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1.0.0 | problem:aim-38756a1f9b537f4591526253cd090490 | problem | aim-38756a1f9b537f4591526253cd090490 | Chern number inequalities in higher rank dHYM | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
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"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Does existence of solutions to the higher rank dHYM equation imply any interesting Chern number inequalities, for example a generalised Bogomolov--Gieseker inequality. For example consider the case of rank 2 on a surface or threefold. The corresponding result is known for dHYM on line bundles in dimensions up to 4. The... | unassessed | {
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"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stabmirror/1/#38756a1f9b537f4591526253cd090490",
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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-38756a1f9b537f4591526253cd090703 | problem | aim-38756a1f9b537f4591526253cd090703 | Isotopy to holomorphic Landau--Ginzburg model | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [
{
"code": "14",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Stability in mirror symmetry. http://aimpl.org/stabmirror/ Not an author-supplied MSC code."
}
] | Suppose $W:X\to \mathbb{C}$ is a symplectic Landau--Ginzburg model. That is, there exists a compact $K\subset \mathbb{C}$ such that on $X\backslash W^{-1}(K)$ the fibers are symplectic, and symplectic parallel transport is well-defined. Are there simple obstructions to $W$ being isotopic to a holomorphic Landau--Ginzbu... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Stability in mirror symmetry",
"type": "workshop-problem-list",
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"aim",
"historical-workshop"
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd09648e | problem | aim-38756a1f9b537f4591526253cd09648e | Bifurcation and inviscid limit · Question 1.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Rigorous derivation of a Hopf bifurcation in Reynolds number for 2D incompressible Navier--Stokes flow or Gross–Pitaevskii flow passing a (cylindrical) obstacle. Can it be proven without computer-assistant proof? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd09648e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Dallas Albritton and Marc Brachet | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd09648e",
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{
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd09a766 | problem | aim-38756a1f9b537f4591526253cd09a766 | Bifurcation and inviscid limit · Question 1.2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Study the bifurcation problem of Taylor--Couette instability. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd09a766",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Bartosz Protas | null | null | null | [
{
"kind": "website",
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{
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1.0.0 | problem:aim-38756a1f9b537f4591526253cd09d215 | problem | aim-38756a1f9b537f4591526253cd09d215 | Bifurcation and inviscid limit · Question 1.3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | In 2D, formulate the random vortex methods analog to the model of a flow past an obstacle (Stochastic ODE). Is there a stability transition (Hopf bifurcation) in the Reynolds number?
\begin{align*}
\frac {dz _i}{dt} = \sum _{j \neq i} v (z _j) + u _{\text{background}}.
\end{align*}
where $v (z _i)$ is... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd09d215",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Gautam Iyer | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd09d215",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e83a5b6a-75c2-4c02-ac9b-209d5fb805bf","format_issues":null,"number":10432} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd09de6d | problem | aim-38756a1f9b537f4591526253cd09de6d | Well-posedness and sharp enstropy bound of quasilinear systems · Question 2.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Prove sharp estimates of the $H ^1$ norm of solutions to the 1D periodic viscous Burger's equation. It is proven the enstrophy $\mathcal E (t) := \left\|{\partial _x u (t)}\right\| _{L ^2} ^2$ obeys
\begin{align*}
\mathcal E' (t) \le C \mathcal E (t) ^\frac53.
\end{align*}
Prove the following bou... | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd09de6d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Bartosz Protas | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd09de6d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"388430fb-1791-41f6-9f33-12ed7f124b04","format_issues":null,"number":10434} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd09fc5f | problem | aim-38756a1f9b537f4591526253cd09fc5f | Long-time dynamics · Question 3.1 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Study the large-time dynamics of 2D Navier--Stokes with high modes forcing. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/3/#38756a1f9b537f4591526253cd09fc5f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Adam Larios | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/3/#38756a1f9b537f4591526253cd09fc5f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
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"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:24:01.219Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d6401288-0978-46ac-a668-fb65b6e58853","format_issues":null,"number":10437} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a05ab | problem | aim-38756a1f9b537f4591526253cd0a05ab | Long-time dynamics · Question 3.2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Doering conjecture: for a transport equation
\begin{align*}
\begin{cases}
\partial _t \theta + u \cdot \nabla \theta = \kappa \Delta \theta, \\
\nabla \cdot u = 0
\end{cases}
\end{align*}
show that
\begin{align*}
\frac{\|\theta\| _{H ^{-1}}}{\|\theta\| _{L ^2}} \to C \text{ as } t \to +\infty.
\end{align*} | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/3/#38756a1f9b537f4591526253cd0a05ab",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Gautam Iyer | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2a4069b2-e804-4a66-833a-da63218e9538","format_issues":null,"number":10438} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a08c0 | problem | aim-38756a1f9b537f4591526253cd0a08c0 | Bifurcation and inviscid limit · Question 1.4 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Study the inviscid limit of the non-unique Leray solution to the forced Navier--Stokes equation. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd0a08c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Alexis Vasseur | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/1/#38756a1f9b537f4591526253cd0a08c0",
"note": null,
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{
"kind": "website",
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.197Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"2cb942eb-ad1d-4b81-ad44-32c676e37673","format_issues":null,"number":10433} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a180d | problem | aim-38756a1f9b537f4591526253cd0a180d | Well-posedness and sharp enstropy bound of quasilinear systems · Question 2.2 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Prove the global existence of the 2D Burger's equation with hyperviscosity.
\begin{align*}
\partial _t u + u \cdot \nabla u = -\nu \Delta ^2 u
\end{align*} | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd0a180d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Adam Larios | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd0a180d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.207Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0731c219-84c0-42bf-93fb-e1a5bf0d3d44","format_issues":null,"number":10435} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a2e6f | problem | aim-38756a1f9b537f4591526253cd0a2e6f | Well-posedness and sharp enstropy bound of quasilinear systems · Question 2.3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Prove the global existence of strong solutions to the 1D surface growth model.
\begin{align*}
\partial _t u + u _{xxxx} + \partial _{xx} (u _x ^2) = 0
\end{align*}
Show the ill-posedness of the inviscid version of this model. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd0a2e6f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Wojciech Ozanski | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/2/#38756a1f9b537f4591526253cd0a2e6f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
"source_record": "38756a1f9b537f4591526253cd0a2e6f",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.213Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b20f26e7-6472-4129-9720-483d91c5e9e1","format_issues":null,"number":10436} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a6243 | problem | aim-38756a1f9b537f4591526253cd0a6243 | Long-time dynamics · Question 3.3 | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "76",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Criticality and stochasticity in quasilinear fluid systems. http://aimpl.org/stochasticfluid/ Not an author-supplied MSC code."
