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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e490ac3 | problem | aim-0df1011a6fa8a3c46e2c977b7e490ac3 | Predictions of the Relative Fontaine-Mazur and Simpson conjectures · Question 4.1 | {
"main": "math",
"sub": "number theory",
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"name": "Number theory",
"original_discipline": "mathematics"
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"basis": "source-map",
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] | Suppose a flat bundle $(\mathcal{E}, \nabla)$ on a smooth projective variety $X / \overline{\mathbb{Q}}$ is defined over $\overline{\mathbb{\mathbb{Q}}}$ and its associated Higgs bundle is $\mathbb{G}_m$-fixed (equivalently the local system $\mathcal{E}^{\nabla}$ underlies a $\mathbb{C}$-VHS) then is it motivic? | unassessed | {
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The relative Fontaine-Mazur conjecture predicts that arithmetic local systems are motivic, or ``arise from geometry'' i.e. they appear in the cohomology of families of smooth projective varieties. In particular, isolated points of the character variety are automatically arithmetic (since each Froben... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
In rank $r = 1$ this is asking if a unitary flat bundle is defined over $\overline{\mathbb{Q}}$ does it have finite monodromy. The... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Yohan Brunebarbe | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e494b2a | problem | aim-0df1011a6fa8a3c46e2c977b7e494b2a | Predictions of the Relative Fontaine-Mazur and Simpson conjectures · Question 4.3 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"basis": "source-map",
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] | Let $X / \mathbb{F}_q$ be a smooth projective variety over a finite field. Given a representation $\rho : \pi_1^{\mathrm{et}}(X_{\overline{\mathbb{F}_q}}, \bar{x}) \to \mathrm{GL}_r(\mathbb{Z}_{\ell})$ (perhaps specified via an oracle returning its action on $(\mathbb{Z} / \ell^n \mathbb{Z})^r$ for each $n$ which is it... | unassessed | {
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Section context
The relative Fontaine-Mazur conjecture predicts that arithmetic local systems are motivic, or ``arise from geometry'' i.e. they appear in the cohomology of families of smooth projective varieties. In particular, isolated points of the character variety are automatically arithmetic (since each Froben... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Again using the work of Litt, we can decide ``no''. Furthermore, one can compute a trace function by point counting and hence dedu... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4950f5 | problem | aim-0df1011a6fa8a3c46e2c977b7e4950f5 | Isolated singularities of the character variety | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Let $X / \mathbb{C}$ be a smooth quasi-projective variety and $x \in M_B(X, r)$ an isolated singularity or isolated point of a cohomology jump loci. Is the corresponding local system motivic? Can we prove any consequences of motivicity for this local system? | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Section context
The relative Fontaine-Mazur conjecture predicts that arithmetic local systems are motivic, or ``arise from geometry'' i.e. they appear in the cohomology of families of smooth projective varieties. In particular, isolated points of the character variety are automatically arithmetic (since each Froben... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Nonabelian Hodge theory shows that the corresponding local system underlies a $\mathbb{C}$-VHS. Hence Simpson's conjecture predict... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"citation": "Motives and mapping class groups · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e49beb2 | problem | aim-0df1011a6fa8a3c46e2c977b7e49beb2 | Geometric proof of a theorem of McMullen--Imayoshi-Shiga | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Is there a proof of this theorem using primarily algebraic geometry? | unassessed | {
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"url": "http://aimpl.org/motivesandmcg/5/#0df1011a6fa8a3c46e2c977b7e49beb2",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
Imayoshi-Shiga (1999) [CITE] proved the following theorem based of the work of McMullen. Let $X \to B$ be a smooth proper family of curves of genus $g \ge 2$ parametrized by a (possibly open) curve $B$ with $\chi(B) < 0$. If the family is not isotrivial then the monodromy representation is irreduci... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
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"url": "http://aimp... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e49c475 | problem | aim-0df1011a6fa8a3c46e2c977b7e49c475 | Monodromy of surface bundles · Question 5.1 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Does the theorem still hold if we drop the adjective ``simple'' from the closed curve? | unassessed | {
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"name": "AIMPL · Motives and mapping class groups",
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"url": "http://aimpl.org/motivesandmcg/5/#0df1011a6fa8a3c46e2c977b7e49c475",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e49cda1 | problem | aim-0df1011a6fa8a3c46e2c977b7e49cda1 | Monodromy of surface bundles · Question 5.15 | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Let $X / K$ be a smooth curve over a field $K$ which is one of the following:
(1) a finite field $\mathbb{F}_q$
(2) a number field $K$
(3) the function field of a curve over $\mathbb{F}_q$
given a $K$-point $x \in X$ and hence an action of $\mathrm{Gal}_K$ on the geometric fundamental group $\pi_1^{et}(X_{\overli... | unassessed | {
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"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
We can ask about arithmetic analogs of the above questions. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Motives and mapping class groups · Original question",
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"url": "http://aimp... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"source-full-text-not-present"
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8a484bd3-1a1b-42d4-bd9b-2797c6bc05f0","format_issues":null,"number":11327} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e49f52e | problem | aim-0df1011a6fa8a3c46e2c977b7e49f52e | Conjecture of Katzarkov-Pantov-Simpson | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Does the monodromy representation of a nonisotrivial family $\mathcal{C} \to B$ of curves of genus $g \ge 2$ (perhaps one arising from a sufficiently ample Lefschetz pencil on a surface) have a dense orbit on the character variety of the fiber?
More precisely, the monodromy group $G \subset \mathrm{Mod}(\Sigma_g)$ of ... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/5/#0df1011a6fa8a3c46e2c977b7e49f52e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Katzarkov-Pantov-Simpson prove that when $H = \mathrm{GL}_{2r+1}(\mathbb{C})$ and $\mathcal{C} \to B$ arises as a sufficiently amp... | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4a0bdf | problem | aim-0df1011a6fa8a3c46e2c977b7e4a0bdf | New examples of finite orbits of homomorphism $\pi_1(\Sigma_{g,n}) \to \mathrm{Mod}(\Sigma_{h})$ | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | What are some examples of finite orbits under the mapping class group $\mathrm{Mod}(\Sigma_{g,n})$ of homomorphisms (considered up to conjugation) $\pi_1(\Sigma_{g,n}) \to \mathrm{Mod}(\Sigma_h)$. Which arise from algebraic surface bundles over an $n$-punctured curve? | unassessed | {
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"url": "http://aimpl.org/motivesandmcg/5/#0df1011a6fa8a3c46e2c977b7e4a0bdf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Some examples arise from Kodaira-Parshin families | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4a1bbf | problem | aim-0df1011a6fa8a3c46e2c977b7e4a1bbf | Isotrivial isogeny factors in families of Jacobians | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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] | Let $\mathcal{C} \to B$ be a nonisotrivial family of proper curves of genus $g$. What is the maximum dimension of an isotrivial isogeny factor in the Jacobian fibration of $\mathcal{C} \to B$? | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4a28d0 | problem | aim-0df1011a6fa8a3c46e2c977b7e4a28d0 | Counterexamples to the Putman-Wieland conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
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] | Can we classify all counterexamples to the Putman-Wieland conjecture in genus $g = 2$? | unassessed | {
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The Putman-Wieland conjecture predicts that if $\Sigma_{g',n'} \to \Sigma_{g,n}$ is an unramified finite $H$-cover of punctured surfaces then the induced action of a finite index subgroup $\Gamma \subset \mathrm{Mod}_{g,n+1}$ on $H_1(\Sigma_{g',n'}, \mathbb{C})$ has no fixed vectors. The action is ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4a64fe | problem | aim-0df1011a6fa8a3c46e2c977b7e4a64fe | Decidability of arithmeticity and motivicty | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
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] | Let $X / \mathbb{C}$ be a smooth projective variety. Is there an algorithm which given an integral point of the character variety $x \in M_B(X, r)(\mathcal{O}_K)$, where $K$ is a number field, can decide if $x$ is (after some embedding $\mathcal{O}_K \subset \mathbb{Q}_p$) an arithmetic local system? Likewise, is there... | unassessed | {
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The relative Fontaine-Mazur conjecture predicts that arithmetic local systems are motivic, or ``arise from geometry'' i.e. they appear in the cohomology of families of smooth projective varieties. In particular, isolated points of the character variety are automatically arithmetic (since each Froben... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Listing all families of smooth projective varieties, one can decide ``yes'' to $x$ being motivic so motivicity is recursively enum... | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4a7573 | problem | aim-0df1011a6fa8a3c46e2c977b7e4a7573 | Stable cohomology of character varieties | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
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] | Prove (or disprove) that the cohomology of $\mathcal{U}_{G,g}$ stabilizes with respect to $g$ and compute its stable value.
