed | {
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"url": "http://aimpl.org/algvision/2/#6ece8953664f1897b245a922130ab8f5",
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"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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-6ece8953664f1897b245a922130ac541 | problem | aim-6ece8953664f1897b245a922130ac541 | Invariants · Question 8 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Find local invariants for a natural (Lie) groupoid action. (e.g. bathroom tiles in an irregular bathroom). How is this related to quasi-invariants? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/algvision/3/#6ece8953664f1897b245a922130ac541",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · Historical workshop question | ## Section context
From a differential geometry perspective we can assign invariants to a smooth curve or surface. This allows us to assign a signature curve to each curve. | 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": "Algebraic vision",
"url": "http://aimpl.org/algvision/3/",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ac88f | problem | aim-6ece8953664f1897b245a922130ac88f | Silhouettes · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Which visual event surfaces appear on visual hulls of algebraic surfaces? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebraic vision",
"type": "workshop-problem-list",
"url": "http://aimpl.org/algvision/4/#6ece8953664f1897b245a922130ac88f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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": "Algebraic vision",
"url": "http://aimpl.org/algvision/4/",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130acb55 | problem | aim-6ece8953664f1897b245a922130acb55 | Silhouettes · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Can we find equations of visual event surfaces? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/algvision/4/#6ece8953664f1897b245a922130acb55",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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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"kind": "website",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130acd60 | problem | aim-6ece8953664f1897b245a922130acd60 | Silhouettes · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | In silhouette reconstruction a duality appears between the visual hull and the convex hull. Is there an algebraic version of this? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/algvision/4/#6ece8953664f1897b245a922130acd60",
"citation": null,
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"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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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] | null | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ad723 | problem | aim-6ece8953664f1897b245a922130ad723 | Silhouettes · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Can we find the fundamental matrix from silhouettes? If the silhouettes are bounded by algebraic curves are there algebraic constraints on the fundamental matrix? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebraic vision",
"type": "workshop-problem-list",
"url": "http://aimpl.org/algvision/4/#6ece8953664f1897b245a922130ad723",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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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"citation": "Algebraic vision",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ada30 | problem | aim-6ece8953664f1897b245a922130ada30 | Reconstruction · Question 45 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | For a reconstruction what does it mean for all the points to be “in front” of the cameras? Can this easily be detected. | unassessed | {
"key": "aimpl",
"name": "AIM · Algebraic vision",
"type": "workshop-problem-list",
"url": "http://aimpl.org/algvision/1/#6ece8953664f1897b245a922130ada30",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · Historical workshop question | ## Section context
A fundamental topic in algebraic vision is that of reconstructing a scene from images. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Two approaches were suggested: That neither of the cameras are contained in the convex hull of the world points; or that $P r_i = \lambda x_i$ and $Q r_i = \mu y_i$ where $\lambda>0$ and $\mu>0$. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130af26b | problem | aim-6ece8953664f1897b245a922130af26b | Carlsson-Weinshall Duality · Question 1 | {
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] | Is there a relationship between Carlsson-Weinshall and Gale duality? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b01d4 | problem | aim-6ece8953664f1897b245a922130b01d4 | Carlsson-Weinshall Duality · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | Is there a Carlsson-Weinshallduality for point and line correspondence? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b03da | problem | aim-6ece8953664f1897b245a922130b03da | Carlsson-Weinshall Duality · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
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] | What is a moduli space description of Carlsson-Weinshall duality? What moduli spaces does this suggest? A framed multiview variety? | unassessed | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b1332 | problem | aim-6ece8953664f1897b245a922130b1332 | Carlsson-Weinshall Duality · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | What can we say about Carlsson-Weinshall duality for other dimensions like $\mathbb{P}^4 \to \mathbb{P}^3$? | unassessed | {
"key": "aimpl",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b2ac5 | problem | aim-6ece8953664f1897b245a922130b2ac5 | Multiview Geometry for Continuous Motion · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Is there a differentiable structure for essential varieties or fundamental varieties over time. Is there a formal structure? Can we use deformation theory and cohomological techniques? | unassessed | {
"key": "aimpl",
"name": "AIM · Algebraic vision",
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"url": "http://aimpl.org/algvision/6/#6ece8953664f1897b245a922130b2ac5",
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"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · 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": "Algebraic vision",
"url": "http://aimpl.org/algvision/6/",