}
] | Investigate global asymptotic behavior of Magnetic relaxation equations (MRE):
\begin{align*}
\begin{cases}
\partial _t B + u \cdot \nabla B = B \cdot \nabla u \\
(- \Delta) ^\gamma u = B \cdot \nabla B + \nabla p \\
\nabla \cdot u = 0
\end{cases}
\end{align*}
with connections to the Magnetohydrodynamics (MHD) equatio... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Criticality and stochasticity in quasilinear fluid systems",
"type": "workshop-problem-list",
"url": "http://aimpl.org/stochasticfluid/3/#38756a1f9b537f4591526253cd0a6243",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list ter... | null | null | null | not-recorded | not-recorded | null | [] | [] | Criticality and stochasticity in quasilinear fluid 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"
] | Susan Friedlander | null | null | null | [
{
"kind": "website",
"citation": "Criticality and stochasticity in quasilinear fluid systems · Original question",
"url": "http://aimpl.org/stochasticfluid/3/#38756a1f9b537f4591526253cd0a6243",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliograp... | {
"source_record": "38756a1f9b537f4591526253cd0a6243",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.230Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a6195f43-dae8-47a2-896e-afeea66196d3","format_issues":null,"number":10439} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0a84c5 | problem | aim-38756a1f9b537f4591526253cd0a84c5 | Ehrhart Positivity · Question 1.05 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Let $[n]:=\{1,\ldots,n\}$ be a groundset, and let $i(P; t)$ denote the Ehrhart polynomial of a lattice polytope $P$. Then coefficient-wise, $$i(T_{r,n}; t) \leq i(\mathsf{Pan}_{s,r,n};t) \leq i(U_{r,n};t),$$ where $T_{r,n}$ is the rank $r$ minimal matroid on $[n]$, $U_{r,n}$ is the rank $r$ uniform matroid on $[n]$, an... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0a84c5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0a84c5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0a84c5",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.157Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"71f39812-fd7e-4920-a222-60b34c44ea66","format_issues":null,"number":10544} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0ac7bb | problem | aim-38756a1f9b537f4591526253cd0ac7bb | Ehrhart Positivity · Question 1.1 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | What is known (or can be shown) about the Ehrhart positivity of polytopes related to Birkhoff polytopes (e.g., transportation polytopes)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0ac7bb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0ac7bb",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0ac7bb",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.164Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fb25d2ab-4b1e-4d8a-90db-70c5078884df","format_issues":null,"number":10545} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0acc49 | problem | aim-38756a1f9b537f4591526253cd0acc49 | Ehrhart Positivity · Question 1.15 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Are $d$-dimensional smooth polytopes with $\leq d+3$ facets Ehrhart positive or satisfy the higher integrality condition? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0acc49",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0acc49",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0acc49",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.170Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9a057abd-c0b8-4511-ba8b-feb18f95c7f1","format_issues":null,"number":10546} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0acca4 | problem | aim-38756a1f9b537f4591526253cd0acca4 | Ehrhart Positivity · Question 1.2 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | - Is there a closed formula for the Ehrhart polynomial of order polytopes of fence posets? Further, are these Ehrhart polynomials Ehrhart positive?
- Is the $h^\ast$-polynomial of the order polytopes from (a) real-rooted?
- Can this be extended to generalized permutahedra? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0acca4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0acca4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0acca4",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.176Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b5639abb-8b98-4aee-a6e9-bb5d6afd35ca","format_issues":null,"number":10547} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b0253 | problem | aim-38756a1f9b537f4591526253cd0b0253 | Ehrhart Positivity · Question 1.25 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Does a rational polygon $P\subseteq \mathbb{R}^2$ with quasi-period 1 satisfy Scott's inequality? That is, assuming $i\geq 1$, is the inequality $b\leq 2i+7$ satisfied, where $b$ and $i$ represent the number of boundary and interior lattice points of $P$, respectively. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b0253",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b0253",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0b0253",
"imported_at": "2026-09-10",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e0443502-a6b6-43b7-b4b9-8d41eaf50398","format_issues":null,"number":10548} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b0cba | problem | aim-38756a1f9b537f4591526253cd0b0cba | Ehrhart Positivity · Question 1.3 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Let $ASM_n$ denote the $n$th alternating sign matrix polytope (defined as the convex hull in $\mathbb{R}^{n^2}$ of the $n\times n$ alternating sign matrices). It is known that $i(ASM_n;t)$ is Ehrhart positive. What further can be said about $i(ASM_n;t)$? Furthermore, what can be said about $h^*(ASM_n;z)$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b0cba",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b0cba",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"69182efb-634d-493d-8c5f-e70ddf9d6739","format_issues":null,"number":10549} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b27d8 | problem | aim-38756a1f9b537f4591526253cd0b27d8 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.02 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Does the Pitman-Stanley polytope have real-rooted $h^*$-polynomial? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b27d8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b27d8",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:24:04.237Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eddc9ac5-82e4-45db-b9e4-a32f7463c428","format_issues":null,"number":10556} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b2856 | problem | aim-38756a1f9b537f4591526253cd0b2856 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.04 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Study the $h^*$-polynomials of (not necessarily convex) $3$-polytopes. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b2856",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b2856",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0b2856",
"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.243Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"9daba627-fb96-4663-9849-3721e96cfe1c","format_issues":null,"number":10557} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b34da | problem | aim-38756a1f9b537f4591526253cd0b34da | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.06 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | For a lattice polytope $P$, let $P^n$ denote the Cartesian product of $P$ with itself $n$ times ($n\in \mathbb{N}$). Investigate what happens to the $h^*$-polynomial of $P^n$. Does it eventually become real-rooted? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b34da",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b34da",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1b5f05f4-4273-4e6a-b406-706f6e46489f","format_issues":null,"number":10558} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b37e3 | problem | aim-38756a1f9b537f4591526253cd0b37e3 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.08 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | For a symmetric edge polytope, can we obtain regular unimodular triangulations using liftings with low heights? If so, how many such triangulations can be obtained? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b37e3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b37e3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.258Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"7b9ce150-6a20-4891-8ac8-3de286bb6647","format_issues":null,"number":10559} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b3bef | problem | aim-38756a1f9b537f4591526253cd0b3bef | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.1 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | What are the ways of ``measuring'' root polytopes, i.e., edge polytopes?
Furthermore, how should Grothendieck polynomials be specialized to obtain Ehrhart $h^*$-polynomials? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b3bef",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b3bef",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.265Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5a38c56a-3549-4335-b910-fa11ad7f4c4e","format_issues":null,"number":10560} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b554d | problem | aim-38756a1f9b537f4591526253cd0b554d | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.12 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Consider the order polynomial, denoted $\Omega(P,t)$, of a finite poset $P$. Let $n$ be the number of elements in $P$.
**Conjecture** [Kahn, Saks] $\frac{\Omega(P,t)}{t^n}$ is nonincreasing for all $t\in \mathbb{Z}_{>0}$.
This statement is known to be true if all coefficients of $\Omega(P,t)$ are positive. Investiga... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b554d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b554d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.272Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f1a35bed-3584-4b8f-a79c-82ee6faa9747","format_issues":null,"number":10561} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b674e | problem | aim-38756a1f9b537f4591526253cd0b674e | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.14 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Note that $i(P;1;n) = i(P;n)$. It is known that $i(P;\omega;n)$ is a polynomial with leading coefficient given by $\int_P \omega$. Investigate $\omega$-Ehrhart function for well-known classes of polytopes. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b674e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b674e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0b674e",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.278Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"023d7d84-63a1-40ee-be9a-fff3ae16fbd6","format_issues":null,"number":10562} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b849f | problem | aim-38756a1f9b537f4591526253cd0b849f | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.16 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Identify polytopes with extremal $h^*$-vectors. That is, for a family of polytopes $\mathcal{P}$ and index $j$, find $P\in \mathcal{P}$ that minimize or maximize $h_j^*$. Potential families of interest include symmetric edge polytopes for a fixed degree sequence and simplices in Hermite normal form with fixed diagonal. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b849f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0b849f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.286Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"de5b1b3f-da6b-447b-bfe0-2ec7df1fa9f2","format_issues":null,"number":10563} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0b9a5a | problem | aim-38756a1f9b537f4591526253cd0b9a5a | Ehrhart Positivity · Question 1.35 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | For lattice polytopes $P$ and $P'$, which Ehrhart-theoretic properties pass through their join? For example, if $P$ and $P'$ are both Ehrhart positive, is $P*P'$ as well? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b9a5a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0b9a5a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0b9a5a",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.196Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0b25c3c2-9c17-4550-a647-807686f32f89","format_issues":null,"number":10550} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0ba7cd | problem | aim-38756a1f9b537f4591526253cd0ba7cd | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.18 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | What relationship, if any, is there between heights of Hilbert basis elements and differences in $h^*$-coefficients? For example, consider $h^*_{j+1} - h^*_j$ or more generally $h^*_j - h^*_i$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0ba7cd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0ba7cd",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0ba7cd",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.293Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"470ad141-c491-4bfb-aa1e-09586c96127a","format_issues":null,"number":10564} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bab63 | problem | aim-38756a1f9b537f4591526253cd0bab63 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.2 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Take the nonnegative hull of $h^*$-vectors of polytopes in a fixed dimension. Does this form a polyhedral cone? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bab63",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bab63",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0bab63",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.300Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"169d0f36-89d1-4781-8461-f2c47fb0a1c7","format_issues":null,"number":10565} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bb0b6 | problem | aim-38756a1f9b537f4591526253cd0bb0b6 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.22 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Are there ``holes'' in the set of $h^*$-vectors of polytopes in a fixed dimension which are not a result of failing known linear inequalities? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bb0b6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bb0b6",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0bb0b6",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.306Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"871f9a65-ce4d-4702-a494-09e4ab4c3dd2","format_issues":null,"number":10566} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bbf0f | problem | aim-38756a1f9b537f4591526253cd0bbf0f | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.24 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | How many facets do symmetric edge polytopes have? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bbf0f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bbf0f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0bbf0f",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.312Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6f948342-b790-44f5-b575-bfa88307e9d1","format_issues":null,"number":10567} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bcc53 | problem | aim-38756a1f9b537f4591526253cd0bcc53 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.26 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Consider the convex hull of parking functions. Does this admit a unimodular triangulation? Furthermore, can the Ehrhart polynomial be obtained from this? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bcc53",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bcc53",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0bcc53",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.318Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"16a5ee2b-7699-4790-96f1-21020a8a4e5d","format_issues":null,"number":10568} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bd14b | problem | aim-38756a1f9b537f4591526253cd0bd14b | Ehrhart Positivity · Question 1.4 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | In types B, C, and D, the stretched Clebsch-Gordon coefficients are period-2 quasi-polynomials. Are the coefficients of the constituent polynomials always positive? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0bd14b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0bd14b",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0bd14b",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.202Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2bd81b45-d555-42a3-8d2c-ce751767e026","format_issues":null,"number":10551} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bd230 | problem | aim-38756a1f9b537f4591526253cd0bd230 | Ehrhart Positivity · Question 1.45 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Consider rational polygons of denominator 2. The Ehrhart quasi-polynomial has two constituent polynomials, one of which is an Ehrhart polynomial. Classify the other constituent polynomial.