A conjecture for the value of the putative stable cohomology should include Chern classes. Does it depend on anything else? What about integral cohomology? | unassessed | {
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Fix an algebraic group $G$, and consider the relative character variety of $G$ local systems for the universal curve over $\mathcal{M}_g$, denoted $\mathcal{U}_{G,g}$ (such that the total monodromy is Zariski dense in $G$). | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
Aaron Landesman conjectures that when $G$ is finite, each component of this space stabilize to the cohomology of $\mathcal{M}_g$. ... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Aaron Landesman | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ac8ee | problem | aim-0df1011a6fa8a3c46e2c977b7e4ac8ee | Log-Calabi-Yau compactifications of character varieties | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
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] | Do there exist ``canonical'' algebraic compactifications of the character variety $M(\Sigma_{g,n}, r)$ of a punctured surface? It is a conjecture (of Simpson?) that $M(\Sigma_{g,n}, r)$ admits a compactification as a log-Calabi-Yau variety. Prove subcases of this conjecture. | unassessed | {
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"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
Quotienting the moduli space of $\lambda$-connections by the canonical algebraic $\mathrm{G}_m$-action alows one to construct a canonical compactification of the Moduli space of flat connections. Hence the Riemann-Hilbert correspondence realizes this as an *analytic* compactification of the charact... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
A theorem of Junho Whang covers the case $r = 2$ when $\Sigma$ has at least one puncture i.e. produces a log-Calabi-Yau compactifi... | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ad918 | problem | aim-0df1011a6fa8a3c46e2c977b7e4ad918 | Hyperbolicity of surface bundles | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
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] | Are there examples in higher dimension given as surface bundles over a surface? Can these be compact examples? In particular, for $g,h \ge 2$ does there exist an $\Sigma_g$-bundle over $\Sigma_h$
$$ \Sigma_g \to E \to \Sigma_h $$
having one of the (increasingly weaker) properties:
(1) $E$ is a hyperbolic $4$-manifold
... | unassessed | {
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4af6c8 | problem | aim-0df1011a6fa8a3c46e2c977b7e4af6c8 | Hyperbolic surface bundles over surfaces | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
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] | Are there examples in higher dimension given as surface bundles over a surface? Can these be compact examples? In particular, for $g,h \ge 2$ does there exist an $\Sigma_g$-bundle over $\Sigma_h$
$$ \Sigma_g \to E \to \Sigma_h $$
having one of the (increasingly weaker) properties:
(1) $E$ is a hyperbolic $4$-manifold
... | unassessed | {
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"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
Thurston gave the following example of a hyperbolic $3$-manifold fibered over $S^1$. Consider $N = S^3 \setminus K$ where $K$ is the figure-eight knot. Then there is a map $N \to S^1$ whose fibers are punctured torii $\Sigma_{1,1}$. This fits into the following general story. For $\phi \in \mathrm{... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4af7fe | problem | aim-0df1011a6fa8a3c46e2c977b7e4af7fe | Examples of MCG-finite irreducible representations of surface groups not arising from abelian varieties | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
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] | Can we find an examples of an irreducible representation $\rho : \pi_1(\Sigma_{g,n}) \to \mathrm{GL}_r(\mathbb{C})$ with finite orbit under $\mathrm{Mod}(\Sigma_{g,n})$ that do not arise from families of abelian varieties?
We say that a representation ``arises from a family of abelian varieties'' if there exists a co... | unassessed | {
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"url": "http://aimp... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4b14d0 | problem | aim-0df1011a6fa8a3c46e2c977b7e4b14d0 | Geometric local systems on $\mathcal{M}_g$ and rigidity | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Consider a local system $\mathbb{L}$ on $\mathcal{M}_g$ (or a space with some level structure) or equivalently a representation of $\mathrm{Mod}(\Sigma_g)$ (or correspondingly a representation of some finite index subgroup). Suppose $\mathbb{L}$ underlies a variation of Hodge structures. Is the period map $\mathcal{M}_... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/2/#0df1011a6fa8a3c46e2c977b7e4b14d0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
There are some big monodromy results in the work of Sawin-Landesman-Litt. These can perhaps be used with a theorem of Peters to ge... | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
{
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4b21d0 | problem | aim-0df1011a6fa8a3c46e2c977b7e4b21d0 | Higher Prym period maps | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Number theory. http://aimpl.org/motivesandmcg/ Not an author-supplied MSC code."
}
] | Is the higher Prym map unique in general? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Motives and mapping class groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/motivesandmcg/2/#0df1011a6fa8a3c46e2c977b7e4b21d0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lis... | null | null | null | not-recorded | not-recorded | null | [] | [] | Motives and mapping class groups · AIMPL workshop record | ## Question context
Let $G$ be a finite group. Let $\mathcal{M}' \to \mathcal{M}_g$ be the universal space of $G$-covers of curves of genus $g$. Given a $G$-cover $\varphi : C_h \to C_g$ we get an exact sequence of abelain varieties
$$ 0 \to \mathrm{Prym}(\varphi) \to \mathrm{Jac}(C_h) \to \mathrm{Jac}(C_g) \to 0 $$
... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
The tools in the previous problem can show it is infinitesimally rigid. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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{
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{
"kind": "website",
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"url": "http://aimp... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d3a31 | problem | aim-0df1011a6fa8a3c46e2c977b7e4d3a31 | Projections and Lorentzian Polynomials | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | If $X \subseteq \mathbb{R}^n$ is an $M$-convex set, and we take a linear projection $L : R^n → R$ that preserves integer points (i.e. $L(x) = \langle v,x \rangle$ with $v \in \mathbb{Z}^n$,and then let
$s_i =|\{x\in X:L(x)=i\}|$. When is this a log-concave sequence? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d3a31",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Section context
These are questions about maps preserving properties of interest for a polynomial, such as stability, Lorentzianity, real rootedness, etc. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d3a31",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"802c7d44-fe2b-4408-9ea6-55364110b24d","format_issues":null,"number":11684} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d487a | problem | aim-0df1011a6fa8a3c46e2c977b7e4d487a | Preserving real roots on a subspace | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | Let $S \subseteq \mathbb{R}[x]_d$ be a subspace of univariate polynomials, characterize linear maps sending real rooted polynomials in $S$ to real rooted polynomials in $S$.
As an example, if $S$ is the space of polynomials with roots summing to 0, then it is conjectured that a diagonal linear map $T$ preserves... | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
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"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d487a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Section context
These are questions about maps preserving properties of interest for a polynomial, such as stability, Lorentzianity, real rootedness, etc. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d487a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5ef7bb07-6921-4831-a6be-68282fc2960a","format_issues":null,"number":11685} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d6a19 | problem | aim-0df1011a6fa8a3c46e2c977b7e4d6a19 | Preservers of Real Rootedness with Nonnegative Roots | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | What are linear maps $T:\mathbb{R}[t] \rightarrow \mathbb{R}[t]$ so that for any real rooted polynomial $f$ with nonnegative real coefficients, $T(f)$ is real rooted. | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d6a19",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Section context
These are questions about maps preserving properties of interest for a polynomial, such as stability, Lorentzianity, real rootedness, etc. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/1/#0df1011a6fa8a3c46e2c977b7e4d6a19",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"0f415626-ba00-433f-95fe-47945d16d50c","format_issues":null,"number":11686} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d770a | problem | aim-0df1011a6fa8a3c46e2c977b7e4d770a | Thin Tree 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/geompolysampling/ Not an author-supplied MSC code."
}
] | There is a $k_0$ (independent of $|V|$) so that every $k_0$-edge connected graph has a $\frac{1}{2}$-thin spanning tree. | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d770a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Question context
If you have a graph $G$, and it is $k$-edge connected for some large $k$. That is, for every partition of the vertices into 2 parts $A \subseteq V(G)$ and $A^c$ there exists at least $k$ edges going from $A$ to $A^c$. A spanning tree is $\alpha$-thin with respect to $G$ if for every cut $A \cup A^c... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d770a",
"note": null,
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{
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"citation": "AIMPL source bibliograp... | {
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.902Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"52d075eb-ce86-4719-a695-c1f747a70efa","format_issues":null,"number":11687} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d92de | problem | aim-0df1011a6fa8a3c46e2c977b7e4d92de | Negative correlation for random forests | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | For what $\epsilon$ is it true that $\Pr(e \in F \text{ and }f \in F) \le (1+\epsilon)\Pr(e \in F)\Pr(f \in F)$ for $F$ a uniformly random spanning forest? | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d92de",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d92de",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"source-full-text-not-present"
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:10.909Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"66b1544c-9168-4ef0-a7e0-6f71e8f9ff56","format_issues":null,"number":11688} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4d9c29 | problem | aim-0df1011a6fa8a3c46e2c977b7e4d9c29 | Graph Theory Motivated Questions · Question 2.3 | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | Let $G = (V,E)$ be a graph of maximum degree $\Delta$. Let $\chi(t)$ be the chromatic polynomial (i.e. $\chi(q)$ is the number of ways of properly coloring the graph $G$ with $q$ colors). Then, is $\chi(t) \neq 0$ for any $t \in \mathbb{C}$ so that $|t| > 2\Delta$. Also if the real part of $\text{Re }t > \Delta + 1$, ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d9c29",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/2/#0df1011a6fa8a3c46e2c977b7e4d9c29",
"note": null,
"sort_order": 0
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{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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"imported_at": "2026-09-10",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4db285 | problem | aim-0df1011a6fa8a3c46e2c977b7e4db285 | Even Delta Matroids, Jump Systems and Fractional Log-Concavity · Question 3.1 | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | Let $J \subseteq \mathbb{Z}^n$ be a jump system so that either every element of $\{\sum_{i=0}^n a_i : a \in J\}$ is even, or every element of it is odd. For every $k \in \mathbb{N}$, let $c_k$ be the number of points in $J$ with the sum of the coordinates equal to $2k$. Is $c_0, \dots, $ ultra-log concave? | unassessed | {
"key": "aimpl",
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"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Question context
A jump-system is given by a subset $J \subseteq \mathbb{Z}^n$ with the following property: define a step from $a$ to $b$ to be a vector $c \in \mathbb{Z}_{\ge 0}^n$ so that $\|a-c\|_1 = 1$ (i.e. $c$ differs from $a$ either by a coordinate vector or the negative of a coordinate vector) and $|b-c| < ... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4dcc02 | problem | aim-0df1011a6fa8a3c46e2c977b7e4dcc02 | Even Delta Matroids, Jump Systems and Fractional Log-Concavity · Question 3.2 | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/geompolysampling/ Not an author-supplied MSC code."
}
] | Suppose that we know that some posinomial $f(x)$ does not vanish whenever it is evaluated when $x$ is in the right half-plane, does that imply that $f(x)$ is log concave on the positive orthant? | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/3/#0df1011a6fa8a3c46e2c977b7e4dcc02",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Question context
A posinomial is a polynomial whose exponents may be fractional,i.e.
$$
f(x) = \sum_{\alpha \in \mathbb{R}_{\ge 0}^n, |\alpha| = d} c_{\alpha}x^{\alpha}\text{ with }c_{\alpha} \ge 0.
$$
for some $d \in \mathbb{Q}_{\ge 0}$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ddcac | problem | aim-0df1011a6fa8a3c46e2c977b7e4ddcac | New Polynomials Arising from Matroids · Question 4.1 | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | Let $M$ be a matroid (say graphic) of rank $d$ with ground set $E$ with $m$ elements.
Let $S_1, \dots, S_n \subseteq E$ (not necessarily disjoint).
Let $\alpha \in \mathbb{Z}^n_{\ge 0}$ with $|\alpha| = \sum_{i=1}^n \alpha_i = d$.
We define $c_{\alpha}$ to be the number of bases $B$ of the matro... | unassessed | {
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"url": "http://aimpl.org/geompolysampling/4/#0df1011a6fa8a3c46e2c977b7e4ddcac",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4de09f | problem | aim-0df1011a6fa8a3c46e2c977b7e4de09f | New Polynomials Arising from Matroids · Question 4.2 | {
"main": "math",
"sub": "combinatorics",
"slug": "combinatorics",
"name": "Combinatorics",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Combinatorics. http://aimpl.org/geompolysampling/ Not an author-supplied MSC code."
}
] | Here, $M_F$ is the result of contracting $F$ in $M$, $M^F$ is the restriction of $M$ to $F$ and $ \overline{\chi_{M^F}}(t)$ is the reduced characteristic polynomial of $M$. Is this polynomial should be real rooted for any matroid? | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/4/#0df1011a6fa8a3c46e2c977b7e4de09f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | ## Question context
To a loopless matroid $M$ of rank $d+1$, we can associated a univariate polynomial of degree $d$ $H_M(t)$ (the Chow polynomial) recursively as follows: if the rank of the matroid is 0, then $H_M$ polynomial is identically 1, otherwise, this polynomial is defined by recursion by
$$
... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"note": null,
"sort_order": 0
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{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4df55f | problem | aim-0df1011a6fa8a3c46e2c977b7e4df55f | Misc · Question 5.1 | {
"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/geompolysampling/ Not an author-supplied MSC code."
}
] | Let $P$ be a convex body with baricenter at 0. Suppose that $P$ contains no integer points in its interior besides 0. The volume of $P$ is at most $\frac{(n+1)^n}{n!}$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · The geometry of polynomials in combinatorics and sampling",
"type": "workshop-problem-list",
"url": "http://aimpl.org/geompolysampling/5/#0df1011a6fa8a3c46e2c977b7e4df55f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | The geometry of polynomials in combinatorics and sampling · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "The geometry of polynomials in combinatorics and sampling · Original question",
"url": "http://aimpl.org/geompolysampling/5/#0df1011a6fa8a3c46e2c977b7e4df55f",
"note": null,
"sort_order": 0
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{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4e29d7 | problem | aim-0df1011a6fa8a3c46e2c977b7e4e29d7 | 2-dimensional ASEP | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
"code": "60",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Probability. http://aimpl.org/roadtokpz/ Not an author-supplied MSC code."
}
] | - Study the two-dimensional asymmetric simple exclusion process (ASEP) on the lattice $\mathbb{Z}^2$, where particles attempt hops to the four cardinal directions (N, S, E, W) with differing asymmetric rates. A key question is whether the resulting fluctuations can be linked to the two-dimensional KPZ universality cla... | unassessed | {
"key": "aimpl",
"name": "AIMPL · All roads to the KPZ universality class",
"type": "workshop-problem-list",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e29d7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem ... | null | null | null | not-recorded | not-recorded | null | [] | [] | All roads to the KPZ universality class · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "All roads to the KPZ universality class · Original question",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e29d7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://a... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e4e29d7",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4e47c0 | problem | aim-0df1011a6fa8a3c46e2c977b7e4e47c0 | Isotropic 2d KPZ | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
"code": "60",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Probability. http://aimpl.org/roadtokpz/ Not an author-supplied MSC code."
}
] | The isotropic two-dimensional KPZ problem remains largely open. A central challenge is to identify the fluctuation exponents and to characterize the fixed point process that would parallel the one-dimensional KPZ FP. | unassessed | {
"key": "aimpl",
"name": "AIMPL · All roads to the KPZ universality class",
"type": "workshop-problem-list",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e47c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem ... | null | null | null | not-recorded | not-recorded | null | [] | [] | All roads to the KPZ universality class · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "All roads to the KPZ universality class · Original question",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e47c0",
"note": null,
"sort_order": 0
},
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"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://a... | {
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"imported_at": "2026-09-10",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"08edbeb9-db47-4148-b502-1ce1a6a2ac6e","format_issues":null,"number":10132} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4e5310 | problem | aim-0df1011a6fa8a3c46e2c977b7e4e5310 | Anisotropic models | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
"code": "60",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Probability. http://aimpl.org/roadtokpz/ Not an author-supplied MSC code."
}
] | - In contrast to the isotropic case, anisotropic KPZ models [Source citation: MR2485688](http://aimpl.org/roadtokpz/bib/), [Source citation: MR3607467](http://aimpl.org/roadtokpz/bib/),
[Source citation: MR3855490](http://aimpl.org/roadtokpz/bib/) are expected to exhibit different scaling behaviors. A key questio... | unassessed | {
"key": "aimpl",
"name": "AIMPL · All roads to the KPZ universality class",
"type": "workshop-problem-list",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e5310",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem ... | null | null | null | not-recorded | not-recorded | null | [] | [] | All roads to the KPZ universality class · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "All roads to the KPZ universality class · Original question",
"url": "http://aimpl.org/roadtokpz/1/#0df1011a6fa8a3c46e2c977b7e4e5310",
"note": null,
"sort_order": 0
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"kind": "website",
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"url": "http://a... | {
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] | There has been success in finding exact formulas for PNG with arbitrary initial conditions [Source citation: arXiv:2209.02643](http://aimpl.org/roadtokpz/bib/). Can this be extended to multilayer PNG? What class of initial conditions can we consider? | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4e6db6 | problem | aim-0df1011a6fa8a3c46e2c977b7e4e6db6 | Multilayer models and multilayer KPZ FP · Question 2.2 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
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] | Find the scaling limit of the multilayer PNG in the spirit of KPZ FP
[Source citation: MR4346267](http://aimpl.org/roadtokpz/bib/), [Source citation: arXiv:2209.02643
](http://aimpl.org/roadtokpz/bib/). | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4e7bd4 | problem | aim-0df1011a6fa8a3c46e2c977b7e4e7bd4 | Multilayer models and multilayer KPZ FP · Question 2.3 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
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] | More generally, consider multilayer models such as the multi-path partition functions in the
O'Connell-Yor semi-discrete directed Brownian polymer, see Theorem~3.1 and subsequent SDEs in [Source citation: MR2952082](http://aimpl.org/roadtokpz/bib/), Definition~4.1.26 in [Source citation: MR3204480](http://aimpl.org... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4eb85f | problem | aim-0df1011a6fa8a3c46e2c977b7e4eb85f | KPZ behavior in quantum spin chains · Question 4.1 | {
"main": "math",
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"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
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}
] | Compute the large-time current fluctuations for the XXZ spin-$1/2$ chain on a 1D lattice.
Some of the progress is the following:
The edge fluctuations for $\Delta=0$ with domain wall initial conditions were computed in [Source citation: MR4573942](http://aimpl.org/roadtokpz/bib/) and shown to have Tracy-Widom GUE d... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ed471 | problem | aim-0df1011a6fa8a3c46e2c977b7e4ed471 | Colored particles on the ring · Question 5.1 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
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}
] | Can one derive an analogue of the TASEP speed process [Source citation: MR2857238](http://aimpl.org/roadtokpz/bib/),
[Source citation: MR4576839](http://aimpl.org/roadtokpz/bib/) for colored particle systems (TASEP or ASEP, for starters) evolving on a ring? | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ed6be | problem | aim-0df1011a6fa8a3c46e2c977b7e4ed6be | Colored particles on the ring · Question 5.2 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
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] | Does a color-position symmetry exist in particle systems on a ring? (Model particular case: Half-open systems?)
For models on the full space or in half-space geometries, such symmetries have been crucial for deriving exact formulas and understanding integrable structures. There are many references
on color-position s... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ee358 | problem | aim-0df1011a6fa8a3c46e2c977b7e4ee358 | Colored particles on the ring · Question 5.3 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
"code": "60",
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"evidence": "Editorial mapping of AIMPL source category: Probability. http://aimpl.org/roadtokpz/ Not an author-supplied MSC code."
}
] | Can the dynamics of colored particles on a ring be recast in terms of an (affine) Hecke algebra structure? | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4eec42 | problem | aim-0df1011a6fa8a3c46e2c977b7e4eec42 | Colored particles on the ring · Question 5.4 | {
"main": "math",
"sub": "probability",
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"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
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] | Is there an analogue of color-position symmetry within the framework of LPP models? Recent works on ``hidden invariance'' cited above hint at deep invariance properties that might extend to colored systems. | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4ef669 | problem | aim-0df1011a6fa8a3c46e2c977b7e4ef669 | Colored particles on the ring · Question 5.5 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
{
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}
] | Within the known stationary measures of ASEP, can we investigate correlations?
Consider the asymmetric simple exclusion process (ASEP) on a
large ring with two particle colors, with particle densities
$\rho_1$ and $\rho_2$. Define $\eta_i(x)$ as the indicator
for the presence of a particle of color $i$ at site $x$
... | unassessed | {
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] | Consider two independent random sequences (strings) of i.i.d.\ Bernoulli(0,1) variables, or more generally, i.i.d.\ variables taking values in a finite alphabet. The main question is to understand the typical size and the fluctuations of their longest common subsequence (LCS). Recent works have studied various regimes ... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4f291b | problem | aim-0df1011a6fa8a3c46e2c977b7e4f291b | Longest common subsequence · Question 6.2 | {
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] | One central object of study is the almost-sure growth rate (or **time constant**) of the LCS as the string lengths grow. Determining this constant precisely remains an open problem in many cases.
A potential approach would be to rephrase the LCS problem in the language close to LPP, and potentially use
Busemann funct... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4f3ca8 | problem | aim-0df1011a6fa8a3c46e2c977b7e4f3ca8 | KPZ line ensemble and random permutations · Question 7.1 | {
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] | Take a vertical slice of the KPZ line ensemble [Source citation: MR3547737](http://aimpl.org/roadtokpz/bib/), how close is the permutation of $\mathbb{Z}_{\ge1}$ to the identity permutation? Is the permutation finite at all? In the Airy line ensemble, the permutation is trivial with probability 1.
Note that there ar... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4f7797 | problem | aim-0df1011a6fa8a3c46e2c977b7e4f7797 | Busemann functions and LPP · Question 8.1 | {
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] | The Airy line ensemble and its Gibbs property [Source citation: MR3152753](http://aimpl.org/roadtokpz/bib/) play a central role in integrable probability.
One intriguing question is what happens when random path
segments are resampled using the Brownian Gibbs property.
As DL is a functional of the Airy line ... | unassessed | {
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A key theme is to explore connections between multipath LPP
partition functions
and Busemann functions defined in several directions.
Busemann functions have long been instrumental in the study of geodesics, current fluctuations, and stationary measures in exactly solvable models such as TA... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4f85a4 | problem | aim-0df1011a6fa8a3c46e2c977b7e4f85a4 | Busemann functions and LPP · Question 8.2 | {
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] | Beyond the original construction via Brownian last passage percolation, alternate descriptions of the DL have begun to emerge, leveraging tools such as Busemann functions, Airy line ensembles, and stationary variants of LPP.
Each of these viewpoints can shed light on the universality and rich geometric behavior inhe... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4f939b | problem | aim-0df1011a6fa8a3c46e2c977b7e4f939b | Relaxing/perturbing integrable models · Question 9.1 | {
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] | Can one can relax the iid Bernoulli random walks that underlie
the nontrivial structure in integrable models like PNG or TASEP,
in formulas around the KPZ FP [Source citation: MR4346267](http://aimpl.org/roadtokpz/bib/), [Source citation: arXiv:2209.02643](http://aimpl.org/roadtokpz/bib/)?
Another example incl... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4fa28a | problem | aim-0df1011a6fa8a3c46e2c977b7e4fa28a | Relaxing/perturbing integrable models · Question 9.2 | {
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] | Characterizing stochastic processes that one can put into formulas instead of random walks. | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4fd74f | problem | aim-0df1011a6fa8a3c46e2c977b7e4fd74f | ASEP on graphs or trees · Question 10.1 | {
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] | Find an explicit formula or expression for large deviation principles for current fluctuation in the case of ASEP on general graphs. | unassessed | {
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On finite trees or graphs, ASEP is an irreducible Markov chain with a unique stationary distribution. Unlike the one-dimensional case, no simple product form generally exists.
In infinite random trees, a nonzero flow can persist if branch capacities exceed the injection rate at the root; ot... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e4fe7a8 | problem | aim-0df1011a6fa8a3c46e2c977b7e4fe7a8 | Log-concavity · Question 3.1 | {
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"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
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}
] | Consider continuous-time TASEP with step initial
condition. There is an associated transition
probability function $f(a)$ into the configuration
$a$. A question arises whether $f(a)$ is log-concave.
While log-concavity appears in many probabilistic
models, it remains unclear how to establish it in this... | unassessed | {
"key": "aimpl",
"name": "AIMPL · All roads to the KPZ universality class",
"type": "workshop-problem-list",
"url": "http://aimpl.org/roadtokpz/3/#0df1011a6fa8a3c46e2c977b7e4fe7a8",
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A function $f$ is log-concave if
$$f(a)f(b) \leq f\left(\frac{a+b}{2}\right)^2.$$
One example of such function is the Gaussian density function.
Note that the variables $a,b$ might be vectors or matrices.
Log-concavity is fundamental in probability theory and combinatorics, e.g.,
[Source citation:... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e504569 | problem | aim-0df1011a6fa8a3c46e2c977b7e504569 | Log-concavity · Question 3.2 | {
"main": "math",
"sub": "probability",
"slug": "probability",
"name": "Probability",
"original_discipline": "mathematics"
} | [] | [
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"code": "60",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Probability. http://aimpl.org/roadtokpz/ Not an author-supplied MSC code."
}
] | The density of the
Tracy--Widom random variable is itself log-concave [Source citation: MR3721641](http://aimpl.org/roadtokpz/bib/).
For a large permutation of size $n$, the
longest increasing subsequence length $L_n$ often (after
suitable centering and scaling) converges to the
Tracy--Widom distribution. Do... | unassessed | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e514a81 | problem | aim-0df1011a6fa8a3c46e2c977b7e514a81 | Boundedness and moduli theory · Question 5.6 | {
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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/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Let $X$ be a Calabi--Yau variety, and let $L$ be a semi-ample Cartier divisor on $X$.
Consider the universal family $(\mathcal X ,\mathcal L) \to \mathrm{Def}(X,L)$ of deformations of $(X,L)$.
Is $\mathcal{L}$ relatively semi-ample over $\mathrm{Def}(X,L)$? | unassessed | {
"key": "aimpl",
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51525c | problem | aim-0df1011a6fa8a3c46e2c977b7e51525c | Boundedness and moduli theory · Question 5.7 | {
"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/higherdimlogcy/ Not an author-supplied MSC code."
}
] | Is the relatie Albanese variety of a Calabi--Yau variety itself Calabi--Yau?
How many abelian fibered Calabi--Yau varieties admit the same relative Albanese fibration? | unassessed | {
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Calabi-Yau varieties and Fano varieties are two of the three fundamental building blocks involved in the (birational) classification of projective algebraic varieties. To improve our knowledge of these classes of varieties, it is natural to introduce numerical and geometrical invariants that m... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51b778 | problem | aim-0df1011a6fa8a3c46e2c977b7e51b778 | Continuation after blowup | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | If solutions of the wave kinetic equation blowup in $L^\infty$, is there continuation of these solutions after the blowup? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/manyparticle/1/#0df1011a6fa8a3c46e2c977b7e51b778",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Section context
Wave kinetic equations (WKE) describe the evolution of the energy spectrum $\mathbb{E}[|\hat{u}(k,t)|^2]$ of a system of weakly nonlinear interacting waves. An example of such an equation is the homogeneous 4-WKE equation,
$$
\partial_tf = \int_{\mathbb{R}^{3d}}\delta(\Sigma)\delta(\Omega)ff_1f_2f_... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51c1e7 | problem | aim-0df1011a6fa8a3c46e2c977b7e51c1e7 | Monotone quantities | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Can we find any monotone hydrodynamic quantities for a wave kinetic equation? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/1/#0df1011a6fa8a3c46e2c977b7e51c1e7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Section context
Wave kinetic equations (WKE) describe the evolution of the energy spectrum $\mathbb{E}[|\hat{u}(k,t)|^2]$ of a system of weakly nonlinear interacting waves. An example of such an equation is the homogeneous 4-WKE equation,
$$
\partial_tf = \int_{\mathbb{R}^{3d}}\delta(\Sigma)\delta(\Omega)ff_1f_2f_... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51d77e | problem | aim-0df1011a6fa8a3c46e2c977b7e51d77e | Conditions for global well-posedness | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Can we find conditions on the initial data so that the homogeneous wave kinetic equation is globally well-posed? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/1/#0df1011a6fa8a3c46e2c977b7e51d77e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Section context
Wave kinetic equations (WKE) describe the evolution of the energy spectrum $\mathbb{E}[|\hat{u}(k,t)|^2]$ of a system of weakly nonlinear interacting waves. An example of such an equation is the homogeneous 4-WKE equation,
$$
\partial_tf = \int_{\mathbb{R}^{3d}}\delta(\Sigma)\delta(\Omega)ff_1f_2f_... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51d8a4 | problem | aim-0df1011a6fa8a3c46e2c977b7e51d8a4 | Example of blowup for inhomogeneous Landau (or Boltzmann) | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Can we find a set of conditions such that the homogeneous equation is globally well-posed, but the inhomogeneous equation blows up? Can this be down for the isotropic Landau equation? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
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"url": "http://aimpl.org/manyparticle/7/#0df1011a6fa8a3c46e2c977b7e51d8a4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jiajie Chen | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51eba7 | problem | aim-0df1011a6fa8a3c46e2c977b7e51eba7 | Regularity of free boundary/obstacle problem | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Consider the following Cauchy problem,
$$\begin{cases}
\max\{\partial_tu + v\cdot \nabla_xu - \mathscr{L}_vu, u - \varphi\} = 0\\
u(0) = u_0.
\end{cases}$$
Determine the regularity of solutions for $\mathscr{L} = \nabla_v^s$ (This is known in $d = 1$)
Determine the regularity of solutions of the free boundary: $\{u =... | unassessed | {
"key": "aimpl",
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51ed9f | problem | aim-0df1011a6fa8a3c46e2c977b7e51ed9f | Alt-Caffarelli type problem | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Find a function that satisfies the Kolmogorov equation
$$\begin{cases}
(\partial_t + v\cdot \nabla_x - \Delta_v)f = 0, & f > 0\\
|\nabla_vf| = 1, & \partial\{f > 0\}.
\end{cases}$$
Derive and study the reasonable Alt-Caffarelli type problem. | unassessed | {
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"url": "http://aimpl.org/manyparticle/2/#0df1011a6fa8a3c46e2c977b7e51ed9f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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"note": null,
"sort_order": 0
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{
"kind": "website",
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"published_at": "2026-09-09T22:24:06.931Z",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e51f37c | problem | aim-0df1011a6fa8a3c46e2c977b7e51f37c | Hele-Shaw: convergence from a particle system | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Find a particle system that converges to $\rho$. That is, $$\frac{1}{N} \sum\limits_{i=1}^N \delta_{X_i(t)} \to \mathbf{1}_{\{p > 0\}}.$$ | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/2/#0df1011a6fa8a3c46e2c977b7e51f37c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consider the following,
$$\begin{cases}
-\Delta p + \Delta \Phi = 0, & \{p > 0\}\\
V = \eta\cdot (\nabla p - \nabla \Phi),& \partial\{p > 0\}
\end{cases}$$
where $\eta$ is the normal, $p$ is the pressure, and $V$ is velocity. This problem can be restated as follows: Let $\rho(t) = \mathbf{1}_{\{p >... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Inwon Kim | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present",
"known-source-format-issue"
] | [] | {
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.936Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"94ff077d-629f-4f0d-9c3c-3f01b709f971","format_issues":{"errors":1,"fields":["background"]},"number":11010} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5227ce | problem | aim-0df1011a6fa8a3c46e2c977b7e5227ce | Asymptotic behavior of nonlinear kinetic Fokker-Planck equations | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove convergence...
Determine convergence rates... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/3/#0df1011a6fa8a3c46e2c977b7e5227ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consider the following nonlinear modifications of Fokker-Planck equations $$\partial_t f = Div(A[f]\nabla_xf) + B[f]\nabla_x V$$ where $A[f]$ is a matrix that depends nonlinearly on $f$ and $V$ is a potential.
Current results are mostly for sampling from a Gaussian where the inverse Hession of the... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/3/#0df1011a6fa8a3c46e2c977b7e5227ce",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e5227ce",
"imported_at": "2026-09-10",
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"current-status-unassessed",
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.945Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"47fd45c3-daef-4bc5-84ec-c8200b0e554e","format_issues":null,"number":11011} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5236ce | problem | aim-0df1011a6fa8a3c46e2c977b7e5236ce | Sampling high dimension distributions | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Find a measure $\mu$ supported on a hypersurface $S \subset \mathbb{R}^n$ and a nonlinear, degenerate, parabolic equation for which solutions converge to $\mu$.
Remark: This should require a diffusion that is degenerate or becomes degenerate in the limit as $t \to \infty$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/3/#0df1011a6fa8a3c46e2c977b7e5236ce",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/3/#0df1011a6fa8a3c46e2c977b7e5236ce",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8e4b265e-5359-499b-a05b-21af78a813f3","format_issues":null,"number":11012} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e524979 | problem | aim-0df1011a6fa8a3c46e2c977b7e524979 | Propagation of regularity | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | In the case of Maxwell molecules, can we propagate regularity of initial data for the cutoff Boltzmann equation? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e524979",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e524979",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e524979",
"imported_at": "2026-09-10",
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"published_at": "2026-09-09T22:24:06.964Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"447cd123-a509-4337-95a2-5fbae9828969","format_issues":null,"number":11014} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e524ec4 | problem | aim-0df1011a6fa8a3c46e2c977b7e524ec4 | Large data global well-posedness for nearly homogeneous non-cutoff Boltzmann | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove large data global well-posedness for the inhomogeneous (3 +1) non-cutoff Boltzmann equation. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e524ec4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Wynter (2023) showed global well-posedness for the inhomogeneous (3 + 1)d cutoff Boltzmann equation for large data. In particular, this result required that the collision kernel to be zero for collisions with small relative velocities. With $x \in \mathbb{R}$ and imposing the cutoff, Wynter is able... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Christopher Henderson | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e524ec4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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"imported_at": "2026-09-10",
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.970Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9b3faed3-cb08-4f57-b0fa-bb7c61d0f21e","format_issues":null,"number":11015} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52868e | problem | aim-0df1011a6fa8a3c46e2c977b7e52868e | Discrete operators to nonlocal operators · Question 5.1 | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | With the above notion of nonlocal derivative, characterize the behavior of the nonlocal transport equation $$\partial_t u + \mathcal{D}_\delta u = 0$$ as $\delta \to 0$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/5/#0df1011a6fa8a3c46e2c977b7e52868e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consider the following nonlocal derivative, $$\mathcal{D}_\delta u(x) = \int_{-\delta}^\delta [u(x + y) - u(x)]K(x,y)dy.$$
If $K(x,y)$ is odd in $y$, then one can show that this converges to a derivative, $$\mathcal{D}_\delta u(x) \to u'(x).$$ | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Petronela Radu | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/5/#0df1011a6fa8a3c46e2c977b7e52868e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e52868e",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
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"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:06.992Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a3b39ff4-0f31-4ed3-98df-5b20bdd7c36b","format_issues":null,"number":11019} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e529616 | problem | aim-0df1011a6fa8a3c46e2c977b7e529616 | Convergence of graph operators to nonlocal operators in $\mathbb{R}^n$ | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Show convergence of graph operators to their nonlocal counterparts in the limit as the $\#$ of vertices ``fills up" $\mathbb{R}^n$. | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Cynthia Flores | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e529c85 | problem | aim-0df1011a6fa8a3c46e2c977b7e529c85 | Construction of large shocks | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Construct traveling wave solutions to the Boltzmann equation with large amplitude (at least amplitude 1) in dimension 1. Is it possible to observed **temperature overshoot**, a well-observed phenomena in physics. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e529c85",
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"doi": null,
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dominic Wynter | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e529f58 | problem | aim-0df1011a6fa8a3c46e2c977b7e529f58 | Caflisch construction for implosion singularity formation | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Study the formation of implosion singularities for the Boltzmann equation via the Caflisch construction of solutions | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e529f58",
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"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
In Caflisch (1980), it is shown that any smooth solution of the Euler equations can be used to make a corresponding solution to the Boltzmann equation. Additionally, the formation of implosion singularities is well-studied for compressible fluids. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52c285 | problem | aim-0df1011a6fa8a3c46e2c977b7e52c285 | Global well-posedness for 3D incompressible axisymmetric Navier-Stokes equation | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove global well-posedness for 3D incompressible axisymmetric Navier-Stokes for large initial data. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/4/#0df1011a6fa8a3c46e2c977b7e52c285",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
$$\begin{cases}
\partial_t u + u\cdot \nabla u - \Delta u + \nabla p = 0\\
\nabla u = 0\end{cases}$$
In cylindrical coordinates, axisymmetric means that $u = u(r,z)$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jiajie Chen | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52e7f3 | problem | aim-0df1011a6fa8a3c46e2c977b7e52e7f3 | General $L^p \to L^\infty$ estimate | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove $L^p \to L^\infty$ estimate for $$\mathscr{L}u = f$$ for $f \in L^p$ and $\mathscr{L}$ a non-divergence, nonlocal form. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/6/#0df1011a6fa8a3c46e2c977b7e52e7f3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/6/#0df1011a6fa8a3c46e2c977b7e52e7f3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibl... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52ecb5 | problem | aim-0df1011a6fa8a3c46e2c977b7e52ecb5 | Continuity of solutions for multi-dimensional $p$-Laplacian | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove continuity of solutions for the system case of the fraction $p$- Laplacian. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/6/#0df1011a6fa8a3c46e2c977b7e52ecb5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
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"note": null,
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52f72d | problem | aim-0df1011a6fa8a3c46e2c977b7e52f72d | Regularity up to boundary for kinetic equations | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | What is the relationship between the regularity of the coefficients and the boundary regularity? Is $C_x^{1/6}C_v^{1/2}$ regularity sharp in the case of constant coefficients? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/8/#0df1011a6fa8a3c46e2c977b7e52f72d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consider a boundary in $\mathbb{R}^d_x$, that is in $x$. Since transport is first order in $x$, one can only define boundary conditions when the velocity points in a particular direction (e.g. normal to the boundary).
In the case of the homogeneous Fokker-Planck equation on the half-space (consta... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Christopher Henderson | null | null | null | [
{
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"note": null,
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e52fbc0 | problem | aim-0df1011a6fa8a3c46e2c977b7e52fbc0 | Schauder estimate for general transport term | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Obtain Schauder estimates for a general transport term, $$(\partial_t + b(v)\cdot \nabla)f - Tr(AD^2_v\cdot).$$
Additionally, kinetic formulation of systems of conservation laws yield transport operators that look like $$(\partial_t + b(t,x,v)\cdot \nabla_x ).$$ Can one obtain Schauder estimates for this further gener... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/6/#0df1011a6fa8a3c46e2c977b7e52fbc0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"note": null,
"sort_order": 0
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"kind": "website",
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:07.014Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"36c0d99e-ab72-4b48-8b8d-8d87ca5b276a","format_issues":null,"number":11023} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e53006a | problem | aim-0df1011a6fa8a3c46e2c977b7e53006a | Regularity of solutions of non-divergence form of a linear kinetic equation | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Study the regularity of solutions a kinetic equation $$\partial_t f + v\cdot \nabla_x f = \mathscr{L}f$$ where $\mathscr{L}$ is linear and of non-divergence form. In the local case, $\mathscr{L} = Tr(AD^2_v\cdot)$.
If $\mathscr{L} = (\Delta)^s$, is there a monotone quantity? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/8/#0df1011a6fa8a3c46e2c977b7e53006a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
"url": "http://aimpl.org/manyparticle/8/#0df1011a6fa8a3c46e2c977b7e53006a",
"note": null,
"sort_order": 0
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{
"kind": "website",
"citation": "AIMPL source bibl... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5318a0 | problem | aim-0df1011a6fa8a3c46e2c977b7e5318a0 | Homogeneous relativistic Landau equation | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove global existence of smooth solutions for the relativistic Landau equation. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/7/#0df1011a6fa8a3c46e2c977b7e5318a0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
The homogeneous relativistic Landau equation is given by $$\partial_t f = \mathcal{C}(f,f)$$ where $$C(h,g)(p) : = \partial_{p_i} \int_{\mathbb{R}^3} \Phi^{ij}(p,q)\left\{h(q)\partial_{p_j}g(p) - \partial_{q_j}h(q)g(p)\right\}dq$$ where Einstein summation convention is used. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stanley Snelson | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5339c0 | problem | aim-0df1011a6fa8a3c46e2c977b7e5339c0 | Uniqueness for porous medium in $d > 1$ | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Prove uniqueness of solutions for the porous medium equation in $d > 1$ with not too smooth initial data. Is the Wasserstein distance contractive? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
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"url": "http://aimpl.org/manyparticle/6/#0df1011a6fa8a3c46e2c977b7e5339c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
The porous medium equation is given by $$\partial_t u = \nabla_x \cdot(u\nabla_x\Delta^{-s}_x u)$$ and lacks a comparison principle in $d > 1$. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e535473 | problem | aim-0df1011a6fa8a3c46e2c977b7e535473 | Consensus based optimization with time dependent temperature | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Can we design a time-dependent global optimization such that you can still prove convergence to the global minimizer? Can we find an optimal cooling schedule? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/manyparticle/3/#0df1011a6fa8a3c46e2c977b7e535473",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consensus based optimization has been proposed to do global optimization of a non-convex objective function without gradient descent.
To do this, one works with the **thermalization** of the measure of the solution of the system at time $t$ and as $T^{-1} \to \infty$, this weighted mean converges... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Franca Hoffman | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2a2ae6ea-799e-40fe-923b-c4563a5bc9eb","format_issues":null,"number":11013} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5364a3 | problem | aim-0df1011a6fa8a3c46e2c977b7e5364a3 | Inverse problem for interacting particle system | {
"main": "math",
"sub": "partial differential equations",
"slug": "partial-differential-equations",
"name": "Partial differential equations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "35",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Partial differential equations. http://aimpl.org/manyparticle/ Not an author-supplied MSC code."
}
] | Assume that one can tune any macroscopic quantity (i.e. $\rho(t,x)$, $E$, $B$ etc.) What is necessary to recover the initial distribution $f_0$ for $d \geq 2$? Is this possible?
There is perhaps a natural extension of this problem to the wave kinetic equation. What would the additional quantity to control be in this ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Integro-differential equations in many-particle interacting systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/manyparticle/8/#0df1011a6fa8a3c46e2c977b7e5364a3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Integro-differential equations in many-particle interacting systems · AIMPL workshop record | ## Question context
Consider the Vlasov-Maxwell equations $$\begin{cases}
(\partial_t + v\cdot \nabla_x)f = -(E + v\times B)\cdot \nabla_v f\\
-\Delta u = \rho\\
\nabla u = E\end{cases}.$$ | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Integro-differential equations in many-particle interacting systems · Original question",
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"note": null,
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},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"84b798ef-457a-49ed-8bd4-0c2f66f8734d","format_issues":null,"number":11029} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e552825 | problem | aim-0df1011a6fa8a3c46e2c977b7e552825 | Uniform stability | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Fix a finite group $G$ and an irreducible representation $\rho: G \to
\operatorname{GL}_r(\mathbb C)$.
One might be interested in understanding homological stability needed for
moments of $L(1/2, \rho_K)$ as $K$ varies over $G$ extensions of $\mathbb
F_q(t)$.
Namely, one can try to understand homological stability on
$... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e552825",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Will Sawin | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e552825",
"note": null,
"sort_order": 0
},
{
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... | {
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"published_at": "2026-09-09T22:24:08.585Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c83b65a3-59a6-498f-9871-b680f51fab2d","format_issues":null,"number":11286} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5533d0 | problem | aim-0df1011a6fa8a3c46e2c977b7e5533d0 | Monodromy images | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | What is the image of the Burau representation specialized at other roots of
unity?
If one specializes to the case of a cyclic group, one may want to know exactly
what the image of the Burau monodromy representation.
What is the exact image of the Burau representation specialized at roots of
unity? It is known in the c... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e5533d0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Petersen | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e5533d0",
"note": null,
"sort_order": 0
},
{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5545d6 | problem | aim-0df1011a6fa8a3c46e2c977b7e5545d6 | Moments of derivatives | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | What do the methods for computing moments of L function give if one tries to
compute moments of derivatives.
Even in the random matrix theory setting computing the distribution of
derivatives is difficult.
What can recent methods tell us about the distribution of values of derivatives
of $L$ functions?
This structure i... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e5545d6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jon Keating | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e5545d6",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.596Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3d38a724-0764-449f-b351-a83752525f00","format_issues":null,"number":11288} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e554a01 | problem | aim-0df1011a6fa8a3c46e2c977b7e554a01 | Higher degree cyclic covers | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | If one starts from the number theoretic side, consider $\chi$ cyclic of order
more than $2$. It is natural to think about
summing
$L(1/2,\chi_d)^r L(1/2, \overline{\chi}_d)^s$
for certain cyclic characters $\chi_d$.
One can find a version of that for higher order cyclic extensions.
This was found by Sean Howe.
(One can... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e554a01",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Petersen | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/4/#0df1011a6fa8a3c46e2c977b7e554a01",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.602Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5662594f-3ebd-4a40-a452-81d0f210c5c8","format_issues":null,"number":11289} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55605d | problem | aim-0df1011a6fa8a3c46e2c977b7e55605d | Hyperelliptic Torelli | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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"code": "11",
"basis": "source-map",
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}
] | Can you give a quadratic presentation of the Maltsev completion
of hyperelliptic Torelli using the computation from
Bergstrom-Diaconu-Petersen-Westerland? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e55605d",
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dan Petersen | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e556bb2 | problem | aim-0df1011a6fa8a3c46e2c977b7e556bb2 | Negative moments | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Can one prove a version of the pair correlation conjecture using topological methods?
Will sawin thinks this should be possible in some range.
Can one use homological stability methods to say anything about negative
moments? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e556bb2",
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alessandro Fazzari | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55755e | problem | aim-0df1011a6fa8a3c46e2c977b7e55755e | Error terms | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | What kind of error terms do people expect for the moments?
Diaconu suggests that there are infinitely many higher order terms.
Could there be interesting secondary stable homology that can be understood?
In which of the polynomial pieces associated to the moments do the relevant classes live?
The simplest setting wher... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
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"citation": null,
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"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jordan Ellenberg | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e558294 | problem | aim-0df1011a6fa8a3c46e2c977b7e558294 | The moments conjecture | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
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}
] | Assume the most optimistic bounds on unstable cohomology.
can we get the full ratios conjecture without a limitation on the size of $q$.
I.e. can we get it for fixed $q$ instead of taking a limit as $q \to \infty$? | unassessed | {
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"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e558294",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Victor Wang | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e558294",
"note": null,
"sort_order": 0
},
{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e5585d5 | problem | aim-0df1011a6fa8a3c46e2c977b7e5585d5 | A conjecture about shifted L functions | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Let $a = \{a_1, \ldots, a_k\}$.
Define
\begin{equation}
\sum_n \tau_a(n) n^{-s} := \prod_{i=1}^k l(s+a_i).
\end{equation}
Then
\begin{equation}
\sum_n \chi_d(n)\tau_a(n) n^{-s} := \prod_{i=1}^k l(s+a_i,\chi_d).
\end{equation}
Observe
\begin{equation}
\sum_{d=1}^d \sum_{n=1}^x \chi_d(n) \tau_a(n)n^{-1/2}\sim \sum_{d=... | unassessed | {
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"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Brian Conrey | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
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"note": null,
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{
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... | {
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e559255 | problem | aim-0df1011a6fa8a3c46e2c977b7e559255 | Twisted averages of $L$ functions | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Consider $\sum_d L(1/2, \chi_d) \cdot \phi(d)$ as $d$ varies over polynomials over $\mathbb
F_q$ generating quadratic fields and $\phi$ is some interesting arithmetic function.
For example, you can take $\phi$ to be the mobius function or some interesting
character.
What would be the relevant homological stability ques... | unassessed | {
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"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jordan Ellenberg | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
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"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"53e70388-67f4-4c2b-a0ec-7f3498fa4545","format_issues":null,"number":11295} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55a217 | problem | aim-0df1011a6fa8a3c46e2c977b7e55a217 | Vanishing of L functions | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | As in
the question by Jordan Ellenberg on twisted averages of $L$ functions,
take $\phi$ to be a quadratic character
and try to compute
$\sum_d L(1/2, \chi_d) \cdot \phi(d)$.
Is there some application to non-vanishing of
$L(1/2, \chi_d)$?
For example, fix $q$.
is the proportion of $d$ so that $L(1/2,\chi_d) \neq 0$ e... | unassessed | {
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"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alexandra Florea | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e55a217",
"note": null,
"sort_order": 0
},
{
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"ffbb0d29-b4e4-4c65-b92a-f709691d46e8","format_issues":null,"number":11296} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55b6c1 | problem | aim-0df1011a6fa8a3c46e2c977b7e55b6c1 | Elliptic Curves | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Take $E$ over $\mathbb F_q(t)$ containing $n$th roots of unity.
one can study the analogous question. what is
$\sum_d L(1/2,e \otimes \chi_d)^r L(1/2, e \otimes \overline{\chi}_d)^s$. for
cubic $\chi_d$ David-Lalin-Nam made a recipe.
What is a homological interpretation of the main term?
can one compute the stable homo... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/5/#0df1011a6fa8a3c46e2c977b7e55b6c1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | ## Section context
This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Adrian Diaconu | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
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"note": null,
"sort_order": 0
},
{
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... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"35177ba9-842f-4d22-bc5f-8537d98f53ff","format_issues":null,"number":11297} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55c1b6 | problem | aim-0df1011a6fa8a3c46e2c977b7e55c1b6 | Vanishing of $L$ functions | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | How often does $L(1/2, E \otimes \chi) = L'(1/2, E \otimes \chi) = 0$, for $E$ an elliptic curve and $\chi$ a quadratic character?
This could perhps be doable if one could solve
question by adrian diaconu on elliptic curves. | unassessed | {
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This is a section on questions related to the BDPW and MPPRW paper, but somewhat less related to a direct generalizations of it. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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] | Jordan Ellenberg | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55ca9b | problem | aim-0df1011a6fa8a3c46e2c977b7e55ca9b | Epsilon factors | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | Fix a finite group $G$ and an irreducible, nontrivial complex representation
$\rho$. study
\begin{align*}
\sum_k \epsilon(1/2, \rho_k),
\end{align*}
where the sum is over $G$-extensions $k$ over $\mathbb F_q(t)$ and $\rho_k:
\operatorname{Gal}(\overline{\mathbb F}_q(t)/\mathbb F_q) \to G
\xrightarrow{\rho}
\operatorna... | unassessed | {
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The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55d4b4 | problem | aim-0df1011a6fa8a3c46e2c977b7e55d4b4 | Representation stability | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
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] | Consider the ordered Hurwitz space where one marks branch points.
is there representation stability?
There is some work in progress by Ellenberg-Shusterman and
Himes-Miller-Wilson-Hoang in the non-splitting case.
Can you do the general case? Can you find the stable value? | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Aaron Landesman | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55d64c | problem | aim-0df1011a6fa8a3c46e2c977b7e55d64c | Rack Hurwitz spaces | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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] | Is there a common generalization of Malle's conjecture and the Davis-Schlank
conjecture that gives asymptotics for $c$ extensions for a rack $c$?
The relevant homological stability result is per component is known due to a result of
Landesman-Levy over $\overline{\mathbb F}_q$.
Namely, there is a hurwitz space $\opera... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Aaron Landesman | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55da14 | problem | aim-0df1011a6fa8a3c46e2c977b7e55da14 | Cohomology coming from quantum shuffle algebras | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
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}
] | Note that racks give braided vector spaces,
which give quantum shuffle algebras whose cohomology agrees with that of the
Hurwitz space associated to $c$, $\operatorname{Hur}^c_n$.
If we consider braided vector spaces whose quantum shuffle algebra has
well-understood cohomology (for example, involving nichols algebras) ... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Craig Westerland | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55e320 | problem | aim-0df1011a6fa8a3c46e2c977b7e55e320 | Finding examples of secondary stability | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
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}
] | Can one find any example of secondary stable homology relating to some
arithmetic statistics question?
For example,
can one understand the secondary stable homology in ordered configuration
spaces?
One interesting example to look at could be Edward Frenkel's computation of the
cohomology of the commutator subgroup of ... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jeremy Miller | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55e7b4 | problem | aim-0df1011a6fa8a3c46e2c977b7e55e7b4 | Predicting secondary stability | {
"main": "math",
"sub": "number theory",
"slug": "number-theory",
"name": "Number theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "11",
"basis": "source-map",
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}
] | Can one use the secondary term for counting cubic extensions to make some guess
for the secondary stable homology of Hurwitz spaces parameterizing (simply
branched) trigonal curves.
In the case of Hurwitz spaces for $S_3$ with transpositions, it would be
interesting to understand secondary stability.
As a preliminary... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jeremy Miller | null | null | null | [
{
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55e94e | problem | aim-0df1011a6fa8a3c46e2c977b7e55e94e | Unstable cohomology | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Can one prove that the unstable cohomology in various questions is exponentially
growing?
Can we prove an exponential lower bound, perhaps using an Euler characteristic
argument?
Can one quantify how miraculous the cancellation of Frobenius eigenvalues has to be when taking the trace
of Frobenius if one wants standard ... | unassessed | {
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"citation": null,
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"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Will Sawin | null | null | null | [
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1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55eb73 | problem | aim-0df1011a6fa8a3c46e2c977b7e55eb73 | Unstable cohomology | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | Let $c$ be a union of conjugacy classes in a group $G$.
What can we say about the Frobenius action on the cohomology of
$\operatorname{Hur}^c_n$?
What can we say about top degree cohomology?
Can one compute $H_{n-1}(\operatorname{Hur}^c_n)$?
Can we use the fact that the Braid group is a duality group?
What should we ev... | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Jeremy Miller | null | null | null | [
{
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"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e55eb73",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.704Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"06e409a0-a2ea-4f7b-a686-ec4940efed98","format_issues":null,"number":11306} |
1.0.0 | problem:aim-0df1011a6fa8a3c46e2c977b7e55f938 | problem | aim-0df1011a6fa8a3c46e2c977b7e55f938 | distribution of discriminants | {
"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/momentsoverff/ Not an author-supplied MSC code."
}
] | This is a question suggested by Jordan Ellenberg at Arizona Winter School
several years ago.
Consider all monic polynomials over $\mathbb F_q$ all of fixed degree $d$.
What is the distribution of discriminants?
Here, we would like to compute the distribution for fixed $q$ and $d$.
Whitehead says he knows how to do this... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Moments in families of L-functions over function fields",
"type": "workshop-problem-list",
"url": "http://aimpl.org/momentsoverff/8/#0df1011a6fa8a3c46e2c977b7e55f938",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Moments in families of L-functions over function fields · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ian Whitehead | null | null | null | [
{
"kind": "website",
"citation": "Moments in families of L-functions over function fields · Original question",
"url": "http://aimpl.org/momentsoverff/8/#0df1011a6fa8a3c46e2c977b7e55f938",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
... | {
"source_record": "0df1011a6fa8a3c46e2c977b7e55f938",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:08.710Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eaf851cf-8f65-4b00-bfb9-4ff7e4afd355","format_issues":null,"number":11307} |
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