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] | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b32b9 | problem | aim-6ece8953664f1897b245a922130b32b9 | Multiview Geometry for Continuous Motion · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | What is the proper algebraic formulation for a continuous multiview variety? $\mathbb{P}^1 \times \mathbb{P}^3 \to (\mathbb{P}^2)^n$? $Hom(\mathbb{A}^1, \text{essential matrices})$? Kontsevich spaces? Or could we use points and optical flow data? | unassessed | {
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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{
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b3b52 | problem | aim-6ece8953664f1897b245a922130b3b52 | Reconstruction · Question 5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
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}
] | The focal lengths of a pair of cameras can be written as a function of their fundamental matrix. During reconstruction fundamental matrices are constructed for which these focal lengths are complex. Is there an efficient way to detect if the this will occur before computing the fundamental matrix? | unassessed | {
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"url": "http://aimpl.org/algvision/1/#6ece8953664f1897b245a922130b3b52",
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"notes": "Problem lists produced at America... | null | null | null | not-recorded | not-recorded | null | [] | [] | Algebraic vision · Historical workshop question | ## Section context
A fundamental topic in algebraic vision is that of reconstructing a scene from images. | 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-6ece8953664f1897b245a922130b41b6 | problem | aim-6ece8953664f1897b245a922130b41b6 | Silhouettes · Question 5 | {
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"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | Which curves with cusps come from rims of algebraic surfaces? | unassessed | {
"key": "aimpl",
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The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b5a71 | problem | aim-6ece8953664f1897b245a922130b5a71 | Reconstruction · Question 55 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Algebraic geometry. http://aimpl.org/algvision/ Not an author-supplied MSC code."
}
] | How can we account for uncertainty, given the geometric structure of these problems? What if we replace points with disks? | unassessed | {
"key": "aimpl",
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A fundamental topic in algebraic vision is that of reconstructing a scene from images. | 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",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130b948b | problem | aim-6ece8953664f1897b245a922130b948b | Density results for PCF polynomials · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Describe
$$
N(x)=\#\{p\leq x : p|f^n(\alpha) \text { for some } n\}
$$
for $p$ prime as $x\rightarrow \infty.$ | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/1/#6ece8953664f1897b245a922130b948b",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Assume $f(z)\in \mathbb{Q}[z]$ is PCF (orbit of critical points is finite) and some reasonable starting point $\alpha\in\mathbb{Q}.$ | 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"
] | Xander Faber | null | null | null | [
{
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ba04d | problem | aim-6ece8953664f1897b245a922130ba04d | Density results for PCF polynomials · Question 2 | {
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"name": "Number theory",
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] | What is the growth rate of $N(x)$ for PCF and non PCF maps? | unassessed | {
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"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Assume $f(z)\in \mathbb{Q}[z]$ is PCF (orbit of critical points is finite) and some reasonable starting point $\alpha\in\mathbb{Q}.$ | 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"
] | Joe Silverman | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ba2ea | problem | aim-6ece8953664f1897b245a922130ba2ea | Density results for PCF polynomials · Question 3 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | If $f(z)\in\mathbb{F}_q(T)$, what happens then? What happens with other fields? | unassessed | {
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"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Assume $f(z)\in \mathbb{Q}[z]$ is PCF (orbit of critical points is finite) and some reasonable starting point $\alpha\in\mathbb{Q}.$ | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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{
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1.0.0 | problem:aim-6ece8953664f1897b245a922130bc30b | problem | aim-6ece8953664f1897b245a922130bc30b | Conjugacy Invariants · Question 1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | Is Pink's generating function $\Phi_w$ always rational for every $\rho(\text{Frob}_p)=w?$ | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Nigel Boston | null | null | null | [
{
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1.0.0 | problem:aim-6ece8953664f1897b245a922130bc7d0 | problem | aim-6ece8953664f1897b245a922130bc7d0 | Conjugacy Invariants · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Cook up other conjugacy invariant things. | unassessed | {
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"url": "http://aimpl.org/galarithdyn/2/#6ece8953664f1897b245a922130bc7d0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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",
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"url": "http://aimpl.org/galarithdyn/2/",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130be8de | problem | aim-6ece8953664f1897b245a922130be8de | Geometric vs. Arithmetic representations · Question 1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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}
] | Is there any example where $G$ does not have finite index in $G'?$ | unassessed | {
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"doi": null,
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"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Take $f(z)\in\mathbb{Q}[z],$ assume $0$ is **not** periodic. Consider two groups
\begin{align}
G &:= \lim_{n\rightarrow\infty} \text{Gal}(f^n)\\
G'&:= \lim \text{Gal}(f^n(z)-t).
