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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592403d763 | problem | aim-6adb9ed5d4e8053cb94017592403d763 | Knot homology theories and categorification · Question 4.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is a B-side construction of Heegaard knot Floer homology? | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mohammed Abouzaid | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592403ecec | problem | aim-6adb9ed5d4e8053cb94017592403ecec | Symplectic topology and dynamics · Question 3.3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is the volume preserving diffeomorphism group of $\mathbb{R}^2$ with respect to the standard volume form $dx \wedge dy$ perfect? | unassessed | {
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Dusa McDuff | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240406f3 | problem | aim-6adb9ed5d4e8053cb9401759240406f3 | Symplectic topology and dynamics · Question 3.4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How about the perfectness for volume-preserving diffeomorphism groups of surfaces of infinite type? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb9401759240406f3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Cheuk Yu Mak | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f74ff249-050d-4604-ba2d-62494288944c","format_issues":null,"number":10688} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240411cd | problem | aim-6adb9ed5d4e8053cb9401759240411cd | Symplectic topology and dynamics · Question 3.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do existing techniques say anything about the structure of $\overline{\text{Ham}}(M, \omega)$ for $\text{dim} M \geq 2$? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb9401759240411cd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sheel Ganatra | null | null | null | [
{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924042909 | problem | aim-6adb9ed5d4e8053cb940175924042909 | Symplectic topology and dynamics · Question 3.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is the group of $C^2$ diffeomorphisms of $S^1$ simple? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924042909",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sobhan Seyfaddini | null | null | null | [
{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"e3759802-ce04-4715-b8ff-5b1d1ca6b819","format_issues":null,"number":10690} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404371e | problem | aim-6adb9ed5d4e8053cb94017592404371e | Knot homology theories and categorification · Question 4.9 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Does Aganagic's Khovanov homology construction have a Lee/Bar-Natan deformation? Does this theory provide a geometric explanation for odd Khovanov homology? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592404371e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Lipshitz-Smith | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592404371e",
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{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924044927 | problem | aim-6adb9ed5d4e8053cb940175924044927 | Symplectic topology and dynamics · Question 3.7 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can one better/explicitly understand the abelianization of the $\overline{\text{Ham}}(\Sigma, \omega)$ for $(\Sigma, \omega)$ a symplectic surface? More generally, how about quotients of $\overline{\text{Ham}}(\Sigma, \omega)$ by other natural normal subgroups? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924044927",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Cheuk Yu Mak | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924044927",
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{
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d69efe2c-f9fc-4622-9c48-d4ecd7e6a3eb","format_issues":null,"number":10691} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924046147 | problem | aim-6adb9ed5d4e8053cb940175924046147 | Quantitative Heegaard Floer theory and ECH · Question 2.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What more can the computational apparatus in Heegaard Floer theory tell us about dynamics? | unassessed | {
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"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb940175924046147",
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"doi": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Robert Lipshitz | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240463a5 | problem | aim-6adb9ed5d4e8053cb9401759240463a5 | Miscellaneous | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | To what degree can link spectral invariants and their applications be generalized to higher dimensions? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/2/#6adb9ed5d4e8053cb9401759240463a5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
Heegaard Floer theory constructs powerful invariants for $3$-manifolds and links therein. Recently, such a theory has found applications in the study of Hamiltonian diffeomorphism groups of surfaces. There is a parallel theory from embedded contact homology. This section records questions not yet an... | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Peng Zhou | null | null | null | [
{
"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"d6c5e783-49a7-4a8c-bf24-61bf1456b611","format_issues":null,"number":10684} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404756f | problem | aim-6adb9ed5d4e8053cb94017592404756f | Spectral refinements (in the sense of algebraic topology) · Question 5.1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Are there spectral refinements of KLRW and nil Hecke algebra? | unassessed | {
"key": "aimpl",
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924049a77 | problem | aim-6adb9ed5d4e8053cb940175924049a77 | Spectral refinements (in the sense of algebraic topology) · Question 5.2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Are there spectral refinements of link spectral invariants and applications? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/5/#6adb9ed5d4e8053cb940175924049a77",
"citation": null,
"doi": null,
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"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Egor Shelukhin | null | null | null | [
{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404c96d | problem | aim-6adb9ed5d4e8053cb94017592404c96d | Knot homology theories and categorification · Question 4.6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a symplectic way to understand the entire $2$-categorical representation theory framework from which, e.g., KLRW or nil Hecke algebra arises? | unassessed | {
"key": "aimpl",
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb94017592404c96d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sheel Ganatra | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404d73d | problem | aim-6adb9ed5d4e8053cb94017592404d73d | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.45 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can one adapt any of the symplectic Khovanov homology constructions to the case of knots in lens spaces? Specifically, what about Aganagic's construction of knot Floer homology? | unassessed | {
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"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592404d73d",
"citation": null,
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... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Robert Lipshitz | null | null | null | [
{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404de1a | problem | aim-6adb9ed5d4e8053cb94017592404de1a | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can one establish a surgery formula (or exact triangle) in Aganagic's construction? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592404de1a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Alexei Oblomkov | null | null | null | [
{
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592404f6e9 | problem | aim-6adb9ed5d4e8053cb94017592404f6e9 | Lagrangian Floer theory of symmetric products and Hilbert schemes · Question 1.55 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can one introduce and then apply the computational tool of ``nice diagrams" of [Source citation: MR2630063](http://aimpl.org/floerhilbert/bib/) to Aganagic's construction and use it to simplify computations? | unassessed | {
"key": "aimpl",
"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592404f6e9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | ## Section context
This section includes problems inspired by Heegaard Floer theory, symplectic Khonvanov homology, and Aganagic’s recent proposal concerning geometric models for knot homology theories. | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Robert Lipshitz | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/floerhilbert/1/#6adb9ed5d4e8053cb94017592404f6e9",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240505e3 | problem | aim-6adb9ed5d4e8053cb9401759240505e3 | Knot homology theories and categorification · Question 4.7 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How does Ekholm--Shende's ``Skeins on Branes" [Source citation: arXiv:1901.08027](http://aimpl.org/floerhilbert/bib/) story fit into a symplectic production of, e.g., (nil) Hecke algebras, and how can we better use it? | unassessed | {
"key": "aimpl",
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"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb9401759240505e3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Ivan Smith | null | null | null | [
{
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"url": "http://aimpl.org/floerhilbert/4/#6adb9ed5d4e8053cb9401759240505e3",
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"kind": "website",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"8712a9f8-1699-4bc9-8887-3d1825d5a06a","format_issues":null,"number":10701} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924050ec3 | problem | aim-6adb9ed5d4e8053cb940175924050ec3 | Symplectic topology and dynamics · Question 3.8 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | It's known that the group of volume-preserving diffeomorphisms on $S^3$ is perfect. Is the commutator length uniformly bounded? | unassessed | {
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"name": "AIMPL · Floer theory of symmetric products and Hilbert schemes ",
"type": "workshop-problem-list",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924050ec3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
... | null | null | null | not-recorded | not-recorded | null | [] | [] | Floer theory of symmetric products and Hilbert schemes · AIMPL workshop record | null | Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.