Note that this is settled for up to 2 interior lattice points. | unassessed | {
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"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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-38756a1f9b537f4591526253cd0be307 | problem | aim-38756a1f9b537f4591526253cd0be307 | Ehrhart Positivity · Question 1.5 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Characterize Ehrhart polynomials of tropical polytopes. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0be307",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0be307",
"note": null,
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"kind": "website",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.216Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"4d16338a-85e4-4341-bda9-8d6252de38be","format_issues":null,"number":10553} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bea8c | problem | aim-38756a1f9b537f4591526253cd0bea8c | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.28 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | - Find $0/1$-polytopes with non-unimodal, non-log-concave, etc. $h^*$-vectors.
- Find $0/1$-polytopes with non-unimodal, non-log-concave, etc. $f$-vectors.
- Find $0/\pm1$-polytopes with non-unimodal, non-log-concave, etc. $h^*$-vectors. | unassessed | {
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"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0bea8c",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
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"published_at": "2026-09-09T22:24:04.325Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"995526d1-f1e7-4686-908f-8514946e6936","format_issues":null,"number":10569} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0becd7 | problem | aim-38756a1f9b537f4591526253cd0becd7 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · 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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Determine a Veronese construction for rational polytopes. | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0becd7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0becd7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.331Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ec11f111-c84a-4aab-8617-255e0a2656b1","format_issues":null,"number":10570} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0bf5b7 | problem | aim-38756a1f9b537f4591526253cd0bf5b7 | Ehrhart Positivity · Question 1.55 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Study the Ehrhart polynomial of Harmonic polytopes and/or bipermutahedra. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0bf5b7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0bf5b7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"published_at": "2026-09-09T22:24:04.223Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5de8f707-ef56-4b65-bf65-4618bc554c33","format_issues":null,"number":10554} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0c011f | problem | aim-38756a1f9b537f4591526253cd0c011f | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.32 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | How many chambers are there for transportation polytopes for $n\times n$ matrices? For example, how many Ehrhart polynomials are needed? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c011f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c011f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.337Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b412f92d-f30a-4933-be6e-d2ca5728f34b","format_issues":null,"number":10571} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0c0ef5 | problem | aim-38756a1f9b537f4591526253cd0c0ef5 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.34 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Identify classes of simplices with unimodal box polynomials. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c0ef5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c0ef5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
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"imported_at": "2026-09-10",
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"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.344Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"06daa3d0-acd7-4efb-9e6e-668e1028bb05","format_issues":null,"number":10572} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0c19fb | problem | aim-38756a1f9b537f4591526253cd0c19fb | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.36 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Investigate $a,b$-decompositions for ``nice'' $h^*$-polynomials. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c19fb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c19fb",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography... | {
"source_record": "38756a1f9b537f4591526253cd0c19fb",
"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:04.350Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b87b32e1-de8b-4190-beb9-9065ac87297b","format_issues":null,"number":10573} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0c2e73 | problem | aim-38756a1f9b537f4591526253cd0c2e73 | Ehrhart Positivity · Question 1.6 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | - Consider the Ehrhart polynomial of a lattice polytope $P$. Below are two well-known representations of $i(P;t)$:
$$i(P;t) = \sum_{i=1}^d c_it^i = \sum_{i=0}^d h_i^* \binom{t+d-i}{d}.$$
Fix $k\in \mathbb{Z}_{>0}$ and write $i(P;t)$ in the basis $\{(t-k)^i\}_i$. (For example, if $\deg(h^*(P;z)) = s$, then $i(P;t)$ is n... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Ehrhart polynomials: inequalities and extremal constructions",
"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/1/#38756a1f9b537f4591526253cd0c2e73",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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-38756a1f9b537f4591526253cd0c6784 | problem | aim-38756a1f9b537f4591526253cd0c6784 | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.4 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | A **spinal graph** $G$ is a connected digraph on vertex set $V=\{1,2,...,n\}$ with edge multiset $E$, where all edges are directed from smaller to larger vertices and $E$ contains all edges of the form $(i,i+1)$ for $i=1,\ldots,n-1$ (i.e., the ``spine'' of $G$).
What can be said about the $h^*$-polynomials of flow pol... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c6784",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c6784",
"note": null,
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{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"914b1aa1-9e16-488d-a6e6-c44edf6a1325","format_issues":null,"number":10574} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0c85fc | problem | aim-38756a1f9b537f4591526253cd0c85fc | Ehrhart $h^\ast$-polynomial: Unimodality and Real-Rootedness · Question 2.38 | {
"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/ehrhartineq/ Not an author-supplied MSC code."
}
] | Investigate Stapledon's Effectiveness Conjecture.
**Conjecture.** [Stapledon] Let $P$ be a lattice polytope invariant under the action of a group $G$. Then the characters of the equivariant $H^*$-series is effective if and only if the equivariant $H^*$-series is a polynomial.
Stapledon proved that $H^*$ effective im... | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c85fc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms... | null | null | null | not-recorded | not-recorded | null | [] | [] | Ehrhart polynomials: inequalities and extremal constructions · AIMPL workshop record | ## Workshop introduction
This workshop was motivated by open questions in **Ehrhart theory**, a fundamental area of discrete geometry concerned with counting lattice points in polytopes and their dilates.
Let $P$ be a $d$-dimensional lattice polytope. For a nonnegative integer $t$ and polytope $P$, the $t$th dilate ... | 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": "Ehrhart polynomials: inequalities and extremal constructions · Original question",
"url": "http://aimpl.org/ehrhartineq/2/#38756a1f9b537f4591526253cd0c85fc",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:24:04.364Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4143262a-d8c8-45b4-b28a-e7f085c7b657","format_issues":null,"number":10575} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0cf944 | problem | aim-38756a1f9b537f4591526253cd0cf944 | Totally Anosov TNS action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\alpha$ be a smooth action on a closed manifold $X$ by $\mathbb{Z}^{k}$, $k\ge 2$. Assume that every elements in $\mathbb{Z}^{k}$ is an Anosov diffeomorphism and the action is totally non symplectic (TNS), that is there are no negatively proportional Lyapunov exponents. Is $X$ diffeomorphic to a nilmanifold and $\... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0cf944",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | B. Kalinin | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0cf944",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0cf944",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.683Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e9298881-eea4-4e6c-98e6-e42b58b6fd38","format_issues":null,"number":10798} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d08c0 | problem | aim-38756a1f9b537f4591526253cd0d08c0 | Classification of Affine Anosov action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $G=\mathbb{Z}^{k}\times \mathbb{R}^{l}$, $k+l\ge 2$.