\end{align} | 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"
] | Tom Tucker | null | null | null | [
{
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1.0.0 | problem:aim-6ece8953664f1897b245a922130bf20b | problem | aim-6ece8953664f1897b245a922130bf20b | Geometric vs. Arithmetic representations · Question 2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | Understand the relation with PCFness. Note this is related to Problem 1.1. Perhaps start with $f(z)=z^2-1.$ | unassessed | {
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"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Take $f(z)\in\mathbb{Q}[z],$ assume $0$ is **not** periodic. Consider two groups
\begin{align}
G &:= \lim_{n\rightarrow\infty} \text{Gal}(f^n)\\
G'&:= \lim \text{Gal}(f^n(z)-t).
\end{align} | 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"
] | Tom Tucker | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130bfb54 | problem | aim-6ece8953664f1897b245a922130bfb54 | Dynatomic Modular Curves · Question 1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | - Analogy between dynatomic and modular curves (See Silverman, ADS Section 4.1 and 4.2 for dynatomic polynomials).
- What are other proxies for level structure, e.g. marked critical points, for which bad primes are more natural? | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Andrew Obus | null | null | null | [
{
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"url": "http://aimpl.org/galarithdyn/4/",
"note": null,
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"published_at": "2026-09-08T03:33:12.136Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e8855889-402a-45d1-867a-44f6ff86769c","format_issues":null,"number":7974} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c125d | problem | aim-6ece8953664f1897b245a922130c125d | Dynatomic Modular Curves · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | - For $p|N,$ $X^{\text{dyn}}(N)$ has bad reduction at $p$ for the standard model, but evidence suggests there exists a different model with good reduction. Is this true? If not, why not? Is there a ``reason" for this to be true?
- (Silverman) In general, what are the primes of bad reduction and why? | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
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"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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",
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"url": "http://aimpl.org/galarithdyn/4/",
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"published_at": "2026-09-08T03:33:12.140Z",
"solved_at": null
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1.0.0 | problem:aim-6ece8953664f1897b245a922130c2328 | problem | aim-6ece8953664f1897b245a922130c2328 | Boundary of $M_d$ · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Give an algebraic description of the boundary and maps in the boundary in characteristic $p$ not necessarily $0.$ (Reference DeMarco). Try $d=3.$ Motivation: results for moduli curves use understanding of the boundary. | unassessed | {
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"url": "http://aimpl.org/galarithdyn/5/#6ece8953664f1897b245a922130c2328",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Rachel Pries | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/galarithdyn/5/",
"note": null,
"sort_order": 0
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] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.145Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d1a8f375-fa85-4f77-91ff-264e306ff123","format_issues":null,"number":7976} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c31e6 | problem | aim-6ece8953664f1897b245a922130c31e6 | Boundary of $M_d$ · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | - (Want to look at a curve in $M_2$). For $f(z)=\frac{z^2-1}{z^2-c},$ there is a collection of PCF maps which approach $c=1$ on the curve. Compare the arboreal representation for $f$ to the representation of the limit map.
- More generally, how do these representations behave as you deform to the boundary? | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Holly Krieger | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130c3a9f | problem | aim-6ece8953664f1897b245a922130c3a9f | Critical Relations · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | What is the influence of critical relations on the image of Galois over a number field (Pink condition)? More specifically which sorts of critical orbit relations force infinite index for the image of Galois? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/6/#6ece8953664f1897b245a922130c3a9f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Ingram, Krieger, Levy | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/6/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-6ece8953664f1897b245a922130c3d71 | problem | aim-6ece8953664f1897b245a922130c3d71 | Critical Relations · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Bad reduction for models of critical orbit relation curves. e.g. $M_2.$ | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/6/#6ece8953664f1897b245a922130c3d71",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Silverman | null | null | null | [
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"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/6/",
"note": null,
"sort_order": 0
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} | 2026-10-10T16:07:49.246Z | {"database_id":"3d7f8b14-2469-449d-9fc4-d7f9b944e451","format_issues":null,"number":7979} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c610d | problem | aim-6ece8953664f1897b245a922130c610d | Dynatomic side · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | If $K_fK_g$ is finite over both $K_f$ and $K_g$, are $f$ and $g$ conjugate, an iterate, or conjugate to something that commutes? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/7/#6ece8953664f1897b245a922130c610d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Let $K$ be a number field $f(z)\in K(z)$ $\deg f\geq 2.$ Let
$$
K_f=K(\text{all preperiodic points of }f).
$$ | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nguyen | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/7/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"published_at": "2026-09-08T03:33:12.164Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"99d150bd-65c0-4be6-b001-adbe19f99c35","format_issues":null,"number":7980} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c6e0e | problem | aim-6ece8953664f1897b245a922130c6e0e | Dynatomic side · Question 2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/galarithdyn/ Not an author-supplied MSC code."