The source supplies no separate status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Tsuboi-Polterovich | null | null | null | [
{
"kind": "website",
"citation": "Floer theory of symmetric products and Hilbert schemes · Original question",
"url": "http://aimpl.org/floerhilbert/3/#6adb9ed5d4e8053cb940175924050ec3",
"note": null,
"sort_order": 0
},
{
"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592405d7b3 | problem | aim-6adb9ed5d4e8053cb94017592405d7b3 | Lagrangian cobordisms from plabic graphs · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For each positroid stratum of a Grassmanian, there is a Legendrian link whose augmentation variety is that stratum. Positroid strata are also ordered with respect to closure.
Is this partial order recoverable on the Legendrian links in terms of topology, for instance by (decomposable) Lagrangian cobordisms? Could the ... | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/7/#6adb9ed5d4e8053cb94017592405d7b3",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
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"created_at": "2026-09-08T03:32:15.935Z",
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"published_at": "2026-09-08T03:33:07.812Z",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592405fcea | problem | aim-6adb9ed5d4e8053cb94017592405fcea | Lagrangian cobordisms from plabic graphs · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a local operation of plabic graphs which induces Lagrangian cobordisms between the associated Legendrian knots? In general, what can be done on the combinatorial side to guarantee a Lagrangian cobordism on the other side? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/7/#6adb9ed5d4e8053cb94017592405fcea",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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] | null | null | null | null | [
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"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406056e | problem | aim-6adb9ed5d4e8053cb94017592406056e | Lagrangian cobordisms from plabic graphs · Question 3 | {
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"name": "Geometry and topology",
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} | [] | [] | Is there a symplectic geometric application of 3d-plabic graphs? Do 3d-plabic graphs give some filling of a Legendrian link? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924060cce | problem | aim-6adb9ed5d4e8053cb940175924060cce | Lagrangian cobordisms from plabic graphs · Question 4 | {
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"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For ADE types, all seeds in the cluster algebra can be realized by Lagrangian fillings. Can this be generalized? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924061994 | problem | aim-6adb9ed5d4e8053cb940175924061994 | Link invariants from quivers · Question 1 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there an association between the mutation equivalence of plabic graphs or the mutation equivalence of quivers to the invariants of isotopy classes of their associated links? Can these be used to produce invariants of quivers up to mutation equivalence? | unassessed | {
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"url": "http://aimpl.org/clusterbraid/1/#6adb9ed5d4e8053cb940175924061994",
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"doi": null,
"arxiv_id": null,
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"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406254a | problem | aim-6adb9ed5d4e8053cb94017592406254a | Link invariants from quivers · Question 2 | {
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"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | To a quiver, we can associate a point count polynomial defined recursively (Galashin-Lam). This is sometimes equal to the HOMFLY-PT polynomial of the related link. For any simple plabic graphs, are these polynomials always equivalent? | unassessed | {
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"url": "http://aimpl.org/clusterbraid/1/#6adb9ed5d4e8053cb94017592406254a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240628e3 | problem | aim-6adb9ed5d4e8053cb9401759240628e3 | Link invariants from quivers · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | In high levels of generality, varieties pick up a mixed Hodge structure (Lam-Speyer). When the cluster variety is adequately nice, the mixed Hodge structure has only two dimensions, and the point count polynomial corresponds to a certain polynomial, but not the HOMFLY-PT.
What is the relationship between the mixed Hod... | unassessed | {
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The source supplies no status note for this question. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240630bd | problem | aim-6adb9ed5d4e8053cb9401759240630bd | Link invariants from quivers · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | When is the plabic cluster algebra locally acyclic? If it is not locally acyclic, is it still a polynomial count and can we say anything about a mixed Hodge structure? | unassessed | {
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"doi": null,
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"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406697d | problem | aim-6adb9ed5d4e8053cb94017592406697d | Stratifications of braid varieties · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | If we consider instead a braid variety, ie. a Legendrian associated to a $(-1)$-closure, does this still hold? | unassessed | {
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"url": "http://aimpl.org/clusterbraid/2/#6adb9ed5d4e8053cb94017592406697d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Given a positive braid, the front projection of a Legendrian link which is its rainbow closure has an augmentation variety with a ruling stratification into $(\mathbb{C}^k)\times (\mathbb{C}^*)^l$ pieces. This stratification is the same as the one coming from the cluster variety. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924066e87 | problem | aim-6adb9ed5d4e8053cb940175924066e87 | Stratifications of braid varieties · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For more general Legendrians, is the augmentation variety cluster? | unassessed | {
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"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/2/#6adb9ed5d4e8053cb940175924066e87",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Given a positive braid, the front projection of a Legendrian link which is its rainbow closure has an augmentation variety with a ruling stratification into $(\mathbb{C}^k)\times (\mathbb{C}^*)^l$ pieces. This stratification is the same as the one coming from the cluster variety. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"citation": "Cluster algebras and braid varieties",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240677c7 | problem | aim-6adb9ed5d4e8053cb9401759240677c7 | Stratifications of braid varieties · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | If $X$ is a general cluster variety, and $T\subset X$ is a cluster torus. What can we say about $X - T$ (Eg. what are the irreducible components, intersections, etc.)? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
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"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Given a positive braid, the front projection of a Legendrian link which is its rainbow closure has an augmentation variety with a ruling stratification into $(\mathbb{C}^k)\times (\mathbb{C}^*)^l$ pieces. This stratification is the same as the one coming from the cluster variety. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924068f6f | problem | aim-6adb9ed5d4e8053cb940175924068f6f | Stratifications of braid varieties · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What can we say if $X$ is the cluster variety of a $(-1)$-closure, but $T$ comes from some weave other than the obvious/natural one? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
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"url": "http://aimpl.org/clusterbraid/2/#6adb9ed5d4e8053cb940175924068f6f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Given a positive braid, the front projection of a Legendrian link which is its rainbow closure has an augmentation variety with a ruling stratification into $(\mathbb{C}^k)\times (\mathbb{C}^*)^l$ pieces. This stratification is the same as the one coming from the cluster variety. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Cluster algebras and braid varieties",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924069d48 | problem | aim-6adb9ed5d4e8053cb940175924069d48 | Lagrangian cobordisms from plabic graphs · Question 5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can mutations of quivers with potentials be realized as a symplectic operation? Could we use this to write down potentials for quivers from braid varieties? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/7/#6adb9ed5d4e8053cb940175924069d48",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406aab7 | problem | aim-6adb9ed5d4e8053cb94017592406aab7 | Combinatorics of cluster structures on braid varieties · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Investigate:
- cluster variables,
- quivers,
- positive parametrizations,
- twist maps and Donaldson-Thomas transformations,
- and the relationship between 3d-plabic graphs and weaves. | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/6/#6adb9ed5d4e8053cb94017592406aab7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Question context
Plabic graphs and weaves give seeds in cluster structures on braid varieties. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"citation": "Cluster algebras and braid varieties",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406d6eb | problem | aim-6adb9ed5d4e8053cb94017592406d6eb | Miscellaneous · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a compactification of the cotangent bundle of Bott-Samelson varieties or the cotangent bundle of Brick manifolds related to all braids? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/10/#6adb9ed5d4e8053cb94017592406d6eb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Question context
Braid varieties are compactified by Brick manifolds. The strata here relate to positive braids. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/10/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406df7b | problem | aim-6adb9ed5d4e8053cb94017592406df7b | Miscellaneous · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What can we say about Soergel bimodules and braid varieties? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/10/#6adb9ed5d4e8053cb94017592406df7b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/10/",
"note": null,
"sort_order": 0
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406e079 | problem | aim-6adb9ed5d4e8053cb94017592406e079 | Miscellaneous · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we study parabolic braid varieties, ie. in $G/P$?
Do these have cluster structures? Do we need to change the definition of a seed? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/10/#6adb9ed5d4e8053cb94017592406e079",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem l... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/10/",
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"sort_order": 0
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406e3e8 | problem | aim-6adb9ed5d4e8053cb94017592406e3e8 | Totally non-negative parts of braid varieties · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Describe the positive real/totally non negative part of the braid variety. Can this be done using motivation from the perspective of algebraic geometry? symplectic topology? linear algebra? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/9/#6adb9ed5d4e8053cb94017592406e3e8",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/9/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406ed8a | problem | aim-6adb9ed5d4e8053cb94017592406ed8a | Totally non-negative parts of braid varieties · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How can we define totally non negative braid varieties in a way which generalizes the totally non negative part of $G(k,n)/\Pi_f$? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/9/#6adb9ed5d4e8053cb94017592406ed8a",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/9/",
"note": null,
"sort_order": 0
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592406f39f | problem | aim-6adb9ed5d4e8053cb94017592406f39f | Totally non-negative parts of braid varieties · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we use different cluster structures or parametrizations to cover braid varieties or other interesting spaces by their different positive parts? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/9/#6adb9ed5d4e8053cb94017592406f39f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/9/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924070134 | problem | aim-6adb9ed5d4e8053cb940175924070134 | Totally non-negative parts of braid varieties · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How can we understand the connected components, topology, etc. of the real points in braid varieties? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/9/#6adb9ed5d4e8053cb940175924070134",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/9/",
"note": null,
"sort_order": 0
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924071040 | problem | aim-6adb9ed5d4e8053cb940175924071040 | The cluster modular group · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Does the cluster modular group act properly discontinuously on the positive real part of the braid variety? Does this group contain the centralizer of our braid? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/8/#6adb9ed5d4e8053cb940175924071040",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/8/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f14e579e-0fa8-4c9b-b074-6c5e0335c21c","format_issues":null,"number":7047} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240714fd | problem | aim-6adb9ed5d4e8053cb9401759240714fd | The cluster modular group · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Given some automorphism of the braid variety, does symplectic geometry help inform if it's a quasi cluster automorphism? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/8/#6adb9ed5d4e8053cb9401759240714fd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924074803 | problem | aim-6adb9ed5d4e8053cb940175924074803 | Compactifications, tropical points, and $\Theta$-functions · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a natural way to compactify a braid variety so that the smaller strata also have cluster structures? | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592407545f | problem | aim-6adb9ed5d4e8053cb94017592407545f | Compactifications, tropical points, and $\Theta$-functions · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can we obtain brick manifolds by cluster-theoretic means? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb94017592407545f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924075b05 | problem | aim-6adb9ed5d4e8053cb940175924075b05 | Compactifications, tropical points, and $\Theta$-functions · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How does this relate to the combinatorics of the subword complex? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb940175924075b05",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Comment: see Laura Escobar's thesis | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924075d2d | problem | aim-6adb9ed5d4e8053cb940175924075d2d | Compactifications, tropical points, and $\Theta$-functions · Question 4 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | How does this relate to compactifications coming from tropical geometry? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb940175924075d2d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592407643e | problem | aim-6adb9ed5d4e8053cb94017592407643e | Compactifications, tropical points, and $\Theta$-functions · Question 5 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What are the tropical points of the braid variety? What are the $\Theta$-functions on the braid variety? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb94017592407643e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Question context
For each cluster torus, take a co-character lattice and glue them by piecewise linear maps coming from exchange relations. These tropical points label the Gross-Hacking-Keel-Kontsevich $\Theta$-basis. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/4/",
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"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924076f9e | problem | aim-6adb9ed5d4e8053cb940175924076f9e | Compactifications, tropical points, and $\Theta$-functions · Question 6 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Does the MV-basis equal the $\Theta$-basis? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb940175924076f9e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Question context
Let $U$ be a unipotent cell. Then $U$ can be thought of as a braid variety. Also $\mathbb{C}[U]$ has a Mirkovi\'c-Vilonen-basis. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Comment: see the appendix of Baumann-Kamnitzer-Knutson. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Cluster algebras and braid varieties",
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240779cd | problem | aim-6adb9ed5d4e8053cb9401759240779cd | Compactifications, tropical points, and $\Theta$-functions · Question 7 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is the relationship between the piecewise linear combinatorics in the Casals-Gorsky-Gorsky-Le-Shen-Simental cluster algebra construction and the PL-combinatorics of MV-polytopes? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/4/#6adb9ed5d4e8053cb9401759240779cd",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
"citation": "Cluster algebras and braid varieties",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924078041 | problem | aim-6adb9ed5d4e8053cb940175924078041 | The peripheral locus · Question 1 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | When is $P$ empty (in $G(2, 2k+1)$)?
What about the big open positroid cell in $G(k,n)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/3/#6adb9ed5d4e8053cb940175924078041",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Let $X$ be a cluster variety. Let $T_1,T_2,\dots$ be the cluster tori. Let $P$ denote the complement $X-\cup T_i$. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/3/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:07.735Z",
"solved_at": null
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240786f4 | problem | aim-6adb9ed5d4e8053cb9401759240786f4 | The peripheral locus · Question 2 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | When $P$ is nonempty, when do we expect the complement of $P$ to be codimension 2? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/3/#6adb9ed5d4e8053cb9401759240786f4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Let $X$ be a cluster variety. Let $T_1,T_2,\dots$ be the cluster tori. Let $P$ denote the complement $X-\cup T_i$. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/3/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:07.739Z",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240792c9 | problem | aim-6adb9ed5d4e8053cb9401759240792c9 | The peripheral locus · Question 3 | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is the converse also true (Is $P$ for the big positroid cell exactly the points with disconnected matroid)? | unassessed | {
"key": "aimpl",
"name": "AIM · Cluster algebras and braid varieties",
"type": "workshop-problem-list",
"url": "http://aimpl.org/clusterbraid/3/#6adb9ed5d4e8053cb9401759240792c9",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem li... | null | null | null | not-recorded | not-recorded | null | [] | [] | Cluster algebras and braid varieties · Historical workshop question | ## Section context
Let $X$ be a cluster variety. Let $T_1,T_2,\dots$ be the cluster tori. Let $P$ denote the complement $X-\cup T_i$.
## Question context
Let $X$ be really full rank. This implies there is a torus of dimension the number of frozen variables acting on $X$ preserving cluster structure. $S$ acts freely ... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Cluster algebras and braid varieties",
"url": "http://aimpl.org/clusterbraid/3/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924081996 | problem | aim-6adb9ed5d4e8053cb940175924081996 | Homotopy colimits in A-homotopy theory | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | The category of graphs with weak equivalences given by the maps inducing isomorphisms on all A-homotopy groups admits (small) homotopy colimits. | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/2/#6adb9ed5d4e8053cb940175924081996",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This statement is wide open. There are other questions that are special cases that are also unknown. We give a simple example below.
For a graph $X$, define the $n$-suspension of $X$ to be the g... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Daniel Carranza, Chris Kapulkin | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/2/",
"note": null,
"sort_order": 0
}
] | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408540f | problem | aim-6adb9ed5d4e8053cb94017592408540f | Higher homotopy groups | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | In $\times$-homotopy theory, what are the higher homotopy groups? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/5/#6adb9ed5d4e8053cb94017592408540f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A proposal was given during the workshop by one of the groups. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/5/",
"note": null,
"sort_order": 0
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] | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924085744 | problem | aim-6adb9ed5d4e8053cb940175924085744 | Eilenberg-Steenrod axioms | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do the Eilenberg-Steenrod axioms or a variant thereof determine the homology theory uniquely for closure spaces (or graphs)? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/4/#6adb9ed5d4e8053cb940175924085744",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Antonio Rieser | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/4/",
"note": null,
"sort_order": 0
}
] | {
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"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c6919d89-6ea9-411b-8373-434bec3a6b99","format_issues":null,"number":8686} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240867d0 | problem | aim-6adb9ed5d4e8053cb9401759240867d0 | Equivariant discrete homotopy theory | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Develop equivariant discrete homotopy theory. | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/6/#6adb9ed5d4e8053cb9401759240867d0",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/6/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.869Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"f666681b-87b1-416e-8f9c-ff67899e9df3","format_issues":null,"number":8692} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240873a6 | problem | aim-6adb9ed5d4e8053cb9401759240873a6 | Homology theory for graphs with loops | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a good homology theory for graphs with loops? How does it interact with homotopy groups of graphs with loops (which also need to be defined). Does it satisfy a variant Eilenberg-Steenrod axioms? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/5/#6adb9ed5d4e8053cb9401759240873a6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
One approach discussed during the workshop was to take homology of $Hom(K_2, X)$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/5/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c57106c0-5ee9-418f-ba11-87c52485b864","format_issues":null,"number":8691} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924087c20 | problem | aim-6adb9ed5d4e8053cb940175924087c20 | Applications to subspace arrangements | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can earlier results of Barcelo on the relation between A-theory and subspace arrangements be extended beyond $A_1$ by showing that the higher $A$-groups vanish? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/2/#6adb9ed5d4e8053cb940175924087c20",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/2/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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} | 2026-10-10T16:07:49.246Z | {"database_id":"1b72712d-5537-461b-927e-d8e98208e765","format_issues":null,"number":8682} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924088433 | problem | aim-6adb9ed5d4e8053cb940175924088433 | Geometric group theory | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | For the free group $F_k$ on $k$ generators, consider the generating set given by the closure of the standard generating set under conjugation. When considered with the word metric, are $F_2$ and $F_3$ quasi-isometric? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/6/#6adb9ed5d4e8053cb940175924088433",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Federico Vigolo | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/6/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.873Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3b5c4d74-b1da-4b56-ab31-2fe535beaabd","format_issues":null,"number":8693} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924088fb6 | problem | aim-6adb9ed5d4e8053cb940175924088fb6 | Cubical homology | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is the Excision Axiom true for cubical homology of Cech closure spaces with respect to interior covers? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/4/#6adb9ed5d4e8053cb940175924088fb6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nikola Milicevic | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/4/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.842Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4b30e92b-93ab-4784-8ed9-2ce04d8d70b8","format_issues":null,"number":8687} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924089e9c | problem | aim-6adb9ed5d4e8053cb940175924089e9c | Manifolds/cobordism | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What are manifolds in Cech closure spaces? What is the notion of cobordism in Cech closure spaces? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/4/#6adb9ed5d4e8053cb940175924089e9c",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Samira Jamil | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/4/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.846Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4cbc87b5-f9cb-4f00-9b62-79a91885577d","format_issues":null,"number":8688} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408a0f4 | problem | aim-6adb9ed5d4e8053cb94017592408a0f4 | Higher homotopy groups | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Define higher homotopy groups in digital topology. As a test case, one should verify that $\pi_2(S^2, *) = \mathbb{Z}$, where $S^2$ is the digital 2-sphere, i.e., a graph with six vertices appropriately embedded in $\mathbb{Z}^3$. | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/1/#6adb9ed5d4e8053cb94017592408a0f4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Gregory Lupton | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6adb9ed5d4e8053cb94017592408a0f4",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.799Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"094b1339-02a5-415e-bca7-045bf6e0afde","format_issues":null,"number":8677} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408a1d4 | problem | aim-6adb9ed5d4e8053cb94017592408a1d4 | Loop spaces | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a good notion of a loop space of a digital space? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/1/#6adb9ed5d4e8053cb94017592408a1d4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Anton Dochtermann | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.803Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f31b3614-012a-4f5b-bf75-237df10957b0","format_issues":null,"number":8678} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408ac3b | problem | aim-6adb9ed5d4e8053cb94017592408ac3b | Algebraic K-theory of digraphs | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Compute $K_0(*)$ and check if it agrees with what one might expect from spaces, i.e., an isomorphism $K_0(*) \cong \mathbb{Z}$, given by taking a class $[X] \in K_0(*)$ to the Euler characteristic of $X$.
Can other K-groups be computed? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/3/#6adb9ed5d4e8053cb94017592408ac3b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | ## Question context
Based on the work of Carranza-Doherty-Kapulkin-Opie-Sarazola-Wong, there is a cofibration category structure on the category of digraphs whose weak equivalences are digraph maps that induce isomorphisms on all path homology groups. One can use it to define a Waldhausen category on (pointed) digraph... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Carranza, Doherty, and Kapulkin defined a map $K_0(*) \rightarrow \mathbb{Z}$ and verified that it is well-defined and injective.
Several assumptions need to be added to have a well-defined map,... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Brandon Doherty | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/3/",
"note": null,
"sort_order": 0
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.832Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7dc73642-3c4f-44aa-8b91-89508e2aef9c","format_issues":null,"number":8685} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408e6e5 | problem | aim-6adb9ed5d4e8053cb94017592408e6e5 | Singular homology of graphs | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Compute $H^{sing}_*(\mathbb{Z}/n, c_k)$. Is it isomorphic to the homomology of the clique complex of $(\mathbb{Z}/n, c_k)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/4/#6adb9ed5d4e8053cb94017592408e6e5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | ## Question context
Every simple graph can be viewed as a closure space as follows: given a graph $X = (V, E)$, we define a closure space by taking its underlying set to be $V$ and $c(A) = \bigcup_{v \in A} c(v)$, where $c(v) = \{ w \in V \ | \ \{ v, w \} \in E\}$.
For $n , k \in \mathbb{Z}$, define the graph $(\mathb... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This was computed by Nikola Milicevic for $n \leq 5$, but is not known for higher values of $n$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Nikola Milicevic | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/4/",
"note": null,
"sort_order": 0
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] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.850Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4bde5b05-ffcc-4dae-85a4-640ef4531dc9","format_issues":null,"number":8689} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408ec1b | problem | aim-6adb9ed5d4e8053cb94017592408ec1b | Topological realization | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Is there a functor $F$ from the category of digital images to that of topological spaces such that the digital invariants of a digital image $X$ agree with the corresponding classical invariants of $FX$, e.g., $\pi_n(X, *) \cong \pi_n(FX, *)$? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/1/#6adb9ed5d4e8053cb94017592408ec1b",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | ## Question context
This problem assumes that higher homotopy groups of digital spaces have been constructed. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Open. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/1/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.807Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"30309206-3489-4924-9020-687f8b2edc1f","format_issues":null,"number":8679} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb94017592408fa8f | problem | aim-6adb9ed5d4e8053cb94017592408fa8f | Computation of cubical homology | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Can cubical homology of a graph be computed using only injective maps $I_1^{\square n} \to X$? Should this restriction be made at the cubical set or chain complex level? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/2/#6adb9ed5d4e8053cb94017592408fa8f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | ## Question context
When computing cubical homology of a simple graph $X$, one builds a cubical set $MX$ whose $n$-cubes are maps $I_1^{\square n} \to X$ and then takes the usual cubical homology of this cubical set. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A similar question in the context of digital topology was considered by Jamil in her Ph.D. dissertation. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Samira Jamil | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6adb9ed5d4e8053cb94017592408fa8f",
"imported_at": "2026-09-08",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.824Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b237ae7d-221f-47a3-b28f-ae7efb5a06c2","format_issues":null,"number":8683} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924090066 | problem | aim-6adb9ed5d4e8053cb940175924090066 | Classifying spaces | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | Do there exist classifying graphs for fibrations with a fixed fiber (up to weak equivalence) in A-theory? Here, by fibrations we mean maps satisfying the graph analogue of the sharp map condition from simplicial sets. | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/2/#6adb9ed5d4e8053cb940175924090066",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Eric Babson | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/2/",
"note": null,
"sort_order": 0
}
] | {
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"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.829Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"918d7f2d-407a-417f-ac31-fdc6efe4f9a2","format_issues":null,"number":8684} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb940175924090f75 | problem | aim-6adb9ed5d4e8053cb940175924090f75 | Digital topology v $x$-homotopy theory | {
"main": "math",
"sub": "geometry and topology",
"slug": "geometry-and-topology",
"name": "Geometry and topology",
"original_discipline": "mathematics"
} | [] | [] | What is the relation between digital topology and $\times$-homotopy theory of reflexive graphs? | unassessed | {
"key": "aimpl",
"name": "AIM · Discrete and combinatorial homotopy theory",
"type": "workshop-problem-list",
"url": "http://aimpl.org/combhomotop/1/#6adb9ed5d4e8053cb940175924090f75",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Probl... | null | null | null | not-recorded | not-recorded | null | [] | [] | Discrete and combinatorial homotopy theory · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "Discrete and combinatorial homotopy theory",
"url": "http://aimpl.org/combhomotop/1/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.811Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"505225ae-1fff-484e-a816-4548f5adea3e","format_issues":null,"number":8680} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a27d5 | problem | aim-6adb9ed5d4e8053cb9401759240a27d5 | Cases of Harassment in the Community | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How can we support people who have been harassed? How do we as a community handle working with people who have been accused (including by way of warnings over the "whisper network")? Is there room for restorative justice? | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a27d5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Selvi Kara, Pamela Harris, Federico Ardila | null | null | null | [
{
"kind": "website",
"citation": "Gems of combinatorics",
"url": "http://aimpl.org/gemscombin/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6adb9ed5d4e8053cb9401759240a27d5",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.585Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b3fa5238-001b-45ef-9cfa-f8ce29d10b68","format_issues":null,"number":8629} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a2d06 | problem | aim-6adb9ed5d4e8053cb9401759240a2d06 | Taking Intent to Action | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How can we go from ideas/intention to action with our DEI work? In particular, can we create a list of ways to take action and/or find literature on best practices for taking intent to action and then translate for mathematicians’ use? | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a2d06",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Laura Colmenarejo | null | null | null | [
{
"kind": "website",
"citation": "Gems of combinatorics",
"url": "http://aimpl.org/gemscombin/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6adb9ed5d4e8053cb9401759240a2d06",
"imported_at": "2026-09-08",
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.589Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c55415c3-e8ea-44f0-9067-0bca7d9be0c6","format_issues":null,"number":8630} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a346e | problem | aim-6adb9ed5d4e8053cb9401759240a346e | The History of Women in Combinatorics | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | What is the history of women in combinatorics? Answering this question might involve researchers from many different areas, including historians, sociologists, mathematicians, and data scientists. As other possible guiding questions: What departments are producing the most women PhDs in math? What are they doing right?... | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a346e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Andrés R. Vindas Meléndez | null | null | null | [
{
"kind": "website",
"citation": "Gems of combinatorics",
"url": "http://aimpl.org/gemscombin/7/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6adb9ed5d4e8053cb9401759240a346e",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.593Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d80fd6a4-6b4f-470b-80c5-ddf40eaa8ef0","format_issues":null,"number":8631} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a386e | problem | aim-6adb9ed5d4e8053cb9401759240a386e | Starting DEI Conversations | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How can we start DEI conversations in departments outside the US? | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a386e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sophie Rehberg | null | null | null | [
{
"kind": "website",
"citation": "Gems of combinatorics",
"url": "http://aimpl.org/gemscombin/7/",
"note": null,
"sort_order": 0
}
] | {
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"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:15.598Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9b310381-a900-4de7-bb63-c42e42ef648a","format_issues":null,"number":8632} |
1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a4745 | problem | aim-6adb9ed5d4e8053cb9401759240a4745 | Improving Conference Organization/Resources for Organizers | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | What might it look like to make our events (conferences, workshops, etc.) accessible to all participants? How can we make it accessible to parent participants, trans participants, participants from the Global South, non-US participants, ? Can we make a "best practices" document for anyone interested in organizing an eq... | unassessed | {
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a4a02 | problem | aim-6adb9ed5d4e8053cb9401759240a4a02 | Less Actionable But Nonetheless Important Issues | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How do we deal with the structural problem of expecting mathematicians to move every 2 years for post-docs? How can we work to change the gender pay gap? How can we financially support mathematicians who would like to have kids, especially those who have kids in ways that are financially draining? How can we provide be... | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
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"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a4a02",
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Katie Waddle, Pamela Harris, Andrés Vindas Meléndez, Kris Shaw | null | null | null | [
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a591f | problem | aim-6adb9ed5d4e8053cb9401759240a591f | Gender Diversity Beyond the Gender Binary | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How can we address and work towards gender diversity outside of the gender binary? Can "Women in Math" organizations clarify what they mean by "women?" And can we push for greater inclusivity in these organizations? | unassessed | {
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"name": "AIM · Gems of combinatorics",
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"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a591f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Mont Cordero | null | null | null | [
{
"kind": "website",
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1.0.0 | problem:aim-6adb9ed5d4e8053cb9401759240a6845 | problem | aim-6adb9ed5d4e8053cb9401759240a6845 | How Does the Gender Binary Influence the Math we Create? | {
"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/gemscombin/ Not an author-supplied MSC code."
}
] | How does the gender binary (and more generally how we perceive the world) influence the math we create? (not just how we teach and share it) | unassessed | {
"key": "aimpl",
"name": "AIM · Gems of combinatorics",
"type": "workshop-problem-list",
"url": "http://aimpl.org/gemscombin/7/#6adb9ed5d4e8053cb9401759240a6845",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced at A... | null | null | null | not-recorded | not-recorded | null | [] | [] | Gems of combinatorics · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Sophie Rehberg | null | null | null | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130094fb | problem | aim-6ece8953664f1897b245a922130094fb | Problems in Low Forcing · Question 05 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent (with the continuum hypothesis) that there is a minimal $\aleph_2$-Countryman line—that is, an $\aleph_2$-Countryman line that order-embeds into all others? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a922130094fb",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
Let $\mathbb{C} = (C,\le)$ be a linear order of size $\kappa$ and consider its Cartesian square under the ordering $(x_1,y_... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Justin Moore | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221300b8ab | problem | aim-6ece8953664f1897b245a9221300b8ab | Problems in Low Forcing · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent with the continuum hypothesis that any two $\aleph_2$-Countryman lines are near or co-near? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221300b8ab",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
Two linear orders $\mathbb{C}_1$ and $\mathbb{C}_2$ are **near** if there is another linear order $\mathbb{C}_0$ that embed... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Justin Moore | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/highlowforcing/1/",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221300cf8d | problem | aim-6ece8953664f1897b245a9221300cf8d | Problems in Low Forcing · Question 15 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is strong homology consistently additive for closed subspaces of Euclidean space, or more generally for locally compact metric spaces? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221300cf8d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
Strong homology is a homology theory satisfying the Eilenberg-Steenrod axioms and is invariant under strong shape. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
CH and PFA both imply a negative answer to this question. It is likely that a positive answer to this question implies that $\mathfrak{d}<\aleph_\omega$, where $\mathfrak{d}$ is the dominating nu... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Justin Moore | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/highlowforcing/1/",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"c681553a-b617-4301-b3af-9444dbbc8a1a","format_issues":null,"number":7249} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213010cc6 | problem | aim-6ece8953664f1897b245a92213010cc6 | Problems in the Overlap of High and Low Forcing · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there a model for $\text{TP}_{\kappa^{++}}$, with $\kappa$ a singular strong limit of countable cofinality, where we use side conditions in place of the Mitchell poset? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a92213010cc6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/3/",
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"sort_order": 0
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1.0.0 | problem:aim-6ece8953664f1897b245a9221301194d | problem | aim-6ece8953664f1897b245a9221301194d | Problems in the Overlap of High and Low Forcing · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there a model for $\text{TP}_{\aleph_2} + \text{TP}_{\aleph_3}$ using side conditions? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a9221301194d",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/3/",
"note": null,
"sort_order": 0
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] | {
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"published_at": "2026-09-08T03:33:08.898Z",
"solved_at": null
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1.0.0 | problem:aim-6ece8953664f1897b245a92213012ec5 | problem | aim-6ece8953664f1897b245a92213012ec5 | Problems in the Overlap of High and Low Forcing · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there a model where both $I[\aleph_2]$ and $I[\aleph_3]$ are trivial? In other words, is $\text{AP}_{\aleph_2} + \text{AP}_{\aleph_3}$ consistent? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a92213012ec5",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
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"kind": "website",
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1.0.0 | problem:aim-6ece8953664f1897b245a9221301438e | problem | aim-6ece8953664f1897b245a9221301438e | Problems in High Forcing · Question 05 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent (relative to large cardinals) that $\text{TP}_{\aleph_{\omega+1}}$ holds along with reflection for all stationary subsets of $\aleph_{\omega+1}$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
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"doi": null,
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"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This is consistent at $\aleph_{\omega^2+1}$. | null | published | incremental | hard | [
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1.0.0 | problem:aim-6ece8953664f1897b245a922130150c6 | problem | aim-6ece8953664f1897b245a922130150c6 | Problems in High Forcing · Question 1 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent to have the failure of both $\text{SCH}$ and $\square_{\aleph_\omega}^\ast$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a922130150c6",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
A positive answer is necessary to get $\text{AP}_{\aleph_{\omega+1}}+\text{AP}_{\aleph_{\omega+2}}$. Since $\text{TP}_{\kappa^+}$ implies $\neg \square_\kappa^\ast$, this is also necessary to get... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
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"published_at": "2026-09-08T03:33:08.844Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ddc4fba8-71ca-4587-b443-a2452e53ad3f","format_issues":null,"number":7263} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213015240 | problem | aim-6ece8953664f1897b245a92213015240 | Problems in High Forcing · Question 15 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is $\neg \square_\kappa^\ast + \neg SCH_\kappa + GCH_{<\kappa}$ consistent for $\kappa$ singular? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a92213015240",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This is known without $\text{GCH}$ from Gitik-Sharon, where Laver preparation disrupts GCH below the cardinal. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
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"url": "http://aimpl.org/highlowforcing/2/",
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"updated_at": "2026-09-08T03:32:15.935Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"cd1938ed-da97-4e7c-af14-f71f33734f7e","format_issues":null,"number":7264} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213015bd4 | problem | aim-6ece8953664f1897b245a92213015bd4 | Problems in Low Forcing · Question 25 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent that there is a poset which adds a club in $\omega_3$ which contains no infinite ground model subset over a model of GCH? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213015bd4",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
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"published_at": "2026-09-08T03:33:08.786Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"b4b6cbcd-fc84-42ec-9fce-0976d64e9381","format_issues":null,"number":7250} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213016e60 | problem | aim-6ece8953664f1897b245a92213016e60 | Problems in Low Forcing · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is there a large cardinal hypothesis that proves the bounded forcing axiom for Namba forcing? | unassessed | {
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"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213016e60",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.790Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"0463f6d6-3487-42f6-8bf7-876a84c4ebd2","format_issues":null,"number":7251} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213017964 | problem | aim-6ece8953664f1897b245a92213017964 | Problems in Low Forcing · Question 35 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Can Namba forcing be iterated with side conditions? Does this work if we replace Namba forcing with a forcing satisfying Shelah's $S$-condition? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213017964",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"published_at": "2026-09-08T03:33:08.794Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"add814c0-5df4-476f-b019-ae71358d627b","format_issues":null,"number":7252} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213017982 | problem | aim-6ece8953664f1897b245a92213017982 | Problems in Low Forcing · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Assume CH. Is there a strongest forcing axiom of $\sigma$-closed posets meeting $\aleph_2$-many dense sets? What if we do not assume CH? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213017982",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.799Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ba5221cd-b5a0-4f15-934e-4a865ef8cc0e","format_issues":null,"number":7253} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301809f | problem | aim-6ece8953664f1897b245a9221301809f | Problems in Low Forcing · Question 45 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | The following is inconsistent: ``For every $\Sigma_1$ statement $\varphi$ with $\aleph_1$ and $\aleph_2$ as parameters, if $\varphi$ can be forced by an $\aleph_1, \aleph_2$-preserving forcing, then $\varphi$ holds.'' | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221301809f",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
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] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.803Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"baf12c8c-d0fa-44da-bf23-d3d8679bb70a","format_issues":null,"number":7254} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213018fe7 | problem | aim-6ece8953664f1897b245a92213018fe7 | Problems in the Overlap of High and Low Forcing · Question 4 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is the forcing axiom for proper posets of size $\aleph_1$ with $\aleph_2$-many dense sets consistent? If so, what if we replace the size-$\aleph_2$ requirement with the $\aleph_2$-chain condition? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a92213018fe7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | null | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/3/",
"note": null,
"sort_order": 0
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.906Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"70175eca-6187-4798-bcf0-fc6f3e101dc3","format_issues":null,"number":7276} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301916e | problem | aim-6ece8953664f1897b245a9221301916e | Problems in the Overlap of High and Low Forcing · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Can this forcing be made proper using side conditions? Does this preserve the $\aleph_2$-chain condition? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/3/#6ece8953664f1897b245a9221301916e",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Question context
There is a coloring $F:[\aleph_2]^2 \rightarrow {0,1}$ of pairs from $\aleph_2$ in $2$ colors so that the poset of finite approximations to a $0$- or $1$-homogeneous set has the $\aleph_2$-chain condition. (We mean either the poset $\mathbb P$ of finite functions $f:\omega \rightarrow F^{-1}(0)$ or... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
If we do obtain properness, then the fprcing axiom for $\aleph_2$-many dense sets proper posets of size $\aleph_1$—and for proper posets with the $\aleph_2$-chain condition—is inconsistent. | null | published | incremental | hard | [
"aim",
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"published_at": "2026-09-08T03:33:08.910Z",
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} | 2026-10-10T16:07:49.246Z | {"database_id":"5cef7d61-022f-42d2-907e-1612b81e3539","format_issues":null,"number":7277} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130196ee | problem | aim-6ece8953664f1897b245a922130196ee | Problems in High Forcing · Question 2 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent that there is a poset turning $\aleph_{\omega+1}$ into $\aleph_2$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a922130196ee",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
}
] | {
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"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
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"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.854Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3a1333a7-dfb6-43b7-a5ea-5dc7425a6061","format_issues":null,"number":7265} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301a567 | problem | aim-6ece8953664f1897b245a9221301a567 | Problems in High Forcing · Question 25 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Find a model of $\text{TP}_\kappa$ for all regular $\kappa \in [\aleph_2,\aleph_{\omega^2+2}]$ where $\aleph_{\omega^2}$ is the first strong limit. | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221301a567",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a9221301a567",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.858Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ead6dc20-9fac-4f31-922c-0473480745d3","format_issues":null,"number":7266} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301b412 | problem | aim-6ece8953664f1897b245a9221301b412 | Problems in High Forcing · Question 3 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Is it consistent that every poset either adds a real or collapses a cardinal? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/2/#6ece8953664f1897b245a9221301b412",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
High forcing has to do with the combinatorics of compactness versus non-compactness.
$\text{TP}_\kappa$ refers to the **tree property** at $\kappa$: Every tree $T$ of height $\kappa$ with levels of size $<\kappa$ has a cofinal branch of length $\kappa$.
$\text{SCH}_\kappa$ is the **singular cardin... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
This question is related to the tree property. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | null | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/2/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a9221301b412",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.863Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6d85e64b-506a-408d-849d-3dfadb14795d","format_issues":null,"number":7267} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301be57 | problem | aim-6ece8953664f1897b245a9221301be57 | Problems in Low Forcing · Question 5 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | When can one obtain $|X|\le 2^{s(X)}$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221301be57",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
If $X$ is a topological space, let $s(X)=\sup\{|Y|:Y \text{ is a discrete subspace of }X\}$. It is a theorem that $|X| \le ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
The answer is negative under $\Diamond$, even for compact Hausdorff spaces. PFA implies that the answer is negative for $X$ with $s(X)=\aleph_0$. PFA also implies that $|X| \le 2^{\aleph_0}$ for ... | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a9221301be57",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.807Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c429b0e6-80f2-47c8-b9bb-4f72b0d43f03","format_issues":null,"number":7255} |
1.0.0 | problem:aim-6ece8953664f1897b245a9221301e8ca | problem | aim-6ece8953664f1897b245a9221301e8ca | Problems in Low Forcing · Question 55 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Do any of the analogs of PFA at $\aleph_2$ give us $|X| \le 2^{\aleph_1}$ for every Hausdorff space with no discrete subspaces of size $\aleph_2$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a9221301e8ca",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a9221301e8ca",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.812Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1092d2db-1662-4994-8201-7ec996872d45","format_issues":null,"number":7256} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130231ef | problem | aim-6ece8953664f1897b245a922130231ef | Problems in Low Forcing · Question 6 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Suppose $X$ is a compact Hausdorff space of tightness $\aleph_1$ (i.e. there are no $\omega_2$-free sequences) and density $\aleph_1$. Is it true that $|X| \le 2^{\aleph_1}$? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a922130231ef",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
It is a fact that a compact Hausdorff space $X$ is countably tight if and only if $X$ contains no $\omega_1$-free sequence. | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a922130231ef",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.816Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"485d252c-990d-4844-9703-c4bd829fc652","format_issues":null,"number":7257} |
1.0.0 | problem:aim-6ece8953664f1897b245a922130238a7 | problem | aim-6ece8953664f1897b245a922130238a7 | Problems in Low Forcing · Question 65 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Under a given analog of PFA for $\aleph_2$, how many cofinal types of directed sets of cardinality $\aleph_2$ are there? | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a922130238a7",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure. | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
Under PFA, $1, \omega, \omega_1, \omega \times \omega_1$, and $(\omega_1)^{<\omega}$ are the cofinal types of directed sets of cardinality $\aleph_1$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a922130238a7",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.821Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"399033bc-ac5a-4b3f-837a-e763cd149948","format_issues":null,"number":7258} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213024955 | problem | aim-6ece8953664f1897b245a92213024955 | Problems in Low Forcing · Question 7 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Can $\omega_2 \rightarrow (\omega_2,\alpha)^2$ be deduced from one of the forcing axioms at $\aleph_2$. | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213024955",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
$\kappa \rightarrow (\alpha,\beta)^n$ means that for every coloring $F:[\kappa]^n \rightarrow \{0,1\}$, then then there is ... | Historical workshop record. Current open/solved status has not been independently reassessed.
## Status note in the source
It is known that PFA implies $\omega_1 \rightarrow (\omega_1,\alpha)^2$ for all $\alpha<\omega_1$. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a92213024955",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.825Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"99f47d29-eb2a-4b48-9f96-33523a01c73f","format_issues":null,"number":7259} |
1.0.0 | problem:aim-6ece8953664f1897b245a92213025b48 | problem | aim-6ece8953664f1897b245a92213025b48 | Problems in Low Forcing · Question 75 | {
"main": "math",
"sub": "mathematics general",
"slug": "mathematics-general",
"name": "Mathematics · general",
"original_discipline": "mathematics"
} | [] | [] | Assuming an appropriate generalization of PFA, determine the gaps spectrum of $P(\omega)/fin$. | unassessed | {
"key": "aimpl",
"name": "AIM · High and low forcing",
"type": "workshop-problem-list",
"url": "http://aimpl.org/highlowforcing/1/#6ece8953664f1897b245a92213025b48",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Editorially moderated; per-list terms",
"notes": "Problem lists produced a... | null | null | null | not-recorded | not-recorded | null | [] | [] | High and low forcing · Historical workshop question | ## Section context
"Low Forcing" refers to the method of side conditions, specifically where the side conditions are elementary submodels of some large transitive structure.
## Question context
It is known under PFA that the gaps-spectrum of $P(\omega)/fin$ consists of $(\omega_1,\omega_1^\ast),(\omega_2,\omega^\ast... | Historical workshop record. Current open/solved status has not been independently reassessed.
The source supplies no status note for this question. | null | published | incremental | hard | [
"aim",
"historical-workshop"
] | Stevo Todorčević | null | null | null | [
{
"kind": "website",
"citation": "High and low forcing",
"url": "http://aimpl.org/highlowforcing/1/",
"note": null,
"sort_order": 0
}
] | {
"source_record": "6ece8953664f1897b245a92213025b48",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Historical list · status unassessed",
"note": "Original numbered AIM workshop question. Section context and source status notes are retained where available. Retrieval date does... | null | [
"current-status-unassessed",
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:33:08.829Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5f8e2dd5-f389-47b1-b464-57005f5de909","format_issues":null,"number":7260} |
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