- Which affine actions of $G$ are Anosov?
- Are there any non-standard ones?
- Which ones have rank one factor?
- Which ones contain ergodic, partially hyperbolic (but not Anosov) elements? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0d08c0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | K. Vinhage | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0d08c0",
"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 | [
"current-status-unassessed",
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"created_at": "2026-09-09T22:23:49.983Z",
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"published_at": "2026-09-09T22:24:05.689Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"bc75cf9e-5392-4cb3-914a-65db9268725b","format_issues":null,"number":10799} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d23d7 | problem | aim-38756a1f9b537f4591526253cd0d23d7 | Centralizer of a diffeomorphism | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a $C^{\infty}$ diffeomorphism of a closed manifold which is transitive, but whose centralizer in $\textrm{Diff}^{\infty}(M)$ is not a finite dimensional Lie group/locally compact? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/3/#38756a1f9b537f4591526253cd0d23d7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | K. Vinhage | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/3/#38756a1f9b537f4591526253cd0d23d7",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.780Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"df4f934e-bf36-428e-8e42-432b02d7600a","format_issues":null,"number":10815} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d2b9f | problem | aim-38756a1f9b537f4591526253cd0d2b9f | Actions on $n$ manifolds by lattices in $\textrm{SL}_{n}(\mathbb{R})$ | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $\textrm{SL}_{n}(\mathbb{R})$. Let $\alpha:\Gamma\to \textrm{Diff}(M)$ be a smooth action on $n$ manifold $M$ by $\Gamma$.
Assume that there is an isolated periodic point with derivative is unbounded.
- Is $\alpha$ linearizable nearby the fixed point?
- Is there an $\alpha$-invarian... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d2b9f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | D. Fisher | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d2b9f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.714Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e3d8f296-c04f-45ca-a3e2-9b9e06bab1c9","format_issues":null,"number":10803} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d659c | problem | aim-38756a1f9b537f4591526253cd0d659c | Higher rank lattice actions · Question 2.1 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $G=\textrm{SL}_{n}(\mathbb{R})$. Let $\alpha:\Gamma\to \textrm{Diff}(M)$ be a smooth action on $n$ manifold $M$ by $\Gamma$.
Assume that $\alpha$ preserves projective structure but there is no affine invariant connection. Does the action $\alpha$ extend to projective structure preserving ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d659c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | K. Melnick | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d659c",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0d659c",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.720Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0fd33337-174a-4ad8-9818-19e54e8494fd","format_issues":null,"number":10804} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d6de9 | problem | aim-38756a1f9b537f4591526253cd0d6de9 | Higher rank lattice actions · Question 2.15 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $\textrm{SL}_{n}(\mathbb{R})$. Let $\alpha:\Gamma\to \textrm{Diff}(M)$ be a smooth action on $n$ manifold $M$ by $\Gamma$.
Assume that there is an $\alpha$ invariant embedded $\mathbb{R}P^{n-1}$ (or $S^{n-1}$) in $M$ which $\Gamma$ acts standard way. Does $\alpha$ extend to a local $G$ ac... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d6de9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | D. Fisher | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d6de9",
"note": null,
"sort_order": 0
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{
"kind": "website",
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"... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1d1411e2-2481-4054-a080-cbd4dc1d2263","format_issues":null,"number":10805} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d7e69 | problem | aim-38756a1f9b537f4591526253cd0d7e69 | Irreducible lattices in product of rank one groups | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma=\textrm{SL}_{2}(\mathbb{Z}[\sqrt{2}])$. $\Gamma$ acts on $4$-torus by automorphism using $\mathbb{Q}$-irreducible representation defined over $\mathbb{Q}$. Is it locally rigid? More generally, any Anosov $\Gamma$ actions on torus is conjugate to an affine action? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d7e69",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Brown | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d7e69",
"note": null,
"sort_order": 0
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{
"kind": "website",
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"... | {
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} | 2026-10-10T16:07:49.246Z | {"database_id":"91e86807-ef07-4c86-b439-e5f2e069997f","format_issues":null,"number":10806} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0d96cf | problem | aim-38756a1f9b537f4591526253cd0d96cf | Actions on manifolds by lattices in p-adic group | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $\textrm{SL}_{n}(\mathbb{Q}_{p})$ with $n\ge 3$. Does $\Gamma$ act smoothly non-isometrically on a closed manifold? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d96cf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Brown | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0d96cf",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0d96cf",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.737Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"34017d4d-9966-41e2-8e52-36f24ba7ff0c","format_issues":null,"number":10807} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0da0b5 | problem | aim-38756a1f9b537f4591526253cd0da0b5 | Lattices in infinite center Lie group | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $G=\widetilde{\textrm{Sp}_{2g}(\mathbb{R})}$.
- Does $G$ act faithfully on a compact manifold?
- If not, does $\Gamma$ act faithfully on a compact manifold? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0da0b5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | W. Van Limbeek | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0da0b5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0da0b5",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.742Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"33283f99-4935-4f09-a00a-66f7a371d95c","format_issues":null,"number":10808} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0dc2a4 | problem | aim-38756a1f9b537f4591526253cd0dc2a4 | Perturbation of rank one factor | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\alpha$ be a $C^{\infty}$ $\mathbb{R}^{k}$ action on a manifold $X$ with $C^{\infty}$ rank one factor $\mathbb{R}$ action $\beta$ on $Y$. Does any perturbation of $\beta$ lift to a perturbation of $\alpha$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0dc2a4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank groups · AIMPL workshop record | ## Question context
Rank one factors are generally considered to be obstructions to rigidity as they can be perturbed. Answering this question would solidify this perspective, since it would show that the original action could also be perturbed once the base is. This is obvious for direct products, but not clear at al... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | K. Vinhage | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0dc2a4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0dc2a4",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.697Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"24ea7de0-5091-4cc2-a278-11dae3e18e59","format_issues":null,"number":10800} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0dcf13 | problem | aim-38756a1f9b537f4591526253cd0dcf13 | Blow up procedure | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $G=\mathbb{Z},\mathbb{Z}^{k} (k\ge 2)$ or a higher rank lattice $\Gamma$. Let $\alpha:G\to \textrm{Aut}(\mathbb{T}^{n})$ be a linear Anosov action. We can blow up along a periodic orbit of $A$. Can you do blow up for infinitely many periodic orbit so that the action is still smooth and there is a nonwhere vanishin... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dcf13",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Brown | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dcf13",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0dcf13",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.747Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"054233f6-1392-4862-9124-9388dd357bb5","format_issues":null,"number":10809} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0ddb35 | problem | aim-38756a1f9b537f4591526253cd0ddb35 | Centralizer of a diffeomorphism | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Which ergodic affine maps $f:X\to X$ of a homogeneous space $X$ have the property that if $g$ is a perturbation of $f$ such that $Z_{\textrm{Diff}(X)}(g)$ and $Z_{\textrm{Diff(X)}}(f)$ are virtually isomorphic, then $g$ is topologically (smoothly) conjugate to an affine perturbation of $f$? Do all partially hyperbolic,... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/3/#38756a1f9b537f4591526253cd0ddb35",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Wilkinson | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/3/#38756a1f9b537f4591526253cd0ddb35",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0ddb35",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.786Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1c9fc62a-4a8c-48f4-950d-91f0a364a686","format_issues":null,"number":10816} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0dee26 | problem | aim-38756a1f9b537f4591526253cd0dee26 | Complex manifold | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $G$ be a higher rank semisimple Lie group and $\Gamma$ be a lattice in it. Does same question hold when we consider biholomorphic actions on an almost complex manifold? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dee26",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | V. Pecastaing | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dee26",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0dee26",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.753Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dd3d4293-4b3b-47dc-993c-7d444b399600","format_issues":null,"number":10810} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0dfba9 | problem | aim-38756a1f9b537f4591526253cd0dfba9 | Bi-Lipschitz action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $\textrm{SL}_{n}(\mathbb{R})$ with $n\ge 3$. Let $X$ be a manifold with $\textrm{dim}(X)\le n-2$. Let $\alpha$ be a bi-lipschitz action on $X$ by $\Gamma$. Is it finite? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dfba9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Brown | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0dfba9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0dfba9",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.759Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f2f71588-f231-4e27-b2b9-e01d3b0cb44e","format_issues":null,"number":10811} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0e12bc | problem | aim-38756a1f9b537f4591526253cd0e12bc | Perturbation of product action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $G=\mathbb{Z}^{k}$ or $\mathbb{R}^{k}$ with $k\ge 2$. Assume that $G$ action $\alpha$ on a closed manifold $X$ is Anosov. Fix a closed manifold $Y$. When is every perturbation of $\alpha\times Id$ on $X\times Y$ is a smooth product? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0e12bc",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | A. Wilkinson | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0e12bc",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0e12bc",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.703Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8f2b5b79-53fc-4dd8-867c-f0fe39f7868f","format_issues":null,"number":10801} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0e227b | problem | aim-38756a1f9b537f4591526253cd0e227b | Cocycle over projective action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a lattice in $\textrm{SL}_{n}(\mathbb{R})$ with $n\ge 3$. Let $$\beta:\Gamma\times \mathbb{R}P^{n-1}\to \textrm{GL}_{d}(\mathbb{R})$$ be a cocycle over a projective action on $\mathbb{R}P^{n-1}$ by $\Gamma$. Is $\beta$ measurably cohomologous to a combination of derivative cocycle and a power of Jacobia... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0e227b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | Z. Wang | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0e227b",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0e227b",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.764Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"41c2acde-0929-423f-8535-9e8a637bd02f","format_issues":null,"number":10812} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0e4ade | problem | aim-38756a1f9b537f4591526253cd0e4ade | Higher rank lattice actions · Question 2.55 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Is there a locally free $\textrm{SL}_{3}(\mathbb{R})$ action on a closed $9$ dimensional manifold $X$ with at least one non-closed orbit? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0e4ade",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | B. Deroin | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0e4ade",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0e4ade",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.770Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c7c93e6c-44c7-4794-99e6-306a82c2da8f","format_issues":null,"number":10813} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0e5c2e | problem | aim-38756a1f9b537f4591526253cd0e5c2e | Higher rank abelian group actions · Question 1.5 | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Suppose $\mathbb{R}^{2}$ acts smoothly on a closed manifold $X$ with invariant foliation $F$. Assume that
- The set of normally hyperbolic elements is dense in $\mathbb{R}^{2}$.
- It satisfies accessibility property.
- Every coarse Lyapunov subspaces is one dimensional.
- Every element is transitive.
Then i... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0e5c2e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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"
] | K. Vinhage | null | null | null | [
{
"kind": "website",
"citation": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/1/#38756a1f9b537f4591526253cd0e5c2e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0e5c2e",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.708Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b5affbb9-70dc-4f03-adc0-db192eca756e","format_issues":null,"number":10802} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd0f98d9 | problem | aim-38756a1f9b537f4591526253cd0f98d9 | Property (T) group action | {
"main": "math",
"sub": "algebra",
"slug": "algebra",
"name": "Algebra",
"original_discipline": "mathematics"
} | [] | [] | Let $\Gamma$ be a discrete group with Kazhdan’s property (T). Let $\Sigma$ be a smooth surface and $\alpha\colon \Gamma\to \textrm{Diff}^{\infty}_{vol}(\Sigma)$ be a smooth volume preserving action on $\Sigma$ by $\Gamma$. Is $\alpha(\Gamma)$ finite? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Global rigidity of actions by higher-rank groups",
"type": "workshop-problem-list",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0f98d9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"no... | null | null | null | not-recorded | not-recorded | null | [] | [] | Global rigidity of actions by higher-rank 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": "Global rigidity of actions by higher-rank groups · Original question",
"url": "http://aimpl.org/rigidhigherrank/2/#38756a1f9b537f4591526253cd0f98d9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"... | {
"source_record": "38756a1f9b537f4591526253cd0f98d9",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:05.775Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"54c133bb-0160-4a5b-b91c-018ebd26cdfe","format_issues":null,"number":10814} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd104463 | problem | aim-38756a1f9b537f4591526253cd104463 | Aaronson-Ambainis conjecture | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Show that there exist $C_1,C_2>0$ such that for all $n\ge 1$, for all $f:\{-1,1\}^n\to [-1,1]$, we have
\begin{equation}
\max_{1\le j\le n}\text{Inf}_j(f)\ge C_1\left(\frac{\text{Var}(f)}{\deg(f)}\right)^{C_2}.
\end{equation} | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd104463",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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 partial cases have been known. For example, it is true when
- the function $f$ is symmetric;
- the function $f$ i... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd104463",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd104463",
"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": "2026-09-09T22:23:57.985Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"094ba4a2-0484-428a-b4d7-b3ca7787845c","format_issues":null,"number":10162} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd109524 | problem | aim-38756a1f9b537f4591526253cd109524 | A stronger form of Aaronson-Ambainis conjecture | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Show that there exists $C>0$ such that for all $n\ge 1$ and for all $f:\{-1,1\}^n\to \mathbb{R}$ we have
\begin{equation}
\text{Var}(f)\le \|f\|_\infty\deg(f)^C \max_{1\le j\le n}\|D_j f\|_2.
\end{equation} | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd109524",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd109524",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd109524",
"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": "2026-09-09T22:23:57.993Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4834216e-9eb9-41cf-92ae-a2b32daf1ccb","format_issues":null,"number":10163} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd10a4c9 | problem | aim-38756a1f9b537f4591526253cd10a4c9 | Some special cases | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Show that the above Aaronson-Ambainis conjecture and its stronger form are valid for
- all homogeneous functions on $\{-1,1\}^n$;
- all functions $f:\{-1,1\}^n\to \mathbb{R}$ whose Fourier coefficients are of the form
\begin{equation*}
|\widehat{f}(S)|=p(|S|),
\end{equation*}
where $p:\mathbb{N}\to ... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd10a4c9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/1/#38756a1f9b537f4591526253cd10a4c9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd10a4c9",
"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": "2026-09-09T22:23:58.028Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d2411cd3-a54b-4127-8796-2c02cfd1b65d","format_issues":null,"number":10164} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd10c48a | problem | aim-38756a1f9b537f4591526253cd10c48a | Heat-smoothing conjecture | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$ and $1< p < \infty$. Show that there exists $c_p>0$ such that for all $n\ge 1$ and all $f:\{-1,1\}^n\to \mathbb{R}$ of the form $f=\sum_{|S|\ge d}\widehat{f}(S)\chi_S$, we have
\begin{equation*}
\|P_t f\|_p\le e^{-tdc_p}\|f\|_p, \qquad t\ge 0,
\end{equation*}
where $P_t=e^{-t\Delta}$ is the heat semi... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd10c48a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd10c48a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd10c48a",
"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": "2026-09-09T22:23:58.036Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"99527694-bae0-42d7-ba3f-5bc6f322346f","format_issues":null,"number":10165} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd111631 | problem | aim-38756a1f9b537f4591526253cd111631 | Heat-smoothing: a weaker form | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$ and $1< p < \infty$. Show that there exists $c_p>0$ such that for all $n\ge 1$ and all $f:\{-1,1\}^n\to \mathbb{R}$ of the form $f=\sum_{|S|\ge d}\widehat{f}(S)\chi_S$, we have
\begin{equation*}
\|\Delta f\|_p\ge dc_p\|f\|_p,
\end{equation*}
where $\Delta$ is the generator of the heat semigroup $P_t... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd111631",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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"
] | Paata Ivanisvili | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd111631",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd111631",
"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": "2026-09-09T22:23:58.071Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c84aaa6-886b-47ca-98f0-5532f2d30f4f","format_issues":null,"number":10166} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd112563 | problem | aim-38756a1f9b537f4591526253cd112563 | Gaussian heat-smoothing | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$ and $1< p < \infty$. Show that there exists $c_p>0$ such that for all $n\ge 1$ and all polynomials $f\in \text{Lin}\{x^k,k\ge d\}$, we have
\begin{equation*}
\|P_t f\|_p\le e^{-tdc_p}\|f\|_p, \qquad t\ge 0,
\end{equation*}
where $P_t=e^{-tN}$ is the Ornstein--Uhlenbeck semigroup on the Gaussian space. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd112563",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd112563",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd112563",
"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": "2026-09-09T22:23:58.078Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"22e6c603-0644-4a48-a7c5-8b3bad9fe6c2","format_issues":null,"number":10167} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd112af4 | problem | aim-38756a1f9b537f4591526253cd112af4 | Gaussian heat-smoothing: a weaker form | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$ and $1< p < \infty$. Show that there exists $c_p>0$ such that for all $n\ge 1$ and all polynomials $f\in \text{Lin}\{x^k,k\ge d\}$, we have
\begin{equation*}
\|Nf\|_p\ge dc_p\|f\|_p,
\end{equation*}
where $N=\Delta-x\nabla$ is the generator of the Ornstein--Uhlenbeck semigroup. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd112af4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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"
] | Paata Ivanisvili | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd112af4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd112af4",
"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": "2026-09-09T22:23:58.115Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"704e06f3-7656-4e6e-801f-2569e225a79a","format_issues":null,"number":10168} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd1137f5 | problem | aim-38756a1f9b537f4591526253cd1137f5 | Reverse heat-smoothing | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$ and $1< p < \infty$. Show that there exists $c_p>0$ such that for all $n\ge 1$,
- and for all polynomials $f$ on $\{-1,1\}^n$ of degree at most $d$, we have
\begin{equation*}
\|\Delta f\|_p\le dc_p\|f\|_p
\end{equation*}
and thus
\begin{equation*}
\|P_t f\|_p\le e^{tdc_p}\|f\|_p, \qqu... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd1137f5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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"
] | Paata Ivanisvili | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/2/#38756a1f9b537f4591526253cd1137f5",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd1137f5",
"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": "2026-09-09T22:23:58.150Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7d2698bc-7aca-432d-ba17-3881df3262a1","format_issues":null,"number":10169} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd114b42 | problem | aim-38756a1f9b537f4591526253cd114b42 | Best constants in Bohnenblust-Hille inequalities for hypercubes | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$. Show that there exists $C>0$ such that for all $n\ge 1$ and all polynomials $f=\sum_{|S|\le d}\widehat{f}(S)\chi_S$ on $\{-1,1\}^n$ of degree at most $d$, we have
\begin{equation*}
\left(\sum_{|S|\le d}|\widehat{f}(S)|^{\frac{2d}{d+1}}\right)^{\frac{d+1}{2d}}\le d^C \|f\|_{\infty}.
\end{equation*} | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/3/#38756a1f9b537f4591526253cd114b42",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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
It is known that the inequality holds with constant $C^{\sqrt{d\log d}}$ for some universal $C>0$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/3/#38756a1f9b537f4591526253cd114b42",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd114b42",
"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": "2026-09-09T22:23:58.187Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6d376aa3-d17e-4890-8466-51be87b86b92","format_issues":null,"number":10170} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd115c39 | problem | aim-38756a1f9b537f4591526253cd115c39 | The sensitivity theorem | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | The sensitivity theorem says that for all $n\ge 1$ and all Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, we have
\begin{equation*}
s(f)\ge \sqrt{\deg (f)}.
\end{equation*}
More proofs of this result? Is it possible to formulate a reasonable problem for real-valued functions $f:\{-1,1\}^n\to \mathbb{R}$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/4/#38756a1f9b537f4591526253cd115c39",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/4/#38756a1f9b537f4591526253cd115c39",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd115c39",
"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": "2026-09-09T22:23:58.260Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"16f182b3-54de-480a-819c-c97f5d70eec7","format_issues":null,"number":10172} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd117532 | problem | aim-38756a1f9b537f4591526253cd117532 | Moment comparison | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Consider the following problems:
- Find the best $C>0$ such that for all $f:\{-1,1\}^n\to \mathbb{R}$,
\begin{equation*}
\|f\|_2\le C^{\deg(f)}\|f\|_1.
\end{equation*}
- For $1< p < q \le 2$, find the best $C_{p,q}>0$ such that
\begin{equation*}
\|f\|_q\le C_{p,q}^{\deg(f)}\|f\|_p.
\end{equation... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/5/#38756a1f9b537f4591526253cd117532",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/5/#38756a1f9b537f4591526253cd117532",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd117532",
"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": "2026-09-09T22:23:58.324Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5c8295c9-23fd-4a79-aa63-715303667806","format_issues":null,"number":10173} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd11f9ba | problem | aim-38756a1f9b537f4591526253cd11f9ba | Homogeneous case | {
"main": "math",
"sub": "analysis",
"slug": "analysis",
"name": "Analysis",
"original_discipline": "mathematics"
} | [] | [
{
"code": "81",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL list topic: Analysis on the hypercube with applications to quantum computing. http://aimpl.org/hypercubequantum/ Not an author-supplied MSC code."
}
] | Fix $d\ge 1$. Show that there exists $C>0$ such that for all $n\ge 1$ and all $d$-homogeneous polynomials $f=\sum_{|S|= d}\widehat{f}(S)\chi_S$ on $\{-1,1\}^n$, we have
\begin{equation*}
\left(\sum_{|S|= d}|\widehat{f}(S)|^{\frac{2d}{d+1}}\right)^{\frac{d+1}{2d}}\le d^C \|f\|_{\infty}.
\end{equation*} | unassessed | {
"key": "aimpl",
"name": "AIMPL · Analysis on the hypercube with applications to quantum computing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/hypercubequantum/3/#38756a1f9b537f4591526253cd11f9ba",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Analysis on the hypercube with applications to quantum computing · AIMPL workshop record | ## Workshop introduction
We fix some notation. For all $n\ge 1$, any function $f:\{-1,1\}^n\to \mathbb{R}$ has the unique Fourier expansion
\begin{equation*}
f=\sum_{S\subset [n]}\widehat{f}(S)\chi_S
\end{equation*}
where for each $S\subset [n]:=\{1,\dots, n\}$, $\widehat{f}(S)\in\mathbb{R}$ and $\chi_S(x):=\prod_{j\... | 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
Similarly, the inequality holds with constant $C^{\sqrt{d\log d}}$ for some universal $C>0$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Analysis on the hypercube with applications to quantum computing · Original question",
"url": "http://aimpl.org/hypercubequantum/3/#38756a1f9b537f4591526253cd11f9ba",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bib... | {
"source_record": "38756a1f9b537f4591526253cd11f9ba",
"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": "2026-09-09T22:23:58.250Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f5c4aca4-ace0-40f7-8a20-9cb1c3c20e28","format_issues":null,"number":10171} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd135f2e | problem | aim-38756a1f9b537f4591526253cd135f2e | Specific questions for graphs of small degree · Question 1.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | What is the $\mu$-measurable chromatic number of $G$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd135f2e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $G$ be the Schreier graph on $X = F(2^{\mathbb{F}_2})$ (The free part of the 2-shift) induced by the standard generating set. Let $\mu$ be the coin flip measure on $X$. Let $a$ and $b$ be the generators. | 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
It is either 3 or 4. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd135f2e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd135f2e",
"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": "2026-09-09T22:24:01.518Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"81899e06-bc89-4e09-890b-7e7ff8ff205e","format_issues":null,"number":10487} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd139b59 | problem | aim-38756a1f9b537f4591526253cd139b59 | Specific questions for graphs of small degree · Question 1.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | What is the approximate $\mu$-measurable chromatic number of $G$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd139b59",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $G$ be the Schreier graph on $X = F(2^{\mathbb{F}_2})$ (The free part of the 2-shift) induced by the standard generating set. Let $\mu$ be the coin flip measure on $X$. Let $a$ and $b$ be the generators. | 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": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd139b59",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd139b59",
"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": "2026-09-09T22:24:01.523Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"25c7f414-7b48-4dc4-8685-d9aa301601ab","format_issues":null,"number":10488} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13a57d | problem | aim-38756a1f9b537f4591526253cd13a57d | Specific questions for graphs of small degree · Question 1.3 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | What is the Borel edge chromatic number of $G$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13a57d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $G$ be the Schreier graph on $X = F(2^{\mathbb{F}_2})$ (The free part of the 2-shift) induced by the standard generating set. Let $\mu$ be the coin flip measure on $X$. Let $a$ and $b$ be the generators. | 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
It is either 5 or 6. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13a57d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13a57d",
"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": "2026-09-09T22:24:01.529Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1aa175df-45dc-4d4b-9887-49a2ee95f287","format_issues":null,"number":10489} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13af0a | problem | aim-38756a1f9b537f4591526253cd13af0a | Specific questions for graphs of small degree · Question 1.4 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | What is the $\mu$-measurable edge chromatic number of $G$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13af0a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $G$ be the Schreier graph on $X = F(2^{\mathbb{F}_2})$ (The free part of the 2-shift) induced by the standard generating set. Let $\mu$ be the coin flip measure on $X$. Let $a$ and $b$ be the generators. | 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
It is either 4 or 5. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13af0a",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13af0a",
"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": "2026-09-09T22:24:01.535Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0c8d4de6-6ff8-4cb6-9dfd-6d54fed01f8d","format_issues":null,"number":10490} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13bd91 | problem | aim-38756a1f9b537f4591526253cd13bd91 | Specific questions for graphs of small degree · Question 1.5 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Is there a Borel partition of the edges of G, say into A, B, and C, such that
[i.]
- For all $x \in X$, $H \cdot x$ contains an edge from $A$ (meaning it contains both endpoints of the edge).
- “ “ $V$ “ “ $B$
- “ “ $D$ “ “ $C$ | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13bd91",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $G$ be the Schreier graph on $X = F(2^{\mathbb{F}_2})$ (The free part of the 2-shift) induced by the standard generating set. Let $\mu$ be the coin flip measure on $X$. Let $a$ and $b$ be the generators.
## Question context
Let
[i.]
- $H = \{\ldots , a^{-1} , 1, a , a^2, \ldots\} = \lan... | 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 is if we weaken Borel to $\mu$-measurable. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/1/#38756a1f9b537f4591526253cd13bd91",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13bd91",
"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": "2026-09-09T22:24:01.541Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9e1e7df9-244a-44cf-a9ad-53e65988442a","format_issues":null,"number":10491} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13dedf | problem | aim-38756a1f9b537f4591526253cd13dedf | Complexity of combinatorial questions and dichotomy theorems · Question 2.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Are the following decidable?
[a.]
- Given a finite set of tiles in $\mathbb{Z}^n$, is there a continuous tiling of $F(2^{\mathbb{Z}^n})$ with those tiles?
- Same as a, but where we are given that there is a (not necessarily definable) tiling. I.e, a tiling of the Cayley graph with those tiles. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13dedf",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
The answer to (a) is no if there are no definability constraints. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13dedf",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13dedf",
"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": "2026-09-09T22:24:01.547Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"861cee36-f958-480a-9436-046fb95540e1","format_issues":null,"number":10492} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13e2f9 | problem | aim-38756a1f9b537f4591526253cd13e2f9 | Complexity of combinatorial questions and dichotomy theorems · Question 2.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Is there a dichotomy characterizing which Borel graphs admit Borel orientations for which every vertex has finite out degree? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13e2f9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13e2f9",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13e2f9",
"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": "2026-09-09T22:24:01.552Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0301eccc-da36-4169-bd29-cfc5baaa20e9","format_issues":null,"number":10493} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13e6f1 | problem | aim-38756a1f9b537f4591526253cd13e6f1 | Complexity of combinatorial questions and dichotomy theorems · Question 2.3 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | What is the complexity of the set of pmp graphs admitting a measurable 3-coloring? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13e6f1",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13e6f1",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13e6f1",
"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": "2026-09-09T22:24:01.557Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"67f54913-80b1-465b-8ed8-ad3b9c923a69","format_issues":null,"number":10494} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd13f598 | problem | aim-38756a1f9b537f4591526253cd13f598 | Complexity of combinatorial questions and dichotomy theorems · Question 2.4 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $G$ be an acyclic analytic Borel graph with uncountable Borel chromatic number. Is there an injective continuous reduction $f$ from $\mathbb{G}_0$ to $G$ ($x \mathbb{G}_0 y$ iff $f(x) G f(y)$)? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13f598",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
The answer is yes if $G$ is contained in a potentially $F_\sigma$ acyclic graph. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/2/#38756a1f9b537f4591526253cd13f598",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd13f598",
"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": "2026-09-09T22:24:01.563Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fc94a965-107c-4471-9001-4dfbdb4a09e5","format_issues":null,"number":10495} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd140b1e | problem | aim-38756a1f9b537f4591526253cd140b1e | Dynamics and measurable combinatorics of group actions · Question 3.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $d < n \in \omega$. Is there a compact subflow of the space of all bounded displacement actions of $\mathbb{Z}^d$ on $\mathbb{Z}^n$ with finitely many orbits? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd140b1e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd140b1e",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
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"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.569Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"95355655-6f90-4d5b-ab62-333aa4864048","format_issues":null,"number":10496} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd140d74 | problem | aim-38756a1f9b537f4591526253cd140d74 | Dynamics and measurable combinatorics of group actions · Question 3.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $G$ be a Schreier graph of a free pmp (probability measure preserving) action of a finitely generated group $\Gamma$.
[a.]
- If $\Gamma$ is non-amenable, does $G$ admit a measurable perfect matching?
- What if $\Gamma$ is just non-two ended and infinite? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd140d74",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd140d74",
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"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
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"imported_at": "2026-09-10",
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"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.575Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b7261b9b-d773-4587-83ed-a135f23c19af","format_issues":null,"number":10497} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd142a1b | problem | aim-38756a1f9b537f4591526253cd142a1b | Dynamics and measurable combinatorics of group actions · Question 3.3 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $\Gamma$ be an infinite property (T) group. Let $G$ be one of the following:
[a.]
- A Borel graphing of the orbit equivalence relation of a free pmp action of $\Gamma$.
- A Cayley graph of $\Gamma$.
Does every finite graph appear as a minor of $G$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd142a1b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd142a1b",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd142a1b",
"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"
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.580Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0294e970-ccd0-4f15-bf40-aa01522d67b6","format_issues":null,"number":10498} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd143447 | problem | aim-38756a1f9b537f4591526253cd143447 | Dynamics and measurable combinatorics of group actions · Question 3.4 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $G$ be a Polish group and $N$ a locally compactable normal subgroup of $G$. Is the translation action of $N$ on $G$ hypersmooth? (It is if $N$ is countable.) | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd143447",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/3/#38756a1f9b537f4591526253cd143447",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd143447",
"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": "2026-09-09T22:24:01.586Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eaab49ec-ea95-4b15-b48e-96a45d5453a0","format_issues":null,"number":10499} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd146404 | problem | aim-38756a1f9b537f4591526253cd146404 | Relationships between different definable settings · Question 4.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $d \in \omega$. Given an SFT (sub-shift of finite type) of $\mathbb{Z}^d$, say $S$ (equivalently, given a LCL (locally checkable labelling problem), say $\Pi$), are any of the following equivalent?
[i.]
- $T$ here is a Borel equivariant map $F(2^{\mathbb{Z}^d}) \rightarrow S$. (Equivalently, a Borel $\Pi$-co... | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/4/#38756a1f9b537f4591526253cd146404",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
## Status note in the source
They are all equivalent for $d = 1$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/4/#38756a1f9b537f4591526253cd146404",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd146404",
"imported_at": "2026-09-10",
"status_as_of": "2026-09-10 source snapshot; not a current-status certification",
"evidence_label": "Workshop record · status unassessed",
"note": "Original numbered question. AIM Problem Lists (AIMPL), original contributors; ... | null | [
"current-status-unassessed",
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] | [] | {
"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.592Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"273b215d-db81-4822-aa34-939a69ab5d66","format_issues":null,"number":10500} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd146a0f | problem | aim-38756a1f9b537f4591526253cd146a0f | Relationships between different definable settings · Question 4.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $\Pi$ be a LCL such that every highly computable graph admits a computable $\Pi$-coloring. Does every locally finite Borel graph admit a Baire measurable $\Pi$-coloring? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/4/#38756a1f9b537f4591526253cd146a0f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/4/#38756a1f9b537f4591526253cd146a0f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd146a0f",
"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": "2026-09-09T22:24:01.598Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"55446eb7-934a-4178-8f8f-1cd18c0de117","format_issues":null,"number":10501} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd148bb4 | problem | aim-38756a1f9b537f4591526253cd148bb4 | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $E$ be treeable.
[a. ]
- Does every Borel graphing, say, $G$ of $E$ contain a Borel subgraph, say $T$, which is a treeing of $E$?
- What if we just want $T$ to be $\mu$-measurable? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd148bb4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd148bb4",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd148bb4",
"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"
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.603Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"eca8283d-5cc9-4f44-bbd5-baa1122067fd","format_issues":null,"number":10502} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd149159 | problem | aim-38756a1f9b537f4591526253cd149159 | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $E$ be pmp and $G$ a Borel graphing of $E$. Does $G$ contain Borel subgraphings (of $E$) whose cost is arbitrarily close to the cost of $E$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd149159",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd149159",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd149159",
"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": "2026-09-09T22:24:01.609Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d721064f-3c34-44ab-a944-9961f9e6fb5c","format_issues":null,"number":10503} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd14a041 | problem | aim-38756a1f9b537f4591526253cd14a041 | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.3 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Is every finite index extension of a hypersmooth equivalence relation hypersmooth? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14a041",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14a041",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd14a041",
"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": "2026-09-09T22:24:01.615Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"07bb7887-19c6-489e-9130-c24c506fed6c","format_issues":null,"number":10504} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd14adad | problem | aim-38756a1f9b537f4591526253cd14adad | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.4 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $E$ be treeable.
[a. ]
- Is every finite index extension of E treeable?
- What if we only require a $\mu$-measurable treeing. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14adad",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14adad",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd14adad",
"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"
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"created_at": "2026-09-09T22:23:49.983Z",
"updated_at": "2026-09-09T22:23:49.983Z",
"published_at": "2026-09-09T22:24:01.624Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"13eeb428-df78-4e9b-aa58-a0a19ca81477","format_issues":null,"number":10505} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd14b15d | problem | aim-38756a1f9b537f4591526253cd14b15d | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.5 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Suppose $E$ and $F$ are treeable of type III_A. do they have class-bijective lifts which are stably orbit equivalent? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14b15d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14b15d",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd14b15d",
"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": "2026-09-09T22:24:01.630Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dacd689a-3dc6-4f99-85b4-ca159ceaf219","format_issues":null,"number":10506} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd14c521 | problem | aim-38756a1f9b537f4591526253cd14c521 | Graphings, Treeings, and CBERs (countable Borel equivalence relations) · Question 5.6 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Is there an “informative” notion of cost in the quasi-pmp setting? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14c521",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space, $E$ and $F$ CBERs on $X$, and $\mu$ a Borel probability measure on $X$. | 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"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/5/#38756a1f9b537f4591526253cd14c521",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd14c521",
"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": "2026-09-09T22:24:01.636Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1fafccf6-3231-4deb-be2f-6a45b2d3b4a3","format_issues":null,"number":10507} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd14f144 | problem | aim-38756a1f9b537f4591526253cd14f144 | Hyperfiniteness and related notions · Question 6.1 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $f_n : X \rightarrow [0,1]$ Borel for $n \in \omega$. Let $I \subset {Borel}(X)$ a $\sigma$-ideal. Let $F_n = \frac{1}{n} \sum_{m < n} f_m$. Does $(F_n)_{n \in \omega}$ admit a subsequence which converges outside a set in $I$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd14f144",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space. | 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
We are especially interested in the case where $I$ is the ideal of Ramsey null sets. The answer is yes if $I$ is the ideal of $\mu... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd14f144",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd14f144",
"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": "2026-09-09T22:24:01.642Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dc8fc2a2-767e-4bd8-b79e-7e41e317af3e","format_issues":null,"number":10508} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd1505cb | problem | aim-38756a1f9b537f4591526253cd1505cb | Hyperfiniteness and related notions · Question 6.2 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Is every orbit equivalence relation induced by a Borel action of the Grigorchuk group hyperfinite? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd1505cb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space. | 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": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd1505cb",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd1505cb",
"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": "2026-09-09T22:24:01.647Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"57e4bf21-7276-44f2-83fa-00e591291dbd","format_issues":null,"number":10509} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd150e7f | problem | aim-38756a1f9b537f4591526253cd150e7f | Hyperfiniteness and related notions · Question 6.3 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | Let $E$ be a CBER on $X$. Suppose there is a Borel binary relation $<$ on $X$ such that the restriction of $<$ to each $E$-class is a linear order isomorphic to $\mathbb{Z}^2$ with the lexicographic order (“A $\mathbb{Z}$-line of $\mathbb{Z}$-lines”). Is $E$ hyperfinite? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd150e7f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space.
## Question context
The following seems closely related to the union problem. Perhaps someone can elaborate on whether there is a direct relationship. | 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": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd150e7f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd150e7f",
"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": "2026-09-09T22:24:01.653Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d02fbb53-0214-4c10-b2ca-90d142793536","format_issues":null,"number":10510} |
1.0.0 | problem:aim-38756a1f9b537f4591526253cd15182f | problem | aim-38756a1f9b537f4591526253cd15182f | Hyperfiniteness and related notions · Question 6.4 | {
"main": "math",
"sub": "logic and foundations",
"slug": "logic-and-foundations",
"name": "Logic and foundations",
"original_discipline": "mathematics"
} | [] | [
{
"code": "03",
"basis": "source-map",
"evidence": "Editorial mapping of AIMPL source category: Logic. http://aimpl.org/descriptgraph/ Not an author-supplied MSC code."
}
] | [a.]
- Which groups are strongly hyperfinite? ($\mathbb{Z}^d$ is for $d \in \omega$.)
- Is strong hyperfiniteness equivalent to the following? : All $E$ as above are topologically orbit equivalent to an action of $\mathbb{Z}$. | unassessed | {
"key": "aimpl",
"name": "AIMPL · Descriptive graph theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd15182f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produ... | null | null | null | not-recorded | not-recorded | null | [] | [] | Descriptive graph theory · AIMPL workshop record | ## Section context
Let $X$ be a Polish space.
## Question context
Call a group $\Gamma$ strongly hyperfinite if every orbit equivalent relation $E$ of a free*** continuous action of $\Gamma$ on a compact, 0-dim. Polish space admits a continuous reduction to $\mathbb{E}_0$.
*** There seemed to be some uncertainty ab... | 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": "Descriptive graph theory · Original question",
"url": "http://aimpl.org/descriptgraph/6/#38756a1f9b537f4591526253cd15182f",
"note": null,
"sort_order": 0
},
{
"kind": "website",
"citation": "AIMPL source bibliography",
"url": "http://aimpl.org/de... | {
"source_record": "38756a1f9b537f4591526253cd15182f",
"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": "2026-09-09T22:24:01.659Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"47ef5c68-8f4b-4b19-8e37-64543e64b313","format_issues":null,"number":10511} |
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