}
] | What do you need to know about $K_f$ to figure out what $f$ was (or how close to $f$ can you get)? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/7/#6ece8953664f1897b245a922130c6e0e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Let $K$ be a number field $f(z)\in K(z)$ $\deg f\geq 2.$ Let
$$
K_f=K(\text{all preperiodic points of }f).
$$ | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/7/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.171Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"63aca768-02a6-4b8c-88b3-395ec2ac4fbd","format_issues":null,"number":7981} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c8bd5 | problem | aim-6ece8953664f1897b245a922130c8bd5 | Dynatomic side · Question 3 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/galarithdyn/ Not an author-supplied MSC code."
}
] | Begin to classify those $f$ for which $\text{Gal}(K_f/K)$ does not have finite index in the thing it's supposed to.
Ask this question again for
$$
K_f'=K(\text{all periodic points of }f)
$$ | unassessed | {
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"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/7/#6ece8953664f1897b245a922130c8bd5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Let $K$ be a number field $f(z)\in K(z)$ $\deg f\geq 2.$ Let
$$
K_f=K(\text{all preperiodic points of }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"
] | Silverman | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/7/",
"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"
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:12.176Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"38f898bc-d6f6-4d23-ae9d-f6cf405b39f4","format_issues":null,"number":7982} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c9214 | problem | aim-6ece8953664f1897b245a922130c9214 | Arboreal side · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | The previous section's problem appropriately phrased for preimage extensions. | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/8/#6ece8953664f1897b245a922130c9214",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/8/",
"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"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.180Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"13ee32b0-a432-40d1-84e1-b10bed2f6907","format_issues":null,"number":7983} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130c9ca1 | problem | aim-6ece8953664f1897b245a922130c9ca1 | At what level do we see deformation? · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Is there a deformation theory for arboreal Galois representations? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/9/#6ece8953664f1897b245a922130c9ca1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Boston | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/9/",
"note": null,
"sort_order": 0
}
] | {
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.185Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"90c3a1bd-0147-49a4-8e8c-33a96e6c7c21","format_issues":null,"number":7984} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130ca414 | problem | aim-6ece8953664f1897b245a922130ca414 | At what level do we see deformation? · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | To what level can the representation associated to two quadratic polynomials agree? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/9/#6ece8953664f1897b245a922130ca414",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes"... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/9/",
"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"
] | [] | {
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:12.189Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ed2b0a28-606d-474b-8047-33eb4c3d1d4b","format_issues":null,"number":7985} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130caa8f | problem | aim-6ece8953664f1897b245a922130caa8f | Find more arboreal Galois representations · 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/galarithdyn/ Not an author-supplied MSC code."
}
] | Find classes of examples of polynomials or rational maps $d\geq 3$ for which we can compute explicitly the arboreal Galois representation up to finite index over various fields. | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/galarithdyn/10/#6ece8953664f1897b245a922130caa8f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · 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"
] | Jones, Manes | null | null | null | [
{
"kind": "website",
"citation": "The Galois theory of orbits in arithmetic dynamics",
"url": "http://aimpl.org/galarithdyn/10/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a922130caa8f",
"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": "2026-09-08T03:33:12.193Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"339f5ddb-7ccc-4c17-bcc0-2f20fbdaebdc","format_issues":null,"number":7986} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130cc2ca | problem | aim-6ece8953664f1897b245a922130cc2ca | Find more arboreal Galois representations · Question 2 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/galarithdyn/ Not an author-supplied MSC code."
}
] | Generalizing: Can you find an example in higher dimensions? | unassessed | {
"key": "aimpl",
"name": "AIM · The Galois theory of orbits in arithmetic dynamics",
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1.0.0 | problem:aim-6ece8953664f1897b245a922130ced76 | problem | aim-6ece8953664f1897b245a922130ced76 | Formal period $n$ · Question 1 | {
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"notes... | null | null | null | not-recorded | not-recorded | null | [] | [] | The Galois theory of orbits in arithmetic dynamics · Historical workshop question | ## Section context
Let $K_n=K$(points of formal period n) and let $G_n=K_n/K.$ Let
$$
\rho_n:G_N\rightarrow \mathbb{Z}/n\mathbb{Z} \wr S_m
$